data were collected on the number of days per week that members visit a certain fitness center. the values varied from 0 to 7, and a distribution of relative frequencies for the values was created. let the random variable x represent the number of days per week that a member visits. the mean of x is 3.12. which of the following statements is the best interpretation of the mean? responses each member visits the fitness center 3 or 4 days per week. each member visits the fitness center 3 or 4 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. for a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.

(a) C(p) is not defined since we can't divide by 0.

(b) The domain of C(p) as given by the equation is (-∞, 100) ∪ (100, ∞)

(c) The domain of C(p) in the context of the application is [0, 100)

(d) The percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100

Here we have given that Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by

C(p) = 8100p / (100 − p)

And we need to find the following.

(a) In general ma the we know that dividing by zero is not possible one.

Therefore, C(p) is undefined when we try to divide it by 0.

(b) The domain of C(p) is the function is not defined at p =100 the domain would be written as,

=> D = (-∞, 100) ∪ (100, ∞)

(c) The domain of C(p) in the context of the application  is calculated as,

=> D = [0, 100)

Therefore, the percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100.

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Answer:

x=9

Step-by-step explanation:

these 2 angles are supplementary angles meaning added together they will equal 180 degrees

so we can add them together and set it equal to 180

(8x-3)+(16x-33)=180

combine like terms

(8x+16x)+(-3-33)=180

24x-36=180

     +36. +36

24x=216

/24.  /24

x=9

hopes this helps

Answer:

a = 4

Step-by-step explanation:

Step 1: Find two numbers that multiply to give 16 and add to give -8.

t²-8t+16 = 0

t² -4t -4t + 16 = 0

The two numbers are 4 and -4.

Step 2: Rewrite the equation in the form (t + 4)(t - 4).

t² - 8t + 16 = (t + 4)(t - 4)

Step 3: Factor the equation to get (t + 4)².

(t + 4)² = (t + 4)(t + 4)

Therefore, a = 4.

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Answer:

A

Step-by-step explanation:

Blue = River Y

Red = River Z

River Y equation: y = 18

River Z equation: y = 10 + 2x

Graph A represents this system of equations.

IF THIS HELPED YOU GIVE ME BRAINLIEST FOR GOOD LUCK FOR 10 YEARS

Answer:

Step-by-step explanation:

3.14 x 3=9.42

The value of width will be;

⇒ 18.5 cm

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The volume of a rectangular prism = 6,618.375 cm³

The height is 13.25 cm and the length is 27 cm.

Now,

We know that,

The volume of rectangular prism = Length x Width x Height

Substitute all the values, we get;

⇒ 6,618.375 = 27 × x × 13.25

⇒ 6,618.375 / 357.75 = x

⇒ x = 18.5 cm

Thus, The value of width = 18.5 cm

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Answer:

The Rate of return would then be 192 / 273 ≈ 70.32%

The measures of the lengths of the sides and angles of the triangles found using the law of cosines and the law of sines are presented as follows;

Question 1

∠A = 47.35°

∠B = 78.65°

c = 3.3

Question  2

∠B = 78.24°

∠C = 29.76°

a = 67.03

Question 3

∠A = 45.77°

∠B = 86.417°

∠C = 47.813°

Question 4

∠A = 36.15°

∠B = 60.48°

∠C = 93.37°

Question 5

a = 258.98

b = 327.41

∠C = 53°

Question 6

a = 34.11

b = 73.987

∠C = 53°

The law of cosines is a relationship between two sides (b and c) and the included angle, (∠A) and the third side (a) of the triangle.

Mathematically; a² = b² + c² - 2·b·c·cos(A)

Question 1

The dimensions of the triangle ΔABC are;

a = 3.0, b = 4.0, ∠C = 54°

The law of cosines indicates that we get;

c² = b² + a² - 2·b·a·cos(∠C)

Therefore;

c² = 3.0² + 4.0² - 2 × 3.0 × 4.0 × cos(54°) ≈ 10.893

The law of sines indicates that we get;

sin(54°)/3.3 = sin(∠A)/3.0

Question 2

b = 69, c = 35, ∠A = 72°

a² = 69² + 35² - 2 × 69 × 35 × cos(72°) ≈ 4493.45

The law of sines indicates that we get;

sin(72°)/67.03 = sin(∠B)/69

∠B = arcsine(69 × sin(72°)/67.03) ≈ 78·24°

∠C = 180° - 72° - 78.24° ≈ 29.76°

Question 3

a = 28, b = 39, c = 29

a² = b² + c² - 2·b·c·cos(A)

cos(A) = (a² - (b² + c²)) ÷ (2·b·c)

