Question in picture below

Answer:

6√2, or about 8.5 meters

The probability that the next person will purchase

more than one costume is 0.05

In the question, we have been given that in a popular online role-playing game, players can create detailed designs for their character's "costumes," or appearance.

Malik sets up a website where players can buy and sell these costumes online.

The information about the number of people who visited the website and the number of costumes purchased in a single day is:

40 visitors purchased no costume.

82 visitors purchased exactly one costume.

6 visitors purchased more than one costume.

We need to find the probability that the next person will purchase

more than one costume.

The total number of visitors the site :

40 + 82 + 6 = 128

The number of visitors purchased more than one costume = 6

Thus, the probability that the next person will purchase no costume would be,

P = 6/128

P = 0.046

P = 0.05

Therefore, the probability that the next person will purchase

more than one costume is 0.05

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Answer:

0.03

Step-by-step explanation:

Answer: 48.1

Step-by-step explanation:

Part a: Range = 4550

Part b: Variance  = 287,034

Part c: Standard deviation =  (287,034)².

For the given question;

The highest net worths (in millions of dollars) for 6 celebrities is shown.

Part a: calculate the range;

Range = highest value - lowest value

Range = George Lucas (5500) - Jerry Seinfeld (950)

Range = 4550

Part b: Calculated the variance;

σ = ∑X²/n - μ² =  ∑(X²- μ²)/n

First find the mean;

μ =  ∑X/n

μ = (5500 + 3700 + 3200 + 1200 + 1000  950)/6

μ = 7775/3

σ =  (5500² + 3700² + 3200² + 1200² + 1000²  950²)/6 - (97775/3)²

σ = 287034

Variance = 287,034

Part c:  Calculated the standard deviation;

standard deviation = σ²

σ² = (287,034)²

Thus, the standard deviation is found as (287,034)².

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According to the solving the value of the given function g(n) = -n² -1 h(n) = -2n + 2:

(g o h)(n)  = 2n³ +4n -2.

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output.

A function is defined technically as a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

g(n) = -n² -1 h(n) = -2n + 2

find  (g o h)(n)

We can write it as:

g o h = g  x h

         = (-n² -1) x (-2n + 2)

        = 2n³ + 2n +2n -2

       = 2n³ +4n -2

According to the solving the value of the given function g(n) = -n² -1 h(n) = -2n + 2:

(g o h)(n)  = 2n³ +4n -2.

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Answer:

6.6666 or 7

Step-by-step explanation:

The new grade of the student will be 70% and the grade reduced by 10 percent.

This is a rate, number, or amount in each hundred. Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

In the given question, we simply need to add the two percentage together and find the average of the value.

This can be done mathematically as

[tex]\frac{60+80}{2} = 70[/tex]

The average grade will be 70% and this shows that the grade dropped by

[tex]80\% - 70\% = 10\%[/tex]

The grade will go down by 10%.

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Answer:

[tex]x=5, y=-2[/tex]

Step-by-step explanation:

[tex]-5y+6x=40 \implies -15y+18x=120 \\ \\ 3y-8x=-46 \implies 15y-40x=-230 \\ \\ \therefore -22x=-110 \implies x=5 \\ \\ \therefore -5y+6(5)=40 \implies y=-2[/tex]

The solutions to all the parts of the question are discussed below.

Inequality in mathematics is a relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given is a rental car company charges a $22 fee to rent a car plus $0.32 per mile.

Assume that [m] represent the number of miles the car is driven by Matt.

Part [A]

We can write the inequality as follows -

22 + 0.32m ≤ 100

Part [B]

The inequality is -

22 + 0.32m ≤ 100

0.32m ≤ 78

m ≤ 78/0.32

m ≤ 243.75

Part [C]

The graph is attached at the end.

Part [D]

22 + 0.32m ≤ 100

22 + 0.32 x 243.75 ≤ 100

22 + 78 ≤ 100

100 ≤ 100             [verified]

Part [E]

The number of miles that can be driven by Matt after renting the car will be 243.5 miles.

Therefore, the solutions to all the parts of the question are discussed above.

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When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula,

y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula t.

Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope intercept form.

The slope-intercept form is provided as y = mx + b, where m is the line's slope and b is the y-intercept. Using this form, we may determine the slope of a line. Here's an illustration. The slope of the line 6x - 3y = 5 should be determined. To convert this into the slope-intercept form, let's solve this for 'y'. The result is y = 2x – (5/3). We calculate the slope to be m = 2 by comparing this to the slope-intercept formula, y = mx + b.

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Considering the average rate of change of the function, the matched pairs are given as follows:

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given according to the following rule:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For the interval given by item 1, between -1 and 2, we have that:

Hence the rate is:

r = (-17 - (-2))/(2 - (-1)) = -15/3 = -5.

Meaning that 1 matches with a.

For the interval given by item 2, between -1 and 0, we have that:

Hence the rate is:

r = (3 - (-2))/(0 - (-1)) = 5/1 = 4.

