2.) Emmanuel is at a sporting goods store. The store
offers a 9% discount on all items. At checkout a 6%
sales tax is added to the discounted price. Select the
two that apply.

A. $25 pants cost $24.12 at checkout

B. $89 cleats cost $76.50 at checkout

C. A $29 basketball costs $37.97 at checkout.

D. $189 glove costs $183.33 at checkout

The equation of parabola in vertex form is [tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]

To write the equation of a parabola in vertex form, we use the following formula:

[tex]$$(x-h)^2=4p(y-k)$$[/tex]

where (h,k) is the vertex and p is the distance between the focus and the vertex.

Given that the focus of the parabola is at (3, 2.5), we can determine that the vertex of the parabola is also at (3, 2.5). Let's substitute these values into the formula:

[tex]$$(x-3)^2=4p(y-2.5)$$[/tex]

To find the value of p, we need to use the fact that the distance between the focus and vertex is p. The distance formula is:

[tex]$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$[/tex]

Substituting the values we know:

[tex]$$\begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ &= \sqrt{(3 - 3)^2 + (2.5 - 2.5)^2} \ &= 0 \end{aligned}$$[/tex]

Since d = 0, we know that p = 0 and the equation simplifies to:

[tex]$$(x-3)^2=0$$[/tex]

Expanding the left side:

[tex]$$x^2 - 6x + 9 = 0$$[/tex]

So the equation of the parabola in vertex form is:

[tex]$$\boxed{(x-3)^2=4 \cdot 0 (y-2.5)}$$[/tex]

Or

[tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]

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The equations in the slope-intercept form are

p = 3b + 2 and p = (5/2)b + 15/2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

From the table and scatter plot;

(a). The line for 'Build it' passes through (1, 10) and (3, 15),

then the equation of the line is,

p = (5/2)b + 15/2

Similarly, the equation of the line-'All things home' is,

p = 3b + 2.

(b) the graphs of the lines are given in the attached image.

(c) The equation in the slope-intercept form;

p = 3b + 2 and p = (5/2)b + 15/2.

(d) When b = 65,

then p = 3(65) + 2 and p = (5/2)(65) + 15/2.

So, p = 197 and p = 170

Therefore, all the required values are given above.

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The width of the river is calculated by the tangent of the angle will be 293 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Observing a river below from the top of a 450-foot cliff, a hiker. Her depression lies at an angle of 80° to the near bank and 50° to the far bank of the river.

The horizontal distance when the angle is 80° is given as,

tan 80° = 450 / x₁

x₁ = 84.64 feet

The horizontal distance when the angle is 50° is given as,

tan 50° = 450 / x₂

x₂ = 377.59 feet

The width of the river is given as,

W = x₂ - x₁

W = 377.59 - 84.64

W = 292.95

W ≈ 293 feet

The width of the river is calculated by the tangent of the angle will be 293 feet.

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Answer:

C i think

Step-by-step explanation:

When performing a t-test assuming unequal variances, the test statistic is a t-value, which is calculated by dividing the difference between the means of the two groups by the standard error of the difference.

To see if the difference in mean mpg between 4 and 8 cylinder cars is statistically significant, compare the estimated t-value to a critical t-value based on degrees of freedom and desired level of significance. The difference is regarded statistically significant if the estimated t-value is bigger than the crucial t-value.

As a result, the right response depends on the estimated t-value, the crucial t-value, and the level of significance utilized in the test.

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Answer: The word "BASKETBALL" has 2 B's and 3 vowels (A, E, A). The probability of choosing the letter B, not replacing it, and then choosing a vowel is:

(2/10) * (2/9) * (3/8) = 6/90 = 1/15

So, the probability of choosing the letter B, not replacing it, and then choosing a vowel is 1/15.

Step-by-step explanation:

Answer:

12.5 in²

Step-by-step explanation:

The distance between the points -3,-8, and 6,-8 is 3 units.

The length of the line segment bridging two points on a plane is known as the distance between the points.

Look at the provided points.

Calculate the distance between the points using the given formula.

Given points are -3,-8 and 6,-8

Given two points lies the parallel to X-axis

The distance between the two points is

A (-3,-8) and B(6,-8) =  X₂ - X₁

6 - 3  = 3 units.

Therefore, the distance between two points -3,-8 and 6,-8 is 3 units.

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x = 5

z = 118°

Step-by-step explanation:

opposite angles are equal

(6x + 32)° = 62°

6x = 62° - 32°

6x = 30°

x = 5°

angles on a straight line add up to 180

180° = 62° + z

z = 180° - 62°

z = 118°

Answer:

Slope: 1

Y-Intercept: -2

y=x-2

Graph it by plotting a point at (0,-2) and then by going up one to the right. One up and then one to the right and repeat twice. Now you can graph this easily. Hope this helped!!

