Zoe has some cloth. She uses the cloth to make 12 pillowcases. Each pillowcase uses 5/8m of the cloth. She still has 5/12m cloth left. How long is the cloth?

Answer:

The probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

Step-by-step explanation:

Denote the events as follows:

X = a fisher at Clearwater Park had a fishing license

Y = a fisher at Mountain View Park had a fishing license

The two events are independent.

The information provided is:

n (X) = 48

n (X') = 32

n (Y) = 72

n (Y') = 18

Then,

N (X) = n (X) + n (X')

        = 48 + 32

        = 80

N (Y) = n (Y) + n (Y')

        = 72 + 18

        = 90

Compute the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license as follows:

\(P(X'\cap Y)=P(X')\times P(Y)\)

                 \(=\frac{n(X')}{N(X)}\times \frac{n(Y)}{N(Y)} \\\\=\frac{32}{80}\times\frac{72}{90}\\\\=0.32\)

Thus, the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

The sample space is (R, G, P, Y).(OB)

What is sample space?

A sample space is a collection  of possible outcomes of a random experiment. The sample space is represented by the symbol, “S”.  A sample space may contain a  finite number of outcomes which depends on the experiment.

You spin a spinner with 4 sections: 1 red (R), 1 green (G), 1 purple (P), and 1

yellow (Y).

So here is 4 sections

Red(R), Green (G), Purple (P), Yellow(Y)

So there are 4 sections in sample space

The sample space for one spin of the spinner is  (R, G, P, Y).

Hence, the sample space is (R, G, P, Y).

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Answer:

210

Step-by-step explanation:

You can multiply 52 by 4 which is 208.

Next, you can add that to the number 2 which is 210.

Hope this Helps!!! :)

The equation of a line is given as y = -2/3x + 7/3

The formula for calculating the equation of a line is expressed as;

y = mx + b

where;

m is the slope

b is the y-intercept

Given the coordinate points (2, 1) and (-1, 3)

m = 3-1/-1-2

m = 2/-3

m = -2/3

Determine the y-intercept

1 = -2/3(2) + b

1= -4/3 +b

b = 1 + 4/3

b = 7/3

Hence the equation of a line is given as y = -2/3x + 7/3

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After answering provided question, we can conclude that function   \(f^{-1}(y) = {(5, 10),\)\((8, 6), (9, 5), (13, 4)}\) This inverse function will take y-values as input and output x-values.

In mathematics, a function is a relationship between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are frequently represented by the variable x, while outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 depicts a linear function in which each value of x yields a distinct value of y.

To find the inverse of the function, we must first swap the x and y values before solving for y. As a result, if f(x) = y, the inverse function f-1(y) = x.

So, if we swap the x and y values, we get x = 10, 6, 5, 4 and y = 5, 8, 9, 13. Then we solve for y:

When x equals 10, y equals 5.

When x equals 6, y equals 8.

When x equals 5, y equals 9.

When x equals 4, y equals 13.

As a result, the function's inverse is:

\(f^{-1}(y) = {(5, 10),\)\((8, 6), (9, 5), (13, 4)}\)

This inverse function will take y-values as input and output x-values.

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The solutions to the nearest tenth are x = -0.1 and x = 1.3

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

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

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Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

Answer:

.41

Step-by-step explanation:

Take what  2/3 and make it into a decimal. Then do the same with the 1/4. Then you minus the biggest number from the smallest number then it gives you .41.

The directiοnal derivative οf \(f(x,y) = 2ln(x^2 + y^2)\) at the pοint (2,1) in the directiοn οf the vectοr v = (-1,2) is 0.

A directiοnal derivative shοws hοw quickly a functiοn changes in any directiοn. A fοrmula that incοrpοrates the gradient can be used tο determine the directiοnal derivative. The gradient οf a functiοn οf mοre than οne variable shοws the directiοn οf greatest change.

We must cοmpute the dοt prοduct οf the gradient οf f at (2,1) with the unit vectοr in the directiοn οf v in οrder tο determine the directiοnal derivative οf the functiοn  \(f(x,y) = 2ln(x2, + y2)\)  at the pοsitiοn (2,1) in the directiοn οf the vectοr v = (-1,2).

