Last year, Ivy's pant measured 12 inches. This year, her plant is 75% taller.

How many inches did her plant grow?

The correct answer is:(c) If we randomly select a student from the population of all students, there would be a 90% chance of selecting a student with a final exam score between 79.4 and 96.3.

The 90% prediction interval represents an interval estimate for an individual student's final exam score, given a homework average of 90. It provides a range of values within which we expect the true final exam score to fall with a 90% confidence level.

Therefore, if we randomly select a student from the population of all students, there is a 90% chance that the student's final exam score will fall within the range of 79.4 and 96.3.

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Answer: D

Step-by-step explanation: The expression can't be factored since there is no such thing as sum of squares. When two squares are being added, you usually can't factor them.

For 2, the answer is D

For 3, the answer is B

For 4, the answer is D

For 5, the answer is B

Answer:

72

Explanation:

First, we can find the top and bottom smaller squares of the rectangular prism. Since we are working with a variety of rectangles, we only need to use the equation L×W.

To start with, let's multiply 2×3, which gives us 6, the surface area of both the bottom and top rectangles, so now we need to multiply it by 2 to account for both of them. 6×2=12

Now, we'll find the surface area of the bigger rectangles in the middle, which are 6 by 3, so again we will need to multiply length times width, then by 2 to count both rectangles. 6×3=18×2=36

Finally, we can find the surface area of the smaller rectangles in the middle, which are 6 by 2. 6×2=12, then multiply by 2 since there are 2 of those rectangles, 12×2=24

Now to find the total surface area, we need to add the gathered surface area from each shape, 12+36+24=72

The solution to the system of equations as an ordered pair is (4, -3).

We are given a system of linear equations in two variables. The first equation is y = (-1/2)x-1. The second equation is (-1/4)x+y+4 = 0.

We need to find the solution of the system of equations. We will use the substitution method to solve for the values of "x" and "y".

y = (-1/2)x - 1

(-1/4)x + y + 4 = 0

Substitute the value of "y" from the first equation into the second equation.

(-1/4)x + (-1/2)x - 1 + 4 = 0

(-3/4)x+3 = 0

(3/4)x = 3

x = 4

Substitute the value of "x" back into the first equation to get the value of "y".

y = (-1/2)x - 1

y = (-1/2)4 - 1

y = -2 - 1

y = -3

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Answer:

The hikers A and B travel at rates of 1.1 miles per hour and 3.3 miles per hour, respectively.

Step-by-step explanation:

Let suppose that each hiker travels at constant speed, such that kinematic formulas are, respectively:

Hiker A

\(x_{A} = x_{A,o}+v_{A}\cdot t\)

Hiker B

\(x_{B} = x_{B,o} +v_{B}\cdot t\)

Relationship

\(v_{A} =- v_{B}-2.2\,mph\) (They walk toward each other)

Where:

\(x_{A,o}\), \(x_{A}\) - Initial and final position of the hiker A, measured in miles.

\(x_{B,o}\), \(x_{B}\) - Initial and final position of the hiker B, measured in miles.

\(t\) - Time, measured in hours.

\(v_{A}\), \(v_{B}\) - Velocities of hikers A and B, measured in miles per hour.

Given that \(x_{A,o} = 0\,mi\), \(x_{B,o} = 22\,mi\), \(x_{A} = x_{B}\) and \(t = 5\,h\), the system of equation is reduced to the following:

\(0\,mi -(v_{B}+2.2\,mph)\cdot (5\,h) = 22\,mi+v_{B}\cdot (5\,h)\)

\(-5\cdot v_{B}-11 = 22+5\cdot v_{B}\)

\(10\cdot v_{B} = -33\)

\(v_{B} = -3.3\,mph\)

Now, the velocity of the hiker A is:

\(v_{A} = - (-3.3\,mph)-2.2\,mph\)

\(v_{A} = 1.1\,mph\)

The hikers A and B travel at rates of 1.1 miles per hour and 3.3 miles per hour, respectively.

Answer:

13

Step-by-step explanation:

using the Pythagorean theorem  a²+b²=c²

or the two shorter sides square added together equal the longest side squared

5²+12²

5²=25

12²=144

144+25=169

then we just have to take the square root of 169

√169=12

have a great day :D

The integral \(\int_{0}x^2 y^2 dxdy\) over the disc D is equal to zero.

In polar coordinates, the area element in the (x, y) plane is given by:

dA = r dr dθ

Let's look at a brief rectangle in the (x, y) plane that is justified by the differential changes in x and y, or dx and dy, respectively.

