A mother explains to her child that the price on the sign is not the total price for a guitar, because the price does not include tax. She points out that a $42 guitar actually costs $44.94 once the sales tax is added. What is the sales tax percentage?

By applying the Gaussian-Jordan algorithm to the given system of equations, we can find the reduced row-echelon form (rref) of the system. The resulting rref shows that the system is consistent, and the solution is x = 1, y = -28/17, and z = -28/17.

We start by writing the augmented matrix of the system:

[ -2 3 1 -2 ]

[ -3 1 3 -4 ]

[ 0 2 -1 0 ]

To obtain the rref, we perform row operations to eliminate the coefficients below and above the pivots. Our goal is to transform the matrix into the following form:

[ 1 0 0 a ]

[ 0 1 0 b ]

[ 0 0 1 c ]

First, we divide the first row by -2 to make the pivot in the first column 1:

[ 1 -3/2 -1/2 1 ]

[ -3 1 3 -4 ]

[ 0 2 -1 0 ]

Next, we perform row operations to eliminate the coefficient -3 in the second row:

[ 1 -3/2 -1/2 1 ]

[ 0 2/2 9/2 -7 ]

[ 0 2 -1 0 ]

Then, we divide the second row by 2 to make the pivot in the second column 1:

[ 1 -3/2 -1/2 1 ]

[ 0 1 9/4 -7/2 ]

[ 0 2 -1 0 ]

Now, we perform row operations to eliminate the coefficient 2 in the third row:

[ 1 -3/2 -1/2 1 ]

[ 0 1 9/4 -7/2 ]

[ 0 0 -17/4 7 ]

Finally, we divide the third row by -17/4 to make the pivot in the third column 1:

[ 1 -3/2 -1/2 1 ]

[ 0 1 9/4 -7/2 ]

[ 0 0 1 -28/17 ]

The resulting rref shows that the system is consistent, and the solution is x = 1, y = -28/17, and z = -28/17.

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Answer:

1. 11

2. -13

3. -6

Step-by-step explanation:

Hope this helps. Have a great day! (I got this correct on edge :})

Answer:

Simplifying

3u = 72

Solving

3u = 72

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Divide each side by '3'.

u = 24

Simplifying

u = 24

3u= 72

three will go to the other side so it will divide

and it well be

u= 24

Answer:

without numbers= 10x + 15y = 120

Step-by-step explanation:

grocery store= 10x (x=8 in this case)

music lessons= 15y

The radius of J is 76. so option A is correct.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

By applying Pythagoras theorem In right triangle,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

(720 + J)² = (648)² + J²

518400+ J² + 1440J = 419904 + J²

1440J = 518400- 419904

J = 76

Therefore, J = 76 units is the answer.

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The most appropriate statistical test for these data from the list below would be: the Wilcoxon Ranked Sum test.

The Wilcoxon Ranked Sum test is the best for the analysis because it does not assume a normal distribution. The Wilcoxon ranked sum test compares two independent populations to determine if there is a statistical significance between them.

In the example given there is no normal distribution, so the Wilcoxon Ranked Sum test will analyze the responses differently to confirm if there is a relationship.

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Answer:

1. Yes

2. Yes

3. No

4. Yes

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees.

For 1, 76+14 = 90.

Etc., you can do the math, I believe you are smarter than addition.

Answer:

pepperoni pizzas = 8

cheese pizzas = 4

Step-by-step explanation:

let x = cheese pizza

2x + x + 1 = 13

3x = 13 -1

3x = 12

x = 4

pepperoni = 2x4 = 8

Answer:

21.952 [tex]yards^{3}[/tex]

Step-by-step explanation:

The volume of a cube is side length cubed.

So [tex]2.8^{3}[/tex] = 21.952

Answer:

s=6.5

Step-by-step explanation:

to check, just substitute s for its value

6.5+10.5+17

so the correct answer is, s=6.5

The gallons of paint that Beth used is 6 gallons.

