16. A gift box has the shape of a rectangular prism.
The length and width of the prism are 10.5 cm
each. The volume of the prism is 1433.25 cm³.
What is the height of the prism?

The second additional Polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

We have a point in polar coordinates (3,-π/6) and we have to find two additional polar representations of this point. Let's recall the formula for converting from Cartesian to polar coordinates :x = rcosθy = rsinθAnd

the formula for converting from polar to Cartesian coordinates :r = √(x²+y²)θ = arctan(y/x)So, we can use the second formula to convert (3,-π/6) to Cartesian coordinates:$$x=3\cos(-\frac{\pi}{6})=3\cdot \frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{2}$$$$y=3\sin(-\frac{\pi}{6})=3\cdot \frac{-1}{2}=-\frac{3}{2}$$

Now we can use the first formula to convert back to polar coordinates:$$r=\sqrt{(\frac{3\sqrt{3}}{2})^2+(-\frac{3}{2})^2}=\frac{3\sqrt{6}}{2}$$$$\theta=\arctan(-\frac{3}{3\sqrt{3}})=-\frac{\pi}{3}$$

So, the first additional polar representation of the point (3,-π/6) is ($\frac{3\sqrt{6}}{2}$, $-\frac{\pi}{3}$).To find the second polar representation,

we need to add or subtract multiples of π to the angle until it is in the range [-2π, 2π].$$-\frac{\pi}{3}+2\pi=\frac{5\pi}{3}$$$$-\frac{\pi}{3}-2\pi=-\frac{7\pi}{3}$$

So, the second additional polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

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If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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The value of the function at -4 is f(-4) = -14.

What is the value of a function?

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The quantity that the function assumes for these argument values is the value of a function, given the value(s) assigned to its argument(s).

Given:

f(x) = 2x - 6

We have to find the value of f(-4).

So, plug x = -4 in the above equation.

Above equation becomes,

f(-4) = 2(-4) - 6

f(-4) = -8 - 6

f(-4) = -14

Hence, the value of the function at -4 is f(-4) = -14.

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Answer:

9060$ is the final amount because 7060 is the interest

The amount of money after 45 years will be $64,060.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Investments increase exponentially by about 26% every 3 years.

If you made a $2,000 investment.

Then the equation will be

\(\rm A = 2000 \times \left (1.26 \right )^{\frac{t}{3}}\)

Where t is the number of years.

Then the amount of money after 45 years will be

\(\rm A = 2000 \times \left (1.26 \right )^{\frac{45}{3}}\)

Simplify the equation, then we have

A = 2000 × (1.26)¹⁵

A = 2000 × 32.03

A = $64,060

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Based on the information given, we know that the two triangles have two pairs of congruent angles. This is sufficient to prove that the two triangles are congruent using the AAS (Angle-Angle-Side) postulate. Therefore, the method I would use to prove the two triangles congruent is **AAS**.

Answer: God

Step-by-step explanation:

The reason it’s god is because god created everything so he know everything. So your answer is god

By definition, the Standard form of the equation of an ellipse is:

Where the center is:

When its center is at the Origin, the equation is:

When:

Where:

It is horizontal.

And when:

Where:

It is vertical.

In this case, you know that this ellipse is centered at the Origin, its vertex is:

And the co-vertex is at:

Analyzing the information given in the exercise, you can idenfity that:

Therefore, you can substitute values into the equation

You get:

The answer is: Last option.

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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Answer: D. $722

Step-by-step explanation:

$2,000 - $375 (initial airfare cost which will only be once)

= 1,625

7 x 129 = 903 (cost of the 7 nights in a hotel)

1,625 - 903 = 722

$722 left for the trip

Answer:

15

Step-by-step explanation:

in multiplication we have given form of expression

Dividend(D) = Quotient(Q) x Divisor(d) + Remainder(r)

The number which is getting divided is called dividend

divisor is the number which divides the dividend.

quotient is the No. of times a dividend is divisible by divisor.

if dividend is not completely divisible by divisor then leftover after quotient * divisor is remainder.

value of remainder should be always less than divisor.

In  the problem given

Dividend is 75

divisor is 5

so by the given above expression

Dividend(D) = Quotient(Q) * Divisor(d) + Remainder(r) ----> 1

we know that 15*5 = 75

75 = 15*5 + 0

comparing with the  expression 1

we have q = 15

r = 0

Thus, quotient is 15.

The technique of repeated addition involves combining equal groups.

4 x ( -3) = 12.

Repeated addition is the combining of equal groupings. It offers a basis for comprehending multiplication. For instance, 3 x 5 can be expressed as 5 + 5 + 5 to represent 3 groups of 5 counters.

We have been given that

4 x ( -3) = 12

By using repeated addition for multiplication

Add 4 three times or add 3 for times ..

In question negative 3 is given so we add negative 4 , three times

(-4) + (-4) + (-4)

-12.

Or

Add negative 3 , four times

(-3) + (-3 )+ (-3) + (-3)

-12.

Hence, we solved given multiplication by the using repeated addition method.

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Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

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Answer:

do the square root off the number

Answer:

$11.40×$3=$34.2

This the price of the stapler

Answer:

The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).

Step-by-step explanation:

Answer:

192 cubic feet

Step-by-step explanation:

The volume V of a triangular pyramid is given by the formula:

V = (1/3) * base area * height

where base area is the area of the triangular base.