In polar coordinates, this rectangle can be represented as a tiny sector with a radius of r and an angle of dθ. The sides of the rectangle are roughly dx and dy, which can be written as follows in terms of r and dθ:

dx = dr cos(θ)

dy = dr sin(θ)

The area of the rectangular region is then given by:

dA = dx dy = (dr cos(θ))(dr sin(θ)) = r dr dθ

Therefore, the area element in the (x, y) plane for polar coordinates is dA = r dr dθ.

Now, let's evaluate the integral \(\int_{0}x^2 y^2 dxdy\) over the disc D of radius a, centered at the origin.

Since the region D is a disc of radius a, we can define the limits of integration for r and θ as follows:

0 ≤ r ≤ a

0 ≤ θ ≤ 2π

Substituting x = r cos(θ) and y = r sin(θ) into the integrand x²y², we have:

x²y² = (r cosθ)² (r sinθ)²

x²y² = r⁴cos²θsin²θ

Now, we can express the integral in polar coordinates as follows:

\(\int\int_{D}x^2 y^2 dxdy = \int\int_{D}r^4 cos^2(\theta) sin^2(\theta)r\ dr d\theta\)

Since D is a disc, the integration limits for r and θ are as mentioned earlier. Therefore, the integral becomes:

\(\int\int_{D}r^4 cos^2\theta sin^2\theta r\ dr d\theta = \int_{\theta=0}^{2\pi} \int_{r=0}^{a} r^5 cos^2\theta sin^2\theta\ dr d\theta\)

The inner integral with respect to r can be evaluated as:

\(\int_{r=0}^{a} r^5 dr = [r^6/6]_{r=0}^{a} = a^6/6\)

Substituting this result back into the expression, the integral becomes:

\(\int_{\theta=0}^{2\pi} (a^6/6) cos^2\theta sin^2\theta d\theta\)

Since cos²θsin²θ is an even function of θ, the integral with respect to θ over the range [0, 2π] will be zero.

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The complete question is:

Give the form of the area element in the (x, y) plane for polar coordinates (r,θ) defined in the standard way and justify your answer with a sketch. Evaluate the integral \(\int_{0}x^2 y^2 dxdy\) where D is a disc of radius a, center the origin, in the (x-y) plane.

The critical value of the test is 2.706. To determine the critical value for the Chi-squared test, we need the degrees of freedom and the significance level.

In this case, we have two categories: gender (male and female) and magazine preference (two types). Therefore, the degrees of freedom will be (number of categories in gender - 1) multiplied by (number of categories in magazine preference - 1).

Degrees of freedom = (2 - 1) * (2 - 1) = 1

The significance level is given as 10% or 0.10.

To find the critical value for a Chi-squared test with 1 degree of freedom at a 10% significance level, we can refer to a Chi-squared distribution table or use statistical software.

Using a Chi-squared distribution table or a calculator, the critical value for a Chi-squared test with 1 degree of freedom at a 10% significance level is approximately 2.706.

Therefore, the critical value of the test is 2.706.

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Answer:

Step-by-step explanation:

14. y = -2/3x + 10. This is parallel to 2x -3y because they have the same slope.

15. y = -1/2x and y = -1/2x + 2. These are perpendicular because the slope is the opposite reciprocal to the slope of y = 2x + 3, which is 2.
The slopes of the lines of the 2 equations are the same. Because of that, we can state that 2 lines that are perpendicular to the same line are parallel. This can be further supported by the Perpendicular Transversal Theorem, which says the same thing.

Hope this helps!

To calculate the standard deviation of the sampling distribution of p-hat, the answer will be 59 students.

By calculating,

600/10=60 and 59 students which is less than 10% of the population.

A sampling distribution, also known as a finite-sample distribution, in statistics is the probability distribution of a given random-sample-based statistic. The sampling distribution is the probability distribution of the values that the statistic takes on if an arbitrarily large number of samples, each involving multiple observations (data points), were used separately to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample. Although only one sample is frequently observed, the theoretical sampling distribution can be determined.

Because they offer a significant simplification before drawing conclusions using statistics, sampling distributions are crucial in the field. They enable analytical decisions to be made based on the probability distribution of a statistic rather than the combined probability distribution of all the individual sample values

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Answer:

Step-by-step explanation:

d/t=mph

Billy's friend's house is 20 miles away from him.

What is Speed?

The ratio of the distance travelled by an object to the time required to travel that distance.

Given that when Billy moves with his normal speed, it takes 40 min for him to reach his friend's house and if he slows his speed to 20 mph he takes 2 hours to reach the same distance.

