Two people are trying to decide whether a die is fair. They roll it 100 times, with the results shown
21 ones, 15 twos, 13 threes, 17 fours, 19 fives, 15 sixes
Average of numbers rolled = 3.43, SD = 1.76 One person wants to make a z-test, the other wants to make a test X^2.
a. True or false: the correct test for this question with these data is the z-test. FALSE No matter what you answer above, carry out the X^2 test.

Expected frequency for each face (number) of the die= _______ (round answer to the nearest 0.1).

c. Number of degrees of freedom: df = ________

d. X^2 = ________
e. P = _________

The velocity of the ball thrown by your friend is approximately 4.17 meters per second.

To ascertain the speed of the ball, we want to utilize the condition of movement that relates distance, time, and speed increase. For this situation, we expect that the ball goes in an orderly fashion, and its speed increase is because of the power applied by your companion's toss. We can utilize the recipe:

distance = speed x time

We realize that the distance among you and your companion is 5 meters, and the time taken for the ball to travel that distance is 1.2 seconds. Hence, we can revise the equation to tackle for the speed:

speed = distance/time

Subbing the qualities, we get:

speed = 5/1.2 = 4.17 meters each second (approx.)

So the speed of the ball tossed by your companion is around 4.17 meters each second.

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Answer:

C

Step-by-step explanation:

'x=' create vertical lines which are not functions whereas

'y=' create horizontal lines which are functions

Answer:

8

Step-by-step explanation:

\(6 + 12 - 5 \times 2 + 2(8 \div 4 - 2)\)

\(6 + 12 - 10 + 2(2 - 2)\)

\(6 + 12 - 10 + 2 \times 0\)

\(6 + 12 - 10 + 0\)

\( = 8\)

Equation of a line is \(x+3y =-3\).

A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.

Given that,

Endpoints of the line segment are (\(x_{1},y_{1}\)) = (4, 1) and (\(x_{2},y_{2}\)) = (2, -5).

First find the midpoints of the given line segment.

M = \(\left(\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2}\Right)\)

    =  \(\left(\frac{4+2 }{2},\frac{1-5 }{2}\Right)\)

M   =  \((3,-2)\)

Now, Find the slope of the line :

It is perpendicular to the line with (4,1) and (2,-5)

Slope between (\(x_{1},y_{1}\)) and (\(x_{2},y_{2}\)) = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

so,

the slope between (4,1) and (2,-5)  =  \(\frac{-5-1 }{2-4 }\)

                                                         = 3

perpendicular lines have slopes the multiply to get -1

3 times m=-1

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

The equation of a line that has a slope of m and passes through the midpoints M(3,-2)  is

\(y-y_{1} =m(x-x_{1} )\)

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

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

if we want slope intercept form

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

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

If we want standard form

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

\(x+3y =-3\)

Hence, Equation of a line is \(x+3y =-3\).

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a. Differentiating the weight function with respect to t, we get:

W'(t) = 25.5(3)(-0.181)(1 - 0.181)2(-0.181')

Simplifying, we get:

W'(t) = -13.92(1 - 0.181)2(0.181')

b. Taking the second derivative of W(t) with respect to t, we get:

W''(t) = -13.92(1 - 0.181)2(0.181'')

Simplifying, we get:

W''(t) = 8.38(0.181'')

c. To find the points of inflection, we need to find the values of t for which W''(t) = 0. Since 0.181'' is always positive, W''(t) will only be zero when t = 0.

To find the corresponding W value, we can use the original weight function:

W(0) = 25.5(1 - 0.181)3 = 25.5(0.819)3 = 15.99 kg

Therefore, the point of inflection is (t, W) = (0, 15.99) years, kg.

d. To find the most rapid rate of growth, we need to find the maximum value of W'(t). We can do this by setting W'(t) = 0 and solving for t:

0 = -13.92(1 - 0.181)2(0.181')

Differentiating , we get:

0.181' = 0.181/3 = 0.06033

Substituting this value back into the expression for W'(t), we get:

W'(t) = -13.92(1 - 0.181)2(0.06033) ≈ -0.229 kg/yr

Therefore, the trout is gaining weight most rapidly at the point of inflection, and the most rapid rate of growth is approximately -0.229 kg/yr.

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Answer:

m< 3 = 180 - 93

m< 3 = 87 degrees

m< 4 = 180 - 87 - 49

m< 4 = 44 degrees

m< 2 is vertically opposite to the 49 degree angle given

m< 2 = 49 degrees

m< 1 = 180- 68 - 49

m< 1 = 63 degrees

The measure of each missing angle are; m< 1 = 63, m< 2 = 49, m< 3 = 87 and m< 4 = 44 degrees

The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

We can determine angle 3 as;

m< 3 = 180 - 93

m< 3 = 87 degrees

Also,

m< 4 = 180 - 87 - 49

m< 4 = 44 degrees

We can see that m< 2 is equal to 49-degree angle by a vertically opposite angle.

m< 2 = 49 degrees

m< 1 = 180- 68 - 49

m< 1 = 63 degrees

Hence, the measure of each missing angle are; m< 1 = 63, m< 2 = 49, m< 3 = 87 and m< 4 = 44 degrees

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Answer:

wow man this is a tough question

Answer:

please ask proper question or repost it

Fisher's Exact Test is used when there are two independent samples of categorical data, and it is a valuable tool for analyzing small sample sizes where other tests may not be appropriate.

