Curated Practice Problem Set #9
1.
It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15
cups of sugar. Double the dimensions of the box. Approximately how much paint would the new
box need? How much sugar would it hold?​

The probability that the company will make less than $2m is 0.8 and b) the probability that the company will make less than $1m or at least $2m is 0.7

Here we are given respective probabilities of the revenue a company could make in a year.

a) Here we need to find the probability that it makes a revenue less than $ 2 million

This means that we need t find the probability that it makes revenue

less than $1M + greater than $1 M but less than $2M

= P(A₁) + P(A₂)

= 0.5 + 0.3

= 0.8

b)

The probability that the company will make less than $1M or at least $2M is

P(A₁ U A₃)

= P(A₁) + P(A₃) - P(A₁ ∩ A₃)

Since A₁ and A₃ are clearly mutually exclusive events, P(A₁ ∩ A₃) will be 0.

Hence we get

P(A₁ U A₃) = 0.5 + 0.2

= 0.7

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Complete Question

Assume the following in regard to a company’s annual revenue:

A₁ : Revenue < $1M; P(A₁) = 0.5

A₂ : Revenue > $1M but < $2M; P(A₂) = 0.3

A₃ : Revenue > $2M; P(A₃) = 0.2

a)What is the probability that the company will make less than $2M?

b)What is the probability that the company will make less than $1M or at least $2M

It describes the Cluster Sampling method.

It is a cluster sampling method because customers are divided into clusters at random and no personal judgment is involved. Thus, each cluster has an equal probability of selection, and sampling is done randomly.

Cluster sampling involves splitting the population into subgroups, but each subgroup should have similar properties to the whole sample.

Cluster sampling is a probability sampling method in which we divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as our sample.

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Answer:

30 groups

Step-by-step explanation:

We can first set 15/4 to have the same denominator as 1/8, which will be 30/8.

Since the question asks for the number of groups of 1/8, 30/8 will consist of 30 groups of 1/8.

Answer: SOME1 ANSWER QUICK

Step-by-step explanation:

Each of the statements should be completed as follows;

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values approach negative infinity (-∞) to positive infinity (∞).

In this context, the purple line on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 1.

Additionally, the base value of this exponential growth function f(x) = 3^x + 1 is equal to 1 and its domain includes all real numbers while its range includes all real numbers that are greater than 1 i.e 1 < y < ∞.

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Answer: We can start solving this problem by using a system of equations. Let x be the number of plain glazed donuts Nicole buys, and y be the number of chocolate cake donuts she buys. We know that:

x + y = 20 (The total number of boxes of donuts she buys is 20)

4x + 5y = 91 (The total amount of money she spends is $91)

We can use the first equation to solve for one variable in terms of the other. For example, we can substitute x = 20 - y into the second equation:

4(20 - y) + 5y = 91

80 - 4y + 5y = 91

-4y + 5y = 91 - 80

y = 11

So Nicole bought 11 boxes of chocolate cake donuts. We can substitute that back into the first equation to find the number of plain glazed donuts she bought:

x + 11 = 20

x = 9

So Nicole bought 9 boxes of plain glazed donuts.

We can check our answer by substituting our values of x and y back into the original equations:

x + y = 9 + 11 = 20 (This is the total number of boxes of donuts she bought, which is 20)

4x + 5y = 4(9) + 5(11) = 91 (This is the total amount of money she spent, which is $91)

Both equations are true, so our solution is correct.

Step-by-step explanation:

The function of u that takes the input u and gives output as v is g(u) = - (8v -2)/ 12.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given that the equation that takes the input and output value to give the function is:

-12u + 3 = 8v + 1

Isolate the value of u.

Subtract 3 from both sides of the equation:

-12u + 3 - 3= 8v + 1 -3

-12u = 8v -2

Divide both sides of the equation with -12.

-12u / -12 = 8v - 2/ -12

u = - (8v -2)/ 12

Hence, the function of u that takes the input u and gives output as v is g(u) = - (8v -2)/ 12.

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Answer:

Step-by-step explanation:

we know the slope and we have a point , so

y = 7x + b

sub in the point ...

-8 = 7(-1) + b

-8 + 7 = b

b = -1

y = 7x - 1

The probability that the 3 eldest children are the 3 girls is 0.05.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To determine the probability, we can use the permutation.

A permutation is an arrangement of a set of objects in a particular order. It is a way of counting the number of ways that a group of items can be arranged in a specific order.

There are a total of 6! ways in which the 6 children can be ordered. If the first 3 children are girls, there are 3! ways to arrange the 3 girls, and 3! ways to arrange the 3 boys. Therefore, the probability that the 3 eldest children are the 3 girls is

(3! x 3!) / 6! = (6 x 6) / 720 = 0.05

Therefore, there is a 0.05 chance or probability that the 3 eldest children are the 3 girls.

