The circumference of a circle is 176 mm. Find the diameter, radius and area. Show your working.

The probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks is 0.1337

The probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks can be calculated using the t-distribution since the population variance is unknown. The formula for t-distribution is:

t = (x-bar - μ) / (s / √n)

where x-bar is the sample mean, μ is the hypothesized population mean (14 years), s is the sample standard deviation (the square root of the sample variance), and n is the sample size (40).

Using the given variance, we can calculate the sample standard deviation as √16 = 4. Plugging in the values, we get:

t = (13.6 - 14) / (4 / √40) = -1.118

Using a t-distribution table with degrees of freedom (df) = n - 1 = 39, we find that the probability of getting a t-value less than -1.118 is 0.1337. Therefore, the probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks is 0.1337 (rounded to four decimal places).

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The estimated radius of the circular object with an area of 40 cm² is 3.57 cm

To find the inverse function r(A), we can start by setting A = πr² and solving for r:

A = πr²

A/π = r²

r = √(A/π)

Therefore, the inverse function is r(A) = √(A/π).

To estimate the radius of a circular object with an area of 40 cm², we can simply substitute A = 40 cm² into the inverse function:

r(40) = √(40/π) ≈ 3.57 cm

Therefore, the estimated radius of the circular object with an area of 40 cm² is approximately 3.57 cm

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The number of hamburgers sold on Sunday was 89

Let's assume that the number of hamburgers sold on Sunday was x.

According to the problem, the number of cheeseburgers sold was three times the number of hamburgers sold.

Therefore, the number of cheeseburgers sold can be expressed as 3x.

The total number of hamburgers and cheeseburgers sold was 356.

Therefore, we can write an equation to represent this information:

x + 3x = 356

Simplifying the left-hand side of the equation, we get:

4x = 356

Dividing both sides by 4, we get:

x = 89

Therefore, the number of hamburgers sold on Sunday was 89, and the number of cheeseburgers sold was 3 times that, or 267.

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Answer:

A: the scale is missing

i hope this helps

Step-by-step explanation:

Answer:

the numbers are supposed to start at zero and the scale is missing

The area of the small triangle is 4 sq.cm.. The area of the medium triangle is 12 sq.cm. The area of the large triangle is 24 sq. cm.

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

Given data:

Dimensions-

area of triangle = 1/2 *base * height

The area of the small triangle = 1/2*2*4 = 4 sq.cm.

The area of the medium triangle = 1/2*4*6 = 12 sq.cm.

The area of the large triangle = 1/2*6*8 = 24 sq. cm

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Complete question:

Dimensions-

small triangle: base = 2 cm, height = 4cm

medium triangle: base = 4 cm , height = 6 cm

Larger triangle: base = 6 cm ,height = 8 cm

The area of the small triangle is_______

The area of the medium triangle is______

The area of the large triangle is______

Increasing the width of a confidence interval can be achieved by:
a) Increasing the confidence level: A higher confidence level requires a wider interval to capture the true population parameter with greater certainty.
b) Decreasing the number in the sample: A smaller sample size results in less precision and a wider confidence interval due to increased sampling variability.
c) Increasing the variance: A larger variance implies greater dispersion in the data, which requires a wider confidence interval to accommodate the increased uncertainty.

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Increasing the confidence level or decreasing the sample size would increase the width of a confidence interval. c

Conversely, decreasing the confidence level or increasing the sample size would decrease the width of the confidence interval.

Decreasing the variance of the data would also decrease the width of the confidence interval.

As it would make the data points more tightly clustered around the mean, reducing the uncertainty of the estimate.

On the other hand, a smaller confidence level or a larger sample size would result in a narrower confidence interval.

The breadth of the confidence interval would be reduced if the data's volatility was reduced.

The data points would become more closely packed around the mean, lowering the estimate's level of uncertainty.

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Since a side of the triangle below has been extended to form an exterior angle of 67°, the value of x is equal to 52°.

