Kyle has a storage box that is 2 ft. Long, 3 ft. High, and has a volume of 12 ft. 3 12 ft.3. Myla has a storage box that is 4 ft. High, 2 ft. Long, and has a volume of 16 ft. 3 16 ft.3. What are the widths of Kyle and Myla's boxes? Explain how you know.

The area of the figure is 644 square inches.

Given,

Figure : triangle + 3 semicircles

We need to find the area of the figure.

Area of a circle: 1/2 x base x height

Area of a circle: \(\pi\)r²

Find the area of the triangle.

We have,

Base = 20 in

Height = 17.3 in

Area = 1/2 x base x height

        = 1/2 x 20 x 17.3

       = 1 x 10 x 17.3

       = 173 square inches

Find the area of a circle

We have,

radius = 10 in

Area = \(\pi\) x 10²

        = 3.14 x 100

        = 314 square inches

Find the area of a semicircle

= area of circle / 2

= 314/2

= 157 square inches

Find the area of the figure

= area of the triangle + 3 x area of the semicircle

= 173 + 3 x 157

= 173 + 471

= 644 square inches.

Thus the area of the figure is 644 square inches.

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Based on the given information, the question is asking about the apparent relationship between two variables: study hours and test score. The correct answer is c.

Test score tends to increase as the number of study hours increases. This suggests a positive correlation between the two variables, meaning that as one variable (study hours) increases, the other variable (test score) also tends to increase.
The apparent relationship between the two variables under consideration, which are study hours and test score, can be described as follows:
Your answer: c. Test score tends to increase as the number of study hours increases.
This is because, generally, the more time a person spends studying, the better their understanding of the material, which often leads to a higher test score.

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To get the maximum profit, Kate should display as many cards from company B as possible, since she makes a higher profit from those cards.

Let x be the number of cards from company A and y be the number of cards from company B.

The constraints are:

The objective function is:

  P = 0.30x + 0.32y (the profit from selling the cards)

To maximize the profit, we need to maximize the value of y. Since the display rack can hold up to 90 cards, we can set y = 90 - x.

Substituting this into the objective function:

  P = 0.30x + 0.32(90 - x)
P = 0.30x + 28.8 - 0.32x
P = -0.02x + 28.8

To maximize P, we need to minimize x. Since x must be at least 40, we can set x = 40.

Substituting this back into the objective function:
P = -0.02(40) + 28.8
P = 28

So the maximum profit Kate can make is $28, by displaying 40 cards from company A and 50 cards from company B.

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The circumference of the outer circle is greater than the circumference of the inner circle by 44/7 feet.

What exactly is a circle?

A circle is a basic closed form made up of all points on a plane that are at a fixed distance from the centre. The radius is the distance between the centre and any point on the circle. A circle is often represented by the mathematical symbol "∘" or the equation (x-a)² + (y-b)² = r², where (a,b) is the center and r is the radius.

Now,

To find the circumference of the outer circle, we need to add the distance between the two circles to the circumference of the inner circle and then calculate the circumference of the resulting larger circle.

Circumference of the inner circle = πd = π*44 = 44π feet

Distance between the circles = 2 ft

Diameter of the larger circle = diameter of inner circle + distance between the circles = 44 ft + 2 ft = 46 ft

Circumference of the larger circle = πd = π(46) = 46π ft

Therefore, the circumference of the outer circle is greater than the circumference of the inner circle

by 46π - 44π

= 2*π feet=

=2*22/7=

=44/7 feet.

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Answer:

x=0.5

My previous answer got deleted

Step-by-step explanation:

11+6x=2x-13

11-11+6x=2x-13-11

6x=2x-24

6x-2x=2x-2x-24

4x=-24

x=-6

The velocity v, in feet per second, of the water pouring out of a small hole in the bottom of a cylindrical tank is given by v = 64h + 10, where h is the height, in feet, of the water in the tank.

The height of the water in the tank when the velocity of the water leaving the tank is 11 ft/s is approximately equal to 0.2 feet.

How to find the height of the water in the tank?