Meaning that 2 matches with b.

For the interval given by item 3, between 1 and 2, we have that:

Hence the rate is:

r = (-17 - (-2))/(2 - 1) = -15/1 = -15.

Meaning that 3 matches with c.

For the interval given by item 4, between -2 and 0, we have that:

Hence the rate is:

r = (3 - (-17))/(0 - (-2)) = 20/2 = 10.

Meaning that 4 matches with d.

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The mean number of individuals per sample who do not exercise regularly = 7

According to the survey 58% of the Americans does not exercise.

Hence probability of not exercising, p = 58/100 = 0.58

Define a random variable X denoting the number of people who does not exercise.

Then X follows the binomial distribution.

If p denotes the probability of success and if n is the sample size or number of trials, then

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ gives the probability of the random variable X.

Here, the sample size, n = 12

For a binomial distribution, mean, μ = np

Therefore,  mean number of individuals per sample who do not exercise regularly = np

               = 12 x 0.58

               = 6.96

               ≈ 7

The question is not complete. Find the complete question below:

According to the Behavioral Risk Factor Surveillance System, 58% of all Americans adhere to a sedentary lifestyle (sedentary means does not exercise).

a. If you selected repeated samples of 12 from the U.S. population, what would be the mean number of individuals per sample who do not exercise regularly?

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The exponent's expression is 5².

Exponent expression:

An exponent refers to the number of times a number is multiplied by itself.

The property of exponents:

[tex]a^{m} / a^{n}[/tex] = [tex]a^{m-n}[/tex]

The expression is:

[tex]5^{8} / 5^{6}[/tex]

Using the property of exponents we have,

[tex]5^{8-6}[/tex]

= 5²

Therefore the exponent expression is 5².

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By using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35

The function is

f(x) = [tex]x^3+4x^2-5x+11[/tex]

The function is defined as the relationship between the one variable and another variable. If one variable is dependent variable and another variable will be independent variable

To find the value of f(-3), first we have to substitute the value x = -3 in the given function

The function is

f(x) = [tex]x^3+4x^2-5x+11[/tex]

Substitute the value of x = -3

f(-3) = [tex](-3)^3+4(-3)^2-5(-3)+11[/tex]

= -27 + 36 + 15 + 11

= 35

Hence, by using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35

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Based on the rate of change and the points, the equation of the line in Point-Slope form was y = 2/3x - 4.17

The equation of the line in point-slope form was y = -1/5x - 2.8

The equation of a line takes the form:

y = mx + b

m is the rate of change

b is the y-intercept

We need to find the y-intercept because we have the rate of change and y and x values:

-6.5 = 2/3(-3.5) + b

-6.5 = -2.33 + b

b = -6.5 + 2.33

b = -4.17

The equation is:

y = 2/3x - 4.17

The equation for the second line takes the same form. So the y-intercept should be found first:

- 3 = - 1/5(1) + b

b = -3 + 1/5

b = -2.8

The equation of the line is:

y = -1/5x - 2.8

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The ratios in their reduced fraction are 4:5  and 9:8 as they are in their simplest form.

a fraction whose lowest terms are obtained by multiplying the numerator by the highest common factor among its denominator and numerator. The reduced fraction of 8/12, for instance, is 2/3.

Divide the numerator and denominator of a fraction by the GCF to reduce it. (Writing a fraction in lowest terms is another name for this.) Sometimes, this is depicted as "cancelling" the common components.

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The information that June says that there should be a decimal point in the quotient below after the 4 is incorrect.

From the information given, it should be noted that it's important to find the division. This will be:

= 43.94 / 5.2

= 8.4.5

Based on the information, June says that there should be a decimal point. It should be noted that from the question, the decimal wasn't illustrated.

Therefore, June is incorrect. This is because the decimal is before 4.

The complete question is written below.

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Given that June says that there should be a decimal point in the quotient below after the 4. The number given is 43.94/5.2 = 845 is she correct?

B)150 km

Step-by-step explanation:

The total distance is 400km

and jim drove 1/4 of this distance so

400 x 1/4 = 100km

then subtract this from the total distance 400 - 100 = 300km

Elaine drove 1/2 of this remaining distance

300 x 1/2 = 150 km

Add this with the first result

100 + 150 = 250 km

this is the total disrance that they have treveled

how much do they have to go

400 - 250 = 150km meaning the answer is b

Function : $8000 = $1200 + $700x

They will raise $700 per month for x months -> $700x is the amount of money they raise per month.

Since $8000 is the sum in the function, it is the goal.
Therefore, $1200 in this case means they started with $1200.

The slope is 1.

