The population of a small town of 29,000 people is expected to grow exponentially at a rate of 1.9% per year. Estimate the population in 2 years' time.

The price that the insurance company should charge for a one-year extended warranty on a Prego SUV is $402.

To determine the price that the insurance company should charge for a one-year extended warranty on a Prego SUV, the company needs to calculate the expected value of the repair costs and then add their desired profit to it.

Let's assume that the price for the warranty is x dollars. Then, the expected value of the repair costs for the insurance company would be:

(0.50)(0) + (0.35)($500) + (0.12)($1500) + (0.03)($4000) = $352

This means that on average, the insurance company can expect to pay out $352 in repair costs for each policy sold. To make an average profit of $50 per policy, the insurance company should charge:

x = $352 + $50 = $402

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Answer:

The equation of the circle with a diameter of 14 and whose center is (-4,6) is  [tex]x^{2}+y^2+8x-12y+3=0[/tex]

Step-by-step explanation:

Given that diameter is 14. So, the radius is 14/2 which is equal to 7.

Also, the center is (-4,6).

We know that the equation of a circle with center (h,k) and radius r units is

[tex](x - h)^2+(y-k)^2=r^2 .[/tex]

Here, h=-4, k=6 and r=7.

Putting these values in the above equation,

[tex](x - (-4))^2+(y-6)^2=7^2 .[/tex]

[tex](x +4)^2+(y-6)^2=49 .[/tex]

On solving, the equation of the circle is

[tex]x^2+y^2+8x+-12y+3=0[/tex].

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So, 3,280 liters of water flows from the tank between the 14 minute mark and the 34 minute mark.

In mathematics, a function is a rule or relationship that assigns a unique output or value for each input or value in its domain. In other words, a function is a mathematical object that takes an input value and produces a corresponding output value. Functions are commonly denoted by f(x), where x represents the input value, and f(x) represents the corresponding output value.

Here,

To find the amount of water that flows from the tank between the 14 minute mark and the 34 minute mark, we need to find the difference between the amount of water at the 14 minute mark and the amount of water at the 34 minute mark. At the 14 minute mark, t = 14, so we can substitute this value into the equation to get:

R(14) = 8000 - 250(14) + 2(14)²

R(14) = 5,720 liters

At the 34 minute mark, t = 34, so we can substitute this value into the equation to get:

R(34) = 8000 - 250(34) + 2(34)²

R(34) = 2,440 liters

Therefore, the amount of water that flows from the tank between the 14 minute mark and the 34 minute mark is:

R(14) - R(34) = 5,720 - 2,440

R(14) - R(34) = 3,280 liters

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Answer:

A trainee requires 3 days of training before they can assemble 9 heaters.

Step-by-step explanation:

We are given the formula for the number of water heaters h that a trainee can assemble per 8-hour shift as:

h = 2.1 0.9t + 4

where t is the number of days of training the trainee has received. We need to find out how many training days are required before a trainee can assemble 9 heaters. So we set h to 9 and solve for t:

9 = 2.1 0.9t + 4

Subtracting 4 from both sides, we get:

5 = 2.1 0.9t

Dividing both sides by 2.1 0.9, we get:

t = (5 / (2.1 0.9))

Using a calculator, we get:

t ≈ 2.49

Rounding up to the nearest day, we get:

t = 3

Therefore, a trainee requires 3 days of training before they can assemble 9 heaters.

The measures of center for this data set are the mean and median. The mean is 5.1 and median is 6.

The measure of variability is the range. The range is 10.

The measures of center describe the typical or central value of the data. For this data set, we can use the mean or the median as measures of center. The mean is the average of all the quiz scores, while the median is the middle value when the scores are arranged in order.

Mean = (0x1 + 1x0 + 2x0 + 3x0 + 4x0 + 5x2 + 6x4 + 7x2 + 8x2 + 9x1 + 10x0) / (1+0+0+0+0+2+4+2+2+1+0) = 5.1

Median = 6 (the middle score)

The measures of variability describe the spread or dispersion of the data. For this data set, we can use the range. The range will be:

= Highest score - Lowest score

= 10 - 0

= 10

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The line plot shows a student's quiz scores.