Let's use the formula given:  v = 64h + 10

To find the height h when the velocity v is given,

substitute v = 11ft/s and solve for h.11 = 64h + 10 ⇒ 64h = 11 - 10 = 1h = 1/64 feet = 0.015625 feet ≈ 0.02 feet (rounded to the nearest hundredth)

Therefore, the height of the water in the tank when the velocity of the water leaving the tank is 11 ft/s is approximately equal to 0.2 feet (rounded to the nearest tenth).

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Answer:

Step-by-step explanation:

Given function:

Find its inverse, substitute x with y and f(x) with x, solve for y:

Substitute y with f⁻¹(x):

Find  f⁻¹(1 ):

Answer:

III

Step-by-step explanation:

Number 3 did. The contains the (-1,1) and (5,-2)

Answer:

lll

Step-by-step explanation:

its the number 3 so A

Answer:

Rate = 56 gal / 7 min

         = 8 gal / min

Step-by-step explanation:

Hope this helps leave a heart ad maybe brailiest

Answer:

Your answer is 0.300 rounded to the thousands place.

Step-by-step explanation:

Hope this helps!

A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.

A random variable is defined as a variable that has posses a single numerical value, and determined for each outcome of an event. That is a variable whose value is either unknown or a function that assigns values to each of an experiment's outcomes. It can be either discrete (having specific values) or continuous (any value in a continuous range). Generally, random variables are represented by capital letters for example, X and Y. For example consider the tossing of coin event, then the values Heads = 0 and Tails= 1 and we have a Random Variable "X". Hence, required answer is random variable.

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Complete question:

a _______ variable is a variable that has a single numerical value, determined bychance, for each outcome of a procedure.

Answer: A

Step-by-step explanation:

Answer: B. 1 yard, 2 feet, 24 inches

Step-by-step explanation: 1 yard is 36 inches. Each feet is 12 inches, but there are 2 feet so 12 times 2 is 24 inches. And the last is just 24 inches. So, 36 + 24 + 24 = 84 inches

To use the Laplace transformation to solve the following differential equation, we will first apply the transformation to the problem and its initial conditions. F(s) denotes the Laplace transform of a function f(x) and is defined as: \(Lf(x) = F(s) = [0,] f(x)e(-sx)dx\)

When the Laplace transformation is applied to the given differential equation, we get:

\(Ld2y/dx2/dx2 + Ly = 0\) .

If we take the Laplace transform of each term, we get: \(s^2Y(s) = 0 - sy(0) - y'(0) + Y(s)\).

Dividing both sides by \((s^2 + 1),\), we obtain:

\(Y(s) = (s + 2) / (s^2 + 1)\).

Now, we can use the partial fraction decomposition to express Y(s) in terms of simpler fractions:

Y(s) = (s + 2) / (\(s^{2}\)+ 1) = A/(s - i) + B/(s + i) .

Multiplying through by (\(s^{2}\) + 1), we have:

s + 2 = A(s + i) + B(s - i).

Expanding and collecting like terms, we get:

s + 2 = (A + B)s + (Ai - Bi).

Comparing the coefficients of s on both sides, we have:

1 = A + B and 2 = Ai - Bi.

From the first equation, we can solve for B in terms of A:B = 1 - A Substituting B into the second equation, we have:

2 = Ai - (1 - A)i

2 = Ai - i + Ai

2 = 2Ai - i

From this equation, we can see that A = 1/2 and B = 1/2. Substituting the values of A and B back into the partial fraction decomposition, we have:

Y(s) = (1/2)/(s - i) + (1/2)/(s + i). Now, we can take the inverse Laplace transform of Y(s) to obtain the solution y(x) in the time domain. The inverse Laplace transform of 1/(s - i) is \(e^(ix).\)

As a result, the following is the solution to the given differential equation:\((1/2)e^(ix) + (1/2)e^(-ix) = y(x).\)

Simplifying even further, we get: y(x) = sin(x)

As a result, given the initial conditions dy(0)/dx = 2 and y(0) = 1, the solution to the above differential equation is y(x) = cos(x).