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The probability that less than 7 of the 30 students are left-handed is given as follows:

0.9742 = 97.42%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

n = 30, p = 0.1.

The probability that less than 7 of the 30 students are left-handed is given as follows:

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

Using a binomial distribution calculator with the parameter, finding each of the probabilities and adding them, we have that:

P(X < 7) = 0.9742 = 97.42%.

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The change represents growth and percentage rate of increase is 95.8%.

The exponential function y = 880(1.958)^x is a function that models growth.

The base of the exponential function, 1.958, is greater than 1. This means that the function is increasing with respect to x, which is the independent variable.

For every unit increase in x, the function increases by a factor of 1.958. This is evident from the fact that 1.958 is raised to the power of x.

The percentage rate of increase is calculated by taking the difference between the base of the exponential function and 1, and then multiplying that difference by 100%.

In this case, the base of the exponential function is 1.958, so the percentage rate of increase is

(1.958- 1)*100 = 95.8%.

This means that for every unit increase in x, the value of y increases by 95.8% of its previous value.

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The axis of symmetry of the graphed function is:

x = -2

Here we want to find the axis of symmetry of the graphed function, which is a quadratic one.

The axis of symmetry is a line of the form:

x = a

Where a is a real number

Such that it divides the graph of the function in two equal parts.

Notice that the parabola is perfectly divided by the line x = -2, so that is the axis of symmetry of the graphed function.

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The length of line segment AB is 8 cm in the above-mentioned diagram.

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Answer: To find the number of seconds it takes for the planes to reach the same altitude, we can use the following formula:

time = (difference in altitude) / (rate of plane B - rate of plane A)

In this case, the difference in altitude is the altitude of plane A (2457 feet) and plane B is just taking off so its altitude is 0 feet.

So, substituting these values into the formula:

time = (2457) / (70.75 - 25.25)

time = 2457 / 45.5

time = 53.7 seconds

So it takes 53.7 seconds for the planes to reach the same altitude. To find out what altitude they will be at when they reach the same altitude, we can use the formula:

Altitude = (rate of plane A x time) + altitude of plane A

Substituting the values we have:

Altitude = (25.25 x 53.7) + 2457

Altitude = 1351.6 + 2457

Altitude = 3809.6 ft

So, both planes will be at 3809.6 ft. when they reach the same altitude.

Step-by-step explanation:

The probability that both bulbs fail the test is 1/9. This is because out of the twelve lights, three of them have already failed the test, leaving nine lights that passed.  

This is because out of the 12 lights tested, 3 have already failed and there is a 1 in 4 chance that the two bulbs selected at random will be the same two failed bulbs.

Since the bulbs are selected at random with replacement, the probability that both bulbs fail the test is 1/9, or 11.11%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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Answer:

Step-by-step explanation:

212+105

We make this the equation because it says he charges 105 and he owes 212, so 212+105=317

Frank owes: $317

Answer:

Check image :D

Step-by-step explanation:

The image is the answer. I hope this helps you out :D

3x-y=2 and 4x+9y=36 make up the graph equation in option F. next we receive [tex]x=\frac{2+y}{3}$$[/tex] and [tex]x=\frac{36-9 y}{4}$$[/tex] .

solve for [tex]$x, 3 x-y=2 \quad: \quad x=\frac{2+y}{3}$[/tex]

Steps

3 x-y=2

Turn y to the right.

3 x=2+y

Divide both sides by 3

[tex]\frac{3 x}{3}=\frac{2}{3}+\frac{y}{3}$$[/tex]

Simplify

[tex]x=\frac{2+y}{3}$$[/tex]

solve for x, 4 x+9 y=36:  x=[tex]\frac{36-9 y}{4}[/tex]

Steps

4 x+9 y=36

Turn 9 y to the right.

4 x=36-9 y

By dividing both sides by 4,

[tex]\frac{4 x}{4}=\frac{36}{4}-\frac{9 y}{4}$$[/tex]

Simplify

[tex]x=\frac{36-9 y}{4}$$[/tex]

Therefore the correct answer is option F ) 3x-y=2 , 4x+9y=36 .

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The inequalities that are equivalent are 3x+6≤8+ 2x and 12-3x ≤18

Inequalities are simply defined as relations that makes a non-equal comparison between two mathematical expressions, equations or numbers.

It is mostly used to compare two numbers or expressions based on the magnitude on the number line.

Inequality signs in mathematic include;

Given the inequalities;

3x + 6 ≤ 8 + 2x

collect like terms

3x - 2x≤ 8 - 6

subtract like terms

x ≤ 2

12-3x ≤18

collect like terms

3x≤ 18 - 12

3x ≤ 6

Divide both sides by 3

x ≤ 2

Hence, the inequalities are 3x+6≤8+ 2x and 12-3x ≤18

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For the given case the full purchase price will be $1,628.92,Principal will be $1,600, Tax will be $101.60,Interest will be  $27.32 and Total is  $1,728.92.

