QUIZ:

Square Roots and Cube Roots to Solve Equations

Question

The volume of a cube can be found using the equation V = s³, where V is the volume and s is the measure of one side of the cube.



Match the equation for how to solve for the side length of a cube to its description.



Drag the equation to the box to match the description.


Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

A cube has a volume of 2560 in³.

Answer:

13.5 would be the answer

The following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.

Like 3x + 5 = 15, for instance.

Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.

So, the given equation is:

3/5(30x-15)=72

Now, we have:
3/5 * 30x - 3/5 * 15 = 72

18x - 9 = 72

Using common 3 as an example, we have the following on the left side of the equation:

3(6x-3) = 72

6x-3 = 72/3

6x-3 = 24

6x = 24+3

6x = 27

x = 27/6

x = 9/2

x = 4.5

Therefore, the following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

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The percentage of rents between $1,300 and $1,720 is 34.13%.

To calculate this, we need to use the z-score formula to convert the rent range into a z-score range. The z-score formula is (x-μ)/σ, where x is the rent range, μ is the mean rent and σ is the standard deviation.

To calculate the lower z-score, the formula becomes (1300-1510)/210 = -1.19.

To calculate the higher z-score, the formula becomes (1720-1510)/210 = 1.14. The z-score of -1.19 to 1.14 corresponds to 34.13% according to the z-table. Therefore, 34.13% of rents are between $1,300 and $1,720.

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If there are 14 people in a club organizing a spaghetti dinner, there can be 364 ways to select 3 people to be ticket takers.

A combination is a selection of things taken from a larger group, where the order in which things are selected is unimportant. A combination is distinct from a permutation, which is a method of organizing objects in which order matters. A combination is a method of selecting things in which order does not matter. In general, the combination formula can be used to determine the number of possible combinations that exist for a given set of things.

Suppose we have to select 3 people out of 14 people. The number of possible combinations can be found using the combination formula, which is given byC(n,r) = n!/(n-r)!r!where n is the total number of objects, and r is the number of objects selected.C(14,3) = 14!/(14-3)!3!C(14,3) = (14 × 13 × 12)/(3 × 2 × 1)C(14,3) = 364Therefore, there are 364 ways to select 3 people to be ticket takers from a group of 14 people.

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The length of the shadow of the second pole is 75 meters, was solved by using the concept of similar triangles.

The concept of similar triangles is based on the idea that if two triangles have the same shape but different sizes, they are called similar triangles. This means that their corresponding angles are equal and their corresponding sides are in proportion.

A triangle is a 2-dimensional geometric shape with three sides, three angles, and three vertices. It is one of the basic shapes in geometry and is used to describe many real-world objects and phenomena.

In the given question,

Length of shadow of first pole / Height of first pole = Length of shadow of second pole / Height of second pole

Substituting the given values, we get:

20√3 / 20 = x / 25√3

Simplifying, we get:

x = (20√3 / 20) * 25√3

x = 25*3

x = 75

Therefore, the length of the shadow of the second pole is 75 meters.

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Answer:

the measure of ∠D is 8°.

Step-by-step explanation:

Since ∠C and ∠D are vertical angles, they have equal measure. So we can set their measures equal to each other and solve for x:

x + 16° = 4x - 5°

6x = 21°

x = 3.5°

Now we can find the measure of ∠D:

∠D = 4x - 5°

∠D = 4(3.5°) - 5°

∠D = 8°

Therefore, the measure of ∠D is 8°.

it will take Bob approximately 47.3 years to save $200,000 for his retirement.

How to find?

To determine the time it will take Bob to reach his retirement goal of $200,000, we can use the formula for compound interest:

A = P(1 + r/n)²(nt)

where:

A = the final amount

P = the initial principal (deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $400 (monthly deposit)

r = 1.8% (annual interest rate, compounded monthly)

n = 12 (compounded monthly)

A = $200,000

We can solve for t by substituting the given values and solving for t:

200,000 = 400(1 + 0.018/12)²(12t)

500 = (1 + 0.0015)²(12t)

log(500) = 12t log(1.0015)

t = log(500) / (12 log(1.0015))

t ≈ 47.3

Therefore, it will take Bob approximately 47.3 years to save $200,000 for his retirement.