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Answer:

the answer will be C

ik this bc I did the math

Answer:

V = 108

Step-by-step explanation:

B = 9 x 4 = 36 Height of Triangular prism is 3 so 36 x 3 = 108

Answer:

Step-by-step explanation:

11 x 6.41

= 70.51

or

= 7051/100

or

=70 50/100

Answer: 3) x = 87°; y = 93°; z = 63°

Step-by-step explanation:

x + 33 + 60 = 180 since they form a triangle.

x + 93 = 180

Subtract 93 from both sides

x = 87°

x and y are linear pairs so they're supplementary.

y + x = 180

y + 87 = 180

Subtract 87 from both sides

y = 93°

z + y + 24 = 180 since they also form a triangle

z + 93 + 24 = 180

z + 117 = 180

Subtract 117 from both sides

z = 63°

Hope this helped!

Oh and nannara nanke demo ii yo, ikasete yaru kara. :p

the set S = {3³ + 2x + 1₁x³ + x, r = -5,³ + 10} is linearly dependent.

B = {[2, 1, 0, 0], [0, 1, 1, -1], [0, -1, 2, -2], [3, 1, 0, -2]} is a basis for R¹.

To test whether the set S = {3³ + 2x + 1₁x³ + x, r = -5,³ + 10} is linearly independent or not, we can use the +1-Test Method. This method involves substituting random values (typically 0 and 1) into the polynomials and checking if the resulting vectors are linearly independent.

Let's substitute 0 and 1 into the given polynomials:

For x = 0:

3³ + 2(0) + 1₁(0)³ + 0 = 3³ = 27

-5³ + 10 = -125 + 10 = -115

For x = 1:

3³ + 2(1) + 1₁(1)³ + 1 = 3³ + 2 + 1₁ + 1 = 27 + 2 + 1 + 1 = 31

-5³ + 10 = -125 + 10 = -115

Now we have two vectors:

v1 = [27, -115]

v2 = [31, -115]

To test for linear independence, we need to see if there exist scalars c1 and c2, not both zero, such that c1 * v1 + c2 * v2 = 0. This can be done by setting up and solving a system of equations.

Let's set up the system of equations:

c1 * [27, -115] + c2 * [31, -115] = [0, 0]

This gives us two equations:

27c1 + 31c2 = 0 (Equation 1)

-115c1 - 115c2 = 0 (Equation 2)

We can solve this system of equations to determine the values of c1 and c2.

Multiplying Equation 1 by 115 and Equation 2 by 27, we get:

3105c1 + 3565c2 = 0 (Equation 3)

-3105c1 - 3105c2 = 0 (Equation 4)

Adding Equation 3 and Equation 4, we obtain:

0 = 0

Since the resulting equation is always true, this means that any values of c1 and c2 would satisfy the system of equations. In other words, there exist non-zero scalars c1 and c2 such that c1 * v1 + c2 * v2 = 0. Therefore, the vectors v1 and v2 are linearly dependent.

Hence, the set S = {3³ + 2x + 1₁x³ + x, r = -5,³ + 10} is linearly dependent.

Now let's show that the set B = {[2, 1, 0, 0], [0, 1, 1, -1], [0, -1, 2, -2], [3, 1, 0, -2]} is a basis for R¹ (the set of all real numbers).

To show that B is a basis, we need to demonstrate two properties:

B spans R¹: Every vector in R¹ can be expressed as a linear combination of vectors in B.

B is linearly independent: The vectors in B are linearly independent.

Spanning R¹:

Let's consider an arbitrary vector v = [a, b, c, d] in R¹, where a, b, c, and d are real numbers.

We need to show that v can be expressed as a linear combination of the vectors in B.

