Cheryl is organizing her movie collection. If each movie case is 3/4 inch wide, how many movies can fit on a shelf 5 1/4 wide?

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

(B) Weak Positive

Step-by-step explanation:

if the points were closer to the line drawn then the stronger the correlation

The type of linear association that the graph show is (B) Weak Positive

If the scattered points lie near to a straight line which has positive slope, then the data represents the linear positive association.

If the scattered points lie near to a U-shaped curve, then the data represents the Nonlinear association

The data that represents no association when the scattered points are not related to each other (neither linear association nor nonlinear  association ), then

The data represents the line, when the scattered points lie near to a straight line which has negative slope,

The type of linear association is (B) Weak Positive

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The augmented matrix for the given system of linear equations is:

[ 4 13 -38 -21 ]

[ 7 23 -67 -37 ]

To find the augmented matrix for the given system of linear equations, we can write the coefficients of the variables and the constants in matrix form. The augmented matrix is formed by appending the constants as an additional column to the coefficient matrix.

The system of equations is:

4x + 13y - 38z = -21

7x + 23y - 67z = -37

Let's represent the variables and constants as follows:

Coefficients: 4 13 -38

7 23 -67

Constants: -21

-37

To form the augmented matrix, we combine the coefficients and constants:

4 13 -38 -21

7 23 -67 -37

This augmented matrix represents the system of equations in a compact matrix form, allowing us to perform matrix operations and solve the system using various methods such as row reduction or matrix inversion.

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Answer:

123

Step-by-step explanation:

We can square and cube the equation, then multiply the results together.

(a + \(\frac{1}{a}\)) = 3 ← square both sides

a² + 2 + \(\frac{1}{a^2}\) = 9 ( subtract 2 from both sides )

a² + \(\frac{1}{a^2}\) = 7 → (1)

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

Now cube both sides

a³ + \(\frac{1}{a^3}\) + 3(a + \(\frac{1}{a}\)) = 27

a³ + \(\frac{1}{a^3}\) + 3(3) = 27

a³ + \(\frac{1}{a^3}\) + 9 = 27 ( subtract 9 from both sides )

a³ + \(\frac{1}{a^3}\) = 18 → (2)

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

Multiply (1) and (2)

(a² + \(\frac{1}{a^2}\) )(a³ + \(\frac{1}{a^3}\) ) = 7(18)

\(a^{5}\)  + ( \(\frac{1}{a}\) + a) + \(\frac{1}{a^5}\) = 126

\(a^{5}\) + 3 + \(\frac{1}{a^5}\) = 126 ( subtract 3 from both sides )

\(a^{5}\) + \(\frac{1}{a^5}\) = 123

answer: the first 1 is y=3x+1  the second 1 is y=-x-3 ⤵

The type of distribution for the proportion of 100 college graduates who believe their degree was a good investment is a binomial distribution.

A binomial distribution is used to describe the outcome of a binomial experiment. A binomial experiment is one that satisfies the following four conditions:

1. The experiment consists of n repeated trials.

2. Each trial results in an outcome that may be classified as a success or a failure (hence the name, binomial).

3. The probability of a success, denoted by P, is the same on every trial.

4. The trials are independent; that is, the outcome of one trial does not influence the outcome of any other trial. In this case, the binomial experiment is the number of college graduates who believe their degree was a good investment out of a sample size of 100.

Each graduate can be classified as either a success (believes their degree was a good investment) or a failure (does not believe their degree was a good investment).

The probability of success is not specified, but it is assumed to be constant across all graduates. The trials (graduates) are also assumed to be independent of each other.

Therefore, the proportion of graduates who believe their degree was a good investment follows a binomial distribution.

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Answer: Yes, 59 is a prime number

Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.

Yes, 59 is a prime number.

What is a prime number?

Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.

In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.

The number in question, which is 59,  has only two factors: 1 and 59.

Therefore 59 is a prime number.

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Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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Answer:

1/y^9= y^-9

1/m^15= m^-15

n^3=n^3

1/m^6=m^-6

n^4

w^12

1/32=2^-5

-6=(-6)^1

1^1

Step-by-step explanation:

Step-by-step explanation:

Use the exponent laws to identify which law to use.

1. y^-4 * y^-5 = y^-9

(add the exponents)

2. (m^-3)^5 = m^-3*5 = m^-15

(multiply the exponents)

3. n^-3 * n^6 = n^3

(add the exponents)

4. m^-12/m^-6 = m^-12-(-6) = m^-6

(subtract exponents)

5. (n^-2)^-2 = n^-2*-2 = n^4

(multiply the exponents)

6. w^5/w^-7 = w^5-(-7) = w^12

(subtract the exponents)

7. 2^-3 * 2^-2 = 2^-5

(add the exponents)

8. (-6)^4 * (-6)^-3 = -6^1

(add the exponents)

9. (4^-6)^0 = 4^-6*0 = 4^0 = 1

(multiply the exponents)

Answer:

It goes by 5 i think so.

