A local screen-printing company sells T-shirts at various prices, in dollars, depending upon how many T-shirts are bought at the time. The piecewise function below represents their pricing structure, where n is the number of T-shirts purchased. The school volleyball team purchased 20 shirts.
How much did the volleyball team spend on shirts?
$480
$180
$220
$260

Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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Answer:

y = e^-4x

Step-by-step explanation:

It might be right im not sure

Answer:

20

Step-by-step explanation:

firstly let's find out the side lengths of the triangle using formula

\(length \: = \: \sqrt{(y₂-y1) + ( y₂-y1)}\)

length of AB

\( \sqrt{( - 6 - 2) {}^{2} + ( - 4 - 1) {}^{2} } = \sqrt{89} \)

length of AC

\( \sqrt{( - 6 - 2) {}^{2} + (1 - 1) {}^{2} } = 8\)

length of BC

\( \sqrt{( - 6 - ( - 6)) {}^{2} + (1 - ( - 4)) {}^{2} } = 5\)

Now we have all three side lengths:

a =√89 b = 8 and c = 5

using this formula to find the semi perimeter where a, b and c are the side lengths, input them in

\(s \: = \: \frac{a + b + c}{2} \)

\(s = \frac{ \sqrt{89} + 8 + 5 }{2} = \frac{13 + \sqrt{89} } {2} \)

Use heron's formula

\(area = \sqrt{s(s - a)(s - b)(s - c)} \)

\(area = \sqrt{ \frac{13 + \sqrt{89} }{2}(\frac{13 + \sqrt{89} }{2} - \sqrt{89})( \frac{13 + \sqrt{89} }{2} - 8)(\frac{13 + \sqrt{89} }{2} - 5 } = 20\)

area = 20

Answer:

Step-by-step explanation:

Answers:

=============================================

Explanation:

The angle theta is between pi and 3pi/2, excluding both endpoints.

This places theta in the third quadrant (Q3) between 180 degrees and 270 degrees. The third quadrant is in the southwest.

Plot point A at the origin. 12 units to the left of this point, will be point B. So B is at (-12,0). Then five units lower is point C at (-12,-5). Refer to the diagram below. Notice how triangle ABC is a right triangle.

The angle theta will be the angle BAC, or simply angle A.

Since cos(theta) = -12/13, this indicates that

AB = -12 = adjacent

AC = 13 = hypotenuse

Technically, AB is should be positive, but I'm making it negative so that we can then say

cos(angle) = adjacent/hypotenuse

cos(theta) = AB/AC

cos(theta) = -12/13

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

If you apply the pythagorean theorem, you should find that BC = 5, which I'll  make negative since we're below the x axis. Then we can say

sin(theta) = opposite/hypotenuse

sin(theta) = BC/AC

sin(theta) = -5/13

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

If you divide sine over cosine, then you'll get 5/12. The 13's cancel out. This is the value of tangent.

Or you could say

tan(theta) = opposite/adjacent

tan(theta) = BC/AB

tan(theta) = (-5)/(-12)

tan(theta) = 5/12

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

To find csc, aka cosecant, you apply the reciprocal to sine

sin = -5/13 which means csc = -13/5

sec, or secant, is the reciprocal of cosine

cos = -12/13 leads to sec = -13/12

and finally cotangent (cot) is the reciprocal of tangent

tan = 5/12 leads to cot = 12/5

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

Note: everything but tan and cot is negative in Q3.

Answer:

Length = 3.56cm

Width = 30.48cm

Step-by-step explanation:

We can use the following equation ty o solve

\(68 = 2(2 + 8x) + 2x\)

Length = x

Width = 2 + 8x

Reduce

68 = 4 + 18x

x = 3.56

We then plug x in width equation and get 30.48

1 whole, 1 whole, 3/5, 1 whole,6/7, 1 whole,6/9, 8/10, 6/13, and 6/7 i think but im not positive

According to the vertical asymptote of the graph, the rational function is:

A. \(F(X) = \frac{1}{x + 4}\)

A vertical asymptote of a function is a point that is outside of it's domain.

