Sam buys several pairs of jeans for $16.50 each, and a shirt for $25. Louis goes to a different store and buys the same number of jeans as Sam for $17.50 each, plus a shirt for $15. Is there a situation where both will pay the same amount for their purchases?
HELP MEEEE I HAVE TO TURN IT IN IN 10 MINUTES

Answer:

see below

Step-by-step explanation:

The commutative property of addition says that changing the order of addends does not change the sum. Here's an example: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+4.

Answer:

The given points isn't define a parallelogram.

Step-by-step explanation:

As we know,

⇒ The opposite sides of a parallelogram are equal.

The given points are:

(x1, y1) = M(2,4)

(x2, y2) = I(1,2)

(x3, y3) = L(5,1)

(x4, y4) = K(4,−1)

Now,

On applying the Distance formula, we get

MI = \(\sqrt{(x 2 - x 1)^2 + (y 2 - y 1)^2}\)

On substituting the given values, we get

    = \(\sqrt{(1 - 2)^2 + (2- 4)^2}\)

    = \(\sqrt{1+4}\)

    = \(\sqrt{5}\)

IL = \(\sqrt{(x 3 - x 2)^2 + (y 3 - y 2)^2}\)

   = \(\sqrt{(5-1)^2+(1-2)^2}\)

   = \(\sqrt{16+1}\)

   = \(\sqrt{17}\)

LK = \(\sqrt{(x 4 - x 3)^2 + (y 4 - y 3)^2}\)

     = \(\sqrt{(4-5)^2+(-1-1)^2}\)

     = \(\sqrt{1+4}\)

     = \(\sqrt{5}\)

KM = \(\sqrt{(x 4 - x 1)^2 + (y 4 - y 1)^2}\)

      = \(\sqrt{(4-2)^2+(-1-4)^2}\)

      = \(\sqrt{4+25}\)

      = \(\sqrt{29}\)

Here, MI = LK = √5

          IL ≠ KM

The measure of the angle indicated is 100 degrees

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

The circle

There are intersecting chords on the circle

Using teh equation of intersecting chords, we have

? = 1/2 * Sum of the intersecting arcs

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

? = 1/2 * (110 + 90)

Evaluate

? = 100 degrees

Hence, the measure of the angle indicated is 100 degrees

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Answer:

use graphs

Step-by-step explanation:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test

Given: Independent group and ordinal data. To find which test to use.

What's the Kruskal Wallis test?

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.

How to calculate the Kruskal Wallis test?

The computation of the Kruskal- Wallis statistic requires

Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.

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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.

We are given an independent group design and ordinate data.

We need to tell which test to use on them.

The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.

The null hypothesis for the Kruskal- Wallis test tells us that:

There are no methodical or harmonious differences among the treatments being compared.

Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.

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Answer:

  138, 139

Step-by-step explanation:

You want the consecutive page numbers whose total is 277.

Consecutive integers differ by 1. If the lesser of two consecutive integers is represented by x, then the next one is (x+1). The sum of these two integers will be ...

  x + (x +1) = 2x +1

We want to find the numbers whose sum is 277:

  2x +1 = 277

  2x = 276

  x = 138

  x+1 = 139

The two page numbers are 138, 139.

__

Additional comment

It is customary for the odd page number to be on the right when the book is open. Fortunately, this problem makes that be the case.

Therefore, two page numbers are 138, 139 of a left and right page numbers of an open book are two consecutive integers whose sum is 277.

Positive numbers, negative numbers, and zero are examples of integers. 'Integer' is a Latin word that means 'complete' or 'completely'. This means that integers exclude fractions and decimals. In this article, we'll learn more about integers, their definition, and their properties.

All whole numbers & negative numbers are considered integers. This means that if we combine negative and whole numbers, we get a set of integers.