We know, Speed = Distance/time

Let x be Billy's normal speed,

Therefore, 2x/3  = 2 (x - 20)

2x/3 = 2x - 40

x = 3x - 60

x = 30

Therefore, Billy's normal speed is 30 mph

Distance covered by him = 2 (30 - 20) = 20 mi

Hence, Billy's friend's house is 20 mi far.

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Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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All you need to do is multiply(or divide).

16/2=8

2/2=1

8:1

16x2=32 2x2=4; 16x3=48 2x3=6; 16x4=64 2x4=8;...

32:4; 48:6; 64:8...

hope it helps!

Answer:

5:7

Step-by-step explanation:

we know that

If y varies inversely as the square of x,

then

the equation that represent this situation is equal to

we have

y=9 when x=12

Find the value of the constant of proportionality k

substitute the value of x and the value of y in the equation above

Find the value of y when the value of x=15

substitute in the equation

therefore

the answer is

y=5.76

The expected value of a binomial random variable is the mean number of successes in a given experiment. In this case, the binomial random variable is denoted by x and the probability of success is 0.84. If 67 trials are conducted, where n=67 and p=0.84. Thus, the expected value of x is 56.28.

This means that, on average, 56.28 successes out of 67 trials are expected to occur when the probability of success is 0.84. This can be visualized as rolling a dice with a 4/5 chance of success 67 times. The expected value represents the average number of times the dice will land on 4 or 5, which is 56.28. This is also the same as saying that 56.28 successes, on average, are expected to occur out of every 67 trials.

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Therefore, (v - w) is orthogonal to u, which implies that the statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true.

The statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true if and only if u is orthogonal to the projection of (v-w) onto the subspace spanned by u.

Since proju(v) and proju(w) are the projections of v and w onto the subspace spanned by u, we can rewrite the statement as "if the projections of v and w onto the subspace spanned by u are equal, then (v - w) is orthogonal to u".

Let proj_u(v - w) be the projection of (v - w) onto the subspace spanned by u. We know that (v - w) can be decomposed as (v - w) = proj_u(v - w) + (v - w - proju(v - w)).

Note that (v - w - proju(v - w)) is orthogonal to the subspace spanned by u, since proju(v - w) is the closest vector in the subspace to (v - w). Therefore, (v - w) is orthogonal to u if and only if proju(v - w) = 0, which is equivalent to saying that the projection of (v - w) onto the subspace spanned by u is the zero vector.

Assuming that proju(v) = proju(w), we have:

proju(v - w) = proju(v) - proju(w) = proju(v) - proju(w) = 0

Therefore, (v - w) is orthogonal to u, which implies that the statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true.

In conclusion, we have proven that if the projections of v and w onto the subspace spanned by u are equal, then (v - w) is orthogonal to u.

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The third prism has dimensions of 3 feet by 3 feet by 3 feet and requires 27 cubes to fill. Since the teacher has only 32 cubes, the first two prisms can be filled completely with some cubes left over, while the third prism cannot be completely filled.

The volume of each cube is (1/4)^3 = 1/64 cubic feet. To determine whether the cubes will completely fill each prism, we need to calculate the volume of each prism and compare it to the total volume of the cubes.

The first prism has dimensions of 2 feet by 2 feet by 2 feet, so its volume is 2 x 2 x 2 = 8 cubic feet. To fill the prism with cubes, we need 8 cubes, which have a total volume of 8 x (1/64) = 1/8 cubic feet. Since 1/8 is less than 8, the first prism can be completely filled with some cubes left over.

The second prism has dimensions of 2 feet by 2 feet by 3 feet, so its volume is 2 x 2 x 3 = 12 cubic feet. To fill the prism with cubes, we need 12 cubes, which have a total volume of 12 x (1/64) = 3/16 cubic feet. Since 3/16 is less than 12, the second prism can be completely filled with some cubes left over.

The third prism has dimensions of 3 feet by 3 feet by 3 feet, so its volume is 3 x 3 x 3 = 27 cubic feet. To fill the prism with cubes, we need 27 cubes, which have a total volume of 27 x (1/64) = 27/64 cubic feet. Since 27/64 is greater than 32, the teacher does not have enough cubes to completely fill the third prism.

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Answer:

1/3.

Step-by-step explanation:

The slope of the given line = (-4 - -7)/(2-3)

= 3 / -1

= -3.

The line perpendicular to this has slope - 1 / (-3)

= 1/3.

the BEST statement is: The serving costs about 40 cents.