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Alyssa and Caleb ate 5/6 of the nachos together.

To calculate the fraction of nachos that Alyssa and Caleb ate together, add the fractions representing the portions that they each ate. However, because the fractions have different denominators, we must first find a common denominator.

2 and 3 share a common denominator of 6. With a denominator of 6, we can rewrite 1/2 and 1/3 as follows:

1/2 = 3/6

1/3 = 2/6

We can now add these fractions:

3/6 + 2/6 = 5/6

As a result, Alyssa and Caleb shared 5/6 of the nachos.

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Answer:

0

Step-by-step explanation:

-2(-3)+27÷(-3)+3

6-9+3

0

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The probability that Mark selects a car key or door key from the key ring is 0.3 or 30%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory provides a framework for understanding random events and the laws of chance, and it is an important tool for modeling and simulating complex systems.

Calculating the probability that he selects a car key or door key :

In this context, we are asked to find the probability of Mark selecting a car key or door key from the key ring. To calculate this probability, we need to first determine the total number of keys on the key ring and then count the number of car keys and door keys.

Total number of keys = 10

Number of car keys = 2

Number of door keys = 1

The probability of selecting a car key or door key can be found by adding the probability of selecting a car key to the probability of selecting a door key. Since there is only one door key and two car keys, the probability of selecting a car key is higher, and we can simplify the calculation by finding the probability of selecting a car key and then adding the probability of selecting a door key that hasn't already been selected.

Probability of selecting a car key = 2/10 = 0.2

Probability of selecting a door key = 1/9 (since one key has already been selected) = 0.1111...

Therefore, the probability of Mark selecting a car key or door key from the key ring is 0.2 + 0.1111... ≈ 0.3 or 30%.

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Since mXOY = mWOV, we can form the following equations so, m--XZ = m--ZV.

An equation is a mathematical statement that states the equality of two expressions. It usually consists of two terms, with an equals sign between them, representing the relationship between the terms. Equations are often used to describe relationships between variables, such as in physics and chemistry, and can be used to calculate unknown values.

Proof:

Since mXOY = mWOV, we can form the following equations:

m--YZ = m--ZW (Given)

Subtract both sides of the equation by m to get:

YZ = ZW

Then, multiply both sides of the equation by X to get:

XZ = XW

Now, substitute Y for V and W for V in the equation to get:

XZ = ZV

Finally, subtract both sides of the equation by m to get:

m--XZ = m--ZV

Therefore, m--XZ = m--ZV.

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Answer:

To create a line plot for this data, we can first convert all the fractions to a common denominator, such as eighths:

Monday: 6/8 of an hour

Wednesday: 4/8 of an hour

Friday: 2/8 of an hour

Sunday: 4/8 of an hour

Then, we can draw a number line with tick marks representing each day of the week and plot a dot for each amount of time spent working out:

0         1         2         3         4

|---------|---------|---------|---------|   <- Number line

         .     .

       .             .

   .                     .

.                             .

To find out how much time June should work out each day to spend an even amount of time working out, we can first find the total amount of time she spent working out:

6/8 + 4/8 + 2/8 + 4/8 = 16/8 = 2 hours

Since there are four days she worked out, to find out how much time she should work out each day, we can divide the total time by four:

2 hours ÷ 4 = 0.5 hours

Therefore, June should work out for 0.5 hours, or 30 minutes, each day to spend an even amount of time working out.

Answer:

[tex]y=3cos(3\pi x)+4[/tex]

Step-by-step explanation:

[tex]f(x)=cos(x)\\[/tex]

[tex]A(f(Bx+C)+D)[/tex]

The outside constants, A & D stretch and shift vertically. The inside constants, B & C stretch and shift horizontally. B & C work oppositely, basically multiplying by B stretches by a factor of 1/B and similarly adding C shifts f(x) horizontally to the left.