Quiz Scores

0 = 1

1,2,3,4 = 0

5 = 2

6 = 4

7 = 2

8 = 2

9 = 1

10 = 0

Which measures of center and variability should be used to describe the data?

The value of P(x=1) from the given discrete data is 0.5.

From the given data

Let P(x=2)=x

p+p+x=1

x=1-2p

E(x²)=∑PiXi²=P(0)²+p(1)²+(1-2p)(2)²

= 0+p+(1-2p)4

= 4-7p

E(x)=∑PiXi=P(0)+P(1)(1-2p)(2)

= 0+p+2-4p

= 2-3p

Given that, E(x²)=E(x)

4-7p=2-3p

4p=2

p=0.5

Therefore, the value of P(x=1) from the given discrete data is 0.5.

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Answer:

a. Let's denote the number of bacterial cultures after n hours by B_n. We know that the number of bacteria triples every hour, so we can write:

- Recursive formula: B_n = 3*B_(n-1) with initial condition B_0 = 250.

- Explicit formula: B_n = 250 * 3^n.

b. To predict the number of bacterial cultures after 8 hours, we can use the explicit formula and substitute n=8:

B_8 = 250 * 3^8 = 250 * 6561 = 1,640,250

Therefore, there will be 1,640,250 bacterial cultures in the dish after 8 hours.

c. Yes, this sequence represents a function. For each input value (number of hours), there is a unique output value (number of bacterial cultures). The explicit formula gives a direct way of computing the output for any input, so it satisfies the definition of a function.

The exponent property of nth roots states that for any real number a and any positive integer n, the nth root of a raised to the nth power equals a.

The property of nth roots, concerning exponents states that if 'a' is a real number and 'n' is a positive integer, then the nth root of 'a' when raised to the nth power will always be equal to 'a':

√ ( a ⁿ ) = a

This can greatly simplify expressions involving nth roots by multiplying the exponent by 'n', taking the nth root of the base:

( √ a ) ⁿ = √ ( a ⁿ )

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We are given that the sample size $\sf\:n = 18$, sample mean $\sf\:\bar{X} = 103$, sample standard deviation $\sf\:S = 10$, and margin of error $\sf\:E = 6.05$ for a 98% confidence interval estimate for the population mean.

Using the formula for the margin of error, we can find the value of the t-score that corresponds to a 98% confidence level with 17 degrees of freedom (since we have 18 samples):

$\sf\:t_{0.01/2, 17} \implies 2.898$

Now, we can use the formula for a confidence interval estimate to find the lower and upper bounds of the interval:

$\sf\:\bar{X} - E \implies 103 - 6.05 < \mu < \bar{X} + E \implies 103 + 6.05$

Substituting in the values we have:

$\sf\:103 - 6.05 < \mu < 103 + 6.05$

Simplifying:

$\sf\leadsto\:96.95 < \mu < 109.05$

Therefore, a 98% confidence interval estimate for the population mean is $\sf\: (96.95, 109.05)$ rounded to two decimal places.

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]{\bigstar{\underline{\underline{\sf{\color{red}{Sumit\:Roy}}}}}}{\bigstar}\\[/tex]

Answer:

x=2

Step-by-step explanation:

f(x) is 89

f(x)=41x+7

89=41x+7

41x+7=89

41x=89-7

41x=81

x=81/41

x=2

The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively. This can be solved by using trigonometric functions.

Trigonometric functions are used to describe relationships involving angles and sides of triangles. They are used to calculate the sizes of angles and distances between points. These include sine, cosine, tangent, secant, cosecant and cotangent.

This can be solved by using trigonometric functions.

First we need to find the length of FA to solve the question further.

FA = 1.5+ FD

AG = FA cos 30

AG = 1.5 √3

AG = 1.5 FD √3/2 = 1.5√3  (as cos 30 = √3/2)

DF = 1.5

Thus, FA = AB+BD+FD

FA = 1 + 0.5 + 1.5

So, the length of FA is 3.