In the graph, the vertical asymptote is at x = -4, hence \(x = -4 \rightarrow x + 4 = 0\) is a root of the denominator, and the correct option is:

A. \(F(X) = \frac{1}{x + 4}\)

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Answer to your question is A. F(X)=1/x+4

Answer:

These tables represent a quadratic function with a vertex at (0,3). What is the

average rate of change for the interval from x = 8 to x = 9?

Interval

х

0

1

2

3

4

5

ilm

у

3

2

-1

-6

-13

-22

--33

0 to 1

1 to 2

2 to 3

3 to 4

4 to 5

5 to 6

Average rate

of change

-1

3-2

-3

1-2

-5

1-2

-7

1-2

-9

1-2

-11

6

O A. -78

O B. -61

C.-2

O D. -17

The average rate of change on the given interval is -17, so the correct option is D.

For a function f(x), the average rate of change on an interval (a, b) is given by:

\(r = \frac{f(b) - f(a)}{b - a}\)

Here we have the table:

x      y

0     3

1      2

2     -1

3     -6

4     -13

5     -22

Using that data we can find the equation of the parabola.

Because of the first point, we know that:

y = a*x^2 + b*x + 3

Using the second and third pairs, we can write:

2 = a + b + 3

-1 = a*2^2 + b*2 + 3

Then we can solve this sytem of equations, if we simplify the equations we get:

a + b = -1

4a + 2b = -4

To solve this, we need to isolate one of the variables, I will isolate a on the first equation:

a = -1 - b

Then we can replace this with the other equation:

4*(-1 - b) + 2b = -4

Now we can solve this for b.

-4 - 4b + 2b = -4

-2b = 0

b = 0

Then:

a = -1 - b = -1 - 0 = -1

Then the quadratic equation is:

y = f(x) = -x^2 + 3

Now, we need to get:

f(8) = -(8)^2 + 3 = -61

f(9) = -(9)^2 + 3 = -78

Then the average rate of change is:

\(r = \frac{-78 - (-61)}{9 - 8} = -17\)

So the correct option is D.

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The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:

\((y-5)^2=12(x+2)\)

Step-by-step explanation:

Since the focus point is directly right of the vertex, the axis of symmetry will be horizontal, which means that we use the equation \((y-k)^2=4p(x-h)\) where \((h,k)\) is the vertex and \((h+p,k)\) is the focus point.

Since we know our vertex to be \((h,k)\rightarrow(-2,5)\) and our focus point to be \((h+p,k)\rightarrow(1,5)\), the distance from the vertex to the focus point is \(p=3\).

Hence, the equation is:

\((y-5)^2=4(3)(x-(-2))\\\\(y-5)^2=12(x+2)\)

The value of the expression is  -8 31/35

The expression is given as:

negative 2 and 3 over 5 minus 6 and 2 over 7.

Rewrite properly as

- 2 3/5  - 6 2/7

Express as improper fraction

-13/5 - 44/7

Take the LCM

(-13 * 7 - 44 * 5)/35

Evaluate the difference of products

-311/35

Express as mixed fraction

-8 31/35

Hence, the value of the expression is  -8 31/35

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Answer:

B

Step-by-step explanation:

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer: 630

Step-by-step explanation:

\(3000 * 21 /100 = 3000 * 0.21 = 630\)

84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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Answer: 45 bags

Step-by-step explanation:

1.5 square yards = 13.5 feet

area sq ft = 600

= 44.44

= 45 bags

Answer:

False.

Step-by-step explanation:

In this equation the first part is correct 2/5 = 0.4 but when you divide 1 by 4 you get 0.25 which is not equal to 0.5, like this:

2 / 5 = 0.4

1/4 = 0.25

But that would mean the equation would look more like this:

0.4 + 0.25 = 0.4 + 0.5

or

0.65 = 0.9

So this equation is false.