The first step is to convert pint to gallon:

1 pint = 0.125 gallon

The second step is to multiply 0.125 by 48 : 0.125 x 48 = 6 gallons

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Answer:

first is no second is yes third is no fourth is yes

Step-by-step explanation:

I'm not sure btw

Answer:

First, multiply the radius by 2 to get the diameter 18 inches. Then, multiply the diameter by 3.14 (an approximation for 1) to get a circumference of about 56.52 inches. If the diameter doubles the circumference doubles.

Step-by-step explanation:

18π = 56.52

36π = 113.04

56.52*2 = 113.04

Answer:

171

Step-by-step explanation:

This is a Right triangle,

So this means that all the sides should add up to 180,

So far we have 9

So we will have to Subtract 9 from 180 which leaves us with 171,

I hope this is correct!!

A standard deviation of 23.16.

In a recent election, where 65% of people supported reelecting the incumbent, a poll was conducted with a sample size of 1390 people.

To approximate the binomial distribution with a normal distribution, we can calculate the mean and standard deviation.

The mean is determined by multiplying the sample size (1390) by the proportion of support (0.65), resulting in a mean of 898.5.

The standard deviation is calculated by taking the square root of the product of the proportion of support (0.65) with the proportion of opposition (0.35), divided by the sample size, and then multiplied by the square root of the sample size.

This yields a standard deviation of approximately 23.16.

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Answer:

2x^2+8x - 16

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

Given

R(x) = 6x ^ 2 + 5x - 8

C(x) = 4x ^ 2 - 3x + 7

P(x) = 6x ^ 2 + 5x - 8-(4x ^ 2 - 3x + 7)

P(x) = 6x ^ 2 + 5x - 8 - 4x ^ 2 + 3x - 8

Collect the like terms;

P(x) = 6x^2-4x^2+5x+3x-8-8

P(x) = 2x^2+8x - 16

Hence the company's profit for the fiscal year is 2x^2+8x - 16

Answer:

139 cm

Step-by-step explanation:

The curves are intersecting at (-1.75, 2.5) and (1.75, 2)

Nonlinear functions include all functions that are not linear. The following are some instances of nonlinear functions: f(x) = x2 - 2x + 2, ln (x), ex, etc.

In the above question, a graphical representation of non-linear system of equations is given

We need to find the solution of this non-linear system of equations based on the graphical representation

We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations

We can clearly see that, the curves are intersecting at

(-1.75, 2.5) and (1.75, 2)

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Answer:

30 ft

Step-by-step explanation:

10 feet = 120 inches

120 in x 3 in = 360 in

360 in ÷ 12 in = 30 ft

Answer:

5 is c 6 is b

Step-by-step explanation:

Answer:

5) C 6) B

Step-by-step explanation:

Yw

The product of 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > is 2x + 1.

The product of the polynomials 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > can be determined using polynomial long division.

To perform the division, we divide 3x³-5x² + 3 by x² + 1. The result of this division gives us the quotient and the remainder. In this case, the quotient is 2x and the remainder is 2x + 1.

The quotient represents the coefficient of x in the resulting product, while the remainder represents the constant term. Therefore, the resulting product is d. 2x + 1.

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B) A high correlation between two or more independent variables would indicate the possible presence of multicollinearity in a regression analysis.

Multicollinearity occurs when two or more independent variables in a regression model have a strong correlation with one another, making it difficult to distinguish the individual influence of each independent variable on the dependent variable.

Poorly constructed experiments, heavily observational data, introducing new variables that are dependent on other factors, including identical variables in the dataset, incorrect use of dummy variables, or inadequate data can all lead to multicollinearity.

Calculating the variance inflation factor (VIF) for each independent variable is one way for detecting multicollinearity; a VIF value more than 1.5 shows multicollinearity.

To correct multicollinearity, one of the highly correlated variables can be removed, combined into a single variable, or a dimensionality reduction approach such as principal component analysis can be used.

