Answer:
Let's start by drawing a diagram of the cornfield with the plowed strip around it:
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The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.
The total area of the cornfield is:
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12 km x 9 km = 108 km^2
If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:
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(12 + 2w) km x (9 + 2w) km
The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:
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(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2
We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:
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108 + 42w + 4w^2 = (1/2)(108)
Simplifying, we get:
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4w^2 + 42w - 54 = 0
We can solve this quadratic equation using the quadratic formula:
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w = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 4, b = 42, and c = -54. Substituting these values, we get:
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w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8
arduino
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w = (-42 ± sqrt(1936)) / 8
makefile
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w = (-42 ± 44) / 8
So we have two possible solutions:
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w = 1/2 km (discarded since it does not satisfy the given condition)
or
makefile
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w = 11/2 km
Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.
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Kareem rented a truck for one day. there was a base fee of $19.99 , and there was an additional charge of 83 cents for each mile driven. kareem had to pay $135.36 when he returned the truck. for how many miles did he drive the truck?
Kareem drove the truck for 150 miles.
As areem rented a truck for one day. there was a base fee of $19.99 , and there was an additional charge of 83 cents for each mile driven we will let the number of miles driven by Kareem be represented by 'x'. The total cost, including the base fee, can be represented as:
Total cost = Base fee + Additional charge per mile * Number of miles driven
$135.36 = $19.99 + $0.83x
Subtracting $19.99 from both sides and then dividing by $0.83, we get:
x = (135.36 - 19.99) / 0.83
x = 150
Therefore, Kareem drove the truck for 150 miles.
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The vector
u
u has magnitude
2
2 and direction
5
5
∘. 55
∘. If vector
v
=
−
2
u
,
v=−2u, then what is the magnitude and direction of vector
v
?
v? Write your direction in degrees in the interval
0
∘
≤
θ
<
36
0
∘. 0
∘
≤θ<
The magnitude of vector v is 4 and the direction is 125 degrees.
Given that vector u has a magnitude of 2 and a direction of 55 degrees, we can determine the magnitude and direction of vector v.
To find the magnitude of vector v, we can use the equation:
|v| = |-2u|
Since u has a magnitude of 2, we can substitute it into the equation:
|v| = |-2 * 2|
|v| = |-4|
|v| = 4
The magnitude of vector v is 4.
To find the direction of vector v, we can note that multiplying a vector by -1 (in this case, multiplying u by -2) reverses its direction. So the direction of v is the exact opposite of the direction of u.
Since the direction of u is 55 degrees, the direction of v is 55 degrees in the opposite direction. In the interval of 0 degrees ≤ θ < 360 degrees, the direction of v can be expressed as:
θ = 180 - 55
θ = 125 degrees
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HELP! BRAINLIST! THIS IS DUE IT IS END OF UNIT ASSESSMENT
The surface area of the cone is approximately 793.10 cm².
What is cone?
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex.
What is area of cone?
The surface area of a cone is given by the formula:
Surface Area = πr² + πrℓ
where r is the radius of the circular base and ℓ is the slant height of the cone.
According to given information:To find the surface area of a cone, we need to find the area of its base and the area of its lateral surface and then add them together.
The formula for the lateral surface area of a cone is given by:
L = πrℓ
where r is the radius of the base and ℓ is the slant height of the cone.
The formula for the area of the base of a cone is given by:
B = πr²
where r is the radius of the base.
Given the slant height ℓ = 19 and the radius r = 9, we can find the lateral surface area of the cone as follows:
L = πrℓ
= π(9)(19)
≈ 538.63 cm²
Next, we can find the area of the base of the cone as follows:
B = πr²
= π(9)²
≈ 254.47 cm²
Therefore, the surface area of the cone is:
A = B + L
≈ 793.10 cm²
So, the surface area of the cone is approximately 793.10 cm².
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The figure below has a net for a right rectangular prism. 15cm 11cm 11cm 11cm 11cm 14cm What is the surface area of the right rectangular prism, in square centimeters
The surface area of the right rectangular prism is 880 cm².
Given Top and bottom measurements of the rectangular prism = 15 cm and 11 cm
The front and back measurements of the rectangular prism = 11cm and 11cm
The two sides measurements of the rectangular prism = 11 cm and 14 cm
To find the surface area of the rectangular prism, we have to substitute the above values in the below equation,
Surface area = (top*bottom) + (front*back) + (sides)
Surface area = (15 cm * 11 cm) + (11 cm * 11 cm) + (11 cm * 14 cm)
Surface area = 330 cm² + 242 cm² + 308 cm²
Surface area = 880cm²
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What is the value of the h in the triangle below?
