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Divide by 2

Y = 2x - 2.5

x intercept: when y = 0

0 = 2x - 2.5

2.5 = 2x, x = 1.25

y intercept: when x = 0

Y = 2(0) - 2.5, y = -2.5

Solution: (1.25, 0) and (0, -2.5)

Answer:

Step-by-step explanation:

\(\angle 2,\angle AEG, \angle GEB\)

Ways can n identical balls be distributed into r bins such that each bin contains at least two balls are 20 ways.

1 ball in each of 3 boxes: 4 ways

3 balls in one box: 4 ways

2 balls in one box and 1 ball in another box: 3*4=12 ways

There are 20 ways to arrange the balls .

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

The combination can also be represented as: –nCr, nCr, C(n,r), Crn

Proof:

nPr = nCr.r!

= [n!/r!(n-r)!].r!

= n!/(n-r)!

Hence the theorem states true.

A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

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Explaining a bar graph

A bar graph graphically displays information. It uses bars that extend to various heights to symbolize value. Bar graphs can be created using any of the following: vertical bars, horizontal bars, grouped bars (several bars that compare values in a category), and stacked bars (bars containing multiple types of information).

Two sketches are shown in Histogram I for Box A.

20 drawings from Box B are represented in Histogram II.

20 drawings from Box A are represented in Histogram III.

Two draws are shown in Histogram IV for Box B.

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The mean of the batting averages is 0.341125.

Mean is used to summarize a set of data, frequently to help determine the overall significance of the data set.

To find the mean of the batting averages, we need to sum up all the batting averages and divide by the total number of players.

Batting averages: .373, .360, .321, .321, .320, .312, .311, .311

Sum of batting averages = .373 + .360 + .321 + .321 + .320 + .312 + .311 + .311

Sum of batting averages = 2.729

Now, we divide the sum by the total number of players, which is 8:

Mean = Sum of batting averages / Total number of players

Mean = 2.729 / 8

Calculating the mean:

Mean ≈ 0.341125

The mean of the batting averages is approximately 0.341125.

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Answer:

(1,4)

Step-by-step explanation:

It was either (1,3) or (1,4) but there was no (1,3) so (1,4).

Hopes This Helps :)

Answer:

She must sell 1026.66666667 kites

Step-by-step explanation:

15,400/15

The number of kites that Ellen needs to sell to complete her annual goal is 1027.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Ellen can make a $15 profit on each kite she sells. Also, Ellen's annual income goal is to have $15,400. Therefore, the number of kites that Ellen needs to sell is,

Number of kites that Ellen will sell = Annual income goal/Profit on each kite

Number of kites that Ellen will sell = $15,400 / $15

                                                     = 1026.6667

Since Ellen can not sell half kites, therefore, she needs to sell 1027 kites to complete her annual income goal.

Hence, the number of kites that Ellen needs to sell to complete her annual goal is 1027.

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The solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

To solve the inequality -5x - 3 + 2x > -18, we need to isolate the variable x on one side of the inequality sign.

Starting with the given inequality:

-5x - 3 + 2x > -18

Simplifying the left-hand side by combining the like terms:

-3x - 3 > -18

Adding 3 to both sides:

-3x > -15

Dividing both sides by -3, and reversing the inequality sign since we are dividing by a negative number:

x < 5

Therefore, the solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

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Answer:

Problem 2) : the gradient is "-2", and the y-intercept is "3"

Problem 3)

A is  \(y=2x+2\)

B is \(y=x+2\)  

Step-by-step explanation:

Problem 2)

In the line given by the equation:   \(y=-2x+3\)

the "gradient" (also known as "slope") is the numerical coefficient that multiplies the variable "x". So in this case the gradient is "-2"

the y-intercept is the numerical term "+3" because that is the y-value result of evaluating the expression for x = 0

\(y=-2x+3\\y=-2\,(0)+3\\y=3\)

Problem 3)

Consider the two lines :

\(y=x+2\)  and  \(y=2x+2\)

notice that both have the same y-intercept (that is the numerical term "2" at the end of both expressions. That means that both lines cross the y-axis at the point y=2.

Now notice that the gradient of one of them is "1"  (for \(y=x+2\) ) that is the coefficient that multiplies the variable "x". While for the other line ( \(y=2x+2\))  the gradient is "2" and therefore steeper than the previous one.

Then, the line identified as "A" which is the one with steeper gradient, corresponds to the equation   \(y=2x+2\), and the line identified with "B" is the one with smaller gradient  \(y=x+2\)  .

Answer:

no.

Step-by-step explanation:

the side of the square garage will be square root of 121 = 11

since the car is wider than the side of the garage, It wouldn't fit.

Answer:

Step-by-step explanation:

Let the length be x and the width be y

The perimeter of a rectangle is give as ; 2 ( L + B) , that is

We know the perimeter formula would be 440=2x+2y. And the area will be A=x*y

We can to take the derivative of the area formula to find where it is a max but we must first substitute something in from the first formula so we only have one variable.