Therefore; cos(A) = (28² - (39² + 29²)) ÷ (-2 × 39 × 29) ≈ 0.6976

sin(45.77)/28 = sin(B)/39

sin(B) = 39 × sin(45.77)/28 ≈ 0.998

Question 4

a = 13, b = 17, c = 22

cos(A) = (13² - (17² + 22²)) ÷ (-2 × 17 × 22) ≈ 0.807

sin(36.15)°/13 = sin(∠B)/17

sin(∠B) = 17 × sin(36.15)°/13

Question 5

The parameters of the triangle are; ∠A = 50°, ∠B = 77°, c = 270

Please find attached the sketch of the triangle in the correct option created with MS Word

a/sin(50°) = 270/sin(53°)

a = sin(50°) × 270/sin(53°) ≈ 258.98

b = sin(77°) × 270/sin(53°) ≈ 329.41

Question 6

The parameters of the triangle are;

∠A = 27°, ∠B = 100°, c = 60

Please find attached the drawing of the correct triangle

∠C = 180° - 27° - 100° = 53°

∠C = 53°

60/sin(53°) = a/sin(27°)

a = sin(27°) × 60/sin(53°) ≈ 34.11

b = sin(100°) × 60/sin(53°) ≈ 73.987

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Answer:

[tex]\dfrac{1}{36n^2+6n}[/tex]

Step-by-step explanation:

Given factorial expression:

[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]

[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]

Apply the factorial rule to the numerator and denominator of the given rational factorial expression:

[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]

[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]

Answer:

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

We know that:

Therefore:

Therefore:

Answer:

non-violence and kindness with animals

Step-by-step explanation:

Using the given formula, we have been able to prove that; the expected value of the students' score is 18 correct responses

1) Let X denote the number of correct guesses, assuming that a student guesses randomly among the five options of all 25 questions. Then X has a binomial probability distribution with;

n = 25

p = 1/5 = 0.2

2) Let Y denote the number of correct responses on the seven questions for which the student guesses randomly from among the five options. Then Y has a binomial probability distribution with n = 7 and p = 0.20. Then the expected value of Y is;

E(Y) = np = 7(0.2) = 1.4

Using the scoring formula given, we have;

Score = (18 + Y) - 0.25(7 - Y) + 0(0)

= 16.25 + 12Y

The expected value of the students' score is;

E(16.25 + 12Y) = 16.25 + 12(1.4)

= 18 correct responses.

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Answer:

-2

Step-by-step explanation:

The line appears to cross through (2,3) and (4,-1)

You can subtract the x values and y values to determine the difference:

[tex]2 - 4= - 2 \\ 3 - ( - 1) = 4[/tex]

These can be used as the y and x values in y over x to find the slope:

[tex] \frac{4}{ - 2} = - 2[/tex]

The slope is -2

a) The number alive after 7 years is given as follows: 48.

b) The percentage of herd that dies each year is of 10%.

The exponential function in the context of this problem is defined as follows:

N(t)=100(0.9)^t.

The parameters of the function are defined as follows:

The amount of herd alive after 7 years is found with the numeric value at t = 7, replacing the lone instance of t in the function by 7, hence:

N(7) = 100 x (0.9)^7 = 48.

(rounding to the nearest whole number).

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10 inches is the scale factor from the drawing to the actual billboard

A scale factor is a ratio of change from a drawing to real life. Typically, a scale factor is unit-less; a scale factor of 48 (or 1:48) is saying that for one unit on the page, it represents 48 of the same units in real life.

A scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Scale drawings show an image either reduced or enlarged in size. The change between the original and the scaled drawing is generally represented by two numbers separated by a colon, like 10:1 (read as “ten to one”).

The difference between the ratio numbers represents the factor by which the scaled image is enlarged or reduced. So for a 10:1 scale ratio, a 1 inch (2.5 cm) drawing will be 10 inches (25 cm) in real life.

Methods are as follows :

Changing Scale Digitally-

Scan the image or snap a pic of it with your phone.

Insert the image into a suitable program or app.

Navigate to the image layout options.

Adjust the height and width under the “Scale” heading.

Save the scaled image and you’re done.

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The two inequalities that describe the total cost and no. of guests are

18a + 9c ≤ 2475 and

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let 'a' be the no. of adults and 'c' be the no. of children.

