You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.

Since the role of young Cosette is played by a child, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette, and alternate girls from night to night. (This is because of restrictions on working hours for children.) You have received headshots and resumes from 25 girls who wish to audition for young Cosette.

When casting the first young Cosette, the casting director has _[blank 1]_ girls to choose from. When casting the second young Cosette, she has _[blank 2]_ girls to choose from, and when casting the third young Cosette, she has _[blank 3]_ girls to choose from.

Match each numbered blank to the answer that correctly satisfies the corresponding blank in the previous sentences.

The volume of the baseball roundibg off to nearest whole number is 14 cube inches.

If radius of a sphere is r and the volume of that spherical figure is given by V then,

[tex]V=\frac{4}{3}\pi r^3[/tex]

So in the problem the object is a baseball which is a sphere for sure.

Given that the diameter of that baseball is 3 inches.

So the radius of that baseball is given by = 3/2 = 1.5 inches.

Hence the volume of that base ball is

[tex]=\frac{4}{3}\pi\times(1.5)^3 \approx 14.1372 \approx 14[/tex]

Thus the volume of the baseball rounding off to nearest whole number is given by 14 cube inches.

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[tex]\bf{-8x+4\leq 36 }[/tex]

Subtract 4 from both sides.

[tex]\bf{-8x\leq 36-4 }[/tex]

Subtract 4 from 36 to get 32.

[tex]\bf{-8x\leq 32 }[/tex]

Divide both sides by −8. Since −8 is <0, the inequality direction is changed.

[tex]\bf{x\geq \dfrac{32}{-8} }[/tex]

Divide 32 by −8 to get −4.

[tex]\bf{x\geq -4 \ \ \Rightarrow \ \ \ Answer }[/tex]

Question :

Solution :

⇒ -8x + 4 ≤ 36

⇒ -8x ≤ 36 - 4

⇒ -8x ≤ 32

⇒ -x ≤ 32 / 8

⇒ -x ≤ 16 / 4

⇒ -x ≤ 8 / 2

⇒ -x ≤ 4

⇒ x ≥ -4

Using the line of best-fit, it is found that:

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are:

(0,0), (1,2), (2,6).

Hence, using a calculator, the estimate for the battery after x minutes is given as follows:

y = 3x - 0.333.

50% power is obtained when y = 50, hence:

50 = 3x - 0.333

x = 50.333/3

x = 16.8 minutes.

90% power is obtained when y = 90, hence:

90 = 3x - 0.333

x = 90.333/3

x = 30.1 minutes.

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The relative frequency of the third class is 3/20.

Relative frequency measures how often a value appears relative to the sum of the total values. It is determined by dividing the frequency of a class by the total frequency.

Relative frequency = frequency of the third class / total frequency

6/(3 + 10 + 6 + 15 + 6)

6/ 40 = 3/20

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Answer: Option (2)

Step-by-step explanation:

[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].

Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].

So, the answer is Option (2).

Pooling can be referred to the process of how an insurance company can pay a large benefit even if it hasn't collected that amount from an individual's or company premium in this type of context.

This is referred to as a type of protection against financial loss or other forms of incidents or risks and there are different types which cater for different purpose or reasons and they include life, vehicle insurance etc. The insurance plan is usually sold by designated insurance companies and are accessible to the public.

Pooling is the process which involves the smaller firms purchasing better interest rates which helps to lessen the cost of coverage. This also ensures that benefits are paid at the right time so as to avoid hassle and other forms of issues which may arise from this important process.

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Answer:

We first need to know the graph of the basic function belonging to the trigonometric family, which is sin x.

Now we need to apply basics of functions to get the graph of y = -sinx from y = sinx

If x is the input in the y = sinx , then sin x will be the output which will be represented on the  y axis. Eg :

If x = pi/2

then output will be y = sin(pi/2) = 1

Hence in the graph of sinx, at x =pi/2 the value of y is 1.

Once we have understood this, we can use the same logic in the case

y = -sinx

If x = pi/2

then output will be y = - sin(pi/2) = -1

Here we can see that the output of y = - sin x will be the exact negative of  of the output of y = sinx

Hence all portions of the graph of  y = sinx in the +y axis will come down to the -y axis for y = -sin x, i.e we will be taking mirror image of the graph along the x axis. Below are the graphs of y=sinx and y= - sinx respectively for your reference:

(image courtesy Microsoft graphic calculator)

Answer:

The choice D.

Step-by-step explanation:

[tex]f(x) = {( \frac{1}{6} })^{x} \\ \\ f(3) = {( \frac{1}{6} })^{3} = \frac{ ({1})^{3} }{( {6})^{3} } = \frac{1}{216} [/tex]

The average rate of change within the function f(x)=[tex]x^{2} -x-1[/tex]is -2.