By multiplying the vectors in B by appropriate scalar coefficients and adding them, we have:

x₁ * [2, 1, 0, 0] + x₂ * [0, 1, 1, -1] + x₃ * [0, -1, 2, -2] + x₄ * [3, 1, 0, -2] = [a, b, c, d]

This leads to the following system of equations:

2x₁ + 0x₂ + 0x₃ + 3x₄ = a

x₁ + x₂ - x₃ + x₄ = b

x₂ + (-x₃) + 2x₃ + 0x₄ = c

-1x₂ - x₃ - 2x₃ - 2x₄ = d

Simplifying the system of equations, we have:

2x₁ + 3x₄ = a

x₁ + x₂ - x₃ + x₄ = b

2x₂ + 2x₃ = c

-1x₂ - 3x₃ - 2x₄ = d

This system of equations has a unique solution for every choice of a, b, c, and d. Therefore, any vector v in R¹ can be expressed as a linear combination of the vectors in B.

Linear Independence:

To show that the vectors in B are linearly independent, we need to demonstrate that the equation:

x₁ * [2, 1, 0, 0] + x₂ * [0, 1, 1, -1] + x₃ * [0, -1, 2, -2] + x₄ * [3, 1, 0, -2] = [0, 0, 0, 0]

only has the trivial solution, where x₁ = x₂ = x₃ = x₄ = 0.

We can rewrite the equation as a system of equations:

2x₁ + 0x₂ + 0x₃ + 3x₄ = 0

x₁ + x₂ - x₃ + x₄ = 0

0x₁ + x₂ + (-x₃) + 2x₃ = 0

0x₁ - x₂ - 2x₃ - 2x₄ = 0

Simplifying the system of equations, we have:

2x₁ + 3x₄ = 0

x₁ + x₂ - x₃ + x₄ = 0

x₂ - x₃ + 2x₃ = 0

-x₂ - 3x₃ - 2x₄ = 0

This system of equations has only the trivial solution x₁ = x₂ = x₃ = x₄ = 0. Therefore, the vectors in B are linearly independent.

Since B satisfies both properties of being a basis (spanning R¹ and linearly independent), we can conclude that B = {[2, 1, 0, 0], [0, 1, 1, -1], [0, -1, 2, -2], [3, 1, 0, -2]} is a basis for R¹.

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Answer:

32

Step-by-step explanation:

9-6 = 3

3 x 6 = 18

18 + 14 = 32

Answer:

b. Complementary gas masks

Step-by-step explanation:

Adjacent means that the two angles are right next to each other and touching. The two angels in the photo are touching. Supplementary means that the two angels can for together to make a 180 degree line. The two angels in the photo make a 180 degree line. Complementary means that the two angels make a 90 degree angel. Since the two angels already make a 180 degree angels then, they cannot make a 90 degree angel. The question is asking for what it is not so, complements would be the answer.

The rate of change of the radius is 1.32cm²/s

The formula for calculating the volume of a sphere is expressed as:

The rate of change of the volume is given as:

Given the following paramters;

dv/dt = 23cm³/s

Volume = 7cm³

Get the radius of the sphere:

7 = 4/3 πr³\

21 = 4πr³

r³ = 21/4π

r = 1.18 cm

Get the rate of change of the radius to have:

\(23 = 4(3.14)(1.18)^2 \frac{dr}{dt} \\23 = 17.48 \frac{dr}{dt} \\\frac{dr}{dt}=1.32cm^2/s\)

Hence the rate of change of the radius is 1.32cm²/s

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Answer:

r² = (2 - (-1))² + (1 - 4)² = 3² + (-3)² = 9 + 9 = 18

(x + 1)² + (y - 4)² = 18

The general form of the equation of the circle is `(x − h)² + (y − k)² = r²`, where the center of the circle is at `(h, k)` and the radius of the circle is `r`.

Given center: `(h, k) = (-1, 4)`Given solution point: `(x, y) = (2, 1)`Let the radius be `r`.

Then, using the distance formula, we can calculate the radius `r`.Distance between center and solution point is `r`i.e. `(x − h)² + (y − k)² = r²

Plugging in the values, we get:`(2 − (-1))² + (1 − 4)² = r²`

Solving for `r`, we get:`3² + (-3)² = r²`

⇒ 18 = r²

⇒ r = ±sqrt(18)`

The center of the circle is `(h, k) = (-1, 4)` and radius of the circle is `r = ±sqrt(18)`.