In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:

base area = length * width = 8 ft * 8 ft = 64 sq ft

Substituting the given values into the formula, we get:

V = (1/3) * 64 sq ft * 9 ft

V = 192 cubic feet.

Therefore, the volume of the triangular pyramid is 192 cubic feet.

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± \(Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )\)

Where  \(d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )\) is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be \(Z_{1-\alpha /2}= Z_{0.975}= 1.96\)

Now using the formula you have to clear the sample size:

\(d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )\)

\(\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }\)

\((\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}\)

\(n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')\)

\(n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2\)

\(n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203\)

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

Answer:

The sample size should be 6157

Step-by-step explanation:

Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.

Let us assume that the guess p = 0.25 as the value of p.

α = 1 - C = 1 - 0.95 = 0.05

\(\frac{\alpha }{2} =\frac{0.05}{2}=0.025\)

The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore \(Z_\frac{\alpha }{2}=Z_{0.025}=1.96\)

To determine the sample size n, we use the formula:

\(Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157\)

The mean weight of the male graders will be 151 pounds.

It should be noted that from the information, the sample of 12 male eleventh graders are: 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165.

We will add the values together and this will be 1812. Also, there are 12 students.

Therefore, the mean will be:

= Total weight / Number of students

= 1812 / 12

= 151 pounds.

Therefore, the mean weight will be 151 pounds.

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Here are weights (in pounds) of sample of 12 male eleventh graders. 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165. Calculate the mean weight.

The gradient of the line joining the points (1,-1) and (4,9) is 10/3, while the gradient of the line joining (5,1) and (2,-2) is 1. The x-intercept of the equation 3y = 2x - 2 is 1, and the y-intercept is -2/3. These calculations follow the formula for gradient and the methods for finding intercepts in linear equations.

1) To find the gradient of a line joining two points, you can use the formula: gradient = (change in y)/(change in x).
Given the points (1,-1) and (4,9), the change in y is 9 - (-1) = 10 and the change in x is 4 - 1 = 3.
Therefore, the gradient of the line joining these points is 10/3.
2) Similarly, to find the gradient of a line joining two points (5,1) and (2,-2), we can use the same formula. The change in y is -2 - 1 = -3 and the change in x is 2 - 5 = -3.
Therefore, the gradient of the line joining these points is -3/-3 = 1.
3) To find the x-intercept, we set y to 0 and solve for x.
Given the equation 3y = 2x - 2, if we substitute y with 0, we have 3(0) = 2x - 2, which simplifies to 0 = 2x - 2.
To solve for x, we can add 2 to both sides: 0 + 2 = 2x - 2 + 2, which gives us 2 = 2x.
Dividing both sides by 2, we get x = 1.
Therefore, the x-intercept of the equation 3y = 2x - 2 is 1.
To find the y-intercept, we set x to 0 and solve for y.
Using the same equation, if we substitute x with 0, we have 3y = 2(0) - 2, which simplifies to 3y = -2.
To solve for y, we can divide both sides by 3: (3y)/3 = (-2)/3, which gives us y = -2/3.
Therefore, the y-intercept of the equation 3y = 2x - 2 is -2/3.
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For binary class classification, assumptions are necessary in a way:

Given that

From Boyer Naive classifier,

We evaluate (ai | vj) is given below

(ai | vj) = n(e) + m(p) / n + m

Here,

m = equivalent sample size

n(e) = number of training examples

for which v = vj and a = ai

n(i) = number of training example for which v = vj

P = a prior estimate for P(ai | vj)

Here, we calculate that

P(SUV | yes), P(Red | yes), P(Domestic | yes)

P(SUV | no), P(Red | no), P(Domestic | no)

We evaluating this value like

yes:

RED :                             SUV:                            DOMESTIC:

n = 5                              n = 5                             n = 5

n(c) = 3                          n(c) = 1                           n(c) = 2

P = 0.5                          P = 0.5                           P = 0.5

m = 3                              m = 3                            m = 3

Therefore, with the above calculation we can justify that the simplifying assumptions are necessary in a binary class classification.

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Answer:

y= 1/5x + 12/5

Step-by-step explanation:

Parallel line to this has same slope and passes through the point (-2, 2)

The required equation in slope- intercept form is:

Answer:

88°

Step-by-step explanation:

Complementary angles have a sum of 90°, just do 90 - 2 and there's your answer.

The point which could represent the player catching the ball is: C. (4, 25).

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

By critically observing the graph (see attachment) which models the given data, we can reasonably infer and logically deduce that the point (4, 45) where the "Distance from Goal" on the y-axis intersect with the "Time after Throw" on the x-axis represents the player catching the ball.

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Answer: 4, 25

Step-by-step explanation:

The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)

Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting\(f(x) = x^2:\)

\(g(x) = (x + 2)^2 - 4\)

Expanding the square:

\(g(x) = x^2 + 4x + 4 - 4\)

Simplifying:

\(g(x) = x^2 + 4x\)

Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:

\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)

Therefore, the function g(x) in the form a(x-h)^2 + k is:

\(g(x) = (x + 2)^2 - 4\)

Where a = 1, h = -2, and k = -4.

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Answer:

Hi... U should do like this

Answer:

60 copies

Step-by-step explanation:

$15/150 = 0.1 each copy costs 1 cent

$6/$0.1 = 60 copies

Answer:

60 copies

Step-by-step explanation:

After using Unitary Method, We find that one copy costs 0.1 dollar. So divide 6.00 dollars by 0.1 and we find 60

For checking, we can multiply 60 by 0.1 and we get the same answer

Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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