William recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 9
Bass 11
Drums 9
Keyboard 11
Eighth Grade Students
Instrument # of Students
Guitar 3
Bass 3
Drums 8
Keyboard 6

Based on these results, express the probability that a seventh grader chosen at random will play the keyboard as a fraction in simplest form.

Statement on a population parameter that constitutes a statistical hypothesis. There's a chance it's true or not.

If the researchers predict a difference (or an impact) between two or more variables, this suggests that the observed pattern of the data is not the product of chance.

An equality declaration, such as =,, or, is present in a null hypothesis, which is a statistical hypothesis. A counterargument to the null hypothesis is an alternate hypothesis.  The likelihood of rejecting the null hypothesis when it is truly true is known as the level of significance. Error Type I is another name for it.

Determine the P-value for a Hypothesis Test

Find the P-value by choosing one of the following options: For a left-tailed test, P= (Area in left tail); For a right-tailed test, P= (Area in right tail); For a two-tailed test, P = 2. ( Area in tail of standardized test statistic)

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It is a convergent series as both component series are geometric with ratios less than 1, so they both converge. The sum is 7/15.

If the sequence is converging (or converges), the series is convergent. The total of its partial sums tends to a limit; that is, while adding one after the other in the sequence specified by the indices, partial sums move closer and closer to a particular number. A divergent series is an infinite series that is not convergent, which means that the infinite sequence of the series' partial sums has no finite limit. If a series converges, the series' individual terms must approach zero.

Here,

sum(3/4ⁿ)₁₋ₓ  -  sum(1/2⁴ⁿ⁺¹)₁₋ₓ

sum(3/4ⁿ)₁₋ₓ=1

sum(1/2⁴ⁿ⁺¹)₁₋ₓ=8/15

=1-8/15

=7/15

It is a convergent series since both component series are geometric and have ratios smaller than one. The total is 7/15.

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Benjamin's walk described as a composition of two translations is (8, 0) and (2, 3) respectively.

The translation walks from his house directly to school is (10, 3)

A translation is a type of transformation that moves every point in a figure by a fixed distance in a certain direction. This can be thought of as sliding the figure along a straight line.

Looking at the image:

The coordinate of  Benjamin's house is (5,4) and he walks to Timothy's house (13, 4) and then to school (15, 7)

The displacement vector from Benjamin's house to Timothy's house is (13, 4) - (5, 4) = (8, 0), which represents an 8 unit move to the right.

The displacement vector from Timothy's house to school is (15, 7) - (13, 4) = (2, 3), which represents a 2 unit move to the right and a 3 unit move up.

Thus, Benjamin's walk can be described as a composition of two translations can be represented using displacement vectors as (8, 0) and (2, 3) respectively.

If Benjamin walks from his house directly to school:

The displacement vector from Benjamin's house directly to Timothy's house is (15, 7) - (5, 4) = (10, 3), which represents 10 units move to the right and 3 units up.

Thus, the translation describes his walk is (10, 3)

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The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

= 40√(10/27) cu in

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Complete Question

(Image Attached)

The width of the shape is 4.2 units

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

Surface Area = 54 square units

Length = 2 units

Height = 3 units

The surface area of the shape can be calculated using the following formula

Surface Area = 2 * (Length * Width + Length * Height + Width * Height)

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

2 * (2 * Width + 2 * 3 + Width * 3) = 54

Divide both sides by 2

So, we have

2 * Width + 2 * 3 + Width * 3 = 27

Subtract 6 from both sides

2 * Width + Width * 3 = 21

This gives

Width * 5 = 21

Divide both sides by 5

Width = 4.2

HEnce, the width is 4.2 units

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Pedro earns $5.1 per hour more than Oliver

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

The hourly rate of Pedro is calculated using

Hourly rate = Amount earned/Number of hours

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

Hourly rate = 521.40/22

Evaluate

Hourly rate = 23.7

Using the points on Oliver's graph

The hourly rate of Oliver is calculated using

Hourly rate = Amount earned/Number of hours

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

Hourly rate = 186/10

Evaluate

Hourly rate = 18.6

The difference between these rates is

Difference = 23.7 - 18.6

Evaluate the difference

Difference = 5.1

Hence, the difference is $5.1

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Answer:

4

Step-by-step explanation:

Because

The chi-square test is 5.02 higher than critical value 3.841 so the two states does not differ with regards of shopping habits, and p value is 0.025.