Fisher's Exact Test is used when there are two independent samples of categorical data. This test is specifically designed to determine if there is a significant association between two categorical variables in a 2x2 contingency table.

It is commonly used when the sample size is small, which can cause issues with other statistical tests such as the chi-square test.

The two independent samples refer to two different groups or populations that are being compared. For example, we might be interested in comparing the success rates of a new drug treatment versus a placebo in a clinical trial, where success and failure are the two categories being considered.

Fisher's Exact Test calculates the probability of observing the data given the null hypothesis of no association between the variables. It does this by considering all possible arrangements of the data that have the same marginal totals. If the calculated probability is very small (typically less than 0.05), we reject the null hypothesis and conclude that there is a significant association between the variables.

In summary, Fisher's Exact Test is used when there are two independent samples of categorical data, and it is a valuable tool for analyzing small sample sizes where other tests may not be appropriate.

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The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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a) Here is a sketch of the region D:

            |\

            | \

            |  \

            |   \

            |    \

            |     \

            |      \

            |       \

   _________|________\_________

            |        \

            |         \

            |          \

            |           \

            |            \

            |             \

b) Possible way to set up this integral is:

∫[0,2π] ∫[1,2] y r dr dθ

(a) The region D is an annulus (a ring-shaped region) with inner radius 1 and outer radius 2. It is neither a type z nor a type y region.

Here is a sketch of the region D:

            |\

            | \

            |  \

            |   \

            |    \

            |     \

            |      \

            |       \

   _________|________\_________

            |        \

            |         \

            |          \

            |           \

            |            \

            |             \

(b) The integral to find the volume under the surface z = y over the region D is:

∬D y dA

where D is the region given by 1 < x² + y² < 4. One possible way to set up this integral is:

∫[0,2π] ∫[1,2] y r dr dθ

where we integrate first with respect to r, the radial variable, and then with respect to θ, the angular variable. Note that the limits of integration for θ are 0 to 2π, the full range of angles, and the limits of integration for r are the radii of the annulus

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Mean height of the students in the class = 65.7 inches

The mean height of all 12 students in the class is 66.0 inches.

So the Total height of 12 students in the class = 66 × 12

                                                                              = 792 inches

As Danielle's height = 62.1 inches

So the total height of 13 students = 792 + 62.1

                                                        = 854.1 inches

Mean of all 13 students in the class = 854.1 / 13

                                                            = 65.7 inches

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The complete question:

Mr. Zuro finds the mean height of all 12 students in his class to be 66.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 62.1 inches tall. What is the mean of the 13 students in the class?

Answer:

A=16

Step-by-step explanation:

formula is 2l+2w=A

First let's find how many kilometers the jeep traveled, by subtracting the odometer readings:

Now, to find the miles per gallon, we just need to divide the kilometers by the amount of gallons of gasoline:

So Harry got 17.8 miles per gallon with the Jeep.

The parametric equations of the line l passing through the given point and perpendicular with the plane p is x = 5 - 3t, y = -8 - 3t, and z = 4 - t.

To find the parametric equations of the line passing through point a (5,-8,4) and perpendicular to the plane p described by the equation 1x - 3y + 3z = 6, we need to first find the direction vector of the line.

The normal vector of the plane p is (1,-3,3), since the coefficients of x, y, and z in the plane equation represent the components of the normal vector.

To find the direction vector of the line, we take the cross product of the normal vector of the plane p and any vector that lies on the line. We can choose the vector (1,0,0) as lying on the line, since it is perpendicular to the normal vector of the plane.

Thus, the direction vector of the line is:

(1,0,0) x (1,-3,3) = (-3,-3,-1)

Now we can write the parametric equations of the line in vector form:

r = a + t*d

where r is the position vector of any point on the line, t is a parameter, a is the position vector of the known point on the line (5,-8,4), and d is the direction vector of the line (-3,-3,-1).

