Answer each one please 20 points! :3 and (brainly)

caden exercises daily by walking on a treadmill. he sets the machine so that he will walk at a steady rate of 3.6 miles per hour.
a. if t represents time in hours and d represents distance in miles, write an equation that models the relationship between these variables.-


b. use your equation to calculate the distance caden will walk in 3/4 of an hour.--


c. use your equation to calculate how long it will take for caden to walk 4.32 miles.--





answer each one please 20 points! :3 and (brainly)

Answers

Answer 1

a. If t represents time in hours and d represents distance in miles, and Caden walks at a steady rate of 3.6 miles per hour, the equation that models the relationship between these variables is:

d = 3.6t

b. To calculate the distance Caden will walk in 3/4 of an hour, plug 3/4 into the equation for t:

d = 3.6(3/4) = 2.7 miles

Caden will walk 2.7 miles in 3/4 of an hour.

c. To calculate how long it will take for Caden to walk 4.32 miles, plug 4.32 into the equation for d and solve for t:

4.32 = 3.6t
t = 4.32/3.6 ≈ 1.2 hours

It will take Caden approximately 1.2 hours to walk 4.32 miles.

To know more about speed and distance refer here:

https://brainly.com/question/31756299?#

#SPJ11


Related Questions

Mr. Lance designed a class banner shaped like a polygon shown what is the name of the polygon

Answers

Step 1: Answer

The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2).

Step 2: Explanation

The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.

Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.

Tim made his mother a quilt. The width is 6 5 /7 ft and the length is 7 3 /5 ft. What is the area of the quilt?

Answers

The quilt's area is approximately 60.74 square feet.

How to calculate the quilt's area?

To calculate the area of the quilt, we need to multiply the width by the length.

First, we need to convert the mixed numbers to improper fractions:

Width: 6 5/7 ft = (7 x 6 + 5)/7 = 47/7 ft

Length: 7 3/5 ft = (5 x 7 + 3)/5 = 38/5 ft

Now, we can multiply the width by the length:

Area = width x length

Area = (47/7) ft x (38/5) ft

Area = 2126/35 sq ft

Area ≈ 60.74 sq ft

Therefore, the area of the quilt is approximately 60.74 square feet.

Learn more about area of the quilt

brainly.com/question/30266367

#SPJ11

one serving of almonds is 1/3 cup. booker bought 2 and 2/3 cups of almonds how many servings of almonds did booker buy

Answers

Booker bought 8 servings of almonds.

How many servings of almonds did Booker buy if he purchased 2 and 2/3 cups of almonds, and one serving of almonds is 1/3 cup?

One serving of almonds is equal to 1/3 cup.

To find how many servings of almonds Booker bought, we can divide the total amount of almonds he purchased by the amount in one serving:

2 and 2/3 cups of almonds = 8/3 cups of almonds

Number of servings = (total amount of almonds purchased) / (amount in one serving)

Number of servings = (8/3) / (1/3)

Number of servings = 8/3 x 3/1

Number of servings = 8

Learn more about servings

brainly.com/question/31639498

#SPJ11

PLEASE HELP EM I WIL GIVE BRAINLIEST TO THE FIRST CORRECT ANSWER EHLP ME FAST PLEASE

Answers

[tex]a = \sqrt{ {8}^{2} - {6}^{2} } \\ \\ = \sqrt{64 - 36 }\\ \\ =\sqrt{ 28} \\ \\ = \sqrt{4 \times 7} \\ \\ = 2 \sqrt{7} [/tex]

How many different simple random samples of size 4 can be obtained from a population whose size is 50?

Answers

The number of random samples, obtained using the formula for combination are 230,300 random samples

What is a random sample?

A random sample is a subset of the population, such that each member of the subset have the same chance of being selected.

The formula for combinations indicates that we get;

nCr = n!/(r!*(n - r)!), where;

n = The size of the population

r = The sample size

The number of different simple random samples of size 4 that can be obtained from a population of size 50 therefore can be obtained using the above equation by plugging in r = 4, and n = 50, therefore, we get;

nCr = 50!/(4!*(50 - 4)!) = 230300

The number of different ways and therefore, the number of random samples of size 4 that can be selected from a population of 50 therefore is 230,300 random samples.

Learn more on combination here: https://brainly.com/question/25718474

#SPJ1

£4500 is shared between 4 charities.
the donation to charity b is 5/6 of the donation to charity d
charity d's donation is twice the donation to charity c.
the ratio of donations for charity c to charity a is 3:4.
work out the donation to charity b.