440-2x=2y

220-x=y

A=(x)*(220-x)

A=220x-x^2

Now we take the derivative:

A'=220-2x (set equal to 0 and solve)

0=220-2x

2x=220

x=110 

Then when we plug this into the perimeter formula, we can solve for y

440=2x+2y

440=2(110)+2y

440=220+2y

220=2y

y=110

So both the length and width are 110 yards, and the area would be 12,100 square yards

The quadratic residues for the given integers are as follows: a) For the integer 3, the quadratic residues are 0 and 1.

b) For the integer 5, the quadratic residues are 0 and 1.

c) For the integer 13, the quadratic residues are 0, 1, 3, 4, 9, and 10.

d) For the integer 19, the quadratic residues are 0, 1, 4, 5, 6, 7, 9, 11, 16, and 17.

In number theory, a quadratic residue of an integer n is an integer x such that there exists an integer y satisfying x^2 ≡ y (mod n), where "≡" denotes congruence.

To find the quadratic residues of a given integer, we can calculate the square of each integer between 0 and n-1 (inclusive) and check if the result is congruent to a residue modulo n.

For example, let's consider the integer 13. We calculate the squares of integers from 0 to 12:

0^2 ≡ 0 (mod 13)

1^2 ≡ 1 (mod 13)

2^2 ≡ 4 (mod 13)

3^2 ≡ 9 (mod 13)

4^2 ≡ 3 (mod 13)

5^2 ≡ 12 (mod 13)

6^2 ≡ 10 (mod 13)

7^2 ≡ 10 (mod 13)

8^2 ≡ 12 (mod 13)

9^2 ≡ 3 (mod 13)

10^2 ≡ 9 (mod 13)

11^2 ≡ 4 (mod 13)

12^2 ≡ 1 (mod 13)

From these calculations, we can see that the quadratic residues of 13 are 0, 1, 3, 4, 9, and 10.

Similarly, we can apply this process to the other given integers (3, 5, and 19) to determine their quadratic residues.

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The hypothesis test to conduct in this situation is a two-sample test for

means, specifically a paired-sample t-test.

This is because the same group of workers is being tested twice, under

two different conditions: without exercise breaks and with exercise breaks.

The two sets of data are dependent because they are coming from the

same group of individuals, and the goal is to determine if there is a

statistically significant difference in their well-being between the two

conditions.

A paired-sample t-test is appropriate because it can compare the means of

two related samples, and it takes into account the correlation between the

data points in each sample.

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For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.

Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know  the formula  for :

volume = x*y*z, as  here it is a square base, so the volume will be

volume =  x²*y, where x and y are the dimension of the base and height

So for the  given reason,  

=>x²*y =  500

=> y = 500/x²

Again, the surface area formula  will be

S=x²+4xy, substituting the value of  y in this question

=>S=x²+4x(500/x²)

=>S=x²+2000/x

Differentiating the above formula with respect to x, we get

=>2x-2000/x²=0

=>2x³= 2000

=>x³= 1000

=>x =10

so the substituting the x values of x in  the equation y , we get

y = 500/x²

=>y = 5

so the dimensions are x= 10 and y=5

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To find the exact value, we would need to evaluate the definite integral, but it may not be practical to do so without further information or using numerical methods.

To find the average value of a function on a closed interval, you need to calculate the definite integral of the function over that interval and divide it by the length of the interval. In this case, we want to find the average value of the function f(x) = 3xsin(x) on the interval 1 ≤ x ≤ 7.

The average value of f on the interval [1, 7] is given by the formula:

Average value = (1/(b - a)) * ∫[a to b] f(x) dx

where a and b are the endpoints of the interval.

In our case, a = 1, b = 7, and f(x) = 3xsin(x). So, we can calculate the average value as follows:

Average value = (1/(7 - 1)) * ∫[1 to 7] (3xsin(x)) dx

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The n-point DFT of the signal x[n] = ax1[n] + bx2[n] is given by the linear combination of the individual DFTs: X[k] = a * X1[k] + b * X2[k], where X[k] is the n-point DFT of x[n], X1[k] is the n-point DFT of x1[n], X2[k] is the n-point DFT of x2[n], and a and b are constants.

The Discrete Fourier Transform (DFT) is a mathematical transformation that converts a discrete-time signal from the time domain to the frequency domain. When we have two signals x1[n] and x2[n] with their respective n-point DFTs X1[k] and X2[k], we can combine them in a linear manner to obtain the DFT of their sum or scaled versions.

In the case of x[n] = ax1[n] + bx2[n], where a and b are constants, we can apply the DFT to both sides of the equation. By linearity property of the DFT, the DFT of the left-hand side (x[n]) can be expressed as the sum of the DFTs of the individual terms on the right-hand side (ax1[n] and bx2[n]).

Thus, the n-point DFT of x[n], denoted as X[k], is given by the linear combination of the individual DFTs:

X[k] = a * X1[k] + b * X2[k],

This equation states that each frequency bin of the DFT of x[n] is obtained by multiplying the corresponding frequency bin of the DFTs of x1[n] and x2[n] by their respective constants (a and b), and then summing these contributions.

