Carter went shopping for a new pair of pants. Sales tax where he lives is 3.75%. The
price of the pair of pants is $36. Find the total price including tax. Round to the
nearest cent.

Answer:

2/10-4/10x

Step-by-step explanation:

Answer: =

2/5 x + -3/5

Step-by-step explanation:

Answer: 6.4 miles/hour

Step-by-step explanation:

Speed = distance/time

19.2/3 = 6.4

Hope this helps!

An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).

In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:

x = a(y - k)² + h.

Where:

By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:

h = 0

k = 0

a = positive.

x = a(y - k)² + h.

x = a(y - 0)² + 0.

x = ay²

Therefore, a possible equation is x = 1/12(y²).

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The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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A vertical parabola with vertex (1,-4) and focus (1,-2) is given. It is required to find the standard form of the equation for the parabola.

Recall that the equation of a Vertical Parabola with vertex (h,k) and focus (h,k+1/4a) is given as:

Compare the given vertex (1,-4) with the form (h,k). It follows that:

Compare the given focus (1,-2) with the form (h,k+1/4a). It follows that:

Substitute k=-4 into the equation and find the value of a:

Substitute k=-4, h=1, and a=1/8 into the equation of a vertical parabola:

Rewrite the equation in standard form as follows:

Recall that the Directrix of a vertical parabola is represented by the equation:

Substitute k=-4 and a=1/8 into the equation of directrix:

Hence, the correct answer is (x-1)²=8(y+4); y=-6.

The correct answer is (x-1)² = 8(y+4) ; y = - 6. (second option)

Answer:

Volume: 1135.82 yd³

Surface Area: 657.12 yd²

Step-by-step explanation:

V = whl

12.2 · 9.8 · 9.5

1135.82

A = 2(wl + hl + hw)

2 · (12.2 · 9.5 + 9.8 · 9.5 + 9.8 · 12.2)

657.12

Total number of monthly payments, not including the final balloon payment is $1,195.77

The monthly payment is the sum that must be paid each month for the duration of the loan to cover the principal balance. When a loan is taken out, not only the principal—the amount that was initially loaned out—but also the interest—which accrues—must be repaid.

Step1

M = 350,000(0.071/12)(1+0.071/12)² /(1+0.071/12)¹² =3,618.02

M = P(r/12) (1+r/12)¹²×n/(1+r/12)¹²×n -1

Step2:

3,618.02 × 12 × 12 = 520,994.88

The total paid is the product of the monthly payment and the number of payments.

520,994.88 - 350,000 = 170,994.88

= 170,994.88÷143

= 1,195.77

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The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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Willka would need 6 liters of paint to cover an area of 27 square meters according to the ratio.

A ratio is a comparison of two or more values or quantities. It is a way of expressing the relationship between two or more quantities in a mathematical form. A ratio is typically expressed in the form of "a:b" or "a to b", where a and b are two values being compared.

According to question:

To find the coverage per liter of paint, we can divide the total area covered by the amount of paint used.

In this case, we can divide 13.5 m² by 3 L:

Coverage per liter = 13.5 m² / 3 L = 4.5 m²/L

This means that with 1 liter of paint, Willka can cover an area of 4.5 square meters.

If we know the area to be painted, we can use this ratio to determine how much paint is needed.

For example, if we want to paint an area of 27 square meters, we can calculate:

Paint needed = area to be painted / coverage per liter = 27 m² / 4.5 m²/L = 6 L

So Willka would need 6 liters of paint to cover an area of 27 square meters.

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mid point =((4+(-4))/2,(-5+5)/2)

=(0,0)

The midpoint between the points (4, -5) and (-4, 5) is (0, 0).

To find the midpoint between two points (\(x_1, y_1\)) and (\(x_2, y_2\)), you can use the midpoint formula:

Midpoint = \(((x_1+ x_2)/2, (y_1+ y_2)/2)\)

In this case, the two points are (4, -5) and (-4, 5).

So, the midpoint using the formula:

\(x_1\) = 4

\(y_1\) = -5

\(x_2\)= -4

\(y_2\) = 5

Midpoint

= ((4 + (-4)) / 2, (-5 + 5) / 2)

= (0 / 2, 0 / 2)

= (0, 0)

Therefore, the midpoint between the points (4, -5) and (-4, 5) is (0, 0).

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Answer:

Step-by-step explanation:

in this triangle

X^2=a^2+b^2

X^2=15^2+8^2

x^2=225+64

x^2=289

x=17

Answer:

X is always equal to 1 no matter the equation. In this it looks like you are using Pyth. Theory. If its not sorry, but X = 1  

Step-by-step explanation:

\(A^{2} +B^{2}=C^{2} \\15^{2}+8^{2} \\225+64\\C^{2}=289\\\sqrt289\\C=17\)  

Answer:

No, triangle B is a reflection of triangle A.

