a triangle has side lengths of a, b, and c centimeters. does each angle in the triangle measure less than 90 degrees?

The best description of the the slope would be D. The slope is 0.8 this means for every 10 hours practiced, the number of baskets scored when up by 8.

In mathematics, a line or curve's steepness is measured by its slope. This indicates the extent of its inclination or transformation. The line or curve increases when moving from left to right if its slope is positive while it reduces when moving in the opposite direction if its slope is negative. A horizontal change with no incline is implied by a zero slope.

In context of this problem therefore, the slope would be the number of baskets made per hour which is 0. 8 baskets. In 10 hours therefore, the baskets would be:

= 0. 8 x 10

= 8 baskets

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Answer:

A

Step-by-step explanation:

y² - 18y + 77

consider the factors of the constant term (+ 77) which sum to give the coefficient of the y- term (- 18)

the factors are - 11 and - 7 , since

- 11 × - 7 = + 77 and - 11 - 7 = - 18 , then

y² - 18y + 77 = (y - 11)(y - 7) ← in factored form

The length of the rectangle is 18 meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Width).

In this case, we are given that the perimeter is 54 meters and the width is 9 meters. We can substitute these values into the formula and solve for the length:

54 = 2 * (Length + 9).

Dividing both sides by 2:

27 = Length + 9.

Subtracting 9 from both sides:

Length = 27 - 9 = 18.

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The radius of the cylinder is approximately 5.25 cm.

We are given the area of the curved surface of a solid circular cylinder, which is 165 cm² (not cm³, as area is measured in square units), and the height of the cylinder, which is 5 cm. We need to find the radius.
The formula for the lateral (curved) surface area of a cylinder is:
Area = 2πr × h
where Area is the lateral surface area, r is the radius, and h is the height of the cylinder. We can plug in the given values and solve for the radius:
165 cm² = 2πr × 5 cm
Divide both sides by 10 (2 × 5):
16.5 cm² = πr
Divide both sides by π to solve for the radius:
r ≈ 16.5 cm² / π ≈ 5.25 cm
So, the radius of the cylinder is approximately 5.25 cm.

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The exact area of the region is 12 square units.

The Riemann sum for the area of the triangle is [tex]A = B\times \sum (1-\frac{h}{H} ) \Delta h[/tex]

The integral that gives the area is [tex]A = B[\int\limits^H_0 {} \, dh - \frac{1}{H} \int\limits^H_0 {h} \ dh[/tex] where a = 0 and b = h,

The exact area of the region is 12 square units.

The Riemann sum of the triangle is described by the following formula:

[tex]A = \sum b(h)\Delta h[/tex].............(i)

Where:

b(h) - Base of the rectangle.

Δh - Height of the rectangle.

A - Area of the rectangle.

Now we derive an expression for the base of the rectangle in terms of the base and height of the triangle:

[tex]b(h) / B = H-h / H[/tex].............(ii)

Where:

B - Base of the triangle.

H - Height of the triangle.

h - Position of the rectangle within the triangle.

Using the equations 1 and 2, we obtain a Riemann sum for the area of the triangle:

[tex]A = B\times \sum (1-\frac{h}{H} ) \Delta h[/tex]...............(3)

The integral that gives the area of the triangle is based on (3):

[tex]A = B[\int\limits^H_0 {} \, dh - \frac{1}{H} \int\limits^H_0 {h} ]\ dh[/tex]

Now we obtain the exact expression by integration:

[tex]A = B. [(H-0) - \frac{1}{2H} (H^2-0^2)]\\\\\\A = B\times H[/tex]

If we know that, B = 3, and H = 8, then the exact area of the region is:

A = 1/2 × 3 × 8

Hence the exact area of the region is 12 square units.

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The point estimate of the population proportion is 0.565.

The point estimate of the population proportion is the proportion of the sample that supports strengthening state laws regarding child safety restraints in vehicles.

