3 A buoy is 30 feet from the shore. You swim 3/5 the way to the buoy. How much farther do you have to swim to reach the buoy?​

The positive integers that are relatively prime to the given numbers less than n are as follows: for n = 4, the numbers are 1 and 3; for n = 5, the numbers are 1, 2, 3, and 4; for n = 8, the numbers are 1, 3, 5, and 7; for n = 12, the numbers are 1, 5, 7.

To find the positive integers that are relatively prime to a given number n, we need to determine the numbers that do not share any common factors (other than 1) with n. This can be done by checking each number less than n and calculating its greatest common divisor (GCD) with n. If the GCD is 1, then the number is relatively prime to n.

For example, for n = 4, the positive integers less than 4 are 1, 2, and 3. The GCD of 1 and 4 is 1, while the GCD of 2 and 4 is 2, and the GCD of 3 and 4 is 1. Therefore, the numbers 1 and 3 are relatively prime to 4.

For n = 4, the numbers are 1 and 3; for n = 5, the numbers are 1, 2, 3, and 4; for n = 8, the numbers are 1, 3, 5, and 7; for n = 12, the numbers are 1, 5, 7, and 11; for n = 15, the numbers are 1, 2, 4, 7, 8, 11, 13, and 14; for n = 16, the numbers are 1, 3, 5, 7, 9, 11, 13, and 15; for n = 20, the numbers are 1, 3, 7, 9, 11, 13, 17, and 19; and for n = 25, the numbers are 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, and 24.

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A new sample size of at least 537 fish to estimate the true mean length with a margin of error of 0.5 centimeters and 95% confidence.

To determine the size of a new sample so that the true mean length is estimated with a margin of error of 0.5 centimeters with 95% confidence, we need to find the standard error of the mean and use it in the formula for the margin of error.

The formula for the margin of error is: ME = z * (σ/√n)

where z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and n is the sample size.

We can estimate the standard deviation of the population using the sample variance, which is given as 34.9.

The standard deviation is the square root of the variance, so σ = √34.9

= 5.91.

To find the standard error of the mean, we divide the standard deviation by the square root of the sample size:

SEM = σ/√n

= 5.91/√n We want the margin of error to be 0.5 centimeters, so we can set up the equation:

0.5 = z * (5.91/√n)

To solve for n, we need to know the value of z for a 95% confidence level.

This corresponds to a z-score of 1.96. Substituting this into the equation gives: 0.5 = 1.96 * (5.91/√n)

Simplifying and solving for n gives: √n = 1.96 * (5.91/0.5) √n

n =(23.18)

n = 537

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Answer:

x = -1/2

Step-by-step explanation:

Given:

Inequality 4 ≥ 2 - 4x

Find:

Value of x

Computation:

4 ≥ 2 - 4x

4x ≥ -2

x ≥ -1/2

x = -1/2

Step-by-step explanation:

The amplitude is the value that the cosine is being multiplied by.

The general equation of a sinusoid is

\( a \cos(b(x + c) ) + d\)

where a is the amplitude

\( \frac{2\pi}{ |b| } \)

is the period

-c is the phase shift

d is the midline(vertical shift)

Here the amplitude is -1/2 so b is the correct answer.

Answer:

the amplitude of the function that is y= -1/2 cos x, is 1/2.

Step-by-step explanation:

The distance between the points J=(-4, 0) and E = (4, 7) In the coordinate plane is, 10.63 units

The distance between two points in the coordinate plane can be calculated using the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

The given points

J=(-4, 0) and E = (4, 7),

we have:

x₁ = -4, y₁ = 0

x₂ = 4, y₂ = 7

Plugging in these values into the distance formula, we get:

d = √((4-(-4))² + (7-0)²)

  = √(8² + 7²)

  = √(64 + 49)

  = √113

  = 10.63 (rounded to the nearest hundredth)

So, the distance between points J and E is approximately 10.63 units.

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Answer:

\( \huge \boxed{ \boxed{ \frac{2}{3} }}\)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question we have

\(m = \frac{3 - 1}{4 - 1} = \frac{2}{3} \\ \)

We have the final answer as

\( \frac{2}{3} \\ \)

Hope this helps you

Answer:

y = 2x – 1

Step-by-step explanation:

i got a 100%

Answer:

A. y = 2x - 1

Step-by-step explanation:

y = mx + b

Plug in your values. (2 for m)

1 = 2(1) + b

Simplify.