O = observed value

E = expected value

n = size of sample = 2

df = degree of freedom = n - 1 = 2 - 1

α = significance level = 5% = 0.05

Chi-square is a one of many test statistic, chi-square is a test to see the different from observed value and expected value.

Chi-square formula is,

[tex]\chi^2[/tex] = [tex]\sum\frac{(O_i - E_i)^2}{E_i}[/tex]

Since, in question only give us the observed value, we need to calculate the expected value first.

Expected value conscientious state A can be calculate by this formula

E(ca) = total of state A value × total of conscientious value ÷ grand total

Repeat this process to all observed value.

We use excel to simplified and for precise calculation. Then, we put the obtained value from excel formula to Chi-square formula,

[tex]\chi^2[/tex] = 0.69 + 1.69 + 0.76 + 1.88

= 5.02

a) Critical value for df = 1 and α = 0.05 from chi-square table is 3.841

Since, the result is 5.02 higher than 3.841, it can be concluded that the two states does not differ with regards of shopping habits.

Assumptions for we use is the study group is independent and the each expected value is higher than 5.

b) We use chi-square p-value calculator with P([tex]\chi^2[/tex] > 5.02) and df = 1, α = 0.05. So, we get 0.025.

Thus, two states doesn't differ with regards of shopping habits since chi-square result is higher than critical value, and p value is 0.025.

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The expensive a car that you can afford is $42666.42.

What is interest rates?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

Given that you can deposit $325 each month. The interest rates is 4.25%.

Future Value of an Ordinary Annuity

[tex]S = R[\frac{(1+i)^n-1}{i}][/tex]

where

S is the future value;

R is the periodic payment;

i is the interest rate per period;

n is the number of periods.

The value of R is $325, i = 0.0425/12 = 0.00354

n = (12 × 9) =108

The future value is

[tex]S = 325[\frac{(1+0.00354)^{108}-1}{0.00354}][/tex]

S = 42666.42

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The equation of the perpendicular line is y = -5x + 18

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

y = 1/5x + 3

Also, from the question;

We have the following points

Point = (4, -2) i.e.  (x, y) = (4, -2)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 1/5

This means that the slope is 1/5

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -5

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = -5

(x₁, y₁) =  (4, -2)

So, we have

y = -5(x - 4) - 2

Evaluate

y = -5x + 18

Hence, the line has an equation of y = -5x + 18

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Answer:

Step-by-step explanation:

The value of f(-2) is -8 and the value of [tex]f(v+1)=\frac{3v+1}{|v+2|}[/tex] for the given function [tex]f(v)=\frac{3v-2}{|v+1|}[/tex].

Given function is

[tex]f(v)=\frac{3v-2}{|v+1|}[/tex]

To evaluate f(-2), we need to substitute v = -2 in the given function.

So, on substituting v = -2, we get

f(-2) = (3(-2) - 2)/|-2+1|

      = (-6 - 2)/|-1|

      = -8/1

Since we know that |-a| = a; we can write |-1| = 1.

Thus, f(-2) = -8

To evaluate f(v+1), we need to substitute v = v+1 in the given function.

So, on substituting v = v+1, we get

f(v+1) = (3(v+1) - 2)/|v+1+1|

        = (3v+3-2)/|v+2|

        = (3v+1)/|v+2|

Thus, f(v+1) = (3v+1)/|v+2|.

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The good practice to protect the classified information is labelling them with markings.

In the question ,

we have been asked about the good practice that can help in protecting the classified information .

we know that ,

the term Classified means when something is arranged in classes. and

the term Labeling means that when something is assign to a category.

So , the best practice is to Ensure the proper labeling by appropriately marking all the classified material and when required, sensitive material.

Therefore , the best practice is Ensure proper labeling by appropriately marking all classified material .

The given question is incomplete , the complete question is

What is a good practice to protect classified information ?

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The best approximation to the solution of the system of equations is (2, 3)

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

Equation 1 is 5 x plus 2 y equals 16.

Equation 2 is x plus 3 y equals 12.

