If Katie started with $40, the remaining balance after purchasing the supplies is $20.
To determine how much money Katie had left after purchasing the supplies, we'll consider the fraction "1/5" for the storybook and "3/10" for the calculator.
1: Calculate the amount spent on the storybook.
Katie spent 1/5 of her initial $40 on the storybook. To find this amount, multiply the fraction by the total amount:
(1/5) x $40 = $8
2: Calculate the amount spent on the calculator.
Katie spent 3/10 of her initial $40 on the calculator. To find this amount, multiply the fraction by the total amount:
(3/10) x $40 = $12
3: Add the amounts spent on both the storybook and calculator.
$8 (storybook) + $12 (calculator) = $20
4: Subtract the total amount spent from Katie's initial amount of money to find the remaining balance.
$40 (initial amount) - $20 (total spent) = $20
After purchasing the supplies, Katie had $20 left.
Note: The question is incomplete. The complete question probably is: Katie started with $40. He spent 1/5 of the money on a storybook and 3/10 on a calculator. how much money did she have left after purchases the supplies.
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A tank in the shape of a hemisphere has a diameter of 8 feet. If the liquid that fills the tank has a density of 86 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
209.07 pounds
Step-by-step explanation:
radius= 8÷2=4 feet
volume of hemisphere=((4/3)×(22/7)×r^3)/2
=134.09 cubic feet
Mass=density × volume
=86×134.09
=209.07 pounds
 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. 
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.
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I need help on this question, and please explain how you did it.
The expression for AB in terms of x and √3 is:
AB = x√3.
What is an expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
In a right triangle ABC, if sin B = 0.5, then we know that:
sin B = opposite / hypotenuse
So, we can write:
0.5 = AB / CB
We also know that:
CB² = AB² + AC²
Substituting the value of AC, we get:
CB² = AB² + (3x)²
CB² = AB² + 9x²
Now, we can substitute the value of CB² from the first equation:
(AB / 0.5)² = AB² + 9x²
4AB² = AB² + 9x²
3AB² = 9x²
AB² = 3x²
The expression for AB in terms of x and √3 is:
AB = x√3
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Which of the following is a typical characteristic of debit cards? (1 point)
O Your bank may charge you a very large fee each time you use one.
O When you buy something from a store, you may be offered a discount if you open one with the store.
O They usually charge a lower interest rate than credit cards.
They are tied directly to your bank account.
A typical characteristic of debit cards is expressed by option D, they are tied directly to your bank account, since money has to be deducted for a purchase to be made.
How debit cards functionWhen you use a debit card to make a purchase, the money is deducted directly from your bank account. Debit cards do not typically charge interest like credit cards do, so C is not correct.
A is also not correct since most banks do not charge a fee for using a debit card, although some may charge fees for using an out-of-network ATM or overdraft fees if you spend more than you have in your account. B is not a typical characteristic of debit cards either, as there is generally no connection between a store's loyalty program or discounts and using a debit card for payment.
Therefore, it is possible to conclude that debit cards have option D as their characteristic. Since they require money in the bank to make the purchase, they are connected to one's account.
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1. $4,076.92
2. Assets = Liabilities + Equity
3. They can be used to make online purchases.
4. by using an emergency fund for this unplanned expense
5. a fund with a minimum investment that tracks the value of cash
6. 1930s
7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.
8. their vacation cabin
9. You should shop around for the best overall deal.
10. If you use a credit card, it is easy to run up huge debts.
11. They are tied directly to your bank account.
12. preventative care
13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage
14. how long the coverage lasts, how much the premium costs, and the cash value
15. 1-year renewable group term life
16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.
17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.
18. 2 year in state community college degree
19. tuition assistance
20. -a sundae, -movie tickets
Explanation: All of these answers are correct!
Personal Finance Semester Exam
5/11/2023
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
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.
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HELPPPPPPP PLEASEEEE
Answer:
The first box and whisker plot
Step-by-step explanation:
A box and whisker plot gives you the five number summary for a set of data. The five number summary is
The minimum/lowest value (looks like the top of capital T turned sideways and is the leftmost part of the box-and-whisker plot The first quartile or Q1, representing 25% of the data (the first point represented in the "box" of the plot and serves as an endpoint of the box)The median or Q2, representing 50%/the middle of the data (the line that splits the box into two parts/the line in the middle of the box)The third quartile or Q3, representing 75% of the data (the last point represented in the "box" of the plot and serves as another endpoint of the box)The maximum/highest value (also looks like the top of capital T turned sideways and is the rightmost part of the box-and-whisker plotMaximum and minimum:
We know from the data that the minimum value is 100 and the maximum value is 200. However, because both boxes available as answer choices have the correct minimum and maximum, we'll need to find more data.