Given The function f(x)=[tex]x^{2} -x-1[/tex]

We have to search out the typical rate of change of function within the interval (-2,1).Interval is largely a variety between numbers lying on the quantity line which may be a line on which different numbers are plotted.

We know that average rate of change =f(b)-f(a)/(b-a)

we have to first know the values of function at different values of x.

f(x)=[tex]x^{2} -x-1[/tex]

f(1)=1-1-1

=-1

f(-2)=4+2-1

=5

b=-2

a=1

put within the formula:

A=-1-5/1+2

=-6/3

=-2

Hence average rate of change of the function within the interval (-2,1) is -2.

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The solution to the inequality is (-4, ∞)

The second inequality is given as:

8 - y < 12

Subtract 8 from both sides

-y < 4

Rewrite as:

y > -4

In interval form, we have:

y = (-4, ∞)

Hence, the solution to the inequality is (-4, ∞)

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Answer:

1. 1/27 2. 1/16

Step-by-step explanation:

First can be rewritten as (1/9)^(1/2 * 3) and anything to the power of 1/2 is a sqrt. So it is sqrt(1/9)^3. Then (1/3)^3 which is 1/27

Second, the negative bring the number to the bottom, 1/(32)^4/5. Then can be written as [tex]\sqrt[5]{1/32}[/tex]^4. 5th root of 1/32 is 1/2 then 1/2^4 is 1/16

Answer:

D. g(x) = 5x^2

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

A point of the function g(x) is known: (1, 5)

The proper function is

[tex]g(x)=5x^{2}[/tex]

Demonstration calculating g(1)

[tex]g(1)=5(1)^{2} =5(1)=5[/tex]

The point (1, 5 ) belongs to this function

Hope this helps

Answer:

all real numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Comment

You are going from a very small number (like - 100000) to a very large number (like + 100000).

But neither of those could be the answer. They are either not small enough or not large enough. The domain must look like this.

- ∞ < x < ∞

Answer: So the domain is all the real numbers.

Answer:

3 is the mode

Step-by-step explanation:

The 98% confidence interval of the proportion of all Americans who think that living on their own makes someone feels like an adult is (29.0%, 31.0%)

The given parameters are:

The number of success is then calculated as;

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 2000 * 28\%[/tex]

Evaluate

[tex]\bar x = 560[/tex]

Hence, 560 successes would be found in the sample of 2000 Americans

The proportion that lives on their own is:

p = 30%

The z-score for 98% confidence interval is

z = 2.326

The confidence interval is calculated as:

[tex]CI = \bar p \pm z * \sqrt{\frac{\bar p(1 - \bar p)}{ n}[/tex]

So, we have:

[tex]CI = 30\% \pm 2.326 * \sqrt{\frac{30\%(1 - 30\%)}{2000}[/tex]

Evaluate

[tex]CI = 30\% \pm 1\%[/tex]

Expand

CI = (30% - 1%, 30% + 1%)

Evaluate

CI = (29%, 31%)

Hence, the 98% confidence interval is (29.0%, 31.0%)

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Answer:

f(5) = 45

Step-by-step explanation:

If f(x) = 2x²-5 , f(5) =

f(5) = 2(5)² - 5

f(5) = 2(25) - 5

f(5) = 50 - 5

f(5) = 45

Answer: [tex]55^{\circ}[/tex]

Step-by-step explanation:

The measure of the third unknown arc is

[tex]360^{\circ}-70^{\circ}-110^{\circ}=180^{\circ}[/tex].

So, [tex]x=\frac{180^{\circ}-70^{\circ}}{2}=\boxed{55^{\circ}}[/tex]

The equation that results from completing the square in the following equation. x^2−20x+75=0 is (x+2)^2 = 10

The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.

GIven;

x^2−20x+75=0

Subtract 75 from each side

x^2−20x+75 - 75 = -75

Take the coefficient of x

20

Divide by 2

10

Square it

100

Add it to each side

x^2 +5x + 100 = -75 + 100

(x+2)^2 = 10

Take the square root of each side

x+2 = 10

x = 8

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The amount loaned at the interest rate of 11% is $3000.

The amount loaned at the interest rate of 7% is $16,500

0.11a + 0.07b = 1485 equation 2

Where:

a = amount loaned at the interest rate of 11%

b = = amount loaned at the interest rate of 7%

In order to determine how much was loaned at 7%, take the following steps:

Multiply equation 1 by 0.11:

.11a + 0.11b = 2145 equation 3

Subtract equation 2 from equation 3:

0.04b = 660

Divide both sides by 0.04:

b = 16,500

Subtract 16,500 from 19,500 :

19,500 - 16,500 = $3000

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The amount going to her savings accounts is $192

The given parameters are:

Drawings = 24

Rate = $12

The total amount earned from selling the drawings is:

Total = 24 * $12

Evaluate

Total = $288

She buys books with 1/3.