Answers

If the donation to charity b is 5/6 of the donation to charity d, charity d's donation is twice the donation to charity c and the ratio of donations for charity c to charity a is 3:4 then the donation to charity b is £1250.

Let's denote the donation to charity a as x. Then the donation to charity c is (3/4)x, and the donation to charity d is 2(3/4)x = (3/2)x.

We know that the donation to charity b is 5/6 of the donation to charity d, so:

donation to charity b = (5/6)(3/2)x = (5/4)x

We also know that the total donation is £4500, so we can set up an equation:

x + (3/4)x + (3/2)x + (5/4)x = £4500

Multiplying through by 4 to get rid of the fractions, we have:

4x + 3x + 6x + 5x = £18,000

18x = £18,000

x = £1000

So the donation to charity b is: (5/4)x = (5/4)(£1000) = £1250

Therefore, the donation to charity b is £1250.

To learn more about  donation : https://brainly.com/question/30868579

#SPJ11

Lourdes could choose to pay an ATM fee to get cash or use a credit card to pay for groceries


that cost $48. The credit card charges interest if the balance is not paid at the end of the month.


Should she use the debit card or credit card? Justify your choice.

Answers

Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.

To determine whether Lourdes should use a debit card or credit card, we need to consider the ATM fee and the potential interest charges from the credit card.

Step 1: Determine the ATM fee
Find out how much Lourdes would be charged for using the ATM to withdraw cash.

Step 2: Determine the interest rate on the credit card
Check the credit card's terms and conditions to find the annual percentage rate (APR). This will help us calculate the potential interest charges.

Step 3: Calculate the potential interest charges
Assuming Lourdes doesn't pay off the credit card balance by the end of the month, divide the APR by 12 to get the monthly interest rate. Multiply this rate by the $48 grocery cost to find the potential interest charges.

Step 4: Compare costs
Compare the ATM fee and potential interest charges to determine the cheaper option. If the ATM fee is less than the potential interest charges, Lourdes should use her debit card. If the potential interest charges are less than the ATM fee, she should use her credit card.

Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.

Learn more about credit card,

https://brainly.com/question/26857829

#SPJ11

25. a state study on labor reported that one-third of full-time teachers in the state also worked part time at another job. for those teachers, the average number of hours worked per week at the part-time job was 13. after an increase in state teacher salaries, a random sample of 400 teachers who worked part time at another job was selected. the average number of hours worked per week at the part-time job for the teachers in the sample was 12. 5 with standard deviation 6. 5 hours. is there convincing statistical evidence at the level of 0. 05, that the average number of hours worked per week at part-time jobs decreased after the salary increase? (a) no. the p-value of the appropriate test is greater than 0. 5. (b) no. the p-value of the appropriate test is less than 0. 5. (c) yes. the p-value of the appropriate test is greater than 0. 5. (d) yes. the p-value of the appropriate test is less than 0. 5. (e) not enough information is given to determine whether there is convincing statistical evidence

Answers

From the solution to the question that we have here, the answer is A. There is no solid proof that the number of hours worked dropped after the income rise.

Let μ be the population mean number of hours worked per week by teachers who work part-time jobs, after the salary increase. Here are the alternate and null hypotheses:

H0: μ = 13

H1: μ < 13

n = 400

[tex]\bar{X}=12.5[/tex]

μ = 13

Formula for the t-test statistics is

[tex]t = \frac{\bar{X}-\mu}{s/\sqrt{n} }[/tex]

t = (12.5 - 13)/(6.5/√400)

t = (- 0.5)/(6.5/20)

t = - 10/6.5

= -1.5388

Degree of freedom is 400 -1 = 399

α = 0.05

The p-value is p(t < -1.5385) = 0.062

The p-value exceeds the level of significance. Therefore, we unable to reject the null hypothesis.

Hence, option a is correct.

Learn more on statistics here:

brainly.com/question/19243813

#SPJ4

Edro, Lena, Harriet, and Yermin each plot a point to approximate StartRoot 0. 50 EndRoot.




Pedro A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 2 and 0. 3.



Lena A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 4 and 0. 5.



Harriet A number line going from 0 to 0. 9 in increments of 0. 1. A point is at 0. 5.



Yermin A number line going from 0 to 0. 9 in increments of 0. 1. A point is just to the right of 0. 7.



Whose point is the best approximation of StartRoot 0. 50 EndRoot?


Pedro


Lena


Harriet


Yermin

Answers

Yermin's point is the best approximation of the square root of 0.50.

To know whose point is the best approximation of the square root of 0.50 on a number line. We have the points plotted by Pedro, Lena, Harriet, and Yermin.