Point estimate = (number of individuals in sample who support the strengthening of laws) / (total number of individuals in the sample)

Point estimate = 1247 / 2208

Point estimate ≈ 0.564 or 56.4% (rounded to one decimal place)

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Therefore, the approximate probability that at least 25 of the 100 American men are shorter than 68 inches is 0.772.

Assuming that the heights of American men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, we can use the normal approximation to the binomial distribution to find the probability that at least 25 of the 100 men are shorter than 68 inches.

Let X be the number of men shorter than 68 inches in a sample of 100 men. Then X follows a binomial distribution with parameters n = 100 and p = P(X < 68), where P(X < 68) is the probability that a randomly chosen American man is shorter than 68 inches.

Using the standard normal distribution, we can find the probability P(Z < (68 - 69)/2.8) ≈ 0.382, where Z is a standard normal random variable. Therefore, we can approximate the probability P(X ≥ 25) as:

P(X ≥ 25) = 1 - P(X < 25)

= 1 - binomcdf(100, 0.382, 24)

≈ 0.772

where binomcdf(100, 0.382, 24) is the cumulative distribution function of the binomial distribution with parameters n = 100 and p = 0.382 evaluated at x = 24.

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The surface integral of xz over the portion x^2 y^2 z^2=a^2 is zero.

To evaluate the surface integral of xz, we need to determine the surface over which the integration is to be performed. The given equation represents an ellipsoid centered at the origin. We can parameterize this surface using spherical coordinates as follows:

x = a sin(phi) cos(theta)

y = a sin(phi) sin(theta)

z = a cos(phi)

where 0 <= phi <= pi and 0 <= theta <= 2pi.

Now, we need to find the unit normal vector to the surface, which is given by:

n = (x/a^2, y/a^2, z/a^2)

The surface integral of xz can be expressed as:

∫∫(xz) ds = ∫∫(xz) ||n|| dA

where ||n|| is the magnitude of the unit normal vector and dA is the surface area element.

Substituting the values of x, y, z, and ||n||, we get:

∫∫(xz) ds = ∫∫(a^2 sin(phi) cos(phi) sin(theta) cos(theta)) a^2 sin(phi) d(phi) d(theta)

Simplifying this expression, we get:

∫∫(xz) ds = 0

Therefore, the surface integral of xz over the given surface is zero.

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The maximum profit the company can make in a week is $1900. The maximum profit is $1900.

To find the maximum profit the company can make in a week, we need to determine the optimal number of hours to allocate to each activity. This can be done by using linear programming, where we maximize the objective function subject to certain constraints.

Let x be the number of hours allocated to activity A, y be the number of hours allocated to activity B, and z be the number of hours allocated to activity C.

The objective function to maximize is:

P = 15x + 20y + 30z

Subject to the following constraints:

x ≤ 40

y ≤ 30

z ≤ 20

2x + y + z ≤ 80

where the first three constraints limit the number of hours available for each activity, and the fourth constraint limits the total number of hours available in a week.

Solving this linear programming problem, we get the optimal solution as x = 20, y = 30, and z = 20. Therefore, the maximum profit the company can make in a week is:

P = 15x + 20y + 30z = 15(20) + 20(30) + 30(20) = $1900

Rounded to the nearest dollar, the maximum profit is $1900.

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The general formula for calculating the doubling time is:

doubling time = ln(2) / growth rate

Here, the growth rate can be found from the given equation as:

q = 100e^(0.5x)

Taking the natural logarithm of both sides:

ln(q/100) = 0.5x

Solving for x:

x = 2 ln(q/100)

The growth rate is therefore 0.5, and the doubling time can be calculated as:

doubling time = ln(2) / 0.5 = 1.3863

Rounding to 4 decimal places, the doubling time is approximately 1.3863 units of x.

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For a normal distribution with a mean equal to µ = 3 and standard deviation equal to σ = 2, P(x>4) : 0.31. The correct option is (b)

We can use the standard normal distribution and the Z-score formula to solve this problem:

Z = (x - µ) / σ

where Z is the standard normal random variable, x is the value we're interested in, µ is the mean, and σ is the standard deviation.