[tex]f(x)=cos(x) \text{ The function which we are transforming}\\\text{It currently has a amplitude of 1, time period of $2\pi$ and mid line at $y=0$}[/tex]

[tex]A=3 \text{ As we want to stretch it by 3 units vertically.}\\\text {To find B:}\\T' = T*(1/B)\\\text{Where $T'$ is new time period and T is existing time period}\\2/3=2\pi*(1/B)\\B=3\pi\\\text{C is not needed}\\D=4 \text{ To shift function by 4 units up}[/tex]

I hope this helps

The value of p from the given equation is 4.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign [tex]=\\[/tex].

The given equation is [tex]0.5p-3.45=-1.2[/tex]

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The equation can be solved as follows

[tex]0.5p-3.45=-1.2[/tex]

[tex]0.5p= -1.2+3.45[/tex]

[tex]0.5p= 2.25[/tex]

[tex]p= 2.25\div0.5[/tex]

[tex]p= 4.5[/tex]

Therefore, the value of p is 4.5.

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Answer:

surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 ...

Surface Area of Triangular Prism - Formula, Examples

Step-by-step explanation:

The probability that a randomly selected loan application takes longer than 11 days to process is 0.1587.

The time taken to process a loan application is uniformly distributed between 5 and 17 days.

We need to determine the probability that a random loan application takes longer than 11 days to process.

To compute the probability, we'll first determine the distribution's parameters;

we have:  a = 5 (minimum value)b = 17 (maximum value)

Mean: μ = (a+b) / 2 = (5+17) / 2 = 11

Variance: σ2 = (b-a)2/12

                     = (17-5)2/12

                     = 12.3333Standard deviation:  

                 σ = 3.516

For the problem, we want to find the probability of a loan application taking more than 11 days to be processed.

In other words, we want to find the probability of the application taking more than one standard deviation from the mean, that is, P(X > μ + σ).

Since the distribution is symmetric, we can also find the probability by calculating P(X < μ - σ) and subtracting the result from 1, since the total probability must be 1.

Using the above formula, we have:

P(X > μ + σ) = P(X > 11 + 3.516)

                  = P(X > 14.516)

To standardize the value of 14.516, we'll convert it to a z-score, which is z = (X - μ) / σ.

Therefore, we have z = (14.516 - 11) / 3.516 = 1

Since we are dealing with a standard normal distribution, we can use the standard normal distribution table to find the probability associated with z = 1.

From the table, we find that the probability of z being less than 1 is 0.8413;

thus, the probability of z being greater than 1 is 1 - 0.8413 = 0.1587.

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The answer to subtracting the two polynomials is 2x2 - 10x - 7.  The process of subtracting polynomials is like that of subtracting any other type of numerical expression.

Polynomials are mathematical expressions consisting of variables, coefficients, and exponents. They are used to represent a variety of functions, such as polynomial equations, rational equations, and trigonometric functions.

In this case, our like terms are 2x2 and 4x2, and -6x and -4x, and -4 and +3. We begin by subtracting the coefficients of the like terms. We subtract the coefficient of the term with the highest power first. In this case, that is 2x2 and 4x2, we subtract 2 from 4 to get 2. Next, we subtract the coefficients of the terms with the second highest power. This is -6x and -4x, so we subtract -6 from -4 to get -2. Thus, our answer now reads 2x2 -2x.

Finally, we subtract the coefficients of the terms with the lowest power. This is -4 and +3, so we subtract -4 from 3 to get -7. Thus, our answer now reads 2x2 -2x -7.

This answer can then be placed in the proper position on the grid.

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The distance of the end of the trip from the starting point is 193.1321 km.

The ship goes 180 kilometers on bearing after 70 km of subsequent journey.

The starting point in this case is A, and the ending point is C.

We now discover distance AC:

As we can see, a right-angled triangle results.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides that make up the right angle is equal to the square of the hypotenuse. This can be expressed mathematically as a^2 + b^2 = c^2, where a and b are the two sides that make up the right angle, and c is the hypotenuse.

Use Pythagoras's principle.

c = √a² + b²

The distance in the Hypotenuse in our case is now.

c = √(70)² + (180)²

c = √4900 + 32400

c = √37,300

c = 193.1321 km

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The complete question is:

A ship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. Find the distance of the end of the trip from the starting point.