The value of h in the triangle shown above is calculated using proportion as: h = 4.
How to Find the Value of h in the Triangle?The two triangles shown are similar to each other based on the Angle-angle (AA) Similarity theorem. This implies that the length of their corresponding pair of sides would be proportional to each other.
Therefore, we have:
8/18 = h/9 [proportional sides of similar triangles]
Cross multiply:
h * 18 = 8 * 9
18h = 72
Divide both sides by 18:
18h/18 = 72/18 [Division property of equality]
h = 4
Therefore, the length of h in the given image is determined as: 4 units.
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· after buying a new car, you decided to sell your old car. you take a 180-day note for
$4,500 at 7.5% simple interest as payment. (principal plus interest due at the end of
180 days.) sixty days later, you need money and sell the note to a third party for
$4,550. what annual interest rate will the third party receive for the investment?
give the answer as a percentage (three decimal places).
The annual interest rate the third party will receive for the investment is approximately 7.7%.
After buying a new car, you sold your old car and took a 180-day note for $4,500 at 7.5% simple interest as payment. The principal plus interest will be due at the end of 180 days.
First, let's calculate the total amount due at the end of the 180 days. To do this, we'll use the formula for simple interest:
Interest = Principal x Rate x Time
Interest = $4,500 x 7.5% x (180/360) [As it's for half a year]
Interest = $4,500 x 0.075 x 0.5
Interest = $168.75
Now, let's add the interest to the principal to find the total amount due:
Total Amount = Principal + Interest
Total Amount = $4,500 + $168.75
Total Amount = $4,668.75
Sixty days later, you sell the note to a third party for $4,550. The third party will receive the remaining interest for 120 days. We need to find the annual interest rate for the third party's investment.
First, let's find the remaining interest:
Remaining Interest = Total Amount - $4,550
Remaining Interest = $4,668.75 - $4,550
Remaining Interest = $118.75
Now, let's find the annual interest rate for the third party's investment using the simple interest formula, but solving for the rate:
Rate = (Remaining Interest) / (Principal x Time)
Rate = $118.75 / ($4,550 x (120/360))
Rate = $118.75 / ($4,550 x 0.3333)
Rate ≈ 0.077 (approximated to 3 decimal places)
So, the annual interest rate the third party will receive for the investment is approximately 7.7%.
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The rate of change dp/dt of the number of bears on an island is modeled by a logistic differential equation. The maximum capacity of the island is 555 bears. At 6 AM, the number of bears on the island is 165 and is increasing at a rate of 29 bears per day. Write a differential equation to describe the situation.
The differential equation that describes the situation is: dp/dt = 41.43 * p * (1 - p/555).
The logistic differential equation is a commonly used model for population growth or decay, taking into account the carrying capacity of the environment. It is given by:
dp/dt = r * p * (1 - p/K)
where p is the population, t is time, r is the growth rate, and K is the carrying capacity.
In this case, the maximum capacity of the island is 555 bears, so we have K = 555. At 6 AM, the number of bears on the island is 165 and is increasing at a rate of 29 bears per day, so we have:
p(0) = 165 and dp/dt(0) = 29
To write the differential equation that describes this situation, we can use the initial conditions and the logistic model:
dp/dt = r * p * (1 - p/555)
Substituting the initial conditions, we get:
29 = r * 165 * (1 - 165/555)
Simplifying this expression, we get:
29 = r * 0.7
r = 41.43
Therefore, the differential equation that describes the situation is:
dp/dt = 41.43 * p * (1 - p/555)
Note that this model assumes that the growth rate of the bear population is proportional to the number of bears present and that the carrying capacity is fixed. Real-life situations may involve more complex models with time-varying carrying capacities or other factors affecting population growth.
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michelle is building a rectangular landing strip for airplanes. she has enough material to cover of a square mile. the landing strip must be of a mile long. with the amount of material that michelle has, what is the greatest possible width of the landing strip, in miles?
The greatest possible width the land strip, in miles with the amount of material that has is 1/250 miles wide.
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.
A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of each rectangle serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.
Let's say that her landing strip is x miles long, then its area would be:
1/6.x
We also know how big it is:
so,
1/6.x = 1/1500
x = 6/1500
x = 3/750
x = 1/250 miles
Therefore, possible width of the landing strip is 1/250 miles.