In this case, we want to find P(x > 4) for a normal distribution with µ = 3 and σ = 2. We first convert 4 to a Z-score:

Z = (4 - 3) / 2 = 0.5

Using a standard normal distribution table or a calculator, we can find the probability that Z is greater than 0.5:

P(Z > 0.5) = 1 - P(Z < 0.5) ≈ 0.3085

Therefore, the answer is (b) 0.31 (rounded to two decimal places).

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The statement 'For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H0: µ = µ0 is (X - µ0)/(σ/√n) when X is the sample mean' is true as in this case Z-test can be used.

For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H0: µ = µ0 is indeed (X - µ0)/(σ/√n) when X is the sample mean. This is because when the population variance is known, we use the Z-test to determine if the null hypothesis should be accepted or rejected. The Z-test statistic formula is given by Z = (X - µ0)/(σ/√n), where X is the sample mean, µ0 is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.

Note: The question is incomplete. The complete question probably is: True or False: For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H0: µ = µ0 is (X - µ0/(σ/√n) when X is the sample mean.

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The Maclaurin series for the following function determines its radius of convergence r. f(x) = ln 1 x 1 − x converges on the interval (-1, 1).

To find the Maclaurin series for f(x) = ln(1-x)/(1-x), we first note that this function is equal to the derivative of ln(1-x) with respect to x. Therefore, the Maclaurin series for f(x) converges on the interval (-1, 1).

Using the power series expansion for ln(1-x), we have:

ln(1-x) = -x - x^2/2 - x^3/3 - ...

f(x) = (1/(1-x))(-1 - x - x^2/2 - x^3/3 - ...) * (1/(1-x))

f(x) = -1 - 2x - 3x^2 - 4x^3 - ...

Since the limit is equal to 1, the radius of convergence is:

r = 1/lim n->infinity |a(n+1)/a(n)| = 1/1 = 1

Therefore, the Maclaurin series for f(x) converges on the interval (-1, 1).

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The term with its description is: 1- comprehensive insurance -(2), 2. Premium - 4, 3. Liability insurance -3 -4. Collision insurance-1.

What is liability insurance?

Liability insurance is a type of insurance coverage that protects individuals and businesses from financial losses resulting from claims or lawsuits filed against them for alleged negligence or wrongdoing. It provides coverage for legal expenses, settlement costs, and judgments that may arise if the insured party is found legally responsible for causing bodily injury, property damage, or other harm to a third party.

Premium: The premium refers to the amount of money an individual or business pays to an insurance company in exchange for insurance coverage. It is typically paid on a regular basis, such as monthly, quarterly, or annually.

Collision Insurance: Collision insurance is a type of auto insurance coverage that helps pay for repairs or replacement of a vehicle if it is damaged in a collision, regardless of who is at fault. It covers the costs of repairing or replacing the insured vehicle up to its actual cash value, minus the deductible.

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the complete question is:

Drag and drop to match the term with its description.1. Comprehensive insurance2. Premium3. Liability insurance4. Collision insurance

1-Covers the cost of your car's collision damage.

2-Covers damage caused by fire, theft, vandalism, and weather

3. Protects you against harm to other people's bodies and possessions.

4- The insurance premiums you pay

Answer:

Step-by-step explanation:

2 squares ( ONLP && PLKH )
2 triangles ( NML && HKJ )

1 semi-circle ( PH )

Area between the curves by integrating with respect to x and y is 20 units.

To find the area between the curve x = y² - 2  and x = 2y with respect to x.

On finding the points of intersection between the two curves by equating them equal

y² - 2 = 2y

y²- 2y - 2 = 0

On solving with the help of quadratic formula we get y = -0.732 , 2.732 and x = -2 , 4.

For integrating with respect to x, we have to find the limits of integration.