Median:
We can start finding the median first by arranging the data from the least to greatest. Then, we find the middle of the data. Because there are 9 points and 9 is odd, we know that there will be 4 points to the left of the median and 4 points to the right of the median:
100, 100, 120, 120, 150, 165, 180, 180, 200
150 has 4 numbers both on its left and right sides so its the median.
Because both of the plots available as answer choices have the correct median, we we'll need to find more data.
First Quartile/Q1:
In order to find Q1, we must find the middle number of the four numbers to the left of the median.
Because we have an even number of points, we will get two middle numbers, 100 and 120. To find the middle of all four points, we average these two numbers:
(100 + 120) / 2 = 220 / 2 = 110
Only the first box has the accurate Q1 value, so it's our answer.
We don't have to find Q3, since both boxes have the correct Q3, but only the first box has the correct minimum, correct Q1, correct median, correct Q3, correct maximum.
5. Rita has a circular hot tub. The hot tub has a circumference 25. 12 feet. It is 3. 5 feet deep.
a. Find the radius of the hot tub. Use 3. 14 for pi
b. How much water can the hot tub hold?
c. The hot tub manual recommends filling the hot tub to 80% of its full capacity. How
much water should rita put in the hot tub in order to follow the recommendation?
a.The radius of the hot tub is 4 feet. b. The amount of water that the hot tub can hold is 176.96 cubic feet c. The amount of water that Rita should put in the hot tub in order to follow the recommendation is 141.57 cubic feet.
a. Find the radius of the hot tub.
Given: Circumference = 25.12 feet
Formula: Circumference = 2 * pi * radius
1: Plug in the given circumference and the value of pi.
25.12 = 2 * 3.14 * radius
2: Solve for the radius.
radius = 25.12 / (2 * 3.14)
radius ≈ 4 feet
So, the hot tub's radius is 4 feet.
b. How much water can the hot tub hold?
Given: Radius = 4 feet, Depth = 3.5 feet
Formula: Volume = pi * radius^2 * depth
1: Plug in the radius, depth, and the value of pi.
Volume = 3.14 * (4^2) * 3.5
2: Calculate the volume.
Volume ≈ 176.96 cubic feet
So, the hot tub can approximately hold 176.96 cubic feet.
c. How much water should Rita put in the hot tub to follow the recommendation?
Given: Recommended capacity = 80% of full capacity
Formula: Recommended water = 0.8 * full capacity
1: Plug in the full capacity (volume) calculated in part b.
Recommended water = 0.8 * 176.96
2: Calculate the recommended water amount.
Recommended water ≈ 141.57 cubic feet
So, Rita should put approximately 141.57 cubic feet of water in the hot tub to follow the recommendation.
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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?
The angle between their courses is 42.02°.
How to calculate angle between 2 moving bodiesIt 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°
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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.)
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
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
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.
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Which system of equations is represented by the graph?
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!
What is the sine ratio for angle A?
A. 10/8
B. 8/10
C. 6/10
D. 6/8
Answer:
C. 6/10
Step-by-step explanation:
Sin A = 6/10
£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.
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.
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Jessica has 300 cm of matenal. She uses 12. 6 cm to make a nght triangular prism She wants to make a second prism that is a
dilation of the first prism with a scale factor of 3
How much more material does Jessica need in order to make the second prism?
Select from the drop-down menu to correctly complete the statement
cm of material to make the second prism
Jessica needs an additional Choose
To make the second prism, Jessica needs an additional 25.2 cm of material.
To answer your question, since Jessica wants to create a second triangular prism with a scale factor of 3, she will need 3 times the material used for the first prism.
She used 12.6 cm for the first prism, so for the second prism, she would need 12.6 cm × 3 = 37.8 cm of material.
Jessica already has 300 cm of material, so to find out how much more she needs, subtract the amount used for the first prism: 37.8 cm - 12.6 cm = 25.2 cm.
Jessica needs an additional 25.2 cm of material to make the second prism.
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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
Answer:
Step-by-step explanation:
Pls answer this, 5 points and brainliest for the one who answers first.
Answer: A
Step-by-step explanation:
It's A because our function of f is multiplied by 3.