So the parametric equations of the line passing through point a (5,-8,4) and perpendicular to the plane p described by the equation 1x - 3y + 3z = 6 are:

x = 5 - 3t

y = -8 - 3t

z = 4 - t

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Answer:

looking at anwser now

Step-by-step explanation:

Answer:

a) 74.3

b) 98.8

Step-by-step explanation:

The tenth decimal place is the first place immediately to the right of the decimal point. When rounding, you first need to look at the number to the right of the place you wish to find. If the number in this spot is 5 - 9, round the number in the tenth decimal place up one unit. If the number is 0 - 4, keep the number in the tenth decimal place the same. Finally, remove all of the numbers to the right of the tenth decimal place.

a) 74.3472

        ^ tenth

The next number to the right (4) is not big enough to round up

a) 74.3

b) 98.759

         ^ tenth

The next number to the right (5) is big enough to round up

b) 98.8

Answer:

a) 74.3

b) 98.8

Step-by-step explanation:

Go to the tenths place, and check the hundredths spot. If the number in the hundredths is less than five, leave the tenths place alone. If it is greater than five, round the tenths place up.

Answer:

15 In²

Step-by-step explanation:

Area of triangle = 1/2 × base × height

1/2 × 6 × 5 = 15

The work done by the vector field F(x, y, z) = xi + 15xyj − (x + z)k on a particle moving along a line segment from (1, 4, 2) to (0, 5, 1) can be found by evaluating the line integral of F along the line segment.

To calculate the work done, we start by parametrizing the line segment as r(t) = (1 - t)i + (4 + t)j + (2 - t)k, where t varies from 0 to 1. Then, we express the line integral of F along the line segment using the dot product of F and the differential of the position vector dr.

After substituting the parametric equations for x, y, and z into the line integral, we simplify the expression and integrate it with respect to t over the interval [0, 1]. The integral involves evaluating terms such as x, xt, and constants. By performing the integration, we obtain the numerical value of the work done by vector field F on the given line segment.

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The probability that it takes 4 people to find one with type O blood is approximately 0.0938 or 9.38%.

Probability is classified into three types:

A randomly selected US adult has a 44% chance of having type O blood. This probability is denoted by the letter p.

The likelihood that the first person you choose does not have type O blood is 1-p (or 56% in this case).

To calculate the probability that it takes exactly four people to find one with type O blood, multiply the odds of the first three people not having type O blood (1-p) by the odds of the fourth person having type O blood (p).

As a result, the likelihood is:

(1-p) * (1-p) * (1-p) * p

= (0.56) * (0.56) * (0.56) * (0.44) (0.44)

= 0.0938

As a result, the probability of finding someone with type O blood is approximately 0.0938, or 9.38%.

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Answer:

B.

Step-by-step explanaBtion:

The answer would be B

(7x+4)(7x-4)

you can tell because when you expand it e.g.

49x^2 +28x - 28x -16

simplify

49x^2 - 16

equals the expression

Answer:

The answer would be B: (7x+4)(7x-4)

Answer:

5.66

Step-by-step explanation:

\(\sqrt{32}\)=5.65685

Answer:

could be wrong. but I belive its B

Step-by-step explanation:

7 X 2 = 14 x pi (3.14) = gives us 43.96. since its 4 tall. you would muiliply 43.96 x 4. it would give you 175.84.

here is the formula because I want you to understand this.

R = radius

D = 2 x radius

Pi = 3.14

C = circumference

C = Pi x (radius x 2)

The band got $300, the chess club got $100, and the environment club got $200.

What are fractions?

A fraction represents a numerical value, which defines the parts of a whole.

The band got 1/2 of the $600, which is:

1/2 x $600 = $300

So, there's $300 left to be shared between the chess club and the environment club.

The chess club got 1/3 of what was left, which is:

1/3 x $300 = $100

So, the environment club got the remaining amount:

$300 - $100 = $200

Therefore, the band got $300, the chess club got $100, and the environment club got $200.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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To find the probability that the mean salary of a person selected at random from Acme Corporation is less than 61,000, we can use the Z-score formula.

First, we need to calculate the Z-score, which measures the number of standard deviations a value is away from the mean. The formula for the Z-score is:

Z = (X - μ) / (σ / √n)

Where:
- X is the value we are interested in (in this case, $61,000)
- μ is the population mean annual salary for Acme Corporation ($63,500)
- σ is the population standard deviation (unknown in this case)
- n is the sample size (unknown in this case)

Since we don't have the population standard deviation or sample size, we cannot calculate the exact Z-score. Therefore, we cannot find the exact probability.

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Based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

The probability of a person selected at random having a salary less than $61,000 can be determined using the z-score and the standard normal distribution.

To calculate the z-score, we need to know the population standard deviation. Since it is not provided, we cannot calculate the exact probability. However, we can use the assumption that the population standard deviation is the same as the sample standard deviation.

Let's assume the sample standard deviation is $5,000.

First, we calculate the z-score:
    \(z = (x - \mu) / (\sigma / \sqrt n)\)
=> z = (61000 - 63500) / (5000 / √1)
=> z = -2500 / 5000
=> z = -0.5

Next, we find the corresponding area under the standard normal curve using a z-table or a calculator. The area to the left of -0.5 is approximately 0.3085.

Therefore, the probability that a person selected at random will have a salary less than $61,000 is approximately 0.3085 or 30.85%.

In conclusion, based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

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