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Complete question:
Michelle is building a rectangular landing strip for airplanes .She has material to cover 1/1,500 of a square mile. The landing strip must be 1/6 of a mile long. With the amount of material that has , what is the greatest possible width the land strip, in miles?
In the figure 11 || 12 and 13 is a transversal. What is the value of |5p - 3q|?
The value of ║5p-3q║=180°.
It is given that line l₁ & l₂ are parallel and l₂ & l₃ are transversal then
they must follow the property that the alternate exterior angles must be equal i.e. ∠ q = 135°.
Also ∠ p + ∠ q = 180°.
Therefore, ∠ p = 45°.
Now to solve ║5p-3q║, substituting the values of p & q in the given equation
║5*45 - 3*135║ = 180°.
Hence, ║5p-3q║=180°.
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the Senators 118 more games than they lost they played 78 games. how many games did they win?
The Number of games lost cannot be negative .
The number of games the Senators won as "W." According to the given information, the Senators won 118 more games than they lost. This can be expressed as:
W = L + 118,
where "L" represents the number of games the Senators lost.
the Senators played a total of 78 games, which means the number of games they won and lost combined should equal 78:
W + L = 78.
Substituting the first equation into the second equation, we have:
(L + 118) + L = 78,
2L + 118 = 78,
2L = 78 - 118,
2L = -40,
L = -40/2,
L = -20.
Since the number of games lost cannot be negative.
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If $x$ is a positive number such that\[\sqrt{8x}\cdot\sqrt{10x}\cdot\sqrt{3x}\cdot\sqrt{15x}=15,\]find all possible values for $x$.
The possible values of x as required to be determined in the task content are; ±½.
What are the possible values of x?It follows from the task content that the possible values of x are to be determined from the given task content.
The given equation can be written algebraically as;
√(8x) • √(10x) • √(3x) • √(15x) = 15
√3600x² = 15
60x² = 15
x² = 15 / 60
x² = 1/4.
x = ± ½.
Ultimately, the possible values of x as required in the task content are; +½ and -½.
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Find all values of x for which the series converges. (Enter your answer using interval notation.)
∑(6x)^n
the series converges for all x in the interval (-1/6, 1/6) in interval notation.
The given series is a geometric series with first term a=1 and common ratio r=6x. The series converges if and only if |r|<1.
So, |6x|<1
Solving this inequality, we get:
-1/6 < x < 1/6
To find all values of x for which the series converges, we need to analyze the given series:
∑(6x)^n
This is a geometric series with a common ratio of 6x. For a geometric series to converge, the absolute value of the common ratio must be less than 1:
|6x| < 1
Now, we can solve for the interval of x:
|-1/6| < |x| < |1/6|
Using interval notation, the range of values for which the series converges is:
(-1/6, 1/6)
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A student at a local high school claimed that three-
quarters of 17-year-old students in her high school had
their driver's licenses. To test this claim, a friend of hers
sent an email survey to 45 of the 17-year-olds in her
school, and 34 of those students had their driver's
license. The computer output shows the significance test
and a 95% confidence interval based on the survey data.
Test and Cl for One Proportion
Test of p = 0. 75 vs p +0. 75
Sample X N Sample p 95% CI Z-Value P-Value
1
34 45 0. 755556 (0. 6300, 0. 086 0. 9315
0. 8811)
Based on the computer output, is there convincing
evidence that p, the true proportion of 17-year olds at this
high school with driver's licenses, is not 0. 75?
O No, the P-value of 0. 9315 is very large.
Yes, the P-value of 0. 9315 is very large.
O Yes, the 95% confidence interval contains 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p > 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p<0. 75.
No, there is not convincing evidence that p, the true proportion of 17-year-olds at this high school with driver's licenses, is not 0.75.
This is because the P-value of 0.9315 is very large, and the 95% confidence interval contains 0.75 (0.6300, 0.8811). This means that there is not enough evidence to reject the null hypothesis that the true proportion of 17-year olds with driver's licenses is 0.75. The 95% confidence interval also supports this, as it includes 0.75. Therefore, there is no convincing evidence to suggest that the student's claim is incorrect.
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A large diamond with a mass of 2138. 7 grams was recently discovered in a mine. If
8
the density of the diamond is 3. 51 cm", what is the volume? Round your answer to
the nearest hundredth. (5 points)
O 1)
141. 84 cm3
2) 609. 3 cm3
3) 717. 06 cm3
O 4
8169. 8 cm3
WILL GIVE BRAINLIEST!!