Step 1: Calculate the square root of 0.50.
[tex]\sqrt{0.50} = 0.707[/tex]

Step 2: Compare the plotted points to the calculated square root value.
Pedro: Between 0.2 and 0.3
Lena: Between 0.4 and 0.5
Harriet: At 0.5
Yermin: Just to the right of 0.7

Step 3: Determine the closest approximation.
Yermin's point (just to the right of 0.7) is the closest to the calculated value of 0.707.

Your answer: Yermin's point is the best approximation of the square root of 0.50.

To know more about "Square root" refer here:

https://brainly.com/question/29775049#

#SPJ11

The table shows the amount of money raised during a car wash for charity.
Number of Cars Washed Money Raised
3 $43.50
13 $279.50
18 $405.00
Which statement is true?

A. The group raised $14.50 per car.
B. The group raised $21.50 per car.
C. The group raised $22.50 per car.
D. The relationship is not a direct proportion.

Answers

Answer:

The correct answer is D. The relationship is not a direct proportion.

We can see that the money raised is not directly proportional to the number of cars washed. For example, when the number of cars washed is doubled from 3 to 13, the money raised is not doubled from $43.50 to $87.00. Instead, it is increased by a factor of 6.5, from $43.50 to $279.50. Similarly, when the number of cars washed is increased by 5 from 13 to 18, the money raised is increased by a factor of 1.4, from $279.50 to $405.00.

This suggests that the amount of money raised is not simply a linear function of the number of cars washed. Instead, it is likely a more complex function that takes into account other factors, such as the time of day, the weather, and the location of the car wash.:

Earthworm Rivals are building the set for

their new music video. There is a tower made

of 9 glowing bricks that stands 5. 4 meters tall. If each of the bricks is the same exact size,

how tall is each brick?

Answers

Since each of the bricks is the same exact size, then each brick is 0.6 meters tall.

To determine the height of each glowing brick, we need to divide the total height of the tower (5.4 meters) by the number of bricks (9). This gives us the average height of each brick.

Using the formula for division, we can write this as:

Height of each brick = Total height of tower / Number of bricks

Plugging in the given values, we get:

Height of each brick = 5.4 meters / 9 bricks

Simplifying this expression, we can cancel out the units of "bricks" to get:

Height of each brick = 0.6 meters

Therefore, each glowing brick in the tower is 0.6 meters tall.

Learn more about division here: https://brainly.com/question/30126004

#SPJ11

I need help! Solve for X

Answers

Answer: x=18
4x + 8 = 80
Take away 8 from both sides
4x = 72
Divide 72 by four
X=18

Albert and Makayla are each renting a car for one day. Albert’s rental agreement states that the car costs $35 per day and $0. 15 per mile driven. Makayla’s agreement states that the car she is renting costs $45 per day and $0. 10 per mile driven. Write an equation to determine the number of miles, m, Albert and Makayla drive if they spend the same amount of money on their rentals

Answers

To determine the number of miles, m, Albert and Makayla drive if they spend the same amount of money on their rentals, we can write an equation using the given information:

Albert's cost = $35 per day + $0.15 per mile driven
Makayla's cost = $45 per day + $0.10 per mile driven

Since they spend the same amount of money, we can set the costs equal to each other:

35 + 0.15m = 45 + 0.10m

Now, we need to solve the equation form, the number of miles driven:

1. Subtract 0.10m from both sides:
35 + 0.05m = 45

2. Subtract 35 from both sides:
0.05m = 10

3. Divide both sides by 0.05:
m = 200

So, if Albert and Makayla spend the same amount of money on their rentals, they both drive 200 miles.

Learn more about rental agreement at https://brainly.com/question/3237108

#SPJ11

Brainliest if correct!_A particle is projected vertically upwards from a fixed point O. The speed of projection is u m/s. The particle returns to O 4 seconds later. Find:

a) the value of u

b) the greatest height reached by the particle

c) the total time of which the particle is at a height greater than half its greatest height

Thank you so much!

Answers

The value of the velocity, u is 19.6 m/s.

The greatest height reached by the particle is 19.6 m.

The total time during which the particle is at a height greater than half its greatest height is 2.33 s.