To calculate the full purchase price, first, you must calculate the sales tax. To do this, multiply the price of the pickup ($1,600) by the sales tax rate (6.5%), which equals $101.60. Next, you must calculate the interest. To do this, multiply the amount borrowed ($1,504) by the interest rate (8%) and the number of years (1), which equals $27.32.

Finally, you must add the principal ($1,600), the sales tax ($101.60), and the interest ($27.32) to get the full purchase price of $1,728.92. Once you subtract the down payment of $200, the total purchase price is $1,628.92.

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As per the given least-square regression line the residual for the player is 12.6.

The term least square regression line in math is defined as  the line that makes the vertical distance from the data points to the regression line as small as possible.

Here we have the least square regression line as y = 280. 3 + 85. 7x.

As we all know that the residual is given by the difference between the observed point and the predicted point.

While we looking into the given problem the expected score over x hours is written as,

=> f(x) = 280.3 + 85.7x.

Here we need to find the residual for the player, then we have to apply the value of x as 3, then we get,

=> f(3) = 280.3 + 85.7 x 3 = 537.4.

As here we know that the observed score was of 550, hence the residual is calculated as,

=> R = 550 - 537.4 = 12.6.

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Answer:

Step-by-step explanation:

Move each point up by 3 points. you should have the same shape moved up on the graph. then move each point to the right by 6 squares. This should be your final square D''E''G''F''

The required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

Now, According to the question:

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Benita buys 2 shirts for the same price, s.

The sales tax rate is 6. 5%.

Write an expression to represent the total cost of the shirts.

1 way, paid the cost of 2 shirts jointly

The total cost of the two shirts becomes,

Total cost = 2[ s + 0.065s]

Total cost = 2.13s

2nd way, paid the cost of two shirts individually,

total cost = s + 0.065s + s + 0.065s

              = 2.13s

Thus, the required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

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For given linear equation x will be 5.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given linear equation is

15-x=10

x=15-10

x=5

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The distributive property of multiplication justifies that 3(x-2) is equivalent to 3x-6.

When a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then the two products added together to produce the same result as multiplying the first number by the sum. When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar terms, we usually add the numbers and then multiply by 5. However, the property states that you must first multiply each addend by 5.

Here,

3(x-2) is equivalent to 3x-6 due to the distributive property of multiplication.

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The ratio of the number of empty tables to the total number of tables is 13:21

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, 8 of the tables at Joy's Italian Restaurant are full, and the other 13 tables are empty, we are asked to find the ratio of the number of empty tables to the total number of tables,

Number of empty table = 13

Total number of tables = 13 + 8 = 21

Ratio of the number of empty tables to the total number of tables = 13 / 21

Hence, the ratio of the number of empty tables to the total number of tables is 13:21

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10-8 is the expression involving absolute value and addition that represents the vertical distance between the top of the slide and the bottom of the deep end of the pool.

An expression is combination of variables, numbers and operators.

Given that the highest point of a pool slide is 10 feet.

The lowest point of the deep end of the pool is 8 feet below water level.

A height of 0 is the water level.

10-8 is the expression involving absolute value and addition that represents the vertical distance between the top of the slide and the bottom of the deep end of the pool.

10-8=2, 2 is the value of the expression in (a)

Hence, 10-8 is the expression involving absolute value and addition that represents the vertical distance between the top of the slide and the bottom of the deep end of the pool.

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The longer crosspiece needs to be about 18 inches long.

To find the length of the longer crosspiece, you need to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).

Let's call the length of the longer crosspiece x. Then, we have two right triangles:

x^2 = (37-24)^2 + (13)^2

x^2 = 13^2 + 13^2

Solving for x:

x = sqrt(13^2 + 13^2) = sqrt(2 * 13^2) = 13 * sqrt(2) = 18.03 inches

So, the longer crosspiece needs to be about 18 inches long.

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Answer:

x=4.5

Step-by-step explanation:

Isolate the variable by dividing by each side by factors that don't contain the variable.

The equation in the simplest form that represents the perimeter of the bookend in centimeters is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Part A :

Perimeter of a closed figure is the sum of the lengths of it's boundary.

Given the lengths of the sides of the bookend as,

5m - 14, 2m - 7, 3/2 m + 2 and 3m + 8.

Perimeter is given as 58 centimeters.

(5m - 14) + (2m - 7) + (3/2 m + 2) + (3m + 8) = 58

(5m + 2m + 3/2 m + 3m) + (-14 - 7 + 2 + 8) = 58

23/2 m - 11 = 58

11 [tex]\frac{1}{2}[/tex] m - 11 = 58

Part B :

We have,

11 [tex]\frac{1}{2}[/tex] m - 11 = 58

11 [tex]\frac{1}{2}[/tex] m = 58 + 11

11 [tex]\frac{1}{2}[/tex] m = 69

23/2 m = 69

m = 6

Hence the required equation is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.

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