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Answer:

the answer is 50

Answer:

50

Step-by-step explanation:

BODMAS/BIDMAS

48 - 5 + 7 x [tex]3^{2}[/tex] ÷ (7-10)²

= 48 - 5 + 7 x [tex]3^{2}[/tex] ÷ (-3)²

= 48 - 5 + 7 x [tex]3^{2}[/tex] ÷ 9

= 48 - 5 + 7 x 9 ÷ 9

= 48 - 5 + 63 ÷ 9

= 48 - 5 + 7

= 43 + 7

= 50

A) The price-demand relationship for a clock radio is given by x=4000-40p. B) The revenue function R(x) is found to be R(x) = x * [(4000 - x) / 40]. C) The marginal revenue at a production level of 2700 clock radios is calculated using the derivative R'(x) = (4000 - 3x) / 40, and D) R'(3200) = -60.00 indicates a decrease in revenue of $60.00 per unit at a production level of 3200 clock radios.

(A) To express the price p in terms of the demand x, we can rearrange the equation x=4000-40p to solve for p. Subtracting x from both sides and dividing by -40, we get p = (4000 - x) / 40. The domain of this function represents the possible values for x, which should be non-negative since it doesn't make sense to have negative demand. Therefore, the domain is x ≥ 0.

(B) The revenue R(x) from selling x clock radios can be calculated by multiplying the price p by the quantity x. Since p = (4000 - x) / 40, we have R(x) = x * p = x * [(4000 - x) / 40]. The domain of the revenue function depends on the domain of x, which we determined in part (A) as x ≥ 0.

(C) The marginal revenue represents the change in revenue resulting from producing one additional unit. To find the marginal revenue at a production level of 2700 clock radios, we need to find R'(x) (the derivative of the revenue function) and evaluate it at x = 2700. Differentiating R(x) = x * [(4000 - x) / 40] with respect to x, we find R'(x) = (4000 - 3x) / 40. Substituting x = 2700 into the derivative, we get R'(2700) = (4000 - 3 * 2700) / 40.

(D) The interpretation of R'(3200) = -60.00 is that the marginal revenue at a production level of 3200 clock radios is -60.00 dollars per unit. This means that producing an additional unit at this level would result in a decrease in revenue by $60.00. The negative value indicates a diminishing marginal revenue, which suggests that the market might be becoming saturated or that there are competitive factors affecting the demand for the clock radios.

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If an equation indicates addition in its presentation, in order to solve for the unknown, you must perform the inverse operation, which is subtraction.

Equations typically involve an equality between two expressions, with one or more unknown variables.

To isolate the unknown variable and determine its value, you need to perform operations on both sides of the equation to simplify and solve for the variable.

When an equation shows addition, you can undo that operation by subtracting the same value from both sides of the equation. This ensures that the equation remains balanced and maintains equality.

For example, consider the equation:

x + 5 = 10

To solve for x, you need to eliminate the 5 added to x. To do so, you subtract 5 from both sides of the equation:

x + 5 - 5 = 10 - 5

x = 5

By subtracting 5 from both sides, you isolate the variable x and find that its value is 5.

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The length of the arc intercepted by a central angle of 140° on a circle with a radius of 14 inches is approximately 34.1557 inches.

To find the length of the arc intercepted by a central angle on a circle, we can use the formula:

Arc Length = (Central Angle / 360°) * Circumference

In this case, the radius of the circle is 14 inches, and the central angle is 140°.

First, we need to calculate the circumference of the circle:

Circumference = 2 * π * radius

Circumference = 2 * π * 14 inches

Now, we can calculate the length of the arc:

Arc Length = (140° / 360°) * Circumference

Arc Length = (140/360) * (2 * π * 14 inches)

Arc Length ≈ (0.3889) * (2 * 3.1416 * 14 inches)

Arc Length ≈ 0.3889 * 87.9648 inches

Arc Length ≈ 34.1557 inches

Therefore, the length of the arc intercepted by a central angle of 140° on a circle with a radius of 14 inches is approximately 34.1557 inches.