In Mathematics, the exterior angle theorem or postulate can be defined as a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the given triangle is equal to the measure of angle x (∠x);

∠y + 67° = 180°

∠y = 180° - 67°

∠y = 113°

∠x = 180° - (15° + 113°)

∠x = 52°

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The given information describes the measures of two angles, A and B. Angle A is represented as ∠A and has a measure of 6x-2 degrees. Angle B is represented as ∠B and has a measure of 4x+48 degrees. These measures are respectively shown in the colors #11accd and #28ae7b.

The question gives us two equations, one for angle A and one for angle B, in terms of x. We will have to solve for x and then find the measure of angle A.

To solve for x, we can set the expressions for ∠A and ∠B equal to each other and solve for x

∠A = ∠B

6x - 2 = 4x + 48

Subtracting 4x from both sides we get

2x - 2 = 48

Adding 2 to both sides we get

2x = 50

Dividing by 2 we get

x = 25

Now that we have found the value of x, we can substitute it into the expression for ∠A

∠A = 6x - 2

∠A = 6(25) - 2

By multiplying 6 with 25 we get

∠A = 150 - 2

By Subtracting we get

∠A = 148

Hence, the measure of angle A is 148 degrees.

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The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.

We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.

Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:

|u| = 20, θu = 45°

The x-component of u is given by:

ux = |u| cos(θu) = 20 cos(45°) = 10√2

The y-component of u is given by:

uy = |u| sin(θu) = 20 sin(45°) = 10√2

Therefore, the component form of vector u is:

u = 10√2 i + 10√2 j

Similarly, for vector v:

|v| = 50, θv = 180°

The x-component of v is given by:

vx = |v| cos(θv) = -50 cos(180°) = -50

The y-component of v is given by:

vy = |v| sin(θv) = 50 sin(180°) = 0

Therefore, the component form of vector v is:

v = -50 i + 0 j

The component form of the sum of u and v is given by the sum of their x- and y-components:

u + v = (10√2 - 50) i + (10√2 + 0) j

Simplifying, we get:

u + v = (10√2 - 50) i + 10√2 j

Therefore, the component form of the sum of u and v is:

u + v = (10√2 - 50) i + 10√2 j

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The question is -

Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.

| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.

The sample may not be representative of the population's preferences for frozen desserts.

Sampling technique that Keziah is using is convenience sampling. Convenience sampling is a non-probability sampling technique.

The researcher selects the easiest and most convenient individuals to participate in the study.

Keziah is simply surveying shoppers who are exiting a grocery store on the west side of her town without any predetermined criteria for selection.

As a result, the sample may not be representative of the population's preferences for frozen desserts.

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The population of unionid mussels start decreasing approximately at the rate of 75% after zebra mussels were introduced .

The change occurs as zebra mussels consuming almost all the resources available  into the Hudson River.

Change in the population of the unionid mussels and zebra mussels over the course of six years are as follow,

population of unionid mussels in 1991 in number per square meter

= 8

Then in the year 1994 it become 3 number per square meter

And finally in the year 1994 it become 2 number per square meter

Change in population of unionid mussels from 1991 to 1997

= [( 2 - 8 )/ 8] × 100

= -75%

Negative sign indicate that decrease in the population.

Now ,

Change in population of zebra mussels is given by,

In 1991 in number per square meter = 4

In 1994 in number per square meter = 1,329

In 1997 in number per square meter = 3,181

Change in population of zebra mussels from 1991 to 1997

= [( 3181 - 4 )/ 4] × 100

= 79425%

There is increase in the population of zebra mussels in thousands.

Reason of change is zebra mussels introduced into the Hudson River

and they eating almost all the resources available in the area.

Zebra mussels consumes large amount of phytoplankton and other small organisms available in the water .

Due to lack of resource availability unionid mussels population decreasing year by year.

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The above question is incomplete, the complete question is:

Unionid mussels are native to the Hudson River in New

York State. In the early 1990s, zebra mussels were

introduced into the Hudson River. The table shows the

number of unionid mussels and zebra mussels over the

course of six years.