In summary, the DFT of a linear combination of signals can be computed by taking the corresponding linear combination of their individual DFTs.

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The alternative hypothesis would be: The proportion of BYU students who identify as Democrat and support the death penalty is significantly less than the proportion of BYU students who identify as Republican and support the death penalty.

The alternative hypothesis for this test would be: The proportion of BYU students who identify as Democrat and support the death penalty (p1) is less than the proportion of BYU students who identify as Republican and support the death penalty (p2). Mathematically, it can be written as:

H1: p1 < p2

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Answer:

between 3 and 4 around 3\(\frac{3\\}{4}\)

Answer: 3.5

Step-by-step explanation:

You want to choose two numbers that have perfect roots. One above 14, and one below 14. The nearest two perfect roots to 14 is 9 and 16. We have the following inequality:

\(\sqrt{9} < \sqrt{14} < \sqrt{16}\)

\(3 < \sqrt{14} < 4\)

This means the square root of 14 is somewhere between 3 and 4. A good estimate would be 3.5

Let R2 have the inner product (u,v) = 2u₁v₁ +5u₂V2, and let x = (3,2) and y = (5, -1). a. Find x, y, and (x,y) |².

(a) Finding x, y, and (x,y) |²: Given the inner product (u,v) = 2u₁v₁ + 5u₂v₂, we have: x = (3, 2) y = (5, -1)

To find (x, y) |², we need to calculate (x, y) first: (x, y) = 2(3)(5) + 5(2)(-1) = 30 - 10 = 20

Now, we can find (x, y) |² by squaring the result: |(x, y)|² = (20)² = 400

Therefore, (x, y) |² = 400.

(b) Describing vectors orthogonal to y: To find vectors orthogonal to y, we need to find vectors (z₁, z₂) such that their inner product with y is zero.

Let (z₁, z₂) be a vector orthogonal to y. The condition for orthogonality is: (y, z) = 2y₁z₁ + 5y₂z₂ = 0

Substituting the values of y, we have: 2(5)z₁ + 5(-1)z₂ = 0 10z₁ - 5z₂ = 0 2z₁ - z₂ = 0

Simplifying the equation, we get: 2z₁ = z₂

This equation shows that all multiples of (1, 2) are orthogonal to y.

Therefore, the correct answer is: OA. All multiples of (1, 2) are orthogonal to y.

For R2 with the inner product (u,v) = 2u₁v₁ +5u₂V2, and let x = (3,2) and y = (5, -1). a. Find x, y, and (x,y) |². (a) x = (3, 2), y = (5, -1), and (x, y) |² = 400.

(b) All multiples of (1, 2) are orthogonal to y.

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Answer:

If you are just wanting to factor out the equation than yes, this is correct! Great job!

Step-by-step explanation:

The third side of the right angle triangle is 5 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, using Pythagoras's theorem,

6² - (√11)² = b²

36 - 11 = b²

b² = 25

square root both sides of the equation

b = √25

b = 5 units

Therefore.

third side = 5 units.

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Answer:

1.00 and -1.00

Step-by-step explanation:

A correlation of 0.0 shows no linear relationship between the movement of two variables.

And the values range between -1.00 and 1.00

Answer:

Step-by-step explanation:

40% is the correct answer

Answer:

250

Step-by-step explanation:

Answer:

Solution is < -18/5

Step-by-step explanation:

1. combine multiplied terms into a single fraction

2. find common denominater

3. multiply the numbers

4. rearrange terms

Answer:

1.) x is greater than or equal to -18/5

Step-by-step explanation:

2 + 4/9x > 4 + x

subtract 4/9x on both sides

subtract 4 on both sides

-2 > 5/9x

mult 9/5 on both sides

-18/5 > x or x < -18/5

The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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Answer:

\(2(x + 1) = 2x + 1 \\ 2x + 2 = 2x + 1 \\ collecting \: like \: terms \\ 2x - 2x = 1 - 2 \\ 1x = - 1 \\ x = - \frac{1}{1} \: \: or \: \: x = - 1\)

Answer:

-1

Step-by-step explanation:

Answer:

$12.90

Step-by-step explanation:

For 40 miles for 0.06 cents with each mile, it would be $2.40 for the extra added with the base fee makes it $12.90.

There are 3,360,276 99-bit strings that contain more ones than zeros.

Consider two cases: strings with exactly 50 ones and strings with exactly 51 ones to determine the number of 99-bit strings that contain more ones than zeros.

Using the formula for combinations, we can calculate the number of 99-bit strings with exactly 50 ones as C(99, 50). This represents choosing 50 positions out of the 99 positions to place the ones.

Calculate the number of 99-bit strings with exactly 51 ones as C(99, 51), which represents choosing 51 positions out of the 99 positions for the ones.

Sum the two cases to find the total number of strings that contain more ones than zeros:

C(99, 50) + C(99, 51) = 99! / (50! × 49!) + 99! / (51! × 48!) = 3,360,276.

Therefore, there are 3,360,276 99-bit strings.

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