What is the value of the velocity, u?

a) To find the value of the velocity, u, we can use the formula for the time of flight of a vertically projected particle:

t = 2u/g

Since the particle returns to the same point after 4 seconds, we have:

2t = 4

Substituting the value of t in the first equation, we get:

u = gt/2 = 9.8 x 2

u = 19.6 m/s

b) To find the greatest height reached by the particle, we can use the formula for the maximum height reached by a vertically projected particle:

h = u^2/2g

Substituting the value of u, we get:

h = 19.6^2/(2 x 9.8)

h = 19.6 m

c) To find the total time during which the particle is at a height greater than half its greatest height, we can first find the height at which the particle is at half its greatest height:

h/2 = (u^2/2g)/2 = u^2/4g

Substituting the value of u, we get:

h/2 = 19.6^2/(4 x 9.8) = 24.01 m

So, the particle is at a height greater than half its greatest height when it is above 24.01 m.

Next, we can find the time taken by the particle to reach this height:

h = ut - (1/2)gt^2

24.01 = 19.6t - (1/2)9.8t^2

Solving this quadratic equation, we get:

t = 2.33 s or t = 4.10 s

The particle takes 2.33 s to reach a height of 24.01 m, and it takes another 1.67 s (4 - 2.33) to return to the ground.

Learn more about velocity at: https://brainly.com/question/80295?source=archive

#SPJ1

 A customer is comparing the size of oil funnels in a store. The funnels are cone shaped. One funnel has a base with a diameter of 8 in. And a slant height of 12 in. What is the height of the funnel? Round your answer to the nearest hundredth. 

Answers

The height of the funnel is 11.31, under the condition that one funnel has a base with a diameter of 8 in. And a slant height of 12 in.

Here we have to apply the Pythagorean theorem to evaluate the height of the funnel. The Pythagorean theorem projects that the square of the hypotenuse (the slant height) is equal to the sum of the squares of the other two sides (the radius and height).

Now, we have a cone that has a base diameter of 8 inches which says that the radius is 4 inches. The slant height is 12 inches. Then the height is
h² + r² = l²
h² + 4² = 12²
h² = 144 - 16
h² = 128
h = √(128)
h ≈ 11.31

Hence, 11.31 inches is the approximate height of the funnel after rounding to the nearest hundredth.
To learn more about Pythagorean theorem,
https://brainly.com/question/343682
#SPJ4

Barbara’s Bigtime Bakery baked the world’s largest chocolate cake. (It was also the world’s worstcake, as 343 people got sick after eating it. ) The length was 600 cm, the width 400 cm, and the height 180 cm. Barbara and her two assistants, Boris and Bernie, applied green peppermint frosting on the four sides and the top. How many liters offrosting did they need for this dieter’s nightmare? One liter of green frosting covers about 1200 cm²

Answers

The total liters of frosting needed is 500, under the condition that the length was 600 cm, the width 400 cm, and the height 180 cm.

In order to evaluate the amount of frosting needed, we have to evaluate the surface area of the cake. The surface area of the cake is the summation of the areas of all its sides.
Here the area of each side is equivalent to its length multiplied by its width. Then the area of the given top is equivalent to its length multiplied by its width.

Then the evaluated surface area of the cake is
2 × (length × height + width × height) + length × width
= 2 × (600 cm × 180 cm + 400 cm × 180 cm) + 600 cm × 400 cm
= 2 × (108000 cm² + 72000 cm²) + 240000 cm²
= 2 × 180000 cm² + 240000 cm²
= 600000 cm²
Hence, one liter of green frosting covers about 1200 cm².
600000 cm² / 1200 cm² per liter = 500 liters

Therefore, Barbara and her assistants needed 500 liters of frosting for their dieter's nightmare.
To learn more about surface area
https://brainly.com/question/951562
#SPJ4

An oil tanker and a cruise ship leave port at the same time and travel straight-line at 32 mph and 46 mph, respectively. Two hours later, they are 63 miles apart. What is the angle between their courses?​

Answers

The angle between their courses is 42.02°.

How to calculate angle between 2 moving bodies

It is important to first find the distance between them after the 2 hours of travel.

Recall the  formula:

speed = distance/time

Make distance the subject of the formula

distance = speed x time

For the oil tanker,

given the following:

speed = 32mph

time = 2hr

distance = 32 mph x 2 hours = 64 miles

For the cruise ship,

given the following:

speed = 46 mph,

time = 2 hr

distance = 46 mph x 2 hours = 92 miles

So after two hours of travel, the two vessels are 63 miles apart. This means that they are forming a triangle with the distance between them as the longest.