How did the population of unionid mussels change

after zebra mussels were introduced? Why did this

change occur?​

attached data.

To solve for x, we can combine like terms on the left side of the equation:

0.35x + 0.40x + 0.05x + 1.2 = 7.12

0.8x + 1.2 = 7.12

Subtracting 1.2 from both sides:

0.8x = 5.92

Dividing both sides by 0.8, we get:

x = 7.4

Therefore, the value of x is actually 7.4

Answer:

191 ounces at the end of 12 weeks

Step-by-step explanation:

A sequence is arithmetic sequence when the first differences are all the same non-zero number.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.

As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.

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The probability that the mean annual salary of a random sample of 64 teachers from state X is less than $52,000 is approximately 0.005 or 0.5%.

The sampling distribution of the mean is normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Here, we are given that the population mean is $54,000 and the population standard deviation is $5,000. We are also told that the sample size is n = 64.

To find the probability that the mean annual salary of a random sample of 64 teachers is less than $52,000, we need to standardize the sample mean using the sampling distribution of the mean.

Z = (x' - μ) / (σ / √n)

where x' is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

Z = (52,000 - 54,000) / (5,000 / √64)

= -2.56

We can then look up the probability of a standard normal variable being less than -2.56 using a standard normal table or calculator, which gives us a probability of approximately 0.005.

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Complete question is:

The annual salary of teachers in a certain state X has a mean of $54,000 and standard deviation of σ = $5,000. What is the probability that the mean annual salary of a random sample of 64 teachers from this state is less than $52,000?

The number of students that would be expected to be unable to complete the exam in the allotted time is 8 students.

To find the number of students who would be unable to complete the exam in the allotted time, we need to calculate the number of students who take more than 90 minutes to complete the exam.

First, we calculate the z-score for the cutoff point of 90 minutes:

z = (90 - 80) / 10 = 1

Using a standard normal distribution table, we find that the probability of a student taking more than 90 minutes is approximately 0.1587.

Therefore, the expected number of students who would be unable to complete the exam in the allotted time is:

0.1587 x 50 = 7.935

Rounding up to the nearest integer, we can expect 8 students to be unable to complete the exam in the allotted time.

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The complete question is :

If a class of 50 students has an examination period of 90 minutes, and the average time a student takes to complete the exam is 80 minutes with a standard deviation of 10 minutes, how many students would be expected to be unable to complete the exam in the allotted time?

The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.

We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".

Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:

|r1 - r2| = √(61) / 3

The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.

We can express the difference between the roots in terms of the sum and product of the roots as follows:

r1 - r2 = √((r1 + r2)² - 4r1r2)

Substituting the expressions we obtained earlier, we have:

r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))

Simplifying, we get:

r1 - r2 = √((25 / a²) + (12 / a))

Taking the absolute value of both sides, we get:

|r1 - r2| = √((25 / a²) + (12 / a))

Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:

√((25 / a²) + (12 / a)) = √(61) / 3

Squaring both sides and simplifying, we get:

25 / a² + 12 / a - 61 / 9 = 0

Multiplying both sides by 9a², we get:

225 + 108a - 61a² = 0

Solving this quadratic equation for "a", we get:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)

Since "a" must be positive, we take the positive root:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83

Therefore, the value of "a" is approximately 1.83.

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The question is -

Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?

The relative frequency of spinning a 1 is 0.32 or 32%.

The given table shows the results of spinning a spinner 50 times. The outcomes of the spins are listed in the first column, and the frequencies are listed in the second column. To find the relative frequency of spinning a 1, we need to divide the frequency of spinning a 1 by the total number of trials (50).

According to the table, the frequency of spinning a 1 is 16. Therefore, the relative frequency of spinning a 1 can be calculated as follows:

Relative frequency of spinning a 1 = (frequency of spinning a 1) / (total number of trials)

Relative frequency of spinning a 1 = 16 / 50

Relative frequency of spinning a 1 = 0.32 or 32%

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The area of the region is 6 square unit.