Step-by-step explanation:

Answer:

The interval estimate is:

41.5 - 2.45 ≤ true average time ≤ 41.5 + 2.45

or

38.05 ≤ true average time ≤ 44.95

Inequality notation:

[38.05, 44.95]

The interval estimate that will estimate the true average time that people spend brushing their teeth is [39.05, 43.95] seconds.

Given that the mean time spent brushing teeth from the sample is 41.5 seconds, and the margin of error is 2.45 seconds, we can construct a confidence interval estimate using the formula:

(sample mean) ± (margin of error)

Substituting the given values, we get:

41.5 ± 2.45

Simplifying, we get:

[39.05, 43.95]

Therefore, we can be 95% confident that the true average time that all people spend brushing their teeth falls within this interval.

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In this case, we must use our trigonometric equations to help us solve this problem:

    ⇒ look at the diagram attached

Let's examine what the problem wants:

Let's examine what the problem gives us:

Let's solve:

  \(tan(41)=\frac{12}{x} \\12=x*tan(41)\\x=\frac{12}{tan(41)} \\x=13.80\)

Answer: 13.8 (rounded to nearest tenth)

Hope that helps!

By surveying a representative sample, the polling agency can estimate the opinions of the entire population without having to survey every single registered voter in the city.

What is statistics?

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical methods to gather, summarize, and interpret data, which can be used to make decisions or draw conclusions about a population based on a sample of that population.

Part A: The population in this survey is the entire registered voter population of the city of Portland. This is because the polling agency wants to survey a representative sample of the entire population to determine their opinions on increasing taxes for investing in a bridge.

Part B: The population parameter in this survey is the maximum percentage increase in municipal taxes that the entire registered voter population of the city of Portland would approve. This is the parameter that the polling agency is interested in estimating through the survey.

Part C: The sample in this survey is the 500 registered voters selected at random by the polling agency.

This sample is a subset of the entire registered voter population of the city of Portland and is used to make inferences about the population parameter.

Hence, By surveying a representative sample, the polling agency can estimate the opinions of the entire population without having to survey every single registered voter in the city.

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The spring stretched from 18 inches to 24 inches, producing a total of 12 joules of work.

The formula: gives the work done on a spring when it is stretched.

W = (1/2)kx²

where W is the amount of work completed, k is the spring's constant, and x is the spring's length change. We can use the equation to determine the spring constant:

F = kx

where F is the spring's applied force and x is the spring's altered length. Since we are aware that a spring with a natural length between 12 and 18 inches will be stretched by a force of 4 pounds, we can enter these numbers into the equation to determine k:

4 = k * (18 - 12)

4 = k * 6

k = 4/6

k = 2/3

Now that we know the spring constant, we can use the work formula to calculate the total amount of work required to extend a spring from 18 inches to 24 inches in length:

W = (1/2)kx²

W = (1/2)(2/3)(24 - 18)²

W = (1/2)(2/3)(6²)

W = (1/2)(2/3)(36)

W = (2/3)(18)

W = 12

So The spring stretched from 18 inches to 24 inches, producing a total of 12 joules of work.

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The actual length of the truck is 72 inches.

To find the length of the actual truck, we need to use the scale factor of 1:12. This means that for every 1 unit on the model, it represents 12 units on the actual truck.
Since the length of the model truck is 6 inches, we can multiply it by the scale factor of 12 to get the length of the actual truck.

1 (model unit) / 12 (actual units) = 6 inches (model length) / x (actual length)
To solve for x, we can cross-multiply:
1 * x = 12 * 6
x = 72 inches
Therefore, the length of the actual truck is 72 inches or 6 feet.

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Answer:

5850 calories

Step-by-step explanation:

Answer:

They ate 17,550 calories in all

Step-by-step explanation:

325 x 3 = 975 calories for the three people in all for one day

975 x 18 = 17,550 calories in all

the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.

What is Taylor series?

The Taylor series is a representation of a function as an infinite sum of terms involving the function's derivatives at a particular point. It provides a way to approximate a function with a polynomial expression.

To find the degree 5 Taylor polynomial, denoted as T₅(x), of the function f(x) = cos(x) at a = 0, we need to compute the polynomial using the derivatives of f evaluated at x = 0.

The Taylor polynomial of degree n for a function f(x) centered at a is given by:

Tₙ(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + ... + (fⁿ(a)/n!)(x - a)ⁿ

In this case, a = 0, so the Taylor polynomial simplifies to:

T₅(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + (f⁴(0)/4!)x⁴ + (f⁵(0)/5!)x⁵

Now, let's calculate the derivatives of f(x) = cos(x) up to the 5th order:

f'(x) = -sin(x)

f''(x) = -cos(x)

f'''(x) = sin(x)

f⁴(x) = cos(x)

f⁵(x) = -sin(x)

Evaluating these derivatives at x = 0:

f(0) = cos(0) = 1

f'(0) = -sin(0) = 0

f''(0) = -cos(0) = -1

f'''(0) = sin(0) = 0

f⁴(0) = cos(0) = 1

f⁵(0) = -sin(0) = 0

Substituting these values into the Taylor polynomial formula:

T₅(x) = 1 + 0x + (-1/2!)x² + (0/3!)x³ + (1/4!)x⁴ + (0/5!)x⁵

Simplifying the expression:

T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴

Therefore, the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.