Since our y intercept is 1, and we are multiplying the function f by 3,
our new y intercept is 3, meaning it is A.
Another way to check this is by using the other two points on your graph.
Please give brainliest + have a good afternoon.
Answer:
Step-by-step explanation:
Your original function has points at
0, 1
1, 2
2,4
if you stretched it by 3, multiply your y by 3
new function:
0, 3
1, 6
2, 12
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?
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.
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In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 10 recent loans is taken. The average calculated from this sample is 6. 40%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a population standard deviation of 0. 5%. Compute 95% and 99% confidence intervals for the population mean 30-year fixed mortgage rate
The 95% confidence interval for the population mean 30-year fixed mortgage rate is (6.091%, 6.709%), and the 99% confidence interval is (5.993%, 6.807%).
To estimate the mean 30-year fixed mortgage rate for a home loan in the United States using a random sample of 10 recent loans with an average of 6.40% and a population standard deviation of 0.5%, you can compute the 95% and 99% confidence intervals as follows:
1: Identify the sample mean (x), sample size (n), and population standard deviation (σ).
x = 6.40%
n = 10
σ = 0.5%
2: Calculate the standard error (SE) using the formula SE = σ/√n.
SE = 0.5%/√10 ≈ 0.158%
3: Determine the critical z-values for 95% and 99% confidence intervals.
For a 95% confidence interval, z = 1.96 (from the z-table)
For a 99% confidence interval, z = 2.576 (from the z-table)
4: Calculate the margin of error (ME) using the formula ME = z * SE.
For 95% CI,
ME = 1.96 * 0.158% ≈ 0.309%
For 99% CI,
ME = 2.576 * 0.158% ≈ 0.407%
5: Compute the confidence intervals by adding and subtracting the ME from the sample mean.
95% CI:
(6.40% - 0.309%, 6.40% + 0.309%) = (6.091%, 6.709%)
99% CI:
(6.40% - 0.407%, 6.40% + 0.407%) = (5.993%, 6.807%)
So, the 95% confidence interval and 99% confidence interval is (6.091%, 6.709%) and (5.993%, 6.807%) respectively.
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Please help I need this done ASAP
Answer:
Domain is all x values
Range is all y values
Step-by-step explanation:
Your image is not clear enough for me to see the x or y coordinates so hope that helps you to figure it out on your own
PLEASE HELP EM I WIL GIVE BRAINLIEST TO THE FIRST CORRECT ANSWER EHLP ME FAST PLEASE
[tex]a = \sqrt{ {8}^{2} - {6}^{2} } \\ \\ = \sqrt{64 - 36 }\\ \\ =\sqrt{ 28} \\ \\ = \sqrt{4 \times 7} \\ \\ = 2 \sqrt{7} [/tex]
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.
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.
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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.
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
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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?
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.
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Find two acute angles that satisfy the equation sin(3x + 9) = cos(x + 5). check that your answers make sense.
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 - 4Dividing 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).
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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
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.
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
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.
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5. The formula below relates the velocity,
v, of a moving object (in meters per
second), to the kinetic energy, E, of the
object (in joules), and the object's mass,
m (in kilograms).
V=
2.E
m
What is the velocity, in meters
per second, of a bowling ball that
has a mass of 5.5 kilograms and is
producing 2223 joules of kinetic
energy?
The velocity of the bowling ball is approximately 20.104 meters per second.
What is velocity?The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity.
The formula given is used to calculate the velocity of a moving object in meters per second, given the object's mass in kilograms and its kinetic energy in joules. The formula is:
V = √(2E/m)
where V is the velocity, E is the kinetic energy, and m is the mass of the object.
To use this formula to find the velocity of the bowling ball, we need to substitute the given values into the formula. The mass of the bowling ball is 5.5 kilograms, and the kinetic energy is 2223 joules. Substituting these values, we get:
V = √(2 × 2223 J / 5.5 kg)
Now, we can simplify the equation:
V = √(404.1818)
Using a calculator, we can find the square root of 404.1818:
V = 20.104 m/s (rounded to three decimal places)
Therefore, the velocity of the bowling ball is approximately 20.104 meters per second.
This formula is useful for calculating the velocity of a moving object when the mass and kinetic energy of the object are known. It can be used in a variety of situations, such as in physics experiments, engineering design, or in understanding the motion of objects in sports.
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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.
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.:
Mr. Lance designed a class banner shaped like a polygon shown what is the name of the polygon
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.
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
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.
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