Step-by-step explanation:

The points of triangle A are reflected across the dotted line. So as a result triangle B is a reflection of triangle A.

Answer:

No

Step-by-step explanation:

Its a reflection because even if you did rotate it it would never be in that orientation.

Answer:

Step-by-step explanation:

GIVEN

4x - 3 = 23 - x

4x + x = 23 +3

5x = 26

x = 26/5

This is because the red and blue lines cross at (0,-2). We don't really need to worry about the y coordinate here. For this problem, all we care about is the x coordinate, which is x = 0.

When x = 0, the outputs of each function f(x) and g(x) are both the same value. So that's why we can say f(0) = g(0). It's the same as saying f(x) = g(x) has the solution x = 0.

Answer:

\(f(-10) = -30\)

Step-by-step explanation:

f(x) = -\(x^{2}\) - 7x (notice the - symbol before the \(x^{2}\))

the first step is to plug in -10 for x

\(f(-10) = -(-10)^{2} - 7(-10)\)

\(f(-10) = -(100) +70\) (-10 * -10 is +100, -7 * -10 is +70)

\(f(-10) = -100 + 70\) (solved parentheses)

\(f(-10) = -30\)

Answer: a) P(3) = 0

              b) P(5<x<9) = 1.28

              c) P(5<x<10) = 1.6

              d) P(6) or P(x>6) = 2.88

              e) P(x<5) = 1.28

              f) E(x) = 8

                 V(x) = 16.34

Step-by-step explanation: Uniform Distribution is a continuous probability distribution in which probability is constant. It is also known as Rectangular Distribution because of the format the graph makes with the axis.

In this case, the probability of adults had been tested for HIV is 0.32.

Let x be the number of adults tested for HIV:

a) x=3

P(x=3) = 0

The graph is a line paralel to x-axis. To calculate probability, you have to calculate the area under the line. Since there is only one point on the x-axis,  there is no variation, so probability is 0.

b) 5<x<9

P(5<x<9) = (9-5)*0.32

P(5<x<9) = 1.28

c) 5<x<10

P(5<x<10) = (10-5)*0.32

P(5<x<10) = 1.6

d) x=6 or x>6

P(x=6) = 0

P(6<x<15) = (15-6)*0.32

P(6<x<15) = 2.88

Using "or" rule:

P(6) + P(6<x<15) = 0 + 2.88 = 2.88

e) x<5

P(1<x<5) = (5-1)*0.32

P(1<x<5) = 1.28

f) Mean or expected value for uniform distribution is

\(E(x) = \frac{b+a}{2}\)

where a and b are the "limits" of the distribution

In the above case, number of adults tested is between 1 and 15. Then

\(E(x) = \frac{15+1}{2}\)

E(x) = 8

Variance of uniform distribution is

\(V(x)=\frac{1}{12} (b-a)^{2}\)

\(V(x)=\frac{1}{12} (15-1)^{2}\)

\(V(x)=\frac{14^{2}}{12}\)

V(x) = 16.34

Answer:

75

Step-by-step explanation:

Step-by-step explanation:

the formula of the "relation" is

x² + y² = r²

this is for circle with its center at the origin.

now that gives us

y² = r² - x²

y = ±sqrt(r² - x²)

a. this ± of the square root gives us the 2 functions.

y = sqrt(r² - x²)

y = - sqrt(r² - x²)

as it is a circle, the ranges and domains are the same.

domain is the allowed number interval for x, and range is the number interval for y (the function results).

both are

-r <= x <= r

outside of that range the square root argument becomes negative, and that is undefined for R (the set of real numbers).

b. if we want to see it that way, we can say that

f(x) = r² - x²

g(x) = sqrt(x)

and so

sqrt(r² - x²) = g(f(x))

a function into function.

c. let's pick the "positive" semicircle

y = g(f(x)) = + sqrt(r² - x²)

f(x) = r² - x²

the domain is all x (-infinity < x < +infinity)

the range is (-infinity < y <= r²), as negative and positive larger x will turn f(x) negative. the functional results cannot get bigger than r² (for x=0).

g(x) = +sqrt(x)

the domain is all positive x incl. 0 (0 <= x < +infinity), as sqrt is not defined for negative values. at least not in R.

the range is also all possible positive values incl. 0

(0 <= y < +infinity).

d.

A one-to-one correspondence function is a function between the elements of the two sets of domain and range, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

that means, every x value creates exactly one y value, and no y value occurs more than once.

this is no true for

f(x) = r² - x²

because for -r <= x <= r we get the same y for -x and +x.

it is true for

g(x) = sqrt(x), as no 2 different numbers have the same square root.