Hope this helps you!!

The correct statement regarding the confidence interval and the test of the hypothesis is given as follows:

B. No. There is not evidence for the population mean to be less than 27, because there are values greater than 27 within the 95% confidence interval.

The 95% confidence interval is given as follows:

19.7 to 27.3 posts.

The claim is given as follows:

The true mean number of posts high school students make is less than 27.

The decision rule is given as follows:

The upper bound of the interval is greater than 27, hence there is not enough evidence that the true mean number of posts high school students make is less than 27.

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The difference between the circumference of the circle and the perimeter of the triangle is 28.2 units. (Option B)

To find the length of each side of triangle, the distance is calculated between the vertices using the formula:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Hence,

AB =√((-4 – 0)^2 + (9 – 0)^2) = 9.85 units

AC = √((9 – 0)^2 + (4 – 0)^2) = 9.85 units

BC = √((9 – (-4))^2 + (4 –9)^2) = 13.93 units

Hence, the perimeter of the triangle = 9.85 + 9.85 + 13.93 = 33.6 units

As AB and AC is the radius of the circle, the circumference of the circle is:

C = 2πr = 2π(9.85) = 61.8 units.

Hence, the difference between the circumference of the circle and the perimeter of the triangle = 61.8 – 33.6 = 28.2 units.

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9514 1404 393

Answer:

Step-by-step explanation:

The third angle can be found from the sum of angles in a triangle.

  A + B + C = 180°

  C = 180° -62° -97°

  C = 21°

__

The remaining side lengths can be found using the Law of Sines.

  a/sin(A) = b/sin(B)

  a = sin(62°)(15/sin(97°)) ≈ 13.34

Similarly, ...

  c/sin(C) = b/sin(B)

  c = sin(21°)(15/sin(97°)) ≈ 5.42

The remaining side lengths are approximately ...

  a ≈ 13.3

  c ≈ 5.4

Approximately 456.3 feet of fence to surround the entire circular yard.

Now, For the amount of fencing needed to surround a circular yard, we have to calculate the circumference of the circle, which is the distance around the circle.

Since, The circumference of a circle is,

⇒ C = πd,

where, C is circumference, d is diameter,

Here, the diameter of the circular yard is 145 feet,

So the radius is half of that,

r = 145/2 = 72.5 feet.

So, Using the formula, we can calculate the circumference as:

C = πd

C = 3.14 x 145

C = 456.3 feet

Therefore, Approximately 456.3 feet of fence to surround the entire circular yard.

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Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

For the given function, it is found that:

The extreme points of a function happen at the values for x for which the first derivative is zero, that is:

y' = 0.

In this problem, the function is:

y = x³ - 6x² + 9x.

Hence the first derivative is:

3x² - 12x + 9.

The extreme values of x are:

3x² - 12x + 9 = 0.

3(x² - 4x + 3) = 0

x² - 4x + 3 = 0

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

Then:

The numeric value of the function at these points is:

Hence the points are:

(3,3) and (1,7).

The extreme points of a function happen at the values for x for which the second derivative is zero, that is:

y'' = 0.

For this problem, the second derivative is given by:

y'' = 6x - 12.

Hence the x-coordinate of the inflection point is:

6x - 12 = 0

6x = 12

x = 2.

The numeric value at x = 2 is:

2³ - 6(2)² + 9(2) + 3 = 5.

Then the inflection point is:

(2,5).

The graph with these points labeled is given at the end of the answer.

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If the position of 5 m below sea level is expressed as -5, then the number that expresses the position of 7 m above sea level would be + 7.

In this particular instance, with the position residing 7 m above sea level, we articulate it as +7. This notation elegantly captures the notion of elevation, affirming the distance above the familiar sea level benchmark.

In the realm of vertical measurements, sea level occupies a crucial position as the reference point, embodying the zero mark on the vertical scale. It is from this fundamental reference point that we navigate the vast spectrum of altitudes.