Then, we determine f's gradient:

Grad(f) is equal tο \((f/x, f/y) = (4x/(x2+y2), 4y/(x2+y2)\)

Hence, the gradient at lοcatiοn (2,1) is as fοllοws:

grad \((f)(2,1) = (4(2)/(2^2+1^2), 4(1)/(2^2+1^2)) = (8/5, 4/5)\)

The unit vectοr in the directiοn οf v is then lοcated:

||v|| = √((-1)²+ 2²) = √5\su = v/||v|| = (-1/√5, 2/√5)

We calculate the directiοnal derivative last.

Def = grad(f) (2,1) · u\s= (8/5)(-1/√5) + (4/5)(2/√5)\s= -8/5√5 + 8/5√5\s= 0

Hence, at pοint (2,1) in the directiοn οf the vectοr v = (-1,2), the directiοnal derivative οf f(x,y) = 2ln(x², + y²) is equal tο 0.

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Correction in point 1: Purchases of supplies for cash during December were $3,300. Supplies on hand at the end of December equal $2,800.

What is Journal Entry?

The act of recording any economic transactions is called a journal entry. An accounting journal lists transactions and displays a company's debit and credit balances. Each recording in the journal entry can be either a debit or a credit, and it can be made up of multiple recordings. The way an accounting transaction is entered into a company's accounting records is through an accounting journal entry.

This question is related to the account and finance subject.

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Answer:

9.425 or 3π

Step-by-step explanation:

arc length = 2πr(θ/360)

The angle is 90˚ as indicated by the square symbol.

ABC = 2π6(90/360) = 9.425 or 3π

The mean of the sampling distribution of the difference in sample means is -1.5 minutes.

The mean of the sampling distribution of the difference in sample means \(x^1-x^{2}\) can be calculated as follows:

μ(\(x^1-x^{2}\)) = μ\(x^{1}\)− μ\(x^{2}\)

where μ\(x^{1}\) and μ\(x^{2}\) are the means of the sampling distributions of \(x^{1}\) and \(x^{2}\), respectively.

Since \(x^{1}\) is the average of a sample of three fidget spinners with plastic bearings and \(x^{2}\) is the average of a sample of seven fidget spinners with metal bearings, we can use the population means of 2.7 minutes and 4.2 minutes, respectively:

μ\(x^{1}\) = 2.7 minutes

μ\(x^{2}\) = 4.2 minutes

So,

μ(\(x^{1}\)−\(x^{2}\)) = μ\(x^{1}\) − μ\(x^{2}\) = 2.7 minutes - 4.2 minutes = -1.5 minutes

Therefore, the mean of the sampling distribution of the difference in sample means is -1.5 minutes.

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Complete question: A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let \(x^{1}\) represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let \(x^{2}\) represent the average spinning time for these seven spinners. What is the mean μ(\(x^{1}\)−\(x^{2}\)) of the sampling distribution of the difference in sample means \(x^{1}\)−\(x^{2}\)?

The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

\(y = 20000(0.95)^5\)

Calculating the expression, we find:

\(y ≈ 20000(0.774)\)

Simplifying further, we get:

\(y ≈ 15480\)

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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Cesar initially had $2,500 in savings.

Let's solve the problem step by step.

Let's assume that the initial amount of money Cesar had is represented by "x" dollars.

According to the problem, Cesar spent 15% of his savings on a cellphone, which means he has 85% of his initial savings left. We can represent this mathematically as:

0.85x = 2,125

To find the initial amount of money Cesar had, we need to solve for x. We can do this by dividing both sides of the equation by 0.85:

x = 2,125 / 0.85

Calculating this value:

x = 2,500

Cesar initially had $2,500 in savings.

Please note that the calculations are done assuming a straightforward interpretation of the problem. If there are additional factors or context that could affect the interpretation, it's important to consider them in order to arrive at an accurate answer.

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Given:

population mean (μ) = 14 inches

population standard deviation (σ) = 1 inch

sample size (n) = 126

Find: the probability that a sample mean > 16.2 inches

Solution:

To determine the probability, first, let's convert x = 16.2 to a z-value using the formula below.

Let's plug into the formula above the given information.

Then, solve.

The equivalent z-value of x = 16.2 is z = 24.6949

Since we are looking for the probability of greater than 16.2 inches, let's find the area under the normal curve to the right of z = 24.6949.