This means that she saved 2/3

So, we have:

Savings = 2/3 * $288

Evaluate

Savings = $192

Hence, the amount going to her savings accounts is $192

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Answer:

C

Step-by-step explanation:

When the run part (the difference between x-coordinates of the two points on the line) is 1, the slope is an integer.

The system of equations is:

x = 2y

x*$10 + y*8 = $84

Solving it, we see that he worked 3 hours landscaping and 6 hours washing cars.

First, we need to define the variables:

We know that Alexander worked twice as many hours washing cars as he worked hours landscaping, then:

x = 2y

We also know that he earned a total of $84, then:

x*$10 + y*8 = $84

So the system of equations is:

x = 2y

x*$10 + y*8 = $84

To solve it, we just replace the first equation into the second one:

(2y)*$10 + y*8 = $84

y*$28 = $84

y = $84/$28 = 3

So He worked 3 hours landscaping, and:

x = 2*y = 2*3 = 6

6 hours washing cars.

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Answer:

160.14  mm^2

Step-by-step explanation:

Area of a circle = pi r^2

subtract the area of the smaller circle from the larger

  note that the smaller radius = 7 mm

pi ( 10^2  - 7^2 ) =

3.14 ( 51) = 160.14 mm^2

The area of the washer is approximately 160.14 square millimeters.

Use the concept of the circle defined as:

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle.

Additionally, every angle possesses rotational symmetry around the center.

Given that,

The outer radius of the washer: 10mm

Diameter of the hole: 14mm

π value to be used: 3.14

To find the area of the washer:

Subtract the area of the hole from the area of the outer circle.

The area of a circle is given by the formula A = πr²,

Where r is the radius.

For the outer circle:

The radius is 10mm, so the area of the outer circle = 10²π.

The area of the outer circle = 100π mm²

For the hole,

The diameter is 14mm,

So the radius of the hole = 7 mm.

The area of the hole = 7²π

The area of the hole = 49π mm²

To find the area of the washer,

Subtract the area of the hole from the area of the outer circle:

Area of washer = Area of the outer circle - Area of hole

Area of washer = (100π - 49π) mm²

Area of washer = 51π mm²

Area of washer ≈ 160.14 mm²

Hence,

The area of the washer is approximately 160.14 square millimeters.

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Answer:

C , D , B

Step-by-step explanation:

Trigonometry is given by three formulas :

SOH - CAH - TOA

Hope this helped and have a good day

There are actually 5040 ways of arranging the letter knitting.

By SSS congruency criteria ΔABC ≅ ΔDEF

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

The given vertices of the triangles are;

ΔABC: A(−4, −3), B(0, 0), C(2, −3)

ΔDEF:  D(3, 1), E(6, -3), F(3, −5)

The lengths of the sides of ΔABC are

AB = √((0+4)² + (0+3)²) = √25 = 5

BC = √((2-0)² + (-3 - 0)²) = √13  

AC = √((2+4)² + (-3 +3)²) = √36 = 6

The lengths of the sides of ΔDEF are;

DE = √25=5

EF = √13

DF = √36 = 6

As,

AB= DE, BC = EF , AC= DF

So, By SSS congruency criteria ΔABC ≅ ΔDEF

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Marisol did a mistake while grouping the terms in Step 1, with the sign. Thus, Marisol should go back and group the terms in Step 1 as (6x³ - 22x²) - (9x - 33). Hence, the second option is the correct choice.

The polynomial Marisol had was 6x³ - 22x² - 9x + 33.

The steps she did in the grouping of terms and factoring out the GFC out of the groups were:

Step 1: (6x³ - 22x²) - (9x + 33).

Step 2: 2x²(3x - 11) -3(3x + 11).

After this Marisol was unable to get a common factor to proceed further.

The mistake that Marisol did was in Step 1, as while grouping -9x and +33, she took the minus sign out, which will make -9x to become 9x, but 33 to become -33.

This is where she made the mistake and writing - (9x + 33) in place of - (9x - 33).

Thus, her steps should have been:

Step 1: (6x³ - 22x) - (9x - 33),

Step 2: 2x²(3x - 11) -3(3x - 11), which gives her a common factor (3x - 11), to continue with the third step:

Step 3: (2x² - 3)(3x - 11).

Refer to the attachment for the complete question, as the given question is incomplete.

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Hence, the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."

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The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.

It should be noted that a inference simply means the conclusion that can be deduced based on the information given.

In this case, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette.

Hence, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts. Therefore, ordering matters.

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