Rewrite the equations properly

So, we have the following representation

5x + 2y = 16

x + 3y = 12

Make x the subject in the second equation

So, we have

x = 12 - 3y

Substitute x =12 - 3y in the equation 5x + 2y = 16

So, we have

5(12 - 3y) + 2y = 16

Open the brakects

This gives

60 - 15y + 2y = 16

Evaluate the like terms

-13y = -44

Divide both sides by -13

y = 3.39

Substitute y = 3.39 in x = 12 - 3y

x = 12 - 3 * 3.39

Evaluate

x = 1.83

Approximate the solutions

x = 2 and y = 3

Hence, the solution is (2, 3)

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A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION  [tex]f(x) = b^{x}[/tex]

-It’s a one-to-one function

-The graph passes through y-intercept of the point (0,1)

-x-intercept: none

-The domain is all real numbers: (−∞,∞)

-The range is y > 0 or (0,∞)

-The graph is increasing

-The graph is asymptotic to the x-axis as x approaches negative infinity

-Horizontal asymptote: y=0

-The graph increases without bound as x approaches positive infinity

-Increasing if b > 1

-Decreasing if b < 1

-The graph is continuous

-The graph is smooth

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The finite population correction factor is not used when you sample without replacement from less than 5% of a finite population.

When you sample without replacement from more than 5% of a finite population, the Finite Population Correction Factor (FPC) is applied.

The Central Limit Theorem does not apply in this situation, and the estimated standard error (such as the mean or proportion) will be excessive. Basic differences between sampling with replacement and sample without replacement are captured by the FPC.

It is employed to modify a variance estimate for an estimated mean or total in order to limit the scope of the variance to that fraction of the population that is not included in the sample.

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Answer:

The slope is [tex]\frac{-2}{3}[/tex]

Step-by-step explanation:

An order pair is in the form (x y).  The slope is the change in y over the change in x.  From the 2 points our y's are 2 and 4.  From the 2 points our x's are  1 and -2.  to find the change you subtract.

[tex]\frac{2-4}{1 - -2}[/tex] = [tex]\frac{-2}{1 + 2}[/tex] [tex]\frac{-2}{3}[/tex]

The pattern that this system detects is a four-digit number that is divisible by 3.

1. The system starts by taking an input of a four-digit number.

2. It then checks if the last digit of the input number is divisible by 3.

3. If it is, the system continues to check if the sum of the remaining three digits is divisible by 3.

4. If this turns out to be true, the system will output a signal indicating that the input number is divisible by 3.

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Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Step-by-step explanation:

The graph of this inequality shows a region to the left at x = 12.

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.

Given, An inequality (1/2)x < 6.

Multiplying both sides of the inequality by 2 we get,

2×(1/2)x < 2×6.

x < 12.

The graph of this inequality shows a dotted line at x = 12 and the region is left side to it.

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So option B. F(x)= 2x3/2- 3/2x² is the correct option of the given statement.

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients.

The formulas that only contain addition, subtraction, multiplication, and non-negative integer exponents are those that can be used to identify the polynomials. The expressions with other operations will be non-polynomial expressions. Justify the expressions' lack of polynomial status.

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.

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Hence, the earnings per share for Aware is [tex]0.25[/tex] $.

What is the ratio?

It is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

Here given that,

The stock of Aware is trading at $[tex]4.90[/tex]. The price-earnings ratio is [tex]4[/tex] times earnings.

So,

The price earning is four times the stock of aware trading is

[tex]4.90(4)=19.6[/tex] $

So, the earnings per share for Aware is

[tex]\frac{4.90}{19.6}=0.25[/tex] $

Hence, the earnings per share for Aware is [tex]0.25[/tex] $.

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No, we do not have enough information to find out the percentage of Americans who either do not follow football or do not follow basketball. We would need to know the percentage of Americans who do follow both sports.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 out of 100 questions correctly on a test, you would have received a 75%.

The percent sign (%), which denotes a division by 100, is used. Therefore, 25% translates to 25/100, or 1/4. Dividing by 100 will change a percentage to a decimal. Therefore, 25% is equal to 25/100, or 0.25. A decimal can be multiplied by 100 to become a percentage (just move the decimal point 2 places to the right)

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Answer:

Find the sum of 4.06 x 1019 and 5.034 x 1017, it equals to 9256.718

4.11034 x 1019 = 4188.43646

9.094 × 1019 = 9266.786

4.11034 x 1036 = 4258.31224

9.094 × 1036 = 9421.384

Step-by-step explanation:

4137.14 + 5119.578 = 9256.718

Answer:

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

Average rate of change for this case is:

The equation of a tangent line to the circle is, [tex]x^{2} +y^{2}[/tex] = 34

Given that,

The equation of a tangent line to the circle with center = (3,6)

The line contains point = (-2,3)

For a circle or curve, the tangent is a line or line segment that touches the circle at one point only. For a circle, the tangent will be perpendicular to a radius drawn to the tangent point.

A tangent to a circle at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c

The equation of circle of radius r and center (h , k) is given by

[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex]         (Equation-1)

And it is given that the center is (3,6) and it passes through (-2,3).