Now we need to find the angle between the two vessels' courses by using the Cosine rule:

Recall that

a² = b² + c² -2bc Cos A

Let C be the angle between the oil tanker and cruise ship

then we can rewrite the equation as:

c² = a² + b² -2bc Cos C

where

a = 64miles (distance of oil tanker)

b = 92miles (dsitance of cruise ship)

c = 63miles (distance between the vessels)

C = angle between the vessels

Plug in the values to the equation

63² = 64² + 92² - 2(64)(92) Cos C

3969 = 4096 + 8464 - 11776 Cos C

3969 = 12560 - 11776 Cos C

Collect like terms

3969 - 12560 = - 11776 Cos C

8591 = 11776 Cos C

Cos C = 8591/11776

Cos C = 0.7295

Apply the inverse Cosine formula

C = Cos⁻¹ (0.7295)

C = 42.02°

Learn more about angle here:

https://brainly.com/question/1309590

#SPJ1

A track has the dimensions shown.
36.5 m
ISTAN
SAMANT
men komm
84.4 m
Ta
inside of track
outside of track
. The track has 8 lanes
• Each lane is 2.1 meters wide
36.5 m
O
TI
16. To the nearest tenth of a meter, what is
the perimeter of the outside of the
track?
Byp
*REQUIRED
ANA
1
√x
Sign out

Answers

Answer:

Step-by-step explanation:

Which system of equations is represented by the graph?

Answers

Answer:

Absoblute value Reflection

Step-by-step explanation:

You can tell it's absolbute value because of the parbolas, and it's reflected acroos the two points. Give brainliest please!

10 foot ladder is leaning against a vertical wall when Jack begins
pulling the foot of the ladder away from the wall at a rate of 0.5
fr/s. how fast is the top of the ladder sliding down the wall?

Answers

We can use the Pythagorean theorem to relate the distances between the ladder, wall, and ground. Let's call the distance from the foot of the ladder to the wall "x", and the distance from the top of the ladder to the ground "y". Then, we know that:

x^2 + y^2 = 10^2

We can differentiate this equation with respect to time to get:

2x(dx/dt) + 2y(dy/dt) = 0

We're interested in finding dy/dt, the rate at which the top of the ladder is sliding down the wall. We know that dx/dt = 0.5 ft/s, so we can plug in these values and solve for dy/dt:

2x(dx/dt) + 2y(dy/dt) = 0
2(8)(0.5) + 2y(dy/dt) = 0 (since x = 8 based on the Pythagorean theorem)
dy/dt = -4 ft/s

So the top of the ladder is sliding down the wall at a rate of 4 ft/s.
When the 10-foot ladder is leaning against a vertical wall, it forms a right-angled triangle with the wall and the ground. As Jack pulls the foot of the ladder away from the wall at a rate of 0.5 ft/s, the top of the ladder slides down the wall. To find the rate at which the top of the ladder slides down, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

where a is the distance from the foot of the ladder to the wall, b is the height of the ladder's top from the ground, and c is the length of the ladder (10 feet).

Differentiating both sides with respect to time (t), we get:

2a(da/dt) + 2b(db/dt) = 0

We know that da/dt = 0.5 ft/s. We need to find db/dt, which is the rate at which the top of the ladder slides down the wall. To do this, we need to find the values of a and b at a given moment. Since the problem doesn't provide this information, it's not possible to determine the exact value of db/dt. However, if you have the values of a and b, you can plug them into the equation and solve for db/dt.

learn more about Pythagorean theorem here: brainly.com/question/343682

#SPJ11

During their team meeting, both managers shared their findings. Complete the statement describing their combined results.



Select the correct answer from each drop-down menu.



The initial number of video views was ____ the initial number of site visits, and the number of video views grew by _____ the number of site visits.



The difference between the total number of site visits and the video views after 5 weeks is _____.



More than


the same as


fewer than



a smaller factor than


the same factor as


a larger factor than



20,825


52,075


15,625


36,450

Answers

The initial number of video views was fewer than the initial number of site visits, and the number of video views grew by a larger factor than the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is 20,825.

During their team meeting, both managers shared their findings. Complete the statement describing their combined results.

The initial number of video views was fewer than the initial number of site visits, and the number of video views grew by a larger factor than the number of site visits.

The difference between the total number of site visits and the video views after 5 weeks is 20,825.

Therefore the correct answer are fewer, larger factor than and 20,825.

Read more about video.

https://brainly.com/question/15245269

#SPJ11

Selika give her garden a makeover. She spends money on plant,materials, and labour in the ratio of 1:5:12. She spends £848. 75. How much money does she spend on labour costs

Answers

Selika spends £565.85 on labour costs.

Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.

Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.

The total amount of money she spends is £848. 75

x + 5x + 12x = 848.75

18x = 848.75

x = 848.75/18

x = 47.15

She spend on labour 12x = 12 × 47.15

= 565.85

Therefore, Selika spends £565.85 on labour costs.