The volume of the diamond is 609.3 cm³.
To find the volume of the diamond, we can use the formula:
Volume = Mass / Density
Given:
Mass = 2138.7 grams
Density = 3.51 g/cm³
Substituting these values into the formula:
Volume = 2138.7 g / 3.51 g/cm³
Calculating the division:
Volume ≈ 609.3 cm³
Therefore, the volume of the diamond is approximately 609.3 cm³.
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Calculate the surface area of the rectangular prism shown. You do not need to provide units as they have been provided for you.
Surface Area = ___ yd2
rectangular prism with the base having all measurements of 7 yards and the height measuring 5 yards
Answer:
238 ft²
Step-by-step explanation:
Base area is l*w and there are two of these so 2(7*7) = 98
Then there 4 faces that have dimensions 4(7*5)=140
98+140=238
Choose the definition for the function acellus
Acellus is a powerful tool for students looking to achieve academic success and gain the skills they need to succeed in today's competitive world.
Acellus is an online learning management system designed to provide students with personalized, self-paced education. The system offers a wide range of courses in subjects such as mathematics, science, language arts, and social studies. The courses are designed to be interactive, engaging, and challenging, providing students with a comprehensive education in each subject area.
Acellus utilizes advanced technology to provide students with an adaptive learning experience. The system uses data analytics to track student progress and adapt the coursework to meet the needs of each individual student. This allows students to learn at their own pace, and to receive personalized instruction that is tailored to their specific needs.
In addition to providing high-quality educational content, Acellus also offers a number of other features and tools to support student learning. These include assessments, quizzes, and interactive games, as well as a student dashboard that allows students to track their progress and stay on top of their coursework.
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Alfonso went to famous Sam’s appliance store and purchased a refrigerator and a stove. The sale price of the refrigerator was 40% off the original price and the sales price of the stove was 20% off the original price
Alfonso received a 30% overall discount on the refrigerator and the stove together if the sale price of the refrigerator was 2/3 of the sale price of the stove. Therefore, statement (c) is the correct answer.
To see why, let's use some algebra. Let R be the original price of the refrigerator and S be the original price of the stove. Then the sale price of the refrigerator is 0.6R and the sale price of the stove is 0.8S. The total amount Alfonso paid is 0.6R + 0.8S.
To receive a 30% overall discount, Alfonso must have paid only 0.7 times the total original price, which is 0.7(R + S). Therefore, we have the equation:
0.6R + 0.8S = 0.7(R + S)
Simplifying this equation gives:
0.1R = 0.1S
R = S
So the original prices of the refrigerator and the stove were the same. This means that statement (C) is true.
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Complete Question:
Alfonso went to famous Sam's Appliances store and purchased a refrigerator and a stove. The sale price of the refrigerator was 40% off the original price and the sale price of the stove was 20% off the original price.
Which statement must be true to conclude that Alfonso received a 30% overall discount on the refrigerator and the stove together?
a) The sale prices of the refrigerator and the stove were the same.
b) The original prices of the refrigerator and the stove were the same.
c) The sale price of the refrigerator was twice the sale price of the stove.
d) The original price of the refrigerator was twice the original price of the stove.
Portfolio for Unit 5
Part 1: Car Wheel Project
For the Portfolio for Unit 5 Part 1, the Car Wheel Project, you'll want to include several key components.
First, be sure to include a detailed description of the project itself, including any goals or objectives you had in mind when you started. This could include things like improving your engineering or design skills, learning more about the materials used in car wheels, or simply creating a visually impressive final product.
Next, include some documentation of your process as you worked on the project. This might include sketches, diagrams, or photos of different stages of the process. Be sure to highlight any challenges or roadblocks you encountered along the way, and how you overcame them.
Finally, be sure to include a final showcase of your completed car wheel project. This might include photos of the finished product from different angles, a video demonstrating how it works or how it was made, or even a physical prototype that you can bring in to show off.
Overall, the key to a successful portfolio for the Car Wheel Project is to demonstrate your creativity, your technical skills, and your ability to work through challenges and solve problems.
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Unit 5 Portfolio Car Wheel Project Answer the following questions: 1. How do you find the area of a circle?