So values of h and k are (3,6) each and values of x and y are 2 and respectively .

Substituting these values in the equation, we will get

(h , k) = (3,6)

We can substitute h , k values in equation-1,

[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex]  

[tex](x-3)^{2}[/tex] + [tex](y-6)^{2}[/tex] = [tex]r^{2}[/tex]

Then we can substitute x , y values,

So,

We can write,

( x , y ) = (-2 , 3)

[tex](-2-3)^{2}[/tex] + [tex](3-6)^{2}[/tex] = [tex]r^{2}[/tex]

[tex](-5)^{2}[/tex] + [tex](-3)^{2}[/tex] = [tex]r^{2}[/tex]

25 + 9 = [tex]r^{2}[/tex]

34 = [tex]r^{2}[/tex]

Substituting the values of h, k and r, we will get

[tex]x^{2} +y^{2}[/tex] = 34

Therefore,

The equation of a tangent line to the circle is, [tex]x^{2} +y^{2}[/tex] = 34

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The best count on the tuition axis will be $5,000.

What is an expression?

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 senior counselor is making a histogram of the yearly cost of tuition of 20 colleges.

And, Tuition ranges from $5,000 to $51,000 a year.

Now,

Since, Tuition ranges from $5,000 to $51,000 a year.

And, There are 20 colleges.

Hence, We get;

The best count on the tuition axis will be $5,000.

Thus, he best count on the tuition axis will be $5,000.

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The probability that the sample mean is less than 5, is 0.92135.

Let X1,X2,...,X32 be a random sample from an exponential distribution with a mean of 4.

We have to find an approximate probability that the sample mean is less than 5.

Let X = [tex]\frac{\Sigma_{i=1}^{n}x_{i}}{n}[/tex]

X = [tex]\frac{\Sigma_{i=1}^{32} x_{i}}{32}[/tex]

Then required probability is P(X<5).

Now we have to find the distribution of X where [tex]x_{i}[/tex]……. x_{32}.

Follow exponential with mean 4.

[tex]x_{i}[/tex]→exponent(λ=1/mean)

[tex]x_{i}[/tex]→exponent(λ=1/4)

[tex]x_{i}[/tex]→exponent(λ=0.25)

Now we have result:

If [tex]x_{1}[/tex] ………… x_{n} are exponential with α.

Then [tex]\Sigma{x_{i}}[/tex] has Gamma Distribution with (α=0.25, n=32)

Now we have result

X→G(α, λ) then c X→G(α/c, λ)

Here, we have

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(α=0.25, n=32)

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(α/(1/n), n)

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(nα, n)

X→Gamma(32*0.25, 32)

X has Gamma distribution with α=8, λ=32.

Required probability is;

P(X<5) = [tex]\int_{0}^{5}f(x) dx[/tex]

P(X<5) =[tex]\int_{0}^{5}\frac{\alpha }{\sqrt{\lambda}}e^{-\alpha x}x^{\lambda-1} dx[/tex]

Now to approximate this probability using normal as

X-mean(X)/SD(X)  = N(0,1)

X→Gamma(α=8, λ=32)

E(X) = λ/α                                            Var(X)= λ/α^2

E(X) = 32/8                                          Var(X)= 32/(8)^2

E(X) = 4                                               Var(X)= 0.5

Now P(X<5)=P[{(X-E(X))/√Var(X)}<{ (5-4)/√0.5}]

P(X<5)=P[{z< 1/√0.5}]

P(X<5) = P(z<1.4142

From the normal probability table

P(X<5) = 0.92135

Hence, the probability that the sample mean is less than 5, is 0.92135.

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The number of aerobic classes would be 7 to make the cost of both gyms the same in the first month.

What are linear equations?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are those in which the linear equation contains two variables.

Let x= number of months, and a=no of aerobic classes.

Let Gym A charge a $10 membership fee plus $20.25 per month plus $5.50 per aerobics class.

So we get the equation:

y= 10+20.25x+5.50a

y=30.25+5.50a ------------ as (x=1)

Next, for Gym B, it charges $46 per month plus $3.25 per aerobics class.

So the equation is:

y=46x+3.25a

y=46+3.25a ------------------as (x=1)

Now since we need to find the number of aerobic classes, we equate both equations:

30.25+5.50a = 46+3.25a

2.25a = 15.75

a = 7

Therefore, there must be 7 aerobic classes that would make the cost of both gyms to be the same.

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