The missing value in the table include the following: B. 4 1/2 in.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

50 5/8 = 5 × W × 2 1/4

Width, W = 4 1/2 inches.

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Complete Question:

The volume of a rectangular prism is 50 5/8 cubic inches.

The dimensions are given below.

What is the missing value in the table?

Length Width Height

5 in. 214 in.

A. 79in.

B. 412in.

C. 134in.

D. 1018in.

The probability of a student being signed up for Algebra 2 but not Chemistry is 0.54 or 54%.

Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.

To find P(Algebra 2 ∩ Not Chemistry), we need to look at the number of students who are signed up for Algebra 2 but not Chemistry. From the table, we can see that there are 260 students who are signed up for Algebra 2 and not Chemistry.

P(Algebra 2 ∩ Not Chemistry) = number of students signed up for Algebra 2 and not Chemistry / total number of students

= 260 / 480

= 0.54

Therefore, the probability of a student being signed up for Algebra 2 but not Chemistry is 0.54 or 54%.

So the answer is 0.54.

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9514 1404 393

Answer:

  0

Step-by-step explanation:

The slope can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (7 -7)/(-5 -4) = 0/-9 = 0

The slope of the line is 0. It is a horizontal line with equation y = 7.

The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

If a polygon is dilated by a scale factor = k

Rule to be followed as;

(x, y) → (kx, ky)

Here, k = Scale factor

If 0 < k < 1, size of the image will be reduced.

Similarly, k > 1, size of the image will be enlarged.

We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.

Rule used for the transformation,

(x, y) → (1/4x, 1/4y)

Here, the scale factor through which MNPQR has been dilated is 1/4.

Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.

Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.

Option (2) is the answer.

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The complete question is: Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'.

Which statement is true?

a. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

b. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

c. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

d. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

Answer:

Range: (negative infinity, 5]

Step-by-step explanation:

The range is the output/y values. The highest output when you plug in x will be 5. Therefore, your range's max will be at 5.

Answer:10c + 9h

Step-by-step explanation: 4 + 6 = 10

5 + 4 = 9

10 C + 9 H

no need for an equal sign, it is an expression with two terms.

For every 1 orange in the fruit bowl there are three bananas.

According to the question,

We have the following information:

In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.

Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:

4 oranges = 12 bananas

Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.

So, we have the following expression:

1 orange = 12/4 bananas

1 orange = 3 bananas

Hence, for every 1 orange in the fruit bowl there are three bananas.

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Answer:

A)

Function A: Exponential

Function B: Linear

Function C: Exponential

Function D: Exponential

B) Function A

Step-by-step explanation:

Function A: This is exponential because- (1, 3)(2,9)(3,27)

It is not going up by the same number each time. However, it is multiplying by 3 each time which means it is exponential.

Function B: This is linear because- (1, 64)(1, 80)(1, 96)

It is going up by 16 each time, (a constant number) which means it is linear.

Function C: This is exponential because- there is a curve, linear is always a straight line. But, this has a curve which means it is exponential.

Function D: This is exponential because- It is increasing by a percentage and not a constant number. It is increasing by 1% which means it is exponential.

The function that has the greatest growth factor is Function A because, Function A multiplies by 3 each time. Function B is linear, exponential functions always pass linear functions despite how "steep" they are. Eventually, the exponential function will surpass it. Function C is also exponential but is not as "steep" as Function A. Function A multiplies by 3 each time but Function C increases less. Function D is also exponential, and for the same reasons as Function C, Function A has the greatest growth factor.

Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed

Answer:

The answer is "\(x_k= -\frac{9}{16} (-2)^k + \frac{9}{16} 2^k +\frac{3}{8} k\times 2^k\\\\\)"

Step-by-step explanation:

\(\to F(Z)=\frac{3z(z-1)}{z^3-2z^2-4z+8}\\\\\to \frac{F(Z)}{z}=\frac{3z(z-1)}{z(z^3-2z^2-4z+8)}\\\\\to \frac{F(Z)}{z}=\frac{3(z-1)}{(z^3-2z^2-4z+8)}\\\\\to \frac{F(Z)}{z}=-\frac{9}{16} \frac{1}{z+2} + \frac{9}{16} \frac{1}{z-2} +\frac{3}{4} \frac{1}{(z-2)^2}\\\\\to F(Z)=-\frac{9}{16} \frac{z}{z+2} + \frac{9}{16} \frac{z}{z-2} +\frac{3}{4} \frac{z}{(z-2)^2}\\\\\to x_k= -\frac{9}{16} (-2)^k + \frac{9}{16} 2^k +\frac{3}{8} k\times 2^k\\\\\)