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Answer:

8.9

Step-by-step explanation:

8.94427191

Answer:

8.9

Step-by-step explanation:

8.94427191 the number 1 spot to the right of the decimal point is tenths. the number is 9 the number to the right of that is 4. unless that number 2 digits to the right of the decimal point is 5 or over the 9 stays the same

c = 1/2 ,the mean is μ = 1/2,  the CDF of f(x) is 2x^2   and the variance is σ² = 1/6.

The given pdf is f(x) = 4xc for 0 ≤ x ≤ 1.

To find the constant c such that f(x) is a pdf: We know that, For f(x) to be a pdf, it must satisfy the following two conditions:

The integral of f(x) over its support should be equal to 1. f(x) must be greater than or equal to 0 for all values of x. So,

Let us find the value of c first integral of f(x) from 0 to 1 should be equal to 1, therefore∫f(x)dx = ∫(4xc)dx for 0 ≤ x ≤ 1∫f(x)dx = 4∫xc dx for 0 ≤ x ≤ 1∫f(x)dx = 4[c(x^2/2)]_0^1∫f(x)dx = 2c

Therefore,∫f(x)dx = 1 implies 2c = 1 or c = 1/2.

Now we know the value of c. Let us find the CDF of f(x): CDF of f(x) = P(x ≤ X) = ∫f(t)dt from -∞ to x= ∫f(t)dt from 0 to x= ∫(4xt)dt from 0 to x= 2x^2 from 0 to x= 2x^2Therefore, the CDF of f(x) is 2x^2.

Graph of the PDF of f(x)For graphing the PDF of f(x), we need to know the values of x for which f(x) is defined as well as its shape and maximum value.f(x) = 4xc for 0 ≤ x ≤ 1The given function is a straight line with a slope of 4c and intersects the x-axis at 0 and the y-axis at 0.

We know that c = 1/2, thus (x) = 2x for 0 ≤ x ≤ 1The graph of f(x) will look as follows: Graph of the CDF of f(x)The graph of the CDF of f(x) will look as follows:

We can find the mean and variance of the PDF of f(x) using the following formulae: Mean, μ = ∫xf(x)dx from -∞ to ∞.Variance, σ² = ∫(x - μ)²f(x)dx from -∞ to ∞.

Substituting f(x) and its limits in the above formulae, we get: Mean, μ = ∫xf(x)dx from 0 to 1= ∫(2x^2)x dx from 0 to 12(1^4 - 0^4)/4= 1/2.

Variance, σ² = ∫(x - μ)²f(x)dx from 0 to 1= ∫(x - 1/2)²(2x)dx from 0 to 1= 1/6.

Therefore, the mean is μ = 1/2, and the variance is σ² = 1/6.

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Answer:

Number of children = x = 330

Number of adults = y = 358

Step-by-step explanation:

Let

Number of children = x

Number of adults = y

x + y = 688 (1)

1.75x + 2.00y = 1293.50 (2)

From (1)

x = 688 - y

Substitute x = 688 - y into (2)

1.75x + 2.00y = 1293.50

1.75(688 - y) + 2.00y = 1293.50

1,204 - 1.75y + 2.00y = 1293.50

- 1.75y + 2.00y = 1293.50 - 1,204

0.25y = 89.50

y = 358

Substitute y = 358 into (1)

x + y = 688

x + 358 = 688

x = 688 - 358

x = 330

Number of children = x = 330

Number of adults = y = 358

Answer:

x = -0.2

Step-by-step explanation:

(5x + 2) = 1

      - 2     -2      

--------------------

5x = -1

Divide each side by 5

-1/5

= -0.2

Check:

(5x + 2) = 1

replace x with -0.2

(-1 + 2) = 1

1 = 1

The equation is true.

Hope this helped :)