2. How do you find the circumference of a circle?
3. What information do you need in order to find the area or circumference of a circle
4. To determine the number of full rotations your tires complete before you need to switch thefront and back tires, will you be working with area or circumference?
Answer:
How do you find an area of a crilce?
-Use the formula A=[tex]\pi r^2[/tex]
How do you find the cirumference of a cirlce?
-Use the formula c=2[tex]\pi r[/tex]
What information do you need in order to find the area or circumference of a cirlce?
-I believe it's the diameter.
To determine the number of full rotations your tires complete before you switch the front and back tires will you be working with area or circumference?
-Circumference. Because ifts the distance around something, like a circle, or a wheel.
(My three examples of the circumference of tires)
Bike:
C=2(3.14)r
C=2 (3.14) 8
C=50.24
Car:
C=2(3.14)r
C=2 (3.14) 20
C=125.6
Scooter:
C=2(3.14)r
C=2 (3.14) 3
C=18.24
(My tire rotations how far you'll go in 10,000 miles)
car-
20x3.1416=62.83
10,000/62.83= 159.2
scooter-
3x3.1416=9.4248
10,000/9.4248=1,061
bike-
8x3.1416=25.13
10,000/25.13=397.9
Using one of your vehicles how far can you get in a week?
-We're driving the car with twenty inch wheels and we're going seventy miles an hour. So in a week we would have driven 490 miles.
When will you need to change your tires?
-When we reach 225 miles we'd change the tires. Because these tires are heavier than the average tire they're wear out faster.
I hope this helps!!! Let me know if you need some help with anything else.
(-10x-4y) and (7x-5y) in simplest form
The simplification of the given algebraic expression is: -3x - 9y
How to simplify Algebraic Expressions?Algebraic expressions are defined as the idea of expressing numbers with the aid of letters or alphabets without really specifying their actual values.
Now, the algebraic operations are known by the acronym PEMDAS which denotes:
P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
We want to find the sum of the algebraic expressions given as (-10x - 4y) and (7x - 5y) in simplest form.
Thus, we have:
(-10x - 4y) + (7x - 5y)
= -10x - 4y + 7x - 5y
= -3x - 9y
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Complete question:
Find an expression which represents the sum of (-10x - 4y) and (7x - 5y) in simplest terms.
During taylor's first test of a car with a mass of 250 grams, she recorded 10 seconds, 10.3 seconds, and 10.4 seconds for her 3 trials. what would be the mean value she would use to compare with the other cars?
The mean value Taylor would use is 10.23 seconds.
What is the mean value of Taylor's recorded times for her car's trials?To calculate the mean value for Taylor's recorded times, we add up the individual times (10 seconds, 10.3 seconds, and 10.4 seconds) to obtain a total of 30.7 seconds.
we divide this total by the number of trials, which in this case is 3.
30.7 seconds divided by 3 equals approximately 10.23 seconds.
The mean value of Taylor's recorded times for her car's trials is approximately 10.23 seconds.
The mean value is often used as a measure of central tendency to represent the average of a set of values.
In this case, it represents the average time recorded by Taylor during her trials.
By calculating the mean, we can compare this value with the mean times of other cars to assess performance.
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A dilation always produces a similar figure. Similar figures have the same ______ but different ______.
Answer:
A dilation always produces a similar figure. Similar figures have the same shape but different sizes.
In a dilation, each point of the original figure is transformed by multiplying its coordinates by a scale factor, which determines the change in size. However, the shape and proportions of the figure remain unchanged. Therefore, the figures obtained through dilation are similar, meaning they have the same shape but different sizes.
Please help -(-4)(-6)-3/5(10+5)/1/3!! I’ll give 30 points.
The solution to the expression -(-4) (-6)-3/5(10+5)/1/3 is 15.
To solve this expression, we need to follow the order of operations, which is also known as PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction):
Start with the parentheses: (-4) (-6)= 24, so we can rewrite the expression as:
24-3/5(15)/(1/3)
Now we need to simplify the expression inside the parentheses by adding 10 and 5, which equals 15. Then we need to simplify the division by multiplying the numerator by the reciprocal of the denominator, which is the same as dividing by 1/3. We can rewrite this expression as:
24-3/5*15*3
Multiply 3/5 and 15 first, then multiply that result by 3: 24-9.
Finally, subtract 9 from 24 to get the final answer: 15.
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A triangular prism is 36 millimeters long and has a triangular face with a base of 36 millimeters and a height of 24 millimeters. The other two sides of the triangle are each 30 millimeters. What is the surface area of the triangular prism?