Now, for the triangle, ΔABC

as ∠BAC= 30

BC = AB/2

= 0.5

This is because the angle of the right triangle is 30°and we know that when the angle of a right triangle is 30° the length of opposite side is exactly equal to half of the length of the hypotenuse.

For ΔADE,

as ∠DAE= 30, and AD= 1.5

DE= AD/2

= 0.75

For ΔGAF,

as ∠GAF= 30, and FA= 3

FG = FA/2

= 1.5

The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively.

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for the first question  answer is 35 , which we can clearly see its pointing 35 degree in the protractor  .second question is incomplete

what is protractor ?

To measure an angle using a protractor instrument, follow these steps:

Place the protractor on the angle: Place the flat side of the protractor on one of the angle's sides, making sure that the vertex (the point where the two sides of the angle meet) is at the center of the protractor.Align the protractor with the angle: Make sure the protractor is aligned with the angle you want to measure. The zero-degree mark on

In the given question,

for the first question  answer is 35 , which we can clearly see in the protractor  

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The median weekly earnings of the data set of the workers in the occupations listed for 2010 is calculated as: $971.

To find the median weekly earnings for the occupations listed in 2010, we need to first arrange the earnings in order from least to greatest:

$501, $900, $971, $977, $1071

The median is the middle value in this ordered list. Since there are an odd number of values, the median is simply the middle value.

Therefore, the median weekly earnings of workers in the occupations listed for 2010 is $971.

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Answer

Construction Model Stats

User

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

ChatGPT

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

User

The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.

ChatGPT

We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:

tan(18 degrees) = h / d

Solving for h, we get:

h = d * tan(18 degrees)

Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:

h = 510 feet * tan(18 degrees)

h ≈ 157.3 feet

Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.

User

The following regular polygon has 15 sides. This distance from its center to any given vertex is 12 inches.

Which of the following is the best approximation for its perimeter?

(1) 68 inches

(3) 84 inches

(2) 75 inches

(4) 180 inches

ChatGPT

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

Answer:

To find the percentage of Virginia's gross pay that she took home after deductions, we need to first calculate her gross pay and then subtract the total amount of deductions to find her net pay. Then, we can divide her net pay by her gross pay and multiply by 100 to find the percentage.

Virginia earns $69,500 per year, so her gross pay per paycheck (assuming she is paid every two weeks) is:

$69,500 / 26 = $2,673.08

Her total deductions from her most recent paycheck were:

$200.20 + $180.65 + $72.00 + $110.00 + $250.00 = $812.85

So her net pay was:

$2,673.08 - $812.85 = $1,860.23

To find the percentage of her gross pay that she took home, we can divide her net pay by her gross pay and multiply by 100:

($1,860.23 / $2,673.08) x 100 ≈ 69.59%

Therefore, the closest option is (3) 69.59%.

The measure of angle A'B'C' in the resulting figure is approximately 142.6 degrees.

The reflection of a point (x, y) across the y-axis is (-x, y). Applying this transformation to the coordinates of A, B, and C, we get:

A' (-2, 1)

B' (-6, 1)

C' (-6, 4)

The rotation of a point (x, y) by 180 degrees counter clockwise is (-x, -y). Applying this transformation to the coordinates of A', B', and C', we get:

A'' (2, -1)

B'' (6, -1)

C'' (6, -4)

Next, we can use the law of cosines to find the measure of angle B:

A'B'C' = 180 - arccos(-7/24)

≈ 142.6 degrees

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2a. To calculate the average number of violations committed, we add up all the violations and divide by the number of offenders:

Average number of violations = (15+20+10+25+5+22+8+12+18+7+23+6+24+19+11) / 15

Average number of violations = 187 / 15

Average number of violations ≈ 12.47

Therefore, the average number of violations committed by the offenders in the sample is approximately 12.47.

2b. To calculate the sample mean for the given data, we add up the five samples and divide by the number of samples:

Sample mean = (22 + 8 + 19 + 7 + 24) / 5

Sample mean = 80 / 5

Sample mean = 16

Therefore, the sample mean for the five samples is 16.