Learn more about ratio here

brainly.com/question/13419413

#SPJ4

Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch.

Answers

The height of the rectangular frame is 30 inches.

How to find the height of the frame?

Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. The rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame.

Hence, the height of the frame can be represented as follows:

using trigonometric ratios,

sin 36.87 = opposite / hypotenuse

sin 36.87 = h / 50

cross multiply

h = 50 sin 36.87

h = 50 × 0.60000142913

h = 30.0000714566

Therefore,

height of the frame = 30 inches

learn more on height here: https://brainly.com/question/31546923

#SPJ1

Find two acute angles that satisfy the equation sin(3x + 9) = cos(x + 5). check that your answers make sense.

Answers

The equation sin(3x + 9) = cos(x + 5) has no solutions in the set of acute angles.

What are the acute angles that satisfy sin(3x + 9) = cos(x + 5)?

To find two acute angles that satisfy the equation sin(3x + 9) = cos(x + 5), we can use the trigonometric identity cos(x) = sin(π/2 - x) to rewrite the right-hand side of the equation as follows:

sin(3x + 9) = cos(x + 5)sin(3x + 9) = sin(π/2 - x - 5)3x + 9 = π/2 - x - 5 + 2πn or 3x + 9 = x + 5 + 2πn + π (where n is an integer)4x = -4 - 2πn or 2x = -2πn - 4 or 2x = π - 2πn - 4

Dividing both sides of the equation by 4, we get:

x = -(1/2)πn - 1

So the solutions are given by:

x = -(1/2)π - 1 and x = -(3/2)π - 1

To check that these solutions make sense, we need to ensure that they are acute angles, i.e., angles that measure less than 90 degrees.

The first solution, x = -(1/2)π - 1, can be written in degrees as:

x ≈ -106.26 degrees

This angle is not acute, so it is not a valid solution.

The second solution, x = -(3/2)π - 1, can be written in degrees as:

x ≈ -286.87 degrees

This angle is also not acute, so it is not a valid solution.

Therefore, there are no acute angles that satisfy the equation sin(3x + 9) = cos(x + 5).

Learn more about acute angles

brainly.com/question/10334248

#SPJ11

Marsha is considering purchasing 3 points on a $350,000 home mortgage for 20 years. If she
purchases the 3 points, at a cost of 1 percent per point, her monthly mortgage would be
approximately $1,878.63. If she decides not to purchase any points, Mercedes' monthly
payment would be approximately $1,987.13. How much money will Mercedes save over the life
of the loan if she purchases the 3 points?

Answers

Marsha would save $26,040 over the life of the loan if she purchases the 3 points.

First, let's calculate the monthly payment if Marsha doesn't purchase any points. We can use a mortgage calculator or the PMT function in Excel to find;

PMT = $1,987.13

Now, let's calculate the monthly payment if Marsha purchases 3 points;

Loan amount = $350,000

Points cost = 3 points × 1% × $350,000 = $10,500

Effective loan amount = $350,000 - $10,500 = $339,500

Interest rate = 4.5% / 12 = 0.375%

Number of payments=20 years × 12 = 240

Using the PMT function, we get;

PMT = $1,878.63

So, by purchasing 3 points, Marsha can save;

$1,987.13 - $1,878.63 = $108.50 per month

Over the life of the loan, which is 20 years or 240 months, the total savings would be;

$108.50 × 240 = $26,040

Therefore, Marsha would save $26,040 amount of money.

To know more about loan here

https://brainly.com/question/31292605

#SPJ1

The bike sarah wants to buy is now 40% off. the original price is $150. decide if you are missing the percent, part or whole. then use the appropriate formula to find the discount amount

Answers

The discount amount of the bike Sarah wants to buy is $60. The calculation was done by using the formula: Discount = Original price x Percent off.

To find the discount amount of the bike, we need to use the formula

Discount = Original Price x Discount Rate

where Discount Rate = Percent Off / 100

We know that the original price of the bike is $150 and it is now 40% off. So, the discount rate is

Discount Rate = 40 / 100 = 0.4

Substituting these values in the formula, we get:

Discount = $150 x 0.4 = $60

Therefore, the discount amount of the bike is $60.

To know more about discount amount:

https://brainly.com/question/29181625

#SPJ4

Find the volume of the solid generated by revolving the region enclosed by x= v5y2, x = 0, y = - 4, and y = 4 about the y-axis.

Answers

To find the volume of the solid generated by revolving the given region about the y-axis, we can use the method of cylindrical shells.