The base of the triangle is the distance between the x-coordinates where the curves y = √x and y = −x + 6 intersect, which is 2. The height of the triangle is the distance between the y-coordinate where y = 0 intersects the y-axis and the y-coordinate where the line y = −x + 6 intersects the y-axis. This distance is 6.

Therefore, the area of the region bounded by the curves y = √x, y = −x + 6, and y = 0 is:

Area = 1/2 * base * height

    = 1/2 * 2 * 6

    = 6

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The variance is equal to the squared value of the standard deviation.(Option a)

The variance is a measure of how spread out a set of data is. It is calculated by taking the average of the squared differences of each data point from the mean. The standard deviation, on the other hand, is the square root of the variance and measures the spread of data in relation to the mean.

Therefore, the variance is equal to the squared value of the standard deviation. Mathematically, Var(X) = σ^2, where Var(X) is the variance and σ is the standard deviation.

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Answer:

Step-by-step explanation:

a) The system of equations modeling this scenario is as follows:

C = 11.50 + 0.9n

C = 13.25 + 0.55n.

b) The number of toppings where the cost is the same at either Pizza Palace or Tasty Pizza is 5.

What is a system of equations?

A system of equations is two or more equations solved concurrently.

A system of equations is also called simultaneous equations because the equations are solved at the same time or simultaneously.

                              Pizza Palace    Tasty Pizza

Pizza cost per unit       $11.50             $13.25

Topping cost per unit  $0.90              $0.55

Let the number of toppings = n

Let the total cost for the pizza at each pizza place = c

Equations:

The total cost at Pizza Palace C = 11.50 + 0.9n... Equation 1

The total cost at Tasty Pizza, C = 13.25 + 0.55n... Equation 2

For the total cost, c, to be the same at the pizza places, Equation 1 must equate Equation 2:

That is, C = C.

Substituting the values of C:

11.50 + 0.9n = 13.25 + 0.55n

0.35n = 1.75

n = 5

The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.

An equation is a mathematical statement that shows that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal is usually to solve for the value of the variable that makes the equation true.

In the given question,

The equations in which 8 is a solution are:

x - 4 = 8 (which simplifies to x = 12)

2x = 16 (which simplifies to x = 8)

x/2 = 16 (which simplifies to x = 32)

x/8 = 1 (which simplifies to x = 8)

Therefore, the correct answers are:

x - 4 = 8

2x = 16

x/2 = 16

x/8 = 1.

The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.

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x² - 16x + 64 = 0 is the equation whose solution is 8.

How to check for which equations is 8 a solution?

To check if 8 is a solution for each equation, we substitute x = 8 into each equation and see if the equation is true or not.

x + 6 = 8 + 6 = 14

and

2x + 2 = 2(8) + 2 = 18, which is not equal to the value of (x+6).

Therefore, 8 is not a solution to this equation.

4x - 4 = 4(8) - 4 = 28,

and

10 - 2x = 10 - 2(8) = -6, which is not equal to 28.

Therefore, 8 is not a solution to this equation.

2x - 4 = 2×8-4 = 12

and

3x-24 = 3×8-24 = 0 which is not equal to 12. Therefore, 8 is not a solution to this equation.

Now,

x² - 16x + 64 = 0 (which can be factored as (x-8)² = 0)

x = 8 (which is always true)

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Correct question is "For which equations is 8 a solution? Select the correct answers from the following,

1) x + 6 = 2 x + 2

2) 10 - 2x = 4 x - 4

3) 2 x-4 = 3 x - 24

4) x² - 16x + 64 = 0

The area of the rectangle is 104 m², area of the triangle is 15 m², and area of the shaded region is equal to 74 m².