To determine the cost of the optimal serving, we need to calculate the cost per serving based on the quantities of chicken and tomatoes used.

Given that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes, we can calculate the cost as follows:

Cost of chicken =\(0.89 ounces * $0.40/ounce\)

Cost of tomatoes = \(0.52 ounces * $0.08/ounce\)

Total cost = Cost of chicken + Cost of tomatoes

Total cost =\((0.89 * $0.40) + (0.52 * $0.08)\)

Total cost =\($0.356 + $0.0416\)

Total cost ≈\($0.3976\)

Rounding to the nearest cent, the cost of the optimal serving is about 40 cents.

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Answer:

See below

Step-by-step explanation:

Hi there!

Mai was given the equation x²+7x=0, and rewrote it as x(x+7)=0 to help solve it

Rewriting the equation in this way helps Mai solve the equation is because it helps make sure none of the answers are missing.

If you look at the equation x²+7x=0, you might think that you are able to divide both sides by x, and then solve x+7=0.

However, this method is incorrect.

The answer to x+7=0 would be x=-7, which if you plug -7 as x into the equation, it would show that it is a correct answer, but it is not the only correct answer.

If you plugged 0 into the equation as well, here is what would happen:

(0)²+7(0)=0

Raise 0 to the second power and multiply 7 by 0

0 + 0 = 0

Add the numbers together

0=0

As you can see, x=0 is also a correct answer to the equation.

However, if you had divided x from both sides, you wouldn't have been able to find that x can also equal 0.

If we factored the equation as Mai did it, x(x+7)=0, then by zero product property, x would equal both 0 and 7

As you can see, both answers are there if we had factored it Mai's way, and  none of the answers are missing.

Hope this helps!

Answer:

x = -2, y = -4

Step-by-step explanation:

Substitution:

y = 2x

3x + 3y = -18

3x + 3(2x) = -18

3x + 6x = -18

9x = -18

x = -2

y = 2(-2)

y = -4

May I please have brainliest? Thank you!

Answer:

24/68 inches

Step-by-step explanation:

Multiply 3 times 8 to get 24. The denominator was multiplied by 8 so you have to do the same thing to the numerator.

Hope This Helps :)

The equivalent of the quantity \(\frac{3}{8}\) inch is \(\frac{24}{64}\) inch.

The given quantity is \(\frac{3}{8}\) inch.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

Here, in equivalent given fraction denominator is 64.

Let the numerator be x.

Now, \(\frac{3}{8}\) inch = \(\frac{x}{64}\) inch

3×64=x×8

x=3×8

x=24

So, the numerator of the fraction is 24.

Hence, the equivalent of the quantity \(\frac{3}{8}\) inch is \(\frac{24}{64}\) inch.

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The length of PR in the triangle is 229 feet.

To indirectly measure the distance across a river, Savannah stands on one side of the river and uses sight lines to a landmark on the opposite bank. Savannah draws  the diagram below to show the lengths and angles that she measured. Let's find PR, the distance across the river.

Triangle PRE is similar to triangle POC. Therefore, similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Hence,

PR = x

165 / 255 = x / x + 125

cross multiply

165(x + 125) = 255x

165x + 20625 = 255x

165x - 255x = - 20625

-90x = - 20625

divide both sides of the equation by -90

x = - 20625 / - 90

x = 229.166666667

Therefore,

PR = 229 ft

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Answer:

Step-by-step explanation:

p:c=10:14

p/c=10/14

p/7=10/14

p=7(10)/14

p=5

Answer:

5 plates

Step-by-step explanation:

First, make two fraction bars, one with the ratio 10/14 the other with the top blank and 7 on the bottom. Next, find how much to multiply 7 by to get 14. Use the number you get to divide 10 by. Then you should get 5. Hope this helped!

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

Answer:

See below

Step-by-step explanation:

the x + 4   will shift the graph 4 units LEFT

the - 8 part will shift the graph 8 units DOWN

Based on the given parameters, the total cost of the TV is  $$214

From the question, we have the following parameters that can be used in our computation:

Original price = $250

Discount = 20% off

Sales tax = 7%

The total cost of the TV is calculated using the following equation

Total cost = Original price * (1 - discount) * (1 + sales tax)

Substitute the known values in the above equation, so, we have the following representation

Total cost = 250 * (1 - 20%) * (1 + 7%)

Evaluate the sum and the difference

Total cost = 250 * (0.80) * (1.07)

Evaluate the products

Total cost = 214

Hence, the cost is $214

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