First, we need to sketch the region and the axis of rotation to visualize the solid. The region is a parabolic shape that extends from y = -4 to y = 4, and the axis of rotation is the y-axis.

Next, we need to set up the integral that represents the volume of the solid. We can slice the solid into thin cylindrical shells, each with radius r = x and height h = dy. The volume of each shell is given by:

dV = 2πrh dy

where the factor of 2π accounts for the full revolution around the y-axis. To express r in terms of y, we can solve the equation x = v5y2 for x:

x = v5y2
r = x = v5y2

Now we can integrate this expression for r over the range of y = -4 to y = 4:

V = ∫-4^4 2πr h dy
 = ∫-4^4 2π(v5y2)(dy)
 = 80πv5

Therefore, the volume of the solid generated by revolving the given region about the y-axis is 80πv5 cubic units.
To find the volume of the solid generated by revolving the region enclosed by x = √(5y²), x = 0, y = -4, and y = 4 about the y-axis, we can use the disk method.

The disk method involves integrating the area of each circular disk formed when the region is revolved around the y-axis. The area of each disk is A(y) = πR², where R is the radius of the disk.

In this case, the radius is the distance from the y-axis to the curve x = √(5y²), which is simply R(y) = √(5y²).

So the area of each disk is A(y) = π(√(5y²))² = 5πy²

Now, we can find the volume by integrating A(y) from y = -4 to y = 4:

Volume = ∫[A(y) dy] from -4 to 4 = ∫[5πy² dy] from -4 to 4

= 5π∫[y²2 dy] from -4 to 4

= 5π[(1/3)y³] from -4 to 4

= 5π[(1/3)(4³) - (1/3)(-4³)]

= 5π[(1/3)(64 + 64)]

= 5π[(1/3)(128)]

= (5/3)π(128)

= 213.67π cubic units

The volume of the solid generated by revolving the region enclosed by x = √(5y²), x = 0, y = -4, and y = 4 about the y-axis is approximately 213.67π cubic units.

Visit here to learn more about volume brainly.com/question/1578538

#SPJ11

If the mean weight of 4 backfield members on the football team is 234 lb and the mean weight of the 7 other players is 192 ​lb, what is the mean weight of the 11​-person​ team?

The mean weight of the team is approximately ___ pounds.
(Round to the nearest​ tenth.)

Answers

Answer: The mean weight of the 11-person team is 207.3 pounds

Step-by-step explanation:

According to the question,

The mean weight of 4 backfield members = 234 lb
Therefore, the total weight of 4 backfield members = 4 × 234 = 936 lb

Similarly,
The mean weight of the 7 players = 192 lb
And the total weight of 7 players = 7 × 192 = 1344 lb

∴ Total weight of 11 players = (936 + 1344) lb = 2280 lb

We know that,

Mean =  [tex]\frac{Total Sum}{Total number of variables}[/tex]    

∴ To find the mean weight of the 11 players we need to divide the total weight by 11 :

Mean = [tex]\frac{2280}{11} = 207.27[/tex]

Rounding off to the nearest tenth we get,
Mean = 207.3

Hence, the mean weight of the team is approximately 207.3 pounds



Under her cell phone plan Yaritza pays a flat cost of $41 and 50 Cent per month and five dollars per gigabyte she wants to keep her bill under $60 per month which inequality can be used to determine ask the minimum number of gigabytes Yahritza can use while staying within her budget

Answers

Answer:3 gigabytes of storage.

Step-by-step explanation: Because you start at $41.50 and add 5 is $46.60 and then add 5 again and you get $51.50 then add 5 more you get $56.50.

A three digit number is such that twice the hundreds digit is more than the tens digit by 2. The unit digit is thrice the hundred digit. When the digits are reversed the number is increased by 594. Find the number.(5 marks)

Answers

Answer:

Step-by-step explanation:

Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.

From the problem, we have two equations:

Equation 1: $2a=b+2$

Equation 2: $c=3a$

We can use these equations to solve for $a$, $b$, and $c$.

Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.

Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.

Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.

Thus, the original three-digit number is $abc=824$.

When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.

Therefore, the answer is $\boxed{824}$.