Step-by-step explanation:

The package that will have enough wrapping paper to cover is package B

Package A has a surface area of 70. 65 in²

Package B has a surface area of 62. 8 in²

The formula for the surface area of a cylinder is expressed as;

SA = 2πrh + 2π

Given that the parameters are;

For Package A, substitute the values

= 2 × 3.14 × 1.5 × 6 + 2 × 3.14 × (1.5)²

Multiply the values, we have;

= 70. 65 in²

For package B, substitute the values, we get;

= 2 × 3.14 × 2 × 3 + 2× 3.14 × (2)²

Multiply the values

= 62. 8 in²

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True. A simple random sample is a type of sampling method that is used to select a subset of observations from a larger population.

The key characteristic of a simple random sample is that each observation in the population has an equal probability of being selected to be part of the sample.

Mathematically, this can be expressed as follows: Let N be the population size, and let n be the sample size. Then, the probability of any specific sample of n observations being selected from the population is given by the formula:

P(Sample) = (n!/N!)/(N-n)!

where n! represents the factorial of n (n factorial), and (N-n)! represents the factorial of N-n.

This means that if we were to draw multiple simple random samples of the same size from the same population, each sample would have an equal probability of being selected.

In conclusion, a simple random sample is a method of selecting a subset of observations from a population that ensures that each observation has an equal probability of being selected, and that each sample has an equal probability of being selected.

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To calculate the percent change in renewable energy investment in the US from 2005 to 2018, you can use the following formula:

Percent change = ((Final value - Initial value) / Initial value) * 100%

In this case, the initial value is $11.4 billion in 2005 and the final value is $46.5 billion in 2018. Plugging these values into the formula, we get:

Percent change = (($46.5 billion - $11.4 billion) / $11.4 billion) * 100%

= ($35.1 billion / $11.4 billion) * 100%

= 3.085 * 100%

= 308.5%

So, the percent change in renewable energy investment in the US from 2005 to 2018 was 308.5%, a substantial increase over the 13-year period.

Answer:

1. Kevin has 12 pieces of paper.

2. Including Sybill and her friends, each person will get 1/8 of the 1/2 slice.

Step-by-step explanation:

1. This is because if 1 piece of paper turned divided into fourths would 4/1 or 4 “fourths” of paper. So multiply that by 3 since there is 3 pieces of paper and we are following the same steps. 3 x 4 = 12. Hence if you divide 3 pieces of paper into fourths, you will have 12 fourths.

2. Since we are splitting the 1/2 piece four (which includes sybill and her 3 friends) ways, the equation would be: 1/2 divided by 4

Divide:

1/2 divided by 4-

 1/2 : 4 = 1/2 · 1/4 = 1 · 1/2 · 4 = 1/8 

Hence, each friend and Sybill her self will receive a 1/8 piece.

The solution for r in the equation is 428.43

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

100000 = 8000(1+ r/12000)^72

Divide through by 8000

So, we have

12.5 = (1+ r/12000)^72

Take the 72th root of both sides

So, we have

1 + r/12000 = 1.03570211065

Subtract 1

r/12000 = 0.03570211065

So, we have

r = 428.4253278

Hence, the value of r is 428.43

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The required measures of length are, as follows:

GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.

A rectangle is defined as a four-sided shape with opposite sides that are equal in length and parallel to each other.

The lengths are given in the question, as follows:

DE = 11

GH = 14

Since DE and GF are opposite sides then both are equal.

So GF = 11

Here GH and HF are equal,

HF = 14

∵ GE = GH + HE = 14 + 14 = 28

As we know that the two lengths of the diagonals are equal in the rectangle.

So GE = DF

So DF = 28

Using the Pythagorean theorem, we have

DG² + GF² = DF²

DG² + 11² = 28²

DG² + 121 = 784

DG² = 663

DG = 25.75

Thus, the measures are, as follows:

GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.

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The value of c lies in the interval [tex](-\infty, -1.5)[/tex]

Inequality is a statement that shows the relationships the two expressions are not equal. It is defined by the symbols like <, >, ≤, ≥.

[tex]\frac{c}{2} < -0.75[/tex]

To find the value of c:

[tex]\frac{c}{2} < -0.75[/tex]

Multiply both sides by 2 we get,

[tex]2\frac{c}{2} < (-0.75)*2[/tex]

⇒c < -1.5

Therefore c<-1.5 is the solution for the given inequality.

It can also be represented in the interval form.

This is given in the interval notation [tex](-\infty, -1.5)[/tex]

Hence, the value of c lies in the interval [tex](-\infty, -1.5)[/tex]

Complete question:

What is the values that c can take when  [tex]\frac{c}{2} < (-0.75)[/tex]?