1 = 2 + b

Subtract 2 from both sides.

-1 = b

Finally, form your equation together.

y = 2x - 1

Answer:

gsjxvsHGVSHGCZJ

Step-by-step explanation:

like you did to me

Answer:

x = -7

Step-by-step explanation:

The interior angles of a triangle should all add up to 180 degrees.

So, we set the equation up as:

(x + 52) + 75 + 60 = 180

Then solve for x:

(x + 52) + 75 + 60 = 180

(x + 52) + 135 = 180

x + 52 = 180 - 135

x = 45 - 52

x = -7

The sampling Distribution of the sample proportion of people who answer yes to the question is normal with mean p = 0.6 and standard deviation σp = 0.049.

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading. We will take a random sample of 100 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is binomial.

The binomial distribution is appropriate since there are two possible outcomes: either a person believes that Martha Stewart is guilty of obstruction of justice and fraud related to insider trading or does not believe so. The sample size is n = 100.

The probability of a person believing that Martha Stewart is guilty is p = 0.6 and the probability of a person not believing is q = 1 - p = 0.4.

The mean of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:μp = p = 0.6

The variance of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:σ²p = pq/n = (0.6)(0.4)/100 = 0.0024

The standard deviation of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:σp = sqrt(σ²p) = sqrt(0.0024) = 0.049

This standard deviation measures how much the sample proportion is likely to vary from one sample to another. The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal by the Central Limit Theorem (CLT) if the sample size is sufficiently large, which is the case here since np and nq are both greater than or equal to 10: np = (100)(0.6) = 60 and nq = (100)(0.4) = 40.

Therefore, the sampling distribution of the sample proportion of people who answer yes to the question is normal with mean p = 0.6 and standard deviation σp = 0.049.

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Answer:

AB = 11.5mm

Step-by-step explanation:

let the hypotenuse be AC = 23mm

Angle of elevation = 30degrees

Required

Opposite AB

Using the SOH CAH TOA identity

Sin theta = opp/hyp

Sin 30 = AB/AC

Sin 30  = AB/23

0.5 = AB/23

AB = 0.5 * 23

AB = 11.5mm

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Answer:

B and E

Step-by-step explanation:

^

Correlations, scatter plots, regression results, and time series analysis are generally associated with predictive analytics.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

Statistical method that links a dependent variable to one or more independent variables.

to separate and go in various direction

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The probability that the batch is accepted if it contains five defectives will be 0.812.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Here,

P(A)=(1-5/100)*(1-5/99)*(1-5/98)*(1-5/97)

=0.812

If the batch has five defects, there is a 0.812 percent chance that it will be approved.

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Answer:

3x^4

Step-by-step explanation:

Answer:

495x^10 y^5

Step-by-step explanation:

The probability of household views between 5 and 11 hours will be 0.7653. Number of hours needed in order to be in top 3% will be 13.03 hours. Probability of views more than 3 hours will be 0.9838.

a) The probability of television views between than 5 and 11 hours.

 P( 5≤X≤11) = P[ (5-μ)/σ ≤ (X-μ)/σ ≤ (11-μ)/σ]

                   = P [ (5-8.35)/2.5 ≤ z ≤ (11-8.35)/2.5)

                    = P ( -1.34 ≤ z ≤ 1.06)

                    = P ( z≤ 1.06) - P(z ≤ -1.34)

Substituting values from the z-table

   P ( 5≤X≤11) = 0.85543 - 0.09012 = 0.76531

Probability that household views between 5 and 11 hours is  0.7653.

b) Hours needed to be in top 3% of all households.

 P( X> h) = 0.03

 P[ (X-μ)/σ > (h-μ)/σ] = 0.03

P ( z >h-8.35/2.5) = 0.03

P ( z ≤ h-8.35/2.5) = 0.97

From the table

  (h - 8.35)/ 2.5 = 1.87

   h = (1.87× 2.5) + 8.35

      = 13.025 = 13.03 hours

So if the viewing time is more than 13.03, the household will be in the top 3%.

c) Probability of viewing more than 3 hours

 P(X> 3) = P[ (X-μ)/σ > (3-μ)/σ]

               = P( z < -2.14) = 0.9838

So probability the household will have views more than 3 hours will be 0.9838.