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Answer:

k750×60x=Ohio

Step-by-step explanation:

Swag like Ohio down in Ohio

Answer:

14

Step-by-step explanation:

200 / 10 = 20

20 miles a gallon

280 / 20 = 14

:)

Answer:

14 gallons

Step-by-step explanation:

200 miles takes ten gallons, and 280 is equal to 100 percent plus 40 percent of 200, and 140 percent of 10 is 14. if that makes sense

The solution is, at 500 miles, will the rental fee be the same under both plans A and B.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, 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.

here, we have,

from the given information, we get,

Plan A:   y = .2x + 75

Plan B:   y = .35x

Find an xy pair that satisfies both (intersection)

Substitute Plan B's y for Plan A

.35x = .2x + 75

.35x - .2x = 75

.15x = 75

x = 500

Hence, The solution is, at 500 miles, will the rental fee be the same under both plans A and B.

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The central limit theorem can be applied to describe the sampling distribution for the sample proportion of children who are nearsighted.

The randomization condition is met because the kindergarten has registered 161 incoming children, which is a sample randomly selected from the population of all children. The 10% condition is also met because 161 is less than 10% of the estimated population size of all children who may have nearsightedness. Finally, the success/failure condition is met because the proportion of children with nearsightedness is estimated to be 13%, which is neither extremely small nor extremely large.

Therefore, no assumptions need to be made to apply the central limit theorem in this case.

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SORRY B GFVBSDJ FS VBDF HVDFSBV FNVFDHS

In multiple regression analysis, the correlation among the independent variables is termed multicollinearity

Multicollinearity in a multivariate regression model refers to the correlations between two or more independent variables. Multicollinearity can lead to skewed or false results when a researcher or analyst attempts to determine how effectively each independent variable can be used to predict or understand the dependent variable in a specific statistical model.

It is the term which is generally used to describe the situation in which two or more explanatory variables in a multiple regression model have strong linear correlations with one another but not with the dependent variable. Many times, the creation of new dependent variables that are reliant on other variables can also result in multicollinearity.

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Answer:

The zeros of f(x)  are -3, 2 , 6

Step-by-step explanation:

f(x) is a polynomial of degree 3.

If the polynomial is not factorized we will either factorize to find the zero or use trial and error method.

Since the f(x) in the question is in the factorized form. we will have to equate each factor to zero.

f(x) = (x+3)(x-2)(x-6)

x + 3 = 0 => x = -3

x - 2 = 0 =>  x = 2

x - 6 = 0 => x = 6

Answer:0.105

Step-by-step explanation:

84-76=8

8/76=0.105

Answer:

substituting  & graphing

Step-by-step explanation:

The length of the frame the width is 22

What is the perimeter of a frame whose length is 22 inches and whose breadth is 14 inches?

The distance around an object is called the perimeter.

For instance, the yard of your home is fenced in. The perimeter is the length of the fence. Your fence is 200 feet long if the yard is 50 feet by 50 feet.

The answer to the above-mentioned difficulty is provided here.

We will search for the length since the frame's breadth is 14 inches and its perimeter is 72 inches. 2L + 2W is the perimeter formula.

Therefore, let's swap the values.

P = 2L + 2w

72 = 2L + 2(14) (14)

72 = 2L + 28

72 -28 = 2L\s44 = 2L \s22 = L

Consequently, the picture frame's length

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From the given figure the value of angle x is 40 degrees

|AC| = | CD |

Δ ( ACD ) = Δ ( DCB )

< ( BAC ) = 70 degrees

Since |AC| = | CD | then the base angles are equal, hence

< ( ADC ) =  < ( BAC ) 70 degrees. ( base angles of isosceles triangle )

< ( ADC ) + < ( BAC ) + < ( ACD ) = 180 degree ( sum of angles in a triangle)

note < ( BAC ) = < ( DAC )

< ( ACD ) = 180 - 70 - 70

< ( ACD ) = 180 - 140

< ( ACD ) = 40 degrees

If Δ ( ACD ) = Δ ( DCB ) then the angles should be equal

Δ ( ACD ) has angles:

< ( ADC )  = 70

< ( DAC ) = 70

< ( ACD ) = 40

Then Δ ( DCB ) should have angles 70, 70, and 40. The figure did not give enough information to put the angles where it should be.

Comparing with the options, only angle 40 degrees is in the option, hence the correct answer

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