The expense for this event must not exceed $2,475.00.

Therefore, 18a + 9c ≤ 2475...(i)

The venue can hold no more than 150 guests.

Therefore, a + c ≤ 150...(ii)

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A translation 3 units left and 2 units up best describes the graph of  f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x

How to solve this problem?

f(x) = log2(x + 3) + 2 (given)

g(x) = log2x (given)

We need to describe the best statement for the graph

The graph is shown in the image

The following steps are shown to describe the graph.

The general equation of f(x) = log2(x-h)+k

When h > 0 (positive)

The graph of the base of the function shift to the right

When  h < 0 (Negative)

The graph of the base function shifts to the left.

When k > 0 (Positive)

The graph of the base function shifts upward.

When k < 0 (Negative)

The graph of the base function shifts downward

Here h = 3 , k = 2

Hence , a translation 3 units left and 2 units up describes the graph.

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The difference of the given polynomials 8x³+5x+6 and 2x²+3x is 8x³-2x²+2x+6. So, the correct answer is D.

To subtract polynomials from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.

Given that, 8x³+5x+6-(2x²+3x)

Group the like terms are perform the addition or subtraction

= 8x³+5x+6-2x²-3x

= 8x³+(5x-3x)-2x²+6 (Here, like terms are 5x and 3x)

= 8x³+2x-2x²+6

= 8x³-2x²+2x+6

So, the standard form of obtained polynomial is 8x³-2x²+2x+6.

The polynomials difference is 8x³-2x²+2x+6. Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Which polynomial represents the difference below?

8x³ + 5x+6-(2x² + 3x)

A. 10x+ 8x² +6

B. -2x² + 8x³ + 8x+6

C. 6x¹⁰+2x+6

D. -2x²+ 8x³+2x+6

The lines that carry the rectangle onto itself are x = 0 and y = 1

The graph that completes the question is added as an attachment

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

The rectangular graph

The coordinates of one end of the graph are

(-3, 3) and (-3, -1)

Next, we calculate the midpoint of these ends

So, we have

Midpoint = 1/2(x₁ + x₂, y₁ + y₂)

Substitute the known values in the above equation, so, we have the following representation

Midpoint = 1/2(-3 + 3, -1 + 3)

Evaluate the like terms

Midpoint = 1/2(0, 2)

So, we have

Midpoint = (0, 1)

So, we have

x = 0 and y = 1

Hence, the reflection lines are x = 0 and y = 1

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The polynomials using synthetic division is [tex]2 y+4+\frac{5}{y+3}[/tex].

What is polynomials?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x^2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

[tex]\frac{\left(2 y^2+10 y+17\right)}{(y+3)}$$[/tex]

[tex]$$\begin{aligned}& \text { Divide } \frac{2 y^2+10 y+17}{y+3}: \frac{2 y^2+10 y+17}{y+3}=2 y+\frac{4 y+17}{y+3} \\& =2 y+\frac{4 y+17}{y+3}\end{aligned}$$[/tex]

Divide [tex]$\frac{4 y+17}{y+3}: \quad \frac{4 y+17}{y+3}=4+\frac{5}{y+3}$[/tex]

[tex]=2 y+4+\frac{5}{y+3}[/tex]

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There is an attachment that includes the graph for the inequality 8x + 5y 100.

How do you calculate the scenario's graph?

The parameters are as follows, taken from the query:

The customer's purchase must not exceed $100.

Each bath towel costs $8.

Each hand towel costs $5.

Inequality among the available combinations is another factor that we have.

8x + 5y ≤ 100

like that

x is the quantity of bath towels, while y is the quantity of hand towels.

Plotting the inequality's graph is the following step.

A graphing tool can be used for this.

In order to attach the graph, we enter the inequality in the graphing tool.

Keep in mind that the inequality is provided as

8x + 5y ≤ 100

See the inequality graph in the attached. 8x + 5y ≤ 100

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A)

A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.

So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414

It is believed that the machine is underfilling the bags.

So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414

Given,

n= 8

Population standard deviation (б) = 18

x= 407

We will use the t-test since n > 8 and we are given the population standard deviation.

t=x-μ / (б/[tex]\sqrt{n-1}[/tex])

t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]

t= -1.028

Use the t table to find p value

p-value = 12.706

Level of significance α = 0.025

p-value>α

It is a two-tailed test.

So, we fail to reject the null hypothesis.

So, its bag-filling machine works correctly at the 414-gram setting.