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The solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.

What is Linear Equation ?

Linear equation can be defined as equation in which highest degree is one.

We can solve for one variable using Equations #1 and #2, but not for all three variables. From Equation #2, we can solve for x in terms of y as x=5y+7. Substituting this expression for x into Equation #1 gives:

3(5y+7)+z+y=8

Simplifying this equation, we get:

16y+z=-13

We still have two unknowns, y and z, so we cannot solve for any variable using only Equations #1 and #2.

b. It is possible to solve for all three variables using Equations #1, #2, and #3. We can use the following steps to solve for the variables:

Use Equation #2 to solve for x in terms of y as x=5y-7.

Substitute this expression for x into Equation #3 to get:

3z+2(5y-7)-2y=15

Simplifying this equation, we get:

13y+3z=29

Substitute the expression for x from Step 1 into Equation #1 to get:

3(5y-7)+z+y=8

Simplifying this equation, we get:

16y+z=29

Solve for z in terms of y by subtracting the equation from Step 3 from the equation from Step 2:

(13y+3z)-(16y+z)=29-(-13)

Simplifying this equation, we get:

-3y+2z=42

Solve for z in terms of y by adding twice the equation from Step 1 to the equation from Step 4:

2(5y-7)+(-3y+2z)=42

Simplifying this equation, we get:

7y+2z=56

Solve for y by adding the equation from Step 4 to twice the equation from Step 5:

(7y+2z)+2(-3y+2z)=56+84

Simplifying this equation, we get:

5z=196

So, z=39.2. Substituting this value for z into the equation from Step 4 gives:

-3y+2(39.2)=42

Solving for y, we get y=-9.6. Finally, substituting the values for y and z into the equation from Step 1 gives:

x=5(-9.6)-7=-55.

Therefore, the solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.

c. To check if the solution found in part b holds for Equation #4, we substitute the values of x, y, and z into Equation #4 and see if the equation is satisfied:

4(-55)+5(-9.6)-2(39.2)=-3

Simplifying this equation, we get:

-220-48-78.4=-3

This equation is not satisfied, so the solution found in part b does not hold for Equation #4. Therefore, the system of equations does not have a unique solution.

Therefore, the solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.

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Answer:

29.2

Step-by-step explanation:

arctan=24/43

Answer:

The correct answer is 65.5

Step-by-step explanation:

Just took a test on DeltaMath.

Answer:

Equation of the straight line passing through the point ( 1,2 ) and having the slope

 x - √3y -1+2√3 =0

Step-by-step explanation:

Step(i):-

Given that the point (1,2) and an angle = ∝ = 30°

The slope of the line

             m = tan 30°

             \(m = \frac{1}{\sqrt{3} } }\)

Step(ii):-

Equation of the straight line passing through the point ( 1,2 ) and having the slope

 \(m = \frac{1}{\sqrt{3} } }\)

           y - y₁ = m(x-x₁)

          y - 2 = \(\frac{1}{\sqrt{3} } }\) ( x -1)

        √3(y-2) = (x-1)

⇒       √3y - 2√3 = x -1

           x - √3y -1+2√3 =0

Answer:

pruduct means multiply so 32.7x0.9=29.43

In real-life writing, objective and subjective styles often coexist, and one example of this can be seen in news articles. News reporting aims to provide objective information and present facts in a neutral manner. However, within the same article, there may be elements of subjective writing, such as the journalist's analysis, interpretation, or personal opinions.

When reporting a news event, journalists strive to convey the facts accurately and objectively. They typically present information using a neutral tone, avoiding personal bias or emotional language. The objective style is employed to ensure that readers receive unbiased information and can form their own opinions based on the presented facts.

However, even in objective news reporting, subjective elements can creep in. Journalists might include quotes from individuals involved in the story, which can introduce subjective viewpoints. Additionally, in analysis or opinion pieces within the article, journalists may express their own subjective thoughts, interpretations, or evaluations of the situation.

The coexistence of objective and subjective writing in news articles is possible because journalism aims to balance providing factual information with offering insights, context, and expert opinions. While the core of the article strives for objectivity, subjective elements can be incorporated to provide a broader understanding of the topic or to prompt critical thinking in readers.