Lower limit will be -2 which is  leftmost point of intersection of x-coordinate  and upper limit will be 4 which is rightmost point of intersection of x-coordinate

Integrating x = y² - 2 from x = -2 to x = 4 , we get

[tex]\int\limits^{4}_{-2} {(y^{2}-2) } \, dx[/tex]

= [tex][ \frac{y^{3}}{3} -2y]\left {{ 4} \atop {-2}} \right.[/tex]

= 20

To find the area between the curve x = y² - 2  and x = 2y with respect to y.

For integrating with respect to y, we have to find the limits of integration.

Lower limit will be[tex][ \frac{2y^{2}}{2} ]\left {{2.732} \atop { -0.732}} \right.[/tex] which is  leftmost point of intersection of y-coordinate and upper limit will be 2.732 which is rightmost point of intersection of y-coordinate.

Integrating x = 2y from y = to y = 2.732, we get

    [tex]\int\limits^{2.732}_{-0.732} {2y} \, dy[/tex]

= 20

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The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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The answer is (b) 0.56. X and Y are independent random variables with pX (0) = 0.5, pX (1) = 0.3, pX (2) = 0.2 and pY (0) = 0.6, pY(1)=0.1,pY(2)=0.25andpY(3)=0.05.

Since X and Y are independent random variables, we can find the probability of their joint event by multiplying their individual probabilities. Therefore, we have:

P(X ≤ 1 and Y ≤ 1) = P(X = 0)P(Y = 0) + P(X = 1)P(Y = 0) + P(X = 0)P(Y = 1) + P(X = 1)P(Y = 1)

Substituting the given probabilities, we get:

P(X ≤ 1 and Y ≤ 1) = (0.5)(0.6) + (0.3)(0.6) + (0.5)(0.1) + (0.3)(0.1)

P(X ≤ 1 and Y ≤ 1) = 0.30 + 0.18 + 0.05 + 0.03

P(X ≤ 1 and Y ≤ 1) = 0.56

Therefore, the answer is (b) 0.56.

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The correct answer is c) 03: 4.

Currently, the ratio of phone agents to chat agents is 5:2, which means for every 5 phone agents, there are 2 chat agents. If there are 250 phone agents, then there are (5/2)*250=625 chat agents.

If the company reduces the phone agents to 50, then the total number of agents will be 50 phone agents + 625 chat agents = 675 agents. The new ratio will be 50:625, which simplifies to 1:12.5.

To invert the ratio, we need to flip it and simplify it. The inverted ratio will be 12.5:1, which simplifies to 25:2.

Therefore, the new ratio after reducing the phone agents to 50 will be 03:04.

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To derive the least-squares fit for the model y = a1x + a2x^2 with a zero intercept, we need to minimize the sum of squared residuals. Let's denote the observed data points as (xi, yi) for i = 1 to n.

The objective is to find the values of a1 and a2 that minimize the following sum of squared residuals:

SSR = ∑(yi - (a1xi + a2xi^2))^2

To find the minimum, we differentiate SSR with respect to a1 and a2 separately and set the derivatives equal to zero.

Partial derivative with respect to a1:

∂SSR/∂a1 = -2∑(yi - (a1xi + a2xi^2))*xi = 0

Partial derivative with respect to a2:

∂SSR/∂a2 = -2∑(yi - (a1xi + a2xi^2))*xi^2 = 0

Expanding the above equations:

∑(yixi) - a1∑(xi^2) - a2∑(xi^3) = 0 ------ (1)

∑(yixi^2) - a1∑(xi^3) - a2∑(xi^4) = 0 ------ (2)

Now, let's solve these equations to find the values of a1 and a2.

From equation (1):

a1∑(xi^2) + a2∑(xi^3) = ∑(yi*xi) ------ (3)

From equation (2):

a1∑(xi^3) + a2∑(xi^4) = ∑(yi*xi^2) ------ (4)

We can express equations (3) and (4) in matrix form as:

| ∑(xi^2) ∑(xi^3) | | a1 | = | ∑(yixi) |

| ∑(xi^3) ∑(xi^4) | | a2 | = | ∑(yixi^2) |

Solving this system of linear equations will give us the values of a1 and a2.