Other Questions
Example 13:0. 29 grams of a hydrocarbon with vapour density 29 when burnt completely in oxygen produce 448 ml of carbon dioxide at S. T. P. From the given information, calculate the (i) mass of carbon dioxide formed. how to remove gas from stomach instantly home remedies The rule is x->y=3x. Copy and fill in the table with atleast 4 points What was the Replacement of the M14 In the Vietnam War?A. M16B. M60C. M4What countries was helping Vietnam in the Vietnam war?A.Soviet Union, China, North Korea and other communist countriesB.Nepal, Kazakhstan, Mongolia and other republic countriesC.None of the aboveWhat Side won in the Vietnam War?A.North VietnamB. South VietnamC.It was a draw.What checkpoint was in East And west Germany?A.Checkpoint CharlieB.Checkpoint CommunistC.Checkpoint "See You In Heaven" I NEED A GOOD GRADE SO I CAN BE A STEPPER NEXT YEAR !!!!! K. canopy, the proprietor of canopy services, withdrew $5,900 from the business during the current year. the entry to close the withdrawals account at the end of the year is: Prepare a mixture of 100g of 8% cream into 200g of 3% cream. What is the resulting concentration? (Pharmacy technician math) Acrostic poem for sacrifice Which narrative technique does this passage NOT use to tell the story of Coach Wilkins? A) the use of a sequential plot B) the introduction of a main character C) character description of Coach Wilkins D) dialogue to reveal the characters' traits If $8000 is invested at 4. 25%, compounded continuously, how long will it take to double?Round the nearest tenth of ayear The education of children and missionaries was the principal goal of. Determine whether the series is convergent or divergent by expressing the nth partial sum sn as a telescoping sum. If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) 2 n2 - If the House wants to take an unscheduled six-day vacation in the middle of the session, what do they need to do? An increase in the quantity supplied can result from an increase in price. an increase in price. decreased demand. decreased demand. an increase in supply. In an effort to encourage Melissa to do well in school, her parents have decided to give her $20 for every "A" she receives on her report card. Melissa's parents are using(A) negative punishment(B) negative reinforcement(C positive reinforcement(D)positive punishment How do I take a picture what is the resulting expression when (7x - 4/3) is subtracted from -3/5x + 5/3? Exam Practice - Analysis of Path-goal theory case studyYou are assigned by the Managing Director of Faxxcom, a mobile phone production company to look into the problems. You have talked to three managers. The first one is Bob, A departments manager, and has a set of leadership challenges. Bob is a supportive leader as seen through his interactions with workers. He remembers his followers birthdays, takes them out for lunch, and praises their performance. However, this approach does not suit their task characteristics as outlined in the path-goal model. Often times, his workers are unsure what and how to do their work. They seem to have ambiguous targets to achieve and have to work under a lot of pressure. Their work environment transforms on a regular basis, so they require a supervisor who can explain the targets. Additionally, these workers feel insecure since they do not know how to cope with the changes which is shown in the way they complain to each other about their work. This scenario requires a directive leader who will provide structure and guide them in their daily tasks. Bob ought to get more involved in his subordinates tasks so as deal with this challenge.The second manager is Arthur who is Department Bs manager, and he has different leadership challenges. His employees are dull and uninterested to work. They also know their tasks inside out. The path goal theory states that directive leadership is suitable to dogmatic subordinates who have unclear, complex and ambiguous tasks. However, B departments workers are already confident about their ability to complete tasks. Additionally, they seem to have an internal locus of control. Therefore, the last thing they need is a directive leader, yet Arthur has selected the directive leadership style. His behaviour is incompatible with his employees and well as their work environment. Thus, Arthur needs to minimize his level of involvement in the workers work. He should behave more like Bob by dealing with his subordinates human needs. Arthur ought to work on his interpersonal relationship by relating to his subordinates. These workers need a human touch because they prefer affiliation and interpersonal relationship, which is the perfect scenario for supportive leadership.Lastly, Carol, is a part-time assistant manager who comes to support the factory of Faxxcom during the peak production seasons for departments A & B, seems to have mastered her situation and her employees quite well. She is a participative leader in certain circumstances, a supportive leader at other times, and an achievement-oriented supervisor in certain circumstances. She knows when to solicit for ideas or when to support workers. Carol represents the ultimate path-goal leader; she works on employees personal needs while focusing on the ultimate goal in the enterprise. She also eliminates obstacles and clarifies path in the way that the matter has been described in the theory.QuestionsWhat are the leadership problems for departments A & B under Bobs and Arthur? (explain it in detail) The smaller of two similar rectangles has dimensions 4 and 6. Find the dimensions of the larger rectangle if the ratio ofthe perimeters is 2 to 3.O 6 by 92/3by 412 by 12O8 by 18 KEY OUEsTION: WHAT WAS THE IMPACT,OF PSEUDOSCIENTIFIC IDEAS OF RACE ON THE JEWISH NATION BY THE NAZI GERMANY DURING THE PERIOD 1933 TO 1946?