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Answer:

Given: [tex]1\frac{1}{3} :2\frac{1}{3}[/tex]

To simplify this ratio, convert the mixed fractions into improper fractions:

[tex]\frac{4}{3}[/tex] : [tex]\frac{7}{3}[/tex]

Then to divide ( because ratio = division ) turn around [tex]\frac{7}{3}[/tex] and multiply:

[tex]\frac{4}{3} * \frac{3}{7}[/tex]

Then multiply:

[tex]\frac{12}{21}[/tex]

Finally simplify this fraction by dividing the denominator & numerator by 3:

= [tex]\frac{4}{7}[/tex]

...

Answer:

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate.

Exact Form:

3√2+2

    7

Decimal Form:

0.89180581

…

In statistics, p represents the true proportion p hat represents the sample proportion

p represents population that has a certain characteristic or falls into a certain category. It is a fixed, unknown value that we are trying to estimate.

p hat represents the sample proportion, which is an estimate of the true proportion based on a sample of the population. It is calculated by dividing the number of individuals in the sample with the characteristic or in the category by the total sample size.

For example, if we want to estimate the proportion of students who prefer chocolate ice cream, we could take a sample of 100 students and find that 60 of them prefer chocolate.

In this case, p hat would be 60/100 or 0.6. This is our estimate of the true proportion, p, of all students who prefer chocolate ice cream.

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Answer: The student correctly wrote an expression to find the total cost of downloading "s" songs. The expression is: 0.99s + 7.99. However, they made a mistake when they simplified the expression to 8.98s. The expression should have remained as 0.99s + 7.99, because the $7.99 membership fee does not change regardless of how many songs are downloaded.

In Part B, the student correctly used the expression to find the cost of downloading 12 songs. They multiplied 8.98 by 12 and got the correct answer of 107.76.

Step-by-step explanation:

Answer:A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Step-by-step explanation:

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

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Answer:

[tex]\frac{2}{30}[/tex]

Step-by-step explanation:

[tex]\frac{4}{6}-\frac{3}{5} \\ \\ =\frac{2}{3}-\frac{3}{5} \\ \\ =\frac{10}{15}-\frac{9}{15} \\ \\ =\frac{1}{15} \\ \\ =\frac{2}{30}[/tex]

It would be 1/15 but thats not an option, if you need help try math  way doht  com, thats the best thing u can use for math problems

Barbara will therefore shell out $171.36 for the cost of shipping and handling.

The amount of money, or its equivalent, for which anything being offered for sale, purchased, or otherwise transacted. A price on someone's head is a sum provided for their capture, whether they are alive or dead.

We must calculate 28% of the chandelier's original purchase price in order to calculate the value Sarah will charge for shipping and handling.

Step 1

Calculate 28% of $612

We can multiply a value by 0.28 to get 28% of it, or reduce it by 100 & then multiply the result by 28. So:

28% of $612 = 0.28 x $612 = $171.36

Step 2

Add the cost of shipping and handling to the purchase price.

Simply include the shipping & handling fee to the original price to get the chandelier's total cost with shipping and handling included:

Total cost = $612 + $171.36 = $783.36

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The answer is 36. you basically add and subtract to the left and right.

32+8= 40

40-4=36

(you get the 8 because 2 x 2 x 2 = 8)

Question: A line passes through the point (9, 5) and has a slope of -4/3. Write an equation in slope-intercept form for this line.

Answer:

[tex]y=-\frac{4}{3}x+17[/tex]

Given:

x = 9

y = 5

m = -4/3

Step-by-step explanation:

Slope intercept form is y = mx+b

Plug in x, y, and m to solve for b.

[tex]5=-\frac{4}{3}(9)+b[/tex]

[tex]b=5+\frac{4}{3}(9)=17[/tex]

Now that you have b, plug in m and b back into the equation

[tex]y=-\frac{4}{3}x+17[/tex]

The total volume of milk would be 1/2 gallons.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that,

Volume = 1/4 gallons

The number of weeks = 2

So, the total volume =

1/4 × 2 = 1/2 gallons

Hence, the total volume of milk would be 1/2 gallons

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The earnings in the simple interest and compound interest for a 5 year period is in the table below where S is for Suzanne and D is for Derrick

            S - annual interest  S - Balance   D - annual interest   D - Balance

Year 1                 147                   3147                      147                    3147

Year 2                294                  3294                     301.2                 3301.2

Year 3                441                   3441                      462.96              3462.96

Year 4                588                  3588                     632.65              3632.65

Year 5                735                   3735                     810.65               3810.65

Simple interest is calculated by the formula

principal x time x rate / 100

In the problem

Principal = $3000

rate = 4.9%

time is varying from 1 to 5

For the first year we have

= 3000 * 1 * 4.9 / 100

= 147

Compound interest the formula is

Principal(1 + rate)^(year) - 1)

For the first year, (the rate is already divided by 100 to get 0.049) we have

= 3000(1 + 0.049)^(1) - 1)

= 147

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Answer:

a: 30%

b: 5%

Step-by-step explanation:

a: (42,000/140,000)*100

b: (7,000/140,000)*100