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Answer:

(p+5)(p-2)

Step-by-step explanation:

We are looking for two numbers that multiply to -10 (the rightmost number) and sum to 3 (the middle number)

These are 5 and -2

So we write

(p ____)(p ____)

and fill in the blanks

(p+5)(p-2)

Check by FOILing:

p^2 -2p + 5p -10

And combine the two middle terms.

p^2 + 3p - 10

The y-intercept (0, 120), and the point (55, 17), on the graph of the exponential function of the population of mammals with the population decreasing at 3.5% per year indicates;

A. The y-intercept represents the number of mammals when they were originally counted was 120

B. The line y = 0 is an asymptote of the graph

D. The y-intercept is 120

F. The asymptote indicates that as years pass, the number of mammals will approach 0

An asymptote is a line on a graph that the curve of a graph approaches as the values of the graph increases to infinity.

The points on the graph of the exponential function are;

(0, 120) and (55, 17)

The rate at which the population is decreasing = -3.5%

The output of the graph, y = The number of mammals x years after counting

The key features of the exponential function are;

The y-intercept of the graph is the point x = 0, which corresponds to year 0, or the time when the mammals were originally counted and the y-value at the y-intercept represents the number of mammals when they were counted originally, therefore option A is correct

The coordinates of the y-intercept is (0, 120)

The y-intercept is therefore the point y = 120

Therefore, option D is correct

The general form of the growth exponential function is presented as follows;

f(x) = a·bˣ + k

r = b - 1

b = 1 + r

Therefore;

b = 1 - 0.035 = 0.965

a = The first term = 120

Plugging in the known values from the graph, we get;

f(0) = 120 = a + k

120 = 120 + k

k = 120 - 120 = 0

k = 0 = The asymptote

Therefore, an asymptote is the line y = 0 option B is therefore correct

The  number of mammals approach the asymptote, y = 0 as the number of mammals approach infinity

Therefore as the years pass the number of mammals will approach 0, option F is correct

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Answer:

y=4/3+2

Step-by-step explanation:

y=mx+b is slope-intercept form

4x-3y=-6

-3y=-4x-6

y=4/3+2

The sum (A+B)(x) and difference (A-B)(x) of two quadratic functions A(x) and B(x) were found, along with their values for x=5, vertices, intercepts, and where they are increasing/decreasing.

To find (A+B)(x), we simply add the two functions:

(A+B)(x) = A(x) + B(x) = (\(-0.25x^2+20x\)) + (\(-0.19x^2+15.2x\)) = \(-0.44x^2\) + 35.2x

To find (A-B)(x), we simply subtract B(x) from A(x):

(A-B)(x) = A(x) - B(x) = (\(-0.25x^2+20x\)) - (\(-0.19x^2+15.2x\)) = \(-0.06x^2\) + 4.8x

When x=5, we can evaluate each expression:

(A+B)(5) = \(-0.44(5)^2\) + 35.2(5) = 60

(A-B)(5) = \(-0.06(5)^2\) + 4.8(5) = 12

To find the vertices and intercepts of the functions A(x) and B(x), we can use the vertex and intercept formulas for quadratic functions:

For A(x):

Vertex = (-b/2a, f(-b/2a)) = (-20/-0.5, A(20/-0.5)) = (40, 400)

x-intercepts: 0 = \(-0.25x^2\) + 20x, so x = 0 or x = 80

y-intercept: A(0) = 0

For B(x):

Vertex = (-b/2a, f(-b/2a)) = (-15.2/-0.38, B(15.2/-0.38)) = (40, 304)

x-intercepts: 0 = \(-0.19x^2\) + 15.2x, so x = 0 or x = 80

y-intercept: B(0) = 0

Both functions are decreasing for x < 40, and increasing for x > 40. The vertex (40, 400) is the maximum point for A(x), and the vertex (40, 304) is the maximum point for B(x).

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