2c. To estimate the mean interval with 95% confidence level, we can use the t-distribution and the formula:

Sample mean ± t-value (α/2, n-1) x (standard deviation / square root of n)

We are not given the standard deviation of the population, so we need to estimate it using the sample standard deviation:

s = sqrt [ Σ(xi - x)^2 / (n - 1) ]

where xi is the i-th sample, x is the sample mean, and n is the number of samples.

Using the five samples given in part (b), we can calculate the sample standard deviation:

s = sqrt [ ((22-16)^2 + (8-16)^2 + (19-16)^2 + (7-16)^2 + (24-16)^2) / (5-1) ]

s = sqrt [ (36 + 64 + 9 + 81 + 64) / 4 ]

s ≈ 9.17

Using a t-distribution table with α/2 = 0.025 and degrees of freedom = n-1 = 4, we find that the t-value is 2.776.

Plugging in the values, we get:

Sample mean ± t-value (α/2, n-1) x (standard deviation / square root of n)

16 ± 2.776 x (9.17 / sqrt(5))

16 ± 9.55

Therefore, with 95% confidence, we estimate that the mean number of violations committed by the population of lawbreakers is between 6.45 and 25.55.

   To estimate the number of violations when the road area is 6 meters, we need to use the regression equation Y = a + bX. However, we are not given the values of a and b.

Without knowing the values of a and b, we cannot estimate the number of violations when the road area is 6 meters or use the regression equation to make any predictions.Answer:

Step-by-step explanation:

For a population of 300 lawbreakers:

2. a. To calculate the average number of violations committed, find the mean of the given data set.

Mean = (15 + 20 + 10 + 25 + 5 + 22 + 8 + 12 + 18 + 7 + 23 + 6 + 24 + 19 + 11) / 15

Mean = 180 / 15

Mean = 12

Therefore, the average number of violations committed is 12.

b. To calculate the sample mean, we need to find the mean of the given sample data set.

Sample mean = (22 + 8 + 19 + 7 + 24) / 5

Sample mean = 80 / 5

Sample mean = 16

Therefore, the sample mean is 16.

c. To estimate the mean interval with 95% confidence level, we can use the t-distribution with n-1 degrees of freedom, where n is the sample size. The formula for the confidence interval is:

Confidence interval = sample mean ± (t-value x standard error)

where t-value is the value obtained from the t-distribution table for a 95% confidence level and n-1 degrees of freedom, and standard error is the standard deviation of the sample data divided by the square root of the sample size.

First, find the standard deviation of the sample data set.

Standard deviation = √[(Σ(x - μ)²) / (n - 1)]

where Σ is the sum of the values, x is each value in the sample data set, μ is the sample mean, and n is the sample size.

μ = 16 (from part b)

n = 5

x values = 22, 8, 19, 7, 24

Standard deviation = √[((22-16)² + (8-16)² + (19-16)² + (7-16)² + (24-16)²) / (5 - 1)]

Standard deviation = √[(36 + 64 + 9 + 81 + 64) / 4]

Standard deviation = √(254 / 4)

Standard deviation = √63.5

Standard deviation ≈ 7.97

Next, find the t-value for a 95% confidence level and 4 degrees of freedom. From the t-distribution table, the t-value is 2.776.

Confidence interval = 16 ± (2.776 x (7.97 / √5))

Confidence interval = 16 ± (2.776 x 3.57)

Confidence interval = 16 ± 9.91

Therefore, the mean interval with 95% confidence level is (16 - 9.91, 16 + 9.91), or approximately (6.09, 25.91).

3. To estimate the number of violations for a road area of 6 meters, we need to use the regression equation Y = a + bX, where Y is the number of violations and X is the road area in meters.

First find the values of a and b from the given data.