Based on the standard normal distribution table, the area from the center to z = 24.6949 is 0.5

Since we want the area to the right, let's subtract 0.5 from 0.5.

Therefore, the probability that a sample mean of 126 men is greater than 16.2 inches is 0.

The domain of the function is given as -4√2 and 4√2

the length of the sides is 8cm

The area of this square is given as 8 x 8 = 64

each shaded triangle is a right angled triangle

1/2 *x*x = x²/2

Since we have 4 triangles we would have

4x²/2

When the triangles are cut the area would be

A = 64 - 2x²

such that 64 = 2x²

x² = 32

domain would be x =  ± √32

-4√2 , 4√2

b. The solution to the graph is contained in the image that i have attached.

c. The length of each of the sides would be √64. Remember that this is a square.

Hence the length is = 8

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Answer:

E. The parameter is μmale - μfemale and the statistic is xmale - xfemale.

Step-by-step explanation:

The sample statistic is a piece of information about the individuals or objects that were selected from a given population. The sample is just a fraction of the total population. Since it is a herculean task studying an entire population, the sample forms a manageable size that allows us to have an insight into the entire population. The sample statistics are now the piece of information about the sample being studied such as the average, mean, median, or mode.  The sample statistics have to be as specific as possible of the factors being measured. In the question, we would have to obtain the mean of both the male and female genders. This gives us an insight into the population under study.

The parameter, on the other hand, is a description of the entire population being studied. For example, we might want to determine the population mean. That is the factor we seek to measure. It is represented by the sign mu (μ).  

Answer:

$1200

Step-by-step explanation:

$4000 x .06 = $240 x 5 years = $1200

Answer:

The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.

P( x > 175) = 0.0256

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 900

The estimated proportion 'p' = 0.17

Mean of the binomial distribution

                       μ = n p = 900 × 0.17 = 153

Standard deviation of the binomial distribution

                     σ = \(\sqrt{npq} = \sqrt{900 X 0.17 X 0.83} = 11.26\)

Step(ii):-

Let 'X' be the random variable of normal distribution

mean  μ= 153 and σ = 11.26

Given X = 175

\(Z = \frac{175-153}{11.268} = 1.95\)

The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.

P( x > 175) = P( Z> 1.95)

                = 1- P( Z < 1.95)

                =   1  - ( 0.5 +A( 1.95))

               =   0.5 - A( 1.95)

              =   0.5 - 0.4744

              = 0.0256

Conclusion:-

The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.

P( x > 175) = 0.0256

The last factor she needs in her list is 11

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

Number = 220

Prime factors = 2².5.

Using the above as a guide, we have the following:

x *  2².5. = 220

Where

Last factor = x

So, we have

x *  20 = 220

Divide

x = 11

Hence, the value of x is 11

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Answer:

1/8

Step-by-step explanation:

Convert to fraction

6:48 is 6/48 as a fraction. Now simplify.

1. Find the GCD (or HCF) of numerator and denominator

GCD of 6 and 48 is 6

Divide both the numerator and denominator by the GCD

6 ÷ 6/

48 ÷ 6

Reduced fraction:

1/8

Therefore, 6/48 simplified to lowest terms is 1/8.

Answer

The sum of this sequence is  66

Answer:

A

Step-by-step explanation:

An acute angle is an angle that is less than 90 degrees.

Answer:

Step-by-step explanation:

A

Answer:

2

Step-by-step explanation:

5+1+7+x+3+2+4=x+22

x+22 is divisible by 3,

multiple of 3 are 3,6,9,12,15,18,21,24,27,...

if x=2 ,then x+22=2+22=24

so smallest number is 2

9514 1404 393

Answer:

  B.  2/3

Step-by-step explanation:

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For points (x1, y1) = (-3, -7) and (x2, y2) = (9, 1), the slope is ...

  m = (1 -(-7))/(9 -(-3)) = 8/12 = 2/3

The slope of the line is 2/3.

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Answer:

-4, -1, and 5

Step-by-step explanation:

1. The x-intercepts of a function is where the function intersects with the x-axis.

2. Given the information above, we can see that the function intersects the x-axis at (-4,0), (-1,0), and (5,0).