Once a1 and a2 are determined, we have the least-squares fit of the model y = a1x + a2x^2 with a zero intercept.

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The given statement "To perform a one-way ANOVA, the populations do not need to be normally distributed" is false because the populations should be normally distributed for a one-way ANOVA to provide accurate results.

One-way ANOVA (Analysis of Variance) is a statistical method used to compare the means of three or more groups to determine if there are any significant differences between them.

In order to perform a one-way ANOVA, certain assumptions must be met, and one of these assumptions is that the populations from which the samples are drawn should be normally distributed.

When the populations are normally distributed, it ensures that the results of the one-way ANOVA are valid and reliable. If the assumption of normality is not met, the conclusions drawn from the one-way ANOVA may be incorrect, and alternative non-parametric tests, such as the Kruskal-Wallis test, may be more appropriate.

So, the given statement is false.

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The expected value as per the probability is $22.75

To calculate the expected value of s1, we need to multiply each payoff by its corresponding probability and then sum the products:

EV(s1) = ($10 x 0.65) + ($20 x 0.65) + ($30 x 0.65) = $22.75

Similarly, we can calculate the expected values of s2 and s3:

EV(s2) = ($5 x 0.15) + ($50 x 0.15) = $7.50

EV(s3) = ($15 x 0.20) + ($25 x 0.20) = $8.00

Now that we have calculated the expected values of each option, we can determine the optimal decision by choosing the option with the highest expected value. In this case, the optimal decision is s1, since it has the highest expected value of $22.75.

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a. The probability that Miami will be hit by a hurricane in any given year can be calculated as the inverse of the historical frequency of hurricane hits, which is 1/25. Therefore:

Probability of Miami being hit by a hurricane in any given year = 1/25

b. The probability that Miami will be hit by hurricanes in both of the next two consecutive years can be calculated as the product of the individual probabilities, assuming that the occurrence of hurricanes in different years is independent. Therefore:

Probability of Miami being hit by hurricanes in both of the next two consecutive years = (1/25) * (1/25) = 1/625

c. The probability that Miami will be hit by hurricanes in either the next year or the year after can be calculated as the sum of the probabilities of each event occurring, minus the probability of both events occurring (since they are not mutually exclusive). Therefore:

Probability of Miami being hit by hurricanes in either the next year or the year after = (1/25) + (1/25) - [(1/25) * (1/25)] = 48/625

d. The probability that Miami will be hit by at least one hurricane in the next seven years can be calculated using the complement rule: the probability of no hurricanes in seven years is (24/25)^7, so the probability of at least one hurricane is 1 minus that value. Therefore:

Probability of Miami being hit by at least one hurricane in the next seven years = 1 - (24/25)^7 ≈ 23.071% (rounded to three decimal places)

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The angle hat has a measure of 46° is angle RWS (∠RWS)

From the question, we are to determine the angle that has the given measure.

From the given information,

The given measure is 46°.

Now, we will determine the angle that has a measure of 46°

From the vertical angles theorem, we know that

"A pair of vertically opposite angles are always equal to each other"

When two lines intersect each other, the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

In the given diagram, angle NWP and angle RWS are vertical angles.

Thus,

m ∠NWP = m ∠RWS

From the given information

m ∠NWP = 46°

Therefore,

m ∠RWS = 46°

Hence,

∠RWS has a measure of 46°

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To determine the sample size required to estimate the population mean with a 97% level of confidence and a margin of error of 0.20 lb., we need to use the formula:

n = (Zα/2 * σ / E)²

where:

n = sample sizeZα/2 = the z-score corresponding to the desired level of confidence (97% in this case) and can be found using a standard normal table or calculator.

level of confidence, Zα/2 is approximately 2.17.

σ = the population standard   deviation    (if known) or an estimate of it from a pilot study or a similar population.E = the margin of error, which is given as 0.20 lb. in this case.