B)

Let μ be the population mean amount of ozone in the upper atmosphere.

As per the given, we have

[tex]H_{0}[/tex]    : μ = 4.8

[tex]H_{1}[/tex] : μ ≠ 4.8

Sample size: n= 26

Sample mean = 4.6

Standard deviation = 1.2

Since population standard deviation is now given, so we use a t-test.

t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]

t= -0.2/0.24

t= -0.833

It is a two-tailed test.

We are accepting the null hypothesis.

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If a store decides to spend $1500 on Sunday TV ads for all-terrain tires, we can predict that 95% of the values for the revenue in those weeks from the sale of these will be between $21863.59 and $25617.41.

A company can use regression analysis to determine statistical relationships between the total sales of its products and the costs associated with promotions and advertising. The outcomes of these analyses can then be used to determine how best to allocate spending funds among, say, various products or sales regions.

n = 41

df = n - 2

df = 41 - 2 = 39

SSₓₓ = (n - 1)S²ₓ

SSₓₓ = (41 - 1) * (400)²

SSₓₓ = 6400000

y = 15531.3086 + 5.4728 * x

If, x = 1500 then:

y = 15531.3086 + 5.4728 * 1500

y = 23740.51

Prediction range of y at 95% = [tex]y + t_{\frac{0.05}{2},39 } * S_{e} * \sqrt{1 + \frac{1}{n} + \frac{(x - x_{1} )^{2}}{SS_{xx} } }[/tex]

Prediction range of y at 95% = [tex]23740.51 + 2.022691 * 915.247 * \sqrt{1 + \frac{1}{41} + \frac{(1500 - 1700)^{2} }{6400000}[/tex]

Prediction range of y at 95% = (2186.1 , 25619.92)

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Answer:

x=38

Step-by-step explanation:

linear par

180-134=46

180-84=96

sum of a triangle is 180

96+46+x=180

142+x=180

x=180-142

x=38

Answer:

$22.50

Step-by-step explanation:

The equation of given graph is y = 2x + 6.

What is equation of line?

The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.

Given:

The graph of the line is given.

From graph we have to find the equation of line.

Let the graph passes through the points (0, 6) and (2, 10).

From these two points to find the slope.

Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here, [tex](x_1, y_1) = (0, 6), (x_2, y_2) = (2, 10)[/tex]

⇒ Slope = m = [tex]\frac{10-6}{2-0}= \frac{4}{2} = 2[/tex]

So, the slope is 2.

Now to find the equation of line.

Consider, the point - slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 2, (x_1, y_1) = (0, 6)[/tex]

⇒

[tex]y-6=2(x-0)\\y-6=2x\\y=2x+6[/tex]

Hence, the equation of given graph is y = 2x + 6.

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Answer:

gh(b)

Step-by-step explanation:

Answer:

shifted to the right

Step-by-step explanation:

By using matrix, it can be calculated that:

[tex]\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]

The term "matrix" refers to any configuration of numbers in the form of rows and columns. a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers.

In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines. Nearly every element of our life uses engineering mathematics.

Here,

[tex]C = \begin{bmatrix} 12 & 16 & -20 \\ 4 & -24 & 28 \end{bmatrix}[/tex]

[tex]\frac{1}{4}C = \begin{bmatrix} 12\times \frac{1}{4} & 16 \times \frac{1}{4} & -20 \times \frac{1}{4} \\ 4 \times \frac{1}{4} & -24 \times \frac{1}{4}& 28 \times \frac{1}{4}\end{bmatrix}\\\\\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]

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Resulting box has the greatest volume for the values  (25 ± 5√7)/6 .

This is a problem that can be solved using derivatives , maxima & minima and common logic.

Hence , going by logic :

Creating a flap of 'a' inches in width, the base of the box will be

 (10 - 2a) by (15 - 2a)

and the depth of the box will be the width of the fold-up flap: a.

Then the volume of the box is

 v = [tex]a(10 -2a)(15 -2a) = 150a -50a^2 +4a^3[/tex]

Using the derivative of the volume will be zero at the maximum volume.

 0 = [tex]dv/da = 150 -100a +12a^2[/tex]

This has roots at

 a = (100 ±√(100² - 4(12)(150)))/(2·12)

 a = (100 ± √2800)/24 = (25 ± 5√7)/6

Only the smaller of these solutions gives a maximum volume.

You should cut (5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.

Similarly , replacing the values of 10 by A and 15 by B , a generalized solution can be formed .

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