Explanation:

The equation of a line is written in "slope-intercept form as

The two variable equation representation of the Jae expenditure of money while buying Video games and gaming accessories will be 60x + 45y = 500

It is given that,

The total money that Jae has =  $500

The cost price of each video game = $60

And, the cost price for each game accessories = $45

We need to find an arithmetic equation representation which is known as equation in two variable

To do that, the question has represented both number of games and gaming accessories that Jae bought with x and y variables

It is given,

Total number of video games he an buy = x

Total number of gaming accessories he an buy = y

Now, the total expenditure that Jae will do in buying Video games and gaming accessories should not exceed $500 as this s the total money he had wit him

Therefore,

60x + 45y = 500

This is the two variable equation representation of the Jae expenditure of money while buying Video games and gaming accessories

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Julie received an amount of $134.4 when she cashed her paycheck.

Let x be the amount of the paycheck.

She gave her brother ten dollars.

She then paid $30 for the car's petrol.

So she departed with an amount equal to x-40.

She now spent half of the remaining accounts on a new camping tent.

Spent camping = (x - 40)/2

Remaining = x - 40 - (x - 40)/2

She paid $29.45 for a pair of running shoes.

Therefore, remaining =  x - 40 - (x - 40)/2 - 29.45

As per the question, she had $17.75 remaining.

So x - 40 - (x - 40)/2 - 29.45 = 17.75

Rearrange the terms and solve for x,

(x - 40)/2 = 47.2

x - 40 = 94.4

x = 134.4

Therefore, she received an amount of $134.4 when she cashed her paycheck.

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A)  The probability that at least one of the two students will be in class on a given day is; 0.92

B)  If at least one of the two students is in class on a given day, the probability that a is in class that day is; 0.8696

In probability theory, the occurrence of the events may depend on its relative events which are called dependent events while the events not dependent on their relative events are referred to as independent events. For dependent events, if conditional probabilities are required , we will make use of the Baye's Theorem and the total probability theorem sometimes.

We are given;

Probability that student A attends class = 80% = 0.8

Probability that student B attends class = 60% = 0.6

A) The probability that at least one of the two students will be in class on a given day is;

P = 1 - Probability that that neither show up to class on any given day.

P(A ∪ B) = 1 - P(A∼ ∩ B∼)

Where  P(A∼ ∩ B∼) = (1 - 0.8) × (1 - 0.6)

P(A∼ ∩ B∼) = 0.08

Thus;

P(A ∪ B) = 1 - 0.08

P(A ∪ B) = 0.92

B) We want to find the probability that student A was in the class given that at least one of them was in the class.

This is obviously a case of conditional probability which will give us the formula;

P(A|A ∪ B) = P(A ∩ (A ∪ B))/P(A ∪ B)

= P(A)/P(A ∪ B)

= 0.8/0.92

= 0.8696

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The inverse function of the function f(x) = 12(x+3)  is f(x) = -2x - 3

A function's inverse is a function that offers us the actual value for which the desired function produces a specific outcome.

The function given is:

To find the inverse, we must perform the following procedures.

y takes the place of f(x);

y = -(x+3)/2

Change the x and y variables.

x = -(y+3)/2

Calculate y

2x = - (y + 3)

2x = -y - 3

y = -2x - 3

We get the following in inverted notation:

f(x)⁻¹ = -2x - 3

Thus the obtained inverse function is f(X) =  -2x - 3

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The ordered pairs that are also functions are listed below.

1. {(2,4),(3,1),(0,5),(-1,-3)}

2. {(2,4),(-4,1),(0,4),(-3,-0)}

4.{(7,-3),(3,-7),(2,4),(4,2)}

The ordered pairs that are not functions are listed below.

3.{(-2,-3),(4,1),(4,4),(-3,2)}

A function is a relation between two sets of ordered pairs that describe that there should be only one output for each input, or that for every element in set A, there should be one and only one relation in set B.

A relation between two sets of ordered pairs can be considered a function when every X value is associated with only one Y value.

Here in the first, second, and fourth sets of ordered pairs

1. {(2,4),(3,1),(0,5),(-1,-3)}

2. {(2,4),(-4,1),(0,4),(-3,-0)}

4.{(7,-3),(3,-7),(2,4),(4,2)}

Hence, every value in X has only one single value in Y. Hence, all these relations can be considered functions.

In the third set, i.e.,

3.{(-2,-3),(4,1),(4,4),(-3,2)}

It can be seen that element 4 has two values as its output, which are 1 and 4 ((4,1),(4,4)). Hence, it cannot be considered a function.  

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Answer:

Step-by-step explanation:

24 : 2 = 12 ft

π12² =

3.14 * 12² =

3.14 * 144 =

452.16 ft²

Answer: 452.16 ft

The formula given is  πr², where π is 3.14, and r is radius.

radius is half the diameter, so first step is 24/2, which is 12. r = 12.

Then we apply it to the formula.

πr² = 3.14 x 12²

3.14 x 144

area = 452.16 ft

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Answer:

about 24.38 feet

Step-by-step explanation:

Graphing window: [0, 30] by [-20, 160]

y1 = 20 + 2x + √(400 + 4x^2)

y2 = 1.6(20 + x + √(400 + x^2))

y1 = y2 when x = 24.3798.

So the length of the smaller garden's longer leg is about 24.38 feet.