The difference between two consecutive integers is 1. The following integer is (x+1) if x is the lesser of two subsequent integers. These two integers' sum will be

x + (x +1) = 2x +1

So for 277 the equation will be

⇒  2x +1 = 277

⇒  2x = 276

⇒  x = 138

⇒  x+1 = 139

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Answer:

C+7d

5+7(8)

5+56=61

Step-by-step explanation:

Answer: 61

Step-by-step explanation:

This is an algebraic equation. You need to replace the variables with their values.

Step 1: Given c=5 and d=8.

5 + 7*8

Step 2: Solve the equation. Following the rules of PEMDAS, first multiply the 7 times the 8. Then, add 5 to that.

7 * 8 = 56

5 + 56 = 61

Answer:

Step-by-step explanation:

- 13x = 26

divide each side by -13

- 13x = 26  

-13      -13

x = -2

Answer:

-2

Step-by-step explanation:

-13x =26

x=-26 :13

x=-2

Answer:

x = 23

7x - 11 = 4x + 58

(7x - 4x) - 11 = (4x - 4x) + 58

3x - 11 = 58

3x (- 11 + 11) = 58 + 11

3x = 69

3x/3 = 69/3

x = 23

Answer:

x=23°

Step-by-step explanation:

(7x - 11)=(4x + 58)

7x-4x=58+11

3x=69

x=23

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

The area of the circle is 9π. Then the radius of the circle is given as,

A = π

πr² = π

r² = 1

The center of the circle is at (-7, -15). Then the equation of the circle is given as,

(x + 7)² + (y + 15)² = 1

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

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Answer:

4x + 7y = 3365

x + y = 578

x = matinees

y = regular

Step-by-step explanation:

Given

$4 = matinees

$7 = regular

Total tickets = 578

Money collected = $3365

If one calls the amount of matinees that when "x" and the amount of regulars that went "y", then one can form the system;

4x + 7y = 3365

x + y = 578

Solving the system;

Multiply the second equation by (-4)

4x + 7y = 3365

-4x - 4y = -2312

Add the equations

4x + 7y = 3365

-4x -4y = -2312

3y = 1053

Inverse operations

3y = 1053

/3        /3

y = 351

x = 227

Answer:

infinite (many)

Step-by-step explanation:

3(2k-5)=6(k-4)+9

6k-15=6k-15

since they are the same on both sides of the equal side any solution for x would work.

The equation 3(2k - 5) = 6(k - 4) + 9 has many solutions.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

3(2k - 5) = 6(k - 4) + 9

6k - 15 = 6k - 24 + 9

6k - 15 = 6k - 15

Both sides of the equation are the same.

This means,

The equation has many solutions.

Thus,

The expression has many solutions.

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Answer: 40

Step-by-step explanation:

38+ 52=90

230-90=40

Total surface area of cylinder is equal to 87.96 yd².

The surface area of cylinder is equal to the lateral surface area added to two time the area of circle which forms the base of the cylinder.

In given question height is 5 yd. and radius 6 yd.

Equating all values in the formula to get surface area:

Total surface area = Lateral surface area + 2 ×area of circle

= 2π(radius)(height) + 2 × π(radius)²

= 2π(2(5) + 2 × π(2)²

= 2π(2)(5+2)

= 28π yd²

= 87.96 yd²

Total surface area of cylinder is equal to 87.96 yd².

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Answer:

The mean is 27.6

Step-by-step explanation:

Formula:   Sum of all data values divided by number of data values.

22+22+28+30+36=138

138/5=27.6

Good Luck! Hope this helps!

Answer: B. h=192÷ (6⋅4)

Step-by-step explanation:

B. h=192÷ (6⋅4)

This equation can be used to find the height of the prism because the volume of a rectangular prism can be represented by the equation V = l*w*h, where l and w are the length and width, respectively, and h is the height. In this case, given that V=192, the equation h=192÷ (l*w) can be used to find the height, where l=6 and w=4.

the Numbers of days = 3

The second statement(She raised $0.50 for each 1/3 of mile that she walked) means

1/3 miles = $0.50

For first day walk we have:

1/3 miles = $0.50

12 miles = 12 x 0.50 x 3 = $18

For Second day walk we have:

1/3 miles = $0.50

8miles = 8 x 0.50 x 3 = $12

For Third day walk we have:

1/3 miles = $0.50

16miles = 16 x 0.50 x 3 = $24

The amount she raised for the three days becomes

$18 + $12 + $24

=$54

Answer:

third option

Step-by-step explanation:

the point ( 98, 56.3 ) is in the form (x, y ) where x is the horizontal axis and y the vertical axis.

the horizontal axis is chirps per minute and vertical axis is temperature.

then (98, 56.3 ) means

an expected temperature of 56.3 ° F when the cricket has chirped 98 times

Answer:

46005.8

Step-by-step explanation:

Because you look to the left of 7 and 5 is higher than 4 so you round up.

So the 7 changes into a 8 and the rest stays the same.

Answer:

-45 + 12 is equal to -33

and Choice A is also equal to -33.

Step-by-step explanation:

Answer:

x(x-2)

Step-by-step explanation:

the common multiple here is the x, notice how it appears in both both terms. thus, we can factor it out of the equation going from x²-2x to x(x-2)

x(x-2)

Im assuming you meant x² - 2x but correct me if i'm wrong!

so x is common in both terms so you can take it out and factorise it.

Hope this helps!

Answer:

\(G=-\frac{5}{4}t+15\)

Slope = \(-\frac{5}{4}\)

Step-by-step explanation:

Let the equation representing the number of gallons left in the gas tank is,

G = mt + b

Where m = slope of the line

b = y-intercept of the line

Slope of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is,

'm' = \(\frac{y_2-y_1}{x_2-x_1}\)

Slope of the line passing through (8, 5) and (4, 10),

m = \(\frac{10-5}{4-8}\)

m = -\(\frac{5}{4}\)

Equation of line will be,

G = \(-\frac{5}{4}t+b\)

Since, point (8, 5) lies on this line,

5 = \(-\frac{5}{4}(8)+b\)

5 = -10 + b

b = 15

Therefore equation of the function will be,

G = \(-\frac{5}{4}t+15\)

Here slope of the function represents the \(\frac{5}{4}\) gallons of gas is consumed to drive the car for one hour.

The new coordinates of the triangle after dilation by a scale factor of 0.5 with the origin as the center of dilation are F'(3, 2.5), H'(1, 0.5), and G'(5, 0.5).

To find the coordinates of the triangle after dilation by a scale factor of 0.5 with the origin as the center of dilation, we can use the following formula:

(x', y') = (0.5 × x, 0.5 × y)

where (x, y) are the original coordinates of the point and (x', y') are the new coordinates after dilation.

Let's apply this formula to each point of the triangle:

For point F(6,5):

x' = 0.5 × 6 = 3

y' = 0.5 × 5 = 2.5

The new coordinates of point F are (3, 2.5)

For point H(2,1):

x' = 0.5 × 2 = 1

y' = 0.5 × 1 = 0.5

The new coordinates of point H are (1, 0.5)

For point G(10,1):

x' = 0.5 × 10 = 5

y' = 0.5 × 1 = 0.5

The new coordinates of point G are (5, 0.5)

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The given question is incomplete, the complete question is:

what are the coordinates of triangle by a scale factor of 0.5 with the origin as the center of dilation ?

The amount of customer deposit on each certificate of deposit (cd) is $12,500 on cd#1, $37,500 on cd#2, $50,000 on cd#3, and $50,000 on cd#4.

We will use the equation to determine the amount of customer deposit on each certificate of deposit (cd) with this rule.

So, for the first rule we can write the equation as below,

cd#1, cd#2, cd#3, cd#4 ≤ 1/3 * 150

cd#1, cd#2, cd#3, cd#4 ≤ 50

The equation for the second rule is,

cd#2 = 3*cd#1

The equation for the third rule is,

cd#2 + cd#1 = cd#3

since cd#2 is 3*cd#1. So,

3*cd#1 + cd#1 = cd#3

4*cd#1 = cd#3

So, to distribute all her money we can write the equation below,

cd#1 + cd#2 + cd#3 + cd#4 = 150

cd#1 + 3*cd#1 + 4*cd#1 + cd#4 = 150

8*cd#1 + cd#4 = 150

since cd#4 can't have more than 50, so we can assume cd#4 is 50.