It's essential for readers to be aware of this combination of objective and subjective styles within news articles. By recognizing the difference between factual information and the journalist's interpretation, readers can critically evaluate the content and form their own opinions based on a more complete understanding of the subject matter.

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Answer:

The inequality for the perimeter to be atleast 300 feet is

Step-by-step explanation:

\(x\geq 142\)

A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is \((-5, -12)\)  .

The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that  \(ZF = ZD + DF = 24 + 28 = 52\)  and \(FH = ZG = 30 and ZH = 36.\)

As a result, Fard ZH's perimeter is as follows:

perimeter = \(= ZF + FH + ZH + ZG\)

perimeter  \(= 52 + 30 + 36 + 30\)

perimeter  \(= 148\)

So the perimeter of Fard ZH is \(148\)  .

(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:

\(V = (xB - xA, yB - yA)\)

Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.

Plugging in the given values, we get:

\(V = (5 - 10, 2 - 14)\)

\(V = (-5, -12)\)

Therefore, The V's direction is \((-5, -12)\) .

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Answer:

x^2 + 8x + 16

Step-by-step explanation:

Given length of square x + 4.

Area of square with side S is given by \(S^2\).

Therefore are of square with side x + 4 is given by \((x + 4)^2\)

Area of square = \((x + 4)^2\\=>(x + 4)*(x + 4)\\=> x(x + 4) + 4(x + 4)\\=> x^2 + 4x + 4x + 4*4\\=> x^2 + 8x + 16\)

Thus, x2 + 8x + 16 expression represents the area of a fabric square.

Answer:

Slope: 4

Intercept: 9

Step-by-step explanation:

Hope this helped! :)

Answer:

\(\frac{11}{45}\)

Step-by-step explanation:

\(\frac{55}{225}\) ( divide numerator and denominator by 5 )

= \(\frac{11}{45}\) ← in simplest form

a fraction is in simplest form when no other number but 1 divides into the numerator and denominator.

The IRA (individual retirement account) of a 22-year-old college student, who deposits $55 into the account each month, will have a total balance at retirement. To calculate this, we need to consider the time period, the monthly deposit, and the annual percentage rate (APR).

The student plans on retiring at age 65, which means the IRA will have 65 - 22 = 43 years to grow. Since the student deposits $55 each month, we can calculate the total number of deposits over the 43-year period: 43 years * 12 months/year = 516 deposits.

To calculate the total balance at retirement, we need to consider the growth of the account due to the APR. The annual growth rate is 6%, which can be expressed as 0.06 in decimal form. To calculate the monthly growth rate, we divide the annual growth rate by 12: 0.06/12 = 0.005.

Using the formula for the future value of an ordinary annuity, we can calculate the total balance at retirement:
FV = PMT * [(1 + r)^n - 1] / r

Where:
FV = future value (total balance at retirement)
PMT = monthly deposit ($55)
r = monthly interest rate (0.005)
n = number of deposits (516)

Plugging in these values into the formula:
FV = 55 * [(1 + 0.005)^516 - 1] / 0.005

Calculating this equation, the IRA will contain $287,740.73 at retirement.

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Answer:

The money Emily spend is 324 dollars

Step-by-step explanation:

Given:

3 pairs of shorts= 25 dollars

5 tank tops = 23 dollars

1 pair of sandal = 54 dollars

2 bathing suits = 40 dollars

The total money spend on 3 pairs of shorts is 3 x 25=75

The total money spend on 5 tank tops is 5 x 23=115

The total money spend on 1 pairs of sandals =54

The total money spend on bathing suits is 2 x 40= 80

Adding them all= 75+115+54+80

                         = 324 dollars

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The amount Emily spent is $324

We are given that

3 pairs of shorts = $25

5 tank tops = $23

1 pair of sandals = $54

2 swimsuits = $40

Total amount spent on 3 pairs of shorts is 3 x 25 = 75

The total amount spent for 5 increased shirts is 5 x 23 = 115

Total amount spent on 1 pair of sandals = 54

Total amount spent on swimwear is 2 x 40 = 80

Add them all up = 75 + 115 + 54 + 80

= $324

The amount Emily spent is $324

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