The shaded region is the remaining area in the rectangle which is outside the triangle, so it is derived by subtracting the area of the triangle from the area of the rectangle as follows:

area of the rectangle = 13 m × 8 m

area of the rectangle = 104 m²

area of the triangle = 1/2 × 5 m × 6 m

area of the triangle = 15 m²

area of the shaded region = 104 m² - 15 m²

area of the shaded region = 89 m²

Therefore, the area of the rectangle is 104 m², area of the triangle is 15 m², and area of the shaded region is equal to 74 m².

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Approximately 0.357 or 35.7% of customers require more than 12 minutes to check out.

Since the checkout times are exponentially distributed with a mean of 5.5 minutes, we can use the exponential distribution formula to find the probability that a customer will take more than 12 minutes to check out:

P(X > 12) = 1 - P(X ≤ 12)

where X is the checkout time.

To find P(X ≤ 12), we can use the cumulative distribution function (CDF) of the exponential distribution, which is:

F(x) = 1 - e^(-λx)

where λ is the rate parameter of the distribution. For an exponential distribution with mean μ, the rate parameter λ is equal to 1/μ.

So, in our case, λ = 1/5.5 = 0.1818, and we can calculate P(X ≤ 12) as:

P(X ≤ 12) = F(12) = 1 - e^(-0.1818 × 12) ≈ 0.643

Therefore, the probability that a customer will take more than 12 minutes to check out is:

P(X > 12) = 1 - P(X ≤ 12) ≈ 1 - 0.643 ≈ 0.357

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Answer:

Step-by-step explanation:

first you divide the shape into 3 parts ;a big triangle, and 2 little squares

after that to get the height of the triangle i gotten by adding

3+5+2+6=16yd

area of a triangle =1/2 × b×h

area =1/2×7×16

area=112/2

area=56yd²

small squre 1=

area=5×5

=25yd²

area of small rectangle=

area=LB

=3×2

=6yd²

total area =triangle+square+rectangle

=56+25+6

TA=87yd²

The drive-thru with typically more wait time is Burger Quick, because it has a larger median. The Option A.

The median is a measure of central tendency that represents the middle value of a set of data. In this case, the median wait time at Burger Quick is 15.5 minutes, while the median wait time at Super Fast Food is 12 minutes.

This indicates that, on average, customers at Burger Quick experience a longer wait time compared to customers at Super Fast Food. The larger median at Burger Quick suggests that there may be some longer wait times skewing the data towards the higher end which could be due to various factors such as slower service, or other operational issues at Burger Quick resulting in a longer wait time for customers at their drive-thru.

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As a result, the response is A .The number of dollars it costs to rent the bowling lane for 3 hours.

The US, Canada, Australia, and some nations in the Pacific, Caribbean, Southeast Asia, Africa, and South America all use the dollar as their primary unit of exchange It is a type of paper money, currency, and monetary unit used in the United States that is equivalent to 100 cents

The total cost (in dollars) for renting a bowling alley for x hours is represented by the function b(x) = 3x + 15.

We change x in the function to 3 to obtain b(3).

B(3) = 3(3) + 15 = 9 + 15 = 24 is the result.

Therefore, b(3) is the amount of money required to rent the bowling alley for three hours.

As a result, the response is A.

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Answer: 2(n6)

And true states are

The two operations are mulitplication and substraction

The constants are 2 and 6

The expression is written as  2(n-6)

Step-by-step explanation:

Answer:

A,C,D,E should be correct.

A. Replace “a number” with the variable, n.

C. The two operations are multiplication and subtraction.

D. The constants are 2 and 6.

E. The expression is written as 2(n – 6).

hope this helped!

You would travel 200 kilometers in 2.5 hours along the Old Geelong Road if you drove at the speed limit of 80 km/h.

If the speed limit along the Old Geelong Road is 80 km/h, it means that you are not allowed to drive faster than 80 km per hour on this road. To find the distance you would travel in 2.5 hours, you need to know how far you can travel in one hour at this speed.

Since the speed limit is 80 km/h, you can travel 80 kilometers in one hour. Therefore, in 2.5 hours, you would travel:

Distance = Speed × Time

Distance = 80 km/h × 2.5 h

Distance = 200 km

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