The surface area of the triangular prism is 4302 mm²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is expressed as;
SA = 2B + ph where B is the base area and h is the height of the prism and p is the perimeter of the base.
Base area = 1/2 bh
= 1/2 × 36 × 24
= 36 × 12
= 432 mm²
Perimeter of the base = 36 + 30+30 = 96 mm²
SA = 2 × 432 + 96 × 36
SA = 846 + 3456
SA = 4302 mm²
Therefore the surface area of the triangular prism is 4302 mm².
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The value of a car that depreciates over time can be modeled by the function
G(t) = 24000(0.95)2t. Write an equivalent function of the form G(t) = abt
An equivalent function of the given function in the form G(t) = [tex]ab^t[/tex] is G(t) = 24000[tex](0.9025)^t[/tex].
The given function for the value of a car that depreciates over time is G(t) = 24000[tex](0.95)^{2t[/tex]. To write an equivalent function of the form G(t) = [tex]ab^t[/tex], we need to rewrite the function using exponent rules.
First, we can rewrite [tex](0.95)^{2t[/tex] as [tex][(0.95)^{2}]^{t[/tex], which simplifies to [tex](0.9025)^t[/tex]. Therefore, we have:
G(t) = 24000[tex](0.9025)^t[/tex]
Next, we need to express 24000 as a product of two factors, a and b. We can choose a = 24000 and b = 0.9025, so we have:
G(t) = 24000[tex](0.9025)^t[/tex] = 24000[tex](0.9025)^t[/tex]
This function gives the value of the car at time t, where t is the number of years after the initial purchase, with a starting value of 24000 and a depreciation rate of 9.75% per year.
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stretch your thinking write a word problem for the following
equation. 4/5 x 1/4+ 3/5=
"A recipe for chocolate chip cookies calls for 4/5 cup of sugar per batch. If a baker wants to make 3 batches of cookies, and only has 1/4 cup of sugar left in the pantry, how much additional sugar will the baker need to buy?" is an example of a word problem for the given equation.
To solve this word problem, we can use the equation 4/5 x 1/4 + 3/5 = to find out how much sugar is needed for one batch of cookies, and then multiply that amount by 3 to get the total amount of sugar needed for 3 batches.
The first part of the equation, 4/5 x 1/4, represents the amount of sugar needed for one batch of cookies, which is 1/5 cup. Adding the remaining 3/5 cup of sugar needed for the recipe gives a total of 4/5 cup of sugar per batch.
To find out how much additional sugar the baker needs to buy, we can multiply 4/5 by 3 (the number of batches), and then subtract the amount of sugar already in the pantry (1/4 cup). This gives us:
4/5 x 3 - 1/4 = 12/5 - 1/4 = 43/20
Therefore, the baker will need to buy 43/20 cups of additional sugar to make 3 batches of chocolate chip cookies.
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Consider the following.
u = -8i - 4j - 2k, v = 2j + 2k
Find the projection of u onto v.
Find the vector component of u orthogonal to v
To find the projection of u onto v, we need to use the formula:
projv(u) = (u · v / |v|^2) * v
where u · v is the dot product of u and v, and |v|^2 is the magnitude of v squared.
First, we calculate u · v:
u · v = (-8i - 4j - 2k) · (0i + 2j + 2k) = 0 + (-8*0) + (-4*2) + (-2*2) = -8
Next, we calculate |v|^2:
|v|^2 = (2)^2 + (2)^2 = 8
Now, we can plug these values into the projection formula:
projv(u) = (-8 / 8) * (2j + 2k) = -1j - 1k
So the projection of u onto v is -1j - 1k.
To find the vector component of u orthogonal to v, we can use the formula:
u - projv(u)
We already found projv(u) to be -1j - 1k, so we just need to subtract that from u:
u - projv(u) = (-8i - 4j - 2k) - (-1j - 1k) = -8i - 3j - k
Therefore, the vector component of u orthogonal to v is -8i - 3j - k.
To find the projection of u onto v, we will use the formula:
proj_v(u) = (u•v / ||v||^2) * v
where u = -8i - 4j - 2k, v = 2j + 2k, and • denotes the dot product.