The garden would require 84 plants, which is the same number of plants as the garden's surface area.

The area of the garden can be determined using the formulas below if it is shaped like a right triangle and has sides that are 7 and 24 yards long.

Area of the garden = (1/2) x Base x Height

Area of the garden = (1/2) x 7 x 24

Area of the garden = 84 square yards

Since there is one square yard of area for each plant, the number of plants needed for the garden would be equal to the area of the garden, which is 84 plants.

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According to a histogram that displays the percentage of replies over time, an April Gallup poll indicated that 55% of Americans think autonomous cars would be widely used in the next ten years.

Whether completely automated "driverless automobiles" would be widely deployed in the United States was the subject of a Gallup Poll conducted in April, which polled Americans ages 18 and older.

How soon, in your opinion, do you believe autonomous cars will be widely used in the US? According to the survey, 55% of Americans think autonomous cars will become commonplace over the next ten years.

The survey's results were displayed as a histogram, displaying the proportion of replies at various time intervals. This indicates how many respondents indicated that driverless cars will be widely utilised within a particular time period (e.g., within 5 years, within 10 years, etc.).

This survey reveals how people feel about autonomous cars in the future and how soon they believe they will be a common sight on the roads.

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The question is -

A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.

Answer:

We can use the slope-intercept form of a linear equation to model the balance y after t months, where the slope represents the rate of change of the balance and the y-intercept represents the initial balance.

The initial balance (y-intercept) is the amount Tina borrowed to buy the refrigerator, which we don't know. But we can find the slope using the two data points provided:

Four months: balance = $630

Six months: balance = $520

The change in the balance over the two-month period is:

$520 - $630 = -$110

The slope of the line is the rate of change of the balance per month, which is:

slope = Δy/Δt = (-$110)/(6-4) = -$55/month

Using the point-slope form of a linear equation, we can plug in one of the data points to find the y-intercept:

y - 630 = -$55(t - 4)

y - 630 = -$55t + 220

y = -$55t + 850

Therefore, the equation that models the balance y after t months is:

y = -$55t + 850.

Answer:

perimeter = 10 mm

Step-by-step explanation:

the perimeter is the sum of the 3 sides.

given perimeter = 24 , that is

w + 6 + 8 = 24

w + 14 = 24 ( subtract 14 from both sides )

w = 10 mm

Answer:

a)30

b)25

Step-by-step explanation:

ratio of red socks and total sock is 1:6 so, lets show this as,

1k and 6k.

1k-------5

6k------x

x=30

a)total socks = 30

b)black socks =total-red socks=30-5=25

Triangle ABC is similar to triangle DEF. The tangent of angle A is equal to 5/12 and the sine of angle F is 1/13.

The sine of the angle is the proportion of a right-angled triangle's hypotenuse to its perpendicular.

Triangle ABC and triangle DEF are similar in that their respective sides are proportional and their corresponding angles are equal. As a result, we have:

BC/EF = AC/DF = AB/DE

To determine the ratio AB/BC, we can utilise the tangent of angle A:

Tan(A) = 5/12 = AB/BC

By multiplying both sides by 12, we may make this simpler:

AB/BC = 12 tan(A).

We can now determine the ratio AB/EF using the ratio BC/EF:

AB/DE = BC/EF

This can be rearranged to yield AB/EF:

BC/EF * DE/AB = AB/EF

Due to the similarity of the triangles, we know that BC/EF = 12/13 and can therefore insert this into the equation:

(12/13) * (AB/DE) = AB/EF

Using the formula AB/DE = 5/12 (from above), we can reduce this:

AB/EF = (12/13) * (5/12) = 5/13

Finally, we may calculate the sine of angle F using the sine ratio:

sinning(F) = EF/DF

Using the ratio AB/EF that we recently discovered, we may rephrase this as follows:

sin(F) = (1/AB) * (AB/EF) = (1/AB) * (5/13)

Simplifying and substituting AB = 5k results in:

sin(F) is equal to (1/5k) x (5/13) x 1/(k*13).