Using the formula:

b = [(nΣXY) - (ΣX)(ΣY)] / [(nΣX²) - (ΣX)²]

a = (ΣY - bΣX) / n

where n is the number of data points, Σ is the sum of the values, and X and Y are the variables.

n = 4

ΣX = 18

ΣY = 15

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Image transcribed:

QUESTIONS

2. There are 300 lawbreaker as a population

X = the number of law violations by the 1st lawbreaker in 1 year. Researched as many as 15 offenders as a random sample. It turns out that the number of violations committed by them is :

15  20  10  25  5

22  8  12  18  7

23  6  24  19  11

Questions:

a. Calculate the average number of violations committed

b. If 5 samples are taken, namely: 22 8 19 7 24

Calculate the sample mean

c. Estimate the mean interval with 95% confidence level

3. The number of traffic violations in city A every day (several times) is:

Road area (X) in meter | 4   3.5   5   5.5

Violation (Y)                 | 3   3   2   7

Approximately how many violations if the road area is 6 meters? If the regression equation is:

Y = a+bX

Answer:

False

Step-by-step explanation:

The reason for it being false is because 2X = 25 should be divided to by 2 to get to X, which should be half of 25.

therefore X should equal 12.5

Answer:

Step-by-step explanation:

11000*14539.95

7.1483737364203627356954981215625 × 10^24

is the answer

The equation of the axis of symmetry of the given quadratic function is x = -2. So, correct option is C.

The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. For a quadratic function in the form y = ax² + bx + c, the equation of the axis of symmetry is given by x = -b/(2a).

In the given equation, y = 2x² + 8x - 3, the coefficients of x² and x are a = 2 and b = 8, respectively. Substituting these values in the equation of the axis of symmetry, we get:

x = -b/(2a)

x = -8/(2*2)

x = -8/4

x = -2

This means that the parabola is symmetric about the vertical line x = -2. So the correct answer is x=-2.

So, correct option is C.

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The polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6 is f(x) = x³ - x² - 30x.

To find a polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6, we start by using the factor theorem. This theorem tells us that if a polynomial function has a zero at some value c, then it is divisible by the linear factor (x - c).

Therefore, the polynomial with zeros at -5, 0, and 6 can be written as:

f(x) = a(x + 5)(x - 0)(x - 6)

where a is a constant coefficient that we need to determine. Since the leading coefficient of the polynomial is 1, we set a = 1.

Multiplying out the factors, we get:

f(x) = (x + 5)(x)(x - 6)

= x³ - x² - 30x

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x = 3.6 units

First, some definitions before working the problem:

The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.

The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.

Working the problem

For the given triangle, the right angle is in the top right, so the side on the bottom left is the hypotenuse.

We know the angle in the lower right corner (angle S), so the side touching it (side ST) with unknown length is the adjacent side.  (notice that the points that form the side include the vertex of the angle -- so, it's the adjacent side).

For this triangle, the "adjacent" leg is unknown, our "goal to find" side.  Additionally, the "hypotenuse" is known.

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "adjacent" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "a" & "h" is "Cah".  So, the desired function to use for this triangle is the Cosine function.

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]cos(69^o)=\dfrac{x}{10}[/tex]

To isolate "x", multiply both sides by 10...

[tex]10*cos(69^o)=x[/tex]

Make sure your calculator is set to degree mode, and calculate:

[tex]10*(0.3583679495453...)=x[/tex]

[tex]x=3.583679495453...[/tex] units

Rounded to the nearest tenth...

x = 3.6 units

Answer:

D. 490

Step-by-step explanation:

We first need to use this formula:

interest = principle × rate × time

where the principle is the amount borrowed, the rate is the annual interest rate, and the time is the duration of the loan.

plugging in the given values, we get:

interest = 3500×0.07×2

simplifying, we get:

interest = 490

the answer is D

When expressed in symbolic form, the original claim would then be H ₀: μ = 68. 9  bpm.

One common approach to express a hypothesis in symbolic form is through the application of logical symbols including "if-then" statements. This symbolized portrayal can be instrumental in directing the design of an experiment aimed at assessing its validity.

The null hypothesis is represented as H₀, with μ describing the mean pulse rate for male adults within the population. The underlying assertion suggests that on average adult males possess a pulse rate equivalent to 68.9 bpm.

H ₀: μ = 68. 9  bpm.