Since we do not have any information about the population standard deviation, we can use a conservative estimate of 1 lb. for σ.

Plugging in the values, we get:

n = (2.17 * 1 / 0.20)² = 297.64

Rounding up to the nearest whole number, we need a sample size of n = 298 to be 97% confident that the sample mean is within 0.20 lb. of the true mean weight.

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The syllogism is invalid because it commits the fallacy of affirming the consequent. The rule that is broken is that the conclusion of a valid syllogism must follow necessarily from the premises.

In this case, the conclusion "all inventors are eccentrics" does not necessarily follow from the premises "all inventors are people who see new patterns in familiar things" and "all eccentrics are people who see new patterns in familiar things."

This is because there could be people who see new patterns in familiar things who are not inventors, and there could be eccentrics who do not see new patterns in familiar things. Therefore, the argument is unsound and illogical.

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The representation of the inequality on the number line is:

←---------------------↓

<-----(-8)---(-7)----(-6)----(-5)-----(-4)----(-3)----(-2)----(-1)-----0----------------->

Here, we have,

given that,

the inequality is: x ≤ -6

here the sign '≤' , represents less than equal to.

so, x is less than equal to -6

i.e. the value of x is -6 or less than -6

so x = { -6, -7, -8,-9,......}

so, representation on the number line is:

←---------------------↓

<-----(-8)---(-7)----(-6)----(-5)-----(-4)----(-3)----(-2)----(-1)-----0----------------->

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The decision rule for this hypothesis test is to reject the null hypothesis if the test statistic is greater than the critical value. For a one-tailed test with a 0.025 significance level and 9 degrees of freedom (n-1), the critical value is 2.306 (found using a t-distribution table or calculator).

To compute the test statistic, we use the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / square root of sample size)
t = (17 - 10) / (4.9 / sqrt(10))
t = 4.48

Since the test statistic (4.48) is greater than the critical value (2.306), we reject the null hypothesis. This means that we have evidence to support the alternative hypothesis that the true population mean is greater than 10. In other words, the sample provides strong evidence that the population mean is larger than 10.

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(a) The unbiased estimate of the total number of errors in the manuscript is approximately 75.83.

(b) Sample average of the errors estimator is used on it.

(c) Yes, this is unbiased for the actual variance of the estimator of the total number of errors

(a) Unbiased estimate of the total number of errors:

To estimate the total number of errors in the manuscript, we need to consider the design used, which involves selecting a systematic sample of pages. The design selects the page with the random number 6 and then includes every 10th page thereafter. We are given the number of errors on the sample pages: 1, 0, 2, 3, 0, and 1.

The average number of errors per page in the sample is calculated as the sum of the errors on the sample pages divided by the number of sample pages:

(1 + 0 + 2 + 3 + 0 + 1) / 6 = 7 / 6 ≈ 1.17.

Now, we can estimate the total number of errors in the manuscript by multiplying the average number of errors per page by the total number of pages:

1.17 * 65 = 75.83.

(b) Estimator used and its unbiasedness:

The estimator used in this case is the sample average of the errors per page, which is calculated by summing the errors on the sample pages and dividing by the number of sample pages. In this case, the person estimated the total number of errors in the manuscript as 75.83 using the formula: 65(1 + 0 + 2 + 3 + 0 + 1) / 6.

(c) Variance of the estimator and its unbiasedness:

The variance of an estimator measures the variability or spread of the estimator's values around its expected value. To estimate the variance of the estimator, the formula used is 65(65 - 6)(1.37) / 6, where 1.37 is the sample variance of the six error counts.

To have an unbiased estimate of the variance, we would need to divide the numerator by (n - 1), where n is the number of sample units. In this case, n is 6 since we have six sample pages.

Therefore, the estimated variance of the estimator provided, 65(65 - 6)(1.37) / 6, is biased for the actual variance of the estimator of the total number of errors.

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the answer is

Y=(X+3)^2-6