We can select k = 1 because we want the response in its simplest form:

sin(F) = 1/13

As a result, 1/13 is the sine of angle F.

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In response to the stated question, we may state that The coordinates of equation triangle ABC in green are: A" (-3,-3); B" (-2,1); C" (1,-4)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The x-axis is horizontal and the y-axis is vertical.

     4   B(−2, 4)

     |   *

     |  / \

     | /   \

     |/_____\

    A(−3, 0) C(1, −1)

     4   B(−2, 4)         C'(4, 1)

     |   *                *

     |  / \              / \

     | /   \            /   \

     |/_____\-3, 0    -1, 1 A'(0, -3)

    A(-3, 0) C(1, −1)   B'(4, -2)

A' (-3,0) ➜ (0,-3)

B' (-2,4) ➜ (4,-2)

C' (1,-1) ➜ (-1,1)

     1   C(1, −1)         C"(1, -4)

     |   *                *

     |  / \              / \

     | /   \            /   \

     |/_____\-3, -3    -2, 1 A'(-3, -3)

    A(-3, 0) B(-2, 4)   B'(-2, 1)

A' (-3,0) ➜ A" (-3,-3)

B' (-2,4) ➜ B" (-2,1)

C (1,-1) ➜ C" (1,-4)

The coordinates of triangle ABC in green are:

A" (-3,-3)

B" (-2,1)

C" (1,-4)

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Figure E is a rotated and reflected version of Figure D that has been shifted to the right and up as a result of this transformation sequence.

The sequence transformation (which may be dependent on n). This is known as a linear sequence transformation. Nonlinear sequence transformations are nonlinear sequence transformations.

We can use the following transformations to map Figure D onto Figure E:

Figure D should be translated 4 units to the right and 1 unit up.

Figure D should be rotated 90 degrees clockwise around the origin.

Cross the y-axis with the resulting figure.

This transformation sequence results in Figure E, which is a rotated and reflected version of Figure D that has been shifted to the right and up.

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Answer: We can use a proportion to solve the problem:

17 gallons / 355 miles = x gallons / 284 miles

Cross-multiplying, we get:

17 * 284 = 355 * x

4844 = 355x

x = 13.66 (rounded to two decimal places)

Therefore, Mai would need approximately 13.66 gallons of gas to drive 284 miles at the same rate.

Step-by-step explanation:

If the amount of jen's monthly phone bill is normally distributed with a mean of $86 and standard deviation of $9, Between the values of $77 and $95 inclusive, 68.26% of Jen's phone bills are expected to fall.

To find the values between which 68.26% of Jen's phone bills lie, we need to use the properties of the normal distribution and the empirical rule.

The empirical rule states that for a normal distribution, approximately 68% of the data lie within one standard deviation of the mean. Therefore, we can find the values between which 68.26% of Jen's phone bills lie by calculating the range of values that are one standard deviation away from the mean.

Using the given population mean of $86 and population standard deviation of $9, we can calculate one standard deviation as follows:

One standard deviation = population standard deviation = $9

To find the lower and upper bounds for 68.26% of Jen's phone bills, we can subtract and add one standard deviation from the mean, respectively:

Lower bound = population mean - one standard deviation = $86 - $9 = $77

Upper bound = population mean + one standard deviation = $86 + $9 = $95

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Answer:

[tex] - 50 + 8i[/tex]

Step-by-step explanation:

[tex]1. \: - 35 - 15i + 21i - 9 - (6 - 2i) \\ 2. \: - 35 - 15i + 21i - 9 - 6 + 2i \\ 3. \: ( - 35 - 9 - 6) + ( - 15i + 21i + 2i) \\ 4. \: - 50 + 8i[/tex]

The expression that best represents the total cost of the charter bus for the field trip is 12n + 50

The total cost of the charter bus for the field trip consists of a $50 reservation fee and an additional $12 per student.

If n represents the number of students going on the field trip, then the expression for the total cost can be written as:

Total cost = 12n + 50

This expression represents the variable cost of the charter bus, which depends on the number of students going on the field trip.

The fixed cost of $50 is added to the variable cost to give the total cost.

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