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First, we need to simplify the expression inside the parentheses:

4v - w = 4(4i - i) - (-9i) = 16i - 4i + 9i = 21i

Now, we can substitute the values of u, v, and w into the expression:

5u - (4v - w) = 5(-7i + 7j) - (21i) = -35i + 35j - 21i = -56i + 35j

Therefore, the final result is -56i + 35j.

Answer:

  -60i +39j

Step-by-step explanation:

You want the value of 5u -(4v -w) given ...

These are added the way any polynomials are added. Like terms can be combined.

  5u -(4v -w)

  = 5(-7i +7j) -(4(4i -j) -(-9i))

  = -35i +35j -(16i -4j +9i)

  = -35i +35j -25i +4j

  = -60i +39j

__

Additional comment

We have assumed a typo in the definition of v, that 4i-j was wanted instead of 4i-i.

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Answer:

O True

Step-by-step explanation:

Unit rate of essays/minute:

40 minutes / 5 essays = 8 essays/minute

256 essays / 32 minutes = 8 essays/minute

The unit rates are equal.

Answer: O True

The best approx. for mean of 10,000 sample means is equal to the population mean which is 84. The Option C is correct.

According to central limit theorem, the distribution of sample means from a large sample size will be normal regardless of the shape of the population distribution.

This is because the 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.

The standard deviation of distribution of sample means will be:

= Population standard deviation / √sample size

= 7.2 / √100

= 0.72

So, the best approximation for the mean of 10,000 sample means is equal to the population mean which is 84.

Full question "Suppose we have a large population with mean = 84 and standard deviation = 7.2. 10 points Let's say we randomly sample 100 values from this population and compute the mean, then repeat this sampling process 10,000 times and record all the means we get.  Which of the following is the best approximation for the mean of our 10,000 sample means? A. 8.4 b. 100 c. 84"

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Answer:

t ≈ 37.76 seconds (rounded to the nearest hundredth)

Step-by-step explanation:

To solve the problem, we can use the equation for the height of a projectile at time t: h(t) = - 16 * t^2 + v0 * t + y0

where v0 is the initial velocity and y0 is the initial height.

In this case, we have:          v0 = 600 ft/sec (upward)

                                             y0 = 160 ft (above the ground)

We want to find the time at which the projectile hits the ground, which is when h(t) = 0.

So we can set up the equation:   0 = -16 * t^2 + 600 * t + 160

We can solve for t using the quadratic formula:

                                           t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -16, b = 600, and c = 160.

Plugging in the values, we get:

                   t = (-600 ± sqrt(600^2 - 4(-16)(160))) / 2(-16)

                   t = (-600 ± sqrt(360000 + 10240)) / (-32)

                   t = (-600 ± sqrt(370240)) / (-32)

We can simplify this expression by taking the negative root since the positive root would give a negative time, which is not physically meaningful in this context: t = (-600 - 608.47) / (-32)

t ≈ 37.76 seconds (rounded to the nearest hundredth)

Therefore, the projectile will be in flight for about 37.76 seconds before hitting the ground.

a. The dependent variable is the number of unit sold. The independent variable is price.

b. The value of r is -0.9965

c. ŷ = -0.68688X + 56.95837

X Values

∑ = 301

Mean = 50.167

∑(X - Mx)2 = SSx = 920.833

Y Values

∑ = 135

Mean = 22.5

∑(Y - My)2 = SSy = 437.5

X and Y Combined

N = 6

∑(X - Mx)(Y - My) = -632.5

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -632.5 / √((920.833)(437.5)) = -0.9965

Meta Numerics (cross-check)

r = -0.9965

c. Regression line calculation

Sum of X = 301

Sum of Y = 135

Mean X = 50.1667

Mean Y = 22.5

Sum of squares (SSX) = 920.8333

Sum of products (SP) = -632.5

Regression Equation = ŷ = bX + a

b = SP/SSX = -632.5/920.83 = -0.68688

a = MY - bMX = 22.5 - (-0.69*50.17) = 56.95837

ŷ = -0.68688X + 56.95837

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