8*cd#1 + 50 = 150

8*cd#1 = 100

cd#1 = 12.5

Thus, the amount in cd#1 is 12.5, cd#2 is 12.5*3 = 37.5, cd#3 is 12.5*4 = 50, and cd#4 is 50.

Your question is incomplete, but most probably your full question was

Fifth national bank offers four different certificates of deposit (cd). the first cd (a) offers a 4% interest rate for amount greater than $10,000. the second cd (b) offers a 4.2% interest rate for amount greater than $25,000. the third cd (c) offers a 4.5% interest rate for amount greater than $30,000. finally, the fourth cd (d) offers a 5% interest rate for amount greater than $35,000. a customer has $150,000 to deposit. she wishes to deposit not more than 1/3 of her money in any of the cds. she likes to deposit exactly three times of her money in cd#2 than cd#1. she wishes the sum of the first and the second cds to be less than or equal to the third cd. you are lowering all amounts by a factor or scale of 1,000. how much does she allocate for each cd?

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Main Answer:  P =\(\left[\begin{array}{cc}4&1\\7&1\end{array}\right]\) is a non-singular matrix P such that( P^−1)AP is diagonal.

Supporting Question and Answer:

How do we determine if a matrix is diagonalizable?

A square matrix is diagonalizable if and only if it has n linearly independent eigenvectors, where n is the dimension of the matrix. To check if a matrix is diagonalizable, we need to find the eigenvalues and corresponding eigenvectors. If the matrix has n linearly independent eigenvectors, then it is diagonalizable; otherwise, it is not.

Body of the Solution:To determine if a nonsingular matrix P exists such that P^(-1)AP is diagonal, we need to check if matrix A is diagonalizable. A square matrix A is diagonalizable if and only if it has n linearly independent eigenvectors, where n is the dimension of the matrix.

Let's find the eigenvalues and eigenvectors of matrix A:

First, we compute the characteristic polynomial by subtracting λ (the eigenvalue) times the identity matrix from matrix A:

A - λI =\(\left[\begin{array}{cc}12-\lambda&-4\\-3&1-\lambda\end{array}\right]\)

The determinant of (A - λI) should be zero to find the eigenvalues:

det(A - λI) = (12-λ)(1-λ) - (-4)(-3) = λ^2 - 13λ + 40 = (λ - 5)(λ - 8)

Setting this expression equal to zero, we find two eigenvalues: λ1 = 5 and λ2 = 8.

To find the eigenvectors corresponding to each eigenvalue, we substitute the eigenvalues back into (A - λI) and solve the resulting system of equations.

For λ1 = 5:

(A - 5I)x = 0

|\(\left[\begin{array}{cc}12-5&-4&\\-3&1-5\end{array}\right] \left[\begin{array}{c}x1\\x2\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right]\)

Simplifying this system of equations, we have: 7x1 - 4x2 = 0 ---> 7x1 = 4x2 ---> x1 = 8/7

Choosing x2 = 7 as a free variable, we obtain the eigenvector:

v1 = \(\left[\begin{array}{c}8/7\\x2\end{array}\right]\)

Choosing x2 = 7, we have v1 = \(\left[\begin{array}{c}4\\7\end{array}\right]\)

Similarly, for λ2 = 8:

(A - 8I)x = 0

(A - 8I)x = 0

\(\left[\begin{array}{cc}12-8&-4\\-3&1-8\end{array}\right] \left[\begin{array}{c}x1\\x2\end{array}\right] =\left[\begin{array}{c}0\\0\end{array}\right]\)

Simplifying this system of equations, we have: 4x1 - 4x2 = 0 ---> 4x1 = 4x2 ---> x1 = x2

Choosing x2 = 1 as a free variable, we obtain the eigenvector: v2 =\(\left[\begin{array}{c}x1\\x2\end{array}\right]\)

Choosing x2 = 1, we have v2 =\(\left[\begin{array}{c}1\\1\end{array}\right]\)

Since we have found two linearly independent eigenvectors, the matrix A is diagonalizable.