First, calculate the dot product (u•v):
u•v = (-8)(0) + (-4)(2) + (-2)(2) = -8 - 4 = -12
Next, calculate the magnitude squared of v (||v||^2):
||v||^2 = (0^2) + (2^2) + (2^2) = 0 + 4 + 4 = 8
Now, use the formula:
proj_v(u) = (-12 / 8) * v = -1.5 * (2j + 2k) = -3j - 3k
Next, to find the vector component of u orthogonal to v, use the formula:
u_orthogonal = u - proj_v(u)
u_orthogonal = (-8i - 4j - 2k) - (-3j - 3k) = -8i - 1j + 1k
So, the projection of u onto v is -3j - 3k, and the vector component of u orthogonal to v is -8i - 1j + 1k.
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Math please help
An insurance company sells a 20-year term life insurance policy with a face value of $200,000 to a 45-year -old woman. Her annual premium is $990. If the woman dies after paying premiums for 6 years, what is the insurance company’s gain or loss?
Loss of $200,990
Loss of $194,060
Gain of $205,940
Gain of $199,010
The company will have a Loss of $194,060
The lady paid premiums for 6 years, which amounts to a total premium of$ 5,940($ 990 * 6).
Still, the insurance company will pay the face value of the policy, which is $ 00, If she dies.
Thus, the company's total payout would be $200,000, while their total income would be $ 5,940 in premiums.
The loss for the company would be the difference between the payout and the income
200,000-$ 5,940 = $ 194,060
Thus, the insurance company's loss in this scenario would be $194,060.
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show, not solve for x
Answer:
Step-by-step explanation:
Roxie plans on purchasing a new desktop computer for $1250. Which loan description would result in the smallest monthly payment when she pays the loan back?
12 months at 6. 25% annual simple interest rate
18 months at 6. 75% annual simple interest rate
24 months at 6. 5% annual simple interest rate
30 months at 6. 00% annual simple interest rate
The loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.
To determine the loan with the smallest monthly payment, we need to calculate the monthly payment for each loan option and compare them.
We can use the formula for monthly payment on a simple interest loan:
monthly payment = (principal + (principal * interest rate * time)) / total number of payments
where:
principal is the amount borrowed (in this case, $1250)interest rate is the annual simple interest rate divided by 12 to get the monthly ratetime is the length of the loan in monthsWe can compute the monthly payments for each loan choice using this formula:
1. 12 Monthly interest rate = 0.0625/12 = 0.00521, monthly payment = (1250 + (1250 * 0.00521 * 12)) / 12 = $107.35
2. 18 months at 6.75%: monthly interest rate = 0.0675/12 = 0.00563, monthly payment = (1250 + (1250 * 0.00563 * 18)) / 18 = $81.96
3. 24 months at 6.5%: monthly interest rate = 0.065/12 = 0.00542, monthly payment = (1250 + (1250 * 0.00542 * 24)) / 24 = $66.14
4. 30 months at 6%: monthly interest rate = 0.06/12 = 0.005, monthly payment = (1250 + (1250 * 0.005 * 30)) / 30 = $45.83
Based on these calculations, the loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.
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let g be a function such that g(9)=0 and g'(9)=2 let h be the function h(x)=square root of x
evaluate d/dx[g(x)*h(x)] at x=9
Work Shown:
First we'll need the derivative of h(x)
[tex]h(\text{x}) = \sqrt{\text{x}}\\\\h(\text{x}) = \text{x}^{1/2}\\\\h'(\text{x}) = (1/2)\text{x}^{-1/2}\\\\h'(\text{x}) = \frac{1}{2\text{x}^{1/2}}\\\\h'(\text{x}) = \frac{1}{2\sqrt{\text{x}}}\\\\[/tex]
Then let f(x) = g(x)*h(x)
Use the product rule to evaluate f ' (9).
[tex]f(\text{x}) = g(\text{x})*h(\text{x})\\\\f'(\text{x}) = \frac{d}{d\text{x}}\left[g(\text{x})*h(\text{x})\right]\\\\f'(\text{x}) = g'(\text{x})*h(\text{x}) + g(\text{x})*h'(\text{x})\\\\f'(\text{x}) = g'(\text{x})*\sqrt{\text{x}} + g(\text{x})*\frac{1}{2\sqrt{\text{x}}}\\\\f'(9) = g'(9)*\sqrt{9} + g(9)*\frac{1}{2\sqrt{9}}\\\\f'(9) = 2*\sqrt{9} + 0*\frac{1}{2\sqrt{9}}\\\\f'(9) = 2*3 + 0\\\\f'(9) = 6\\\\[/tex]