Hence, the equation of the circle in the general form is`(x − (-1))² + (y − 4)² = (±sqrt(18))²`

On simplifying, we get:`(x + 1)² + (y − 4)² = 18`Therefore, the required equation of the circle in the general form is `(x + 1)² + (y − 4)² = 18`.

Thus, the equation of the circle in the general form is `(x + 1)² + (y − 4)² = 18`.

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Answer:

The first choice.

Step-by-step explanation:

The volume must be about 226.19 in^3.

Volume of a cylinder = area of base * height4

= πr^2h  = 226.19

r^2 = 226.19 / πh.

Consider the first of the choices:-

When h = 8 , r^2 = 226.19 /8π = 8.9998

So r = 3.00  to nearest hundredth.

So this is the required image.

Answer: It a

Step-by-step explanation:

The linear function of the graph is written as: y = 4/3x + 2.

The most common form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept.

To write a linear function in this form, you will need to find the slope and y-intercept of the line.

The slope is the ratio of the change in y to the change in x, and the y-intercept is the point at which the line crosses the y-axis. Once you have these two values, you can substitute them into the equation and write the linear function.

Using the given graph:

Slope (m) = rise/run = 8/6

Slope (m) = 4/3

The y-intercept (b) = 2.

To write the linear function, substitute m = 4/3 and b = 2 into y = mx + b:

y = 4/3x + 2

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Answer:

(5,3)

Step-by-step explanation:

Well to solve the following,

y = 8 - x

y = x - 2

Graphically.

We need to graph both equations,

Look at the image below ↓

By looking at the graph we can tell the intercept point is at (5,3).

Thus,

the solution is (5,3).

Hope this helps :)

The estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

What is population variance?

Each data point's distance from the population mean is quantified by the population variance, which is a measure of dispersion. The average of the squares of the deviations from the data's mean value is known as population variance.

Hence, when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes, the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

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Answer:

A

Step-by-step explanation:

Using Pythagoras' identity on the large right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(x + 32)² = 30² + 40² = 900 + 1600 = 2500 ( take the square root of both sides)

x + 32 =\(\sqrt{2500}\) = 50 ( subtract 32 from both sides )

x = 18 → A

The function y = -tcost-t is a solution to the initial-value problem t(dy/dt) = y + t^2sin(t), with the initial condition y(pi) = 0.

To verify whether the given function y = -tcos(t) - t is a solution of the initial-value problem t(dy/dt) = y + t^2sin(t) and y(pi) = 0, we need to follow these steps:

Step 1: Calculate dy/dt

Differentiate y = -tcos(t) - t with respect to t to find dy/dt:

dy/dt = -cos(t) + tsin(t) - 1

Step 2: Substitute the values of y and dy/dt into the differential equation

Replace y and dy/dt in the differential equation t(dy/dt) = y + t^2sin(t) with their corresponding values:

t(-cos(t) + tsin(t) - 1) = (-tcos(t) - t) + t^2sin(t)

Step 3: Simplify the equation

Distribute t on the left side:

-tcos(t) + t^2sin(t) - t = -tcos(t) - t + t^2sin(t)

Combine like terms on both sides:

-tcos(t) + t^2sin(t) - t = -tcos(t) - t + t^2sin(t)

Step 4: Verify if the equation holds true

The equation is an identity, as the left side is equal to the right side for all values of t. Therefore, the function y = -tcos(t) - t satisfies the differential equation t(dy/dt) = y + t^2sin(t).

Step 5: Check the initial condition

We also need to verify if y(pi) = 0. Substitute pi into the function y = -tcos(t) - t:

y(pi) = -(pi)cos(pi) - pi

= -(-pi) - pi

= 0

Since y(pi) = 0, the initial condition is satisfied as well.

Therefore, the function y = -tcos(t) - t is indeed a solution of the initial-value problem t(dy/dt) = y + t^2sin(t), y(pi) = 0.

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