To construct the diagonal matrix D, we place the eigenvalues on the diagonal in the same order as the corresponding eigenvectors. Thus, we have:

D =\(\left[\begin{array}{cc}5&0\\0&8\end{array}\right]\)

To construct the matrix P, we place the eigenvectors of A as columns in the same order as the eigenvalues in D. Thus, we have:

P =\(\left[\begin{array}{cc}4&1\\7&1\end{array}\right]\)

Finally, we need to find the inverse of P

(P^(-1)):

P^(-1) = (1/(-3))\(\left[\begin{array}{cc}1&-1\\-7&4\end{array}\right]\)

Therefore, the non-singular matrix P such that P^(-1)AP is diagonal exists.

Final Answer: Thus, the non-singular matrix P such that P^(-1)AP is diagonal exists.

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Answer:40

Step-by-step explanation:

A graph of this parallelogram is shown below.

The perimeter of a parallelogram is equal to 31.8 units.

In Mathematics and Geometry, the perimeter of a parallelogram can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

For the length, we have:

Distance UX = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance UX = √[(2 + 2)² + (3 + 5)²]

Distance UX = √80

Distance UX = 8.9 units

For the width, we have:

Distance WX = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance WX = √[(2 - 9)² + (3 - 3)²]

Distance WX = √49

Distance WX = 7 units.

P = 2(UX + WX)

P = 2(8.9 + 7)

P = 31.8 units.

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At 95% CI, the difference between the population means is -238 ± 14.99

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

x₁ = 5079  x₂ = 5317

s₁ = 125       s₂ = 100

Also, we have

Sample size, n = 438

The difference between the population means can be calculated using

CI = (x₁ - x₂) ± z * √((s₁² / n₁) + (s₂² / n₂))

Where

z = 1.96 i.e z-score at 95% confidence interval

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

CI = (5079 - 5317) ± 1.96 * √((125² / 438) + (100² / 438))

Evaluate

CI = -238 ± 14.99

Hence, the difference between the population means is -238 ± 14.99

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Question

In order to compare the means of two populations, independent random samples of 438 observations are selected from each population, with the following results:

   Sample 1 Sample 2

x₁ = 5079  x₂ = 5317

s₁ = 125       s₂ = 100

Use a 95% confidence interval to estimate the difference between the population means (μ₁ −μ₂)

The velocity of the top of the ladder is 20.62 feet per second.

We can use the Pythagorean theorem to relate the distance between the wall and the base of the ladder to the height of the ladder. Let h be the height of the ladder, then we have:

h² + 7² = 25²

h² = 576

h = 24 feet

We can then use the chain rule to find the velocity of the top of the ladder. Let v be the velocity of the base of the ladder, then we have:

h² + (dx/dt)² = 25²

2h (dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Simplifying and plugging in h = 24 and dx/dt = -2, we get:

(24)(dh/dt) - 2(d²x/dt²) = 0

Solving for (d²x/dt²), we get:

(d²x/dt²) = (12)(dh/dt)

We can find (dh/dt) using the Pythagorean theorem and the fact that the ladder is sliding down the wall at a rate of 2 feet per second:

h² + (dx/dt)² = 25²

2h(dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Substituting h = 24, dx/dt = -2, and solving for (dh/dt), we get:

(dh/dt) = -15/8

Finally, we can find (d²x/dt²) by plugging in (dh/dt) and solving:

(d²x/dt²) = (12)(dh/dt) = (12)(-15/8) = -45/2

Therefore, the velocity of the top of the ladder is 20.62 feet per second.

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Answer:

29

Step-by-step explanation:

P = 2l + 2w

64 = 6 + 2w

58/2 = w

=29