Find Vector A + B

….

The statement "this is an example of sampling without replacement" is true. When it is mentioned that there are 130 eligible people, and out of those, 60 are women, it implies that the selection is done without replacement.

This means that once someone is selected or chosen, they are removed from the pool of eligible people for subsequent selections.

b) To calculate the probability that all four of the excused potential jurors are women, we need to consider the number of women in the eligible pool and the reduced pool after each excusal.

Initially, there are 60 women out of 130 eligible people. After the first excusal, there are 129 eligible people remaining, with 59 women. After the second excusal, there are 128 eligible people remaining, with 58 women. After the third excusal, there are 127 eligible people remaining, with 57 women. Finally, after the fourth excusal, there are 126 eligible people remaining, with 56 women.

To calculate the probability, we multiply the probabilities of each excusal:

P(all four are women) = (60/130) * (59/129) * (58/128) * (57/127)

Calculating this expression gives us the probability that all four excused potential jurors are women.

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So the altitude of the pile is increasing at a rate of 8/(45π) feet per minute when the pile is 6 feet high.

Let's call the radius of the conical pile at any given time "r" and the altitude "h". We are given that the altitude is always twice the radius, so we can write:

h = 2r

We are also given that water is pouring from a chute into the pile at a rate of 8 cubic feet per minute. The volume of a cone is given by the formula V = (1/3)πr^2h, so the rate of change of the volume of the pile is:

dV/dt = (1/3)πr^2 dh/dt + (2/3)πrh^2 dr/dt

We want to find the rate at which the altitude is increasing, so we need to solve for dh/dt when h = 6. We can also find r when h = 6 by using the equation h = 2r:

6 = 2r

r = 3

Now we can substitute the values we know into the equation for dV/dt:

8 = (1/3)π(3^2) dh/dt + (2/3)π(3)(6)^2 dr/dt

Simplifying:

8 = 9π dh/dt + 72π dr/dt

We can use the fact that h = 2r to eliminate r from this equation. Taking the derivative of both sides with respect to time:

dh/dt = 2 dr/dt

Now we can substitute this into the equation for dV/dt:

8 = 9π (2 dr/dt) + 72π dr/dt

Simplifying:

8 = 90π dr/dt

Solving for dr/dt:

dr/dt = 8/(90π) = 4/(45π)

Finally, we can use the equation h = 2r to find dh/dt:

dh/dt = 2 dr/dt = 8/(45π)

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There are 160 different combinations of 2 snacks and 1 drink that can be chosen if you can't pick the same snack twice.

What is the combination?

Combinations are a way to count the number of ways to choose a subset of objects from a larger set, where the order of the objects does not matter.

Since you can't pick the same snack twice, the first snack can be chosen in 5 ways, and the second snack can be chosen in 4 ways (since there are only 4 remaining choices after choosing the first snack). The drink can be chosen in 8 ways.

Using the multiplication principle of counting, the total number of different combinations of 2 snacks and 1 drink is:

5 × 4 × 8 = 160

Therefore, there are 160 different combinations of 2 snacks and 1 drink that can be chosen if you can't pick the same snack twice.

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Answer:on what

Step-by-step explanation: L

Therefore, the only critical number of g(y) is y = -1/12.

To find the critical numbers of a function, we need to find the values of the independent variable (in this case, y) at which the derivative of the function is zero or undefined.

First, we find the derivative of g(y):

g'(y) = 1 - 12y - 2

Setting g'(y) = 0, we get:

1 - 12y - 2 = 0

-12y = 1

y = -1/12

Since the derivative is defined for all values of y, there are no values of y at which it is undefined.

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Taylor will pay $1.60 for the grapes and $1.49 for the oranges, totaling $3.09 for both.

To calculate the cost of the grapes, we multiply the weight (1/4 lb) by the cost per pound ($3.20):

Grapes cost = (1/4) lb * $3.20/lb = $0.80.

Similarly, to calculate the cost of the oranges, we multiply the weight (1/2 lb) by the cost per pound ($2.98):

Oranges cost = (1/2) lb * $2.98/lb = $1.49.

To find the total amount Taylor will pay for the grapes and oranges, we add the individual costs together:

Total cost = Grapes cost + Oranges cost = $0.80 + $1.49 = $2.29.

Therefore, Taylor will pay $1.60 for the grapes and $1.49 for the oranges, totaling $3.09 for both.

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1/2

HHH HHT THH HTH Rest of then are: TTT TTH THT HTT so the answer is 1/2

The maximum annual retirement benefit that Dr. Zinab can receive during her retirement years depends on the balance in her retirement fund account at the time of retirement. Based on the given information, Dr. Zinab will make annual deposits of $10,000 for 10 years, which will earn an annual interest rate of 12%.

     To calculate the maximum annual retirement benefit, we need to use the formula for the present value of an annuity due, which takes into account the annual payments made at the beginning of each year and the interest earned on those payments.

Using the formula, the maximum annual retirement benefit that Dr. Zinab can receive during her retirement years is approximately $54,305. This assumes that Dr. Zinab's retirement fund account has a balance of $1,449,787 at the time of her retirement, which is calculated based on the 10-year period of annual deposits and the interest earned on those deposits. This amount can be further adjusted based on Dr. Zinab's specific retirement needs and circumstances.

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The maximum annual retirement benefit that Dr. Zinab can receive during her retirement years depends on the balance in her retirement fund account at the time of retirement. Based on the given information, Dr. Zinab will make annual deposits of $10,000 for 10 years, which will earn an annual interest rate of 12%.

    To calculate the maximum annual retirement benefit, we need to use the formula for the present value of an annuity due, which takes into account the annual payments made at the beginning of each year and the interest earned on those payments.

Using the formula, the maximum annual retirement benefit that Dr. Zinab can receive during her retirement years is approximately $54,305. This assumes that Dr. Zinab's retirement fund account has a balance of $1,449,787 at the time of her retirement, which is calculated based on the 10-year period of annual deposits and the interest earned on those deposits. This amount can be further adjusted based on Dr. Zinab's specific retirement needs and circumstances.

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Answer: C

Step-by-step explanation:

Median is the middle number out of the distribution. Cancel out the numbers at each end of the distribution until you get the median number. You will get 42 cm for Cityview and 40 cm for Countryside, thus making C correct.

Answer:

2,5,11,19,29,41,47

Step-by-step explanation:

The sequence can be generated by starting with 2 and adding increasing odd numbers successively.

Starting with 2, the first odd number is 3. So, adding 3 to 2 gives 5.

The second odd number is 5. So, adding 5 to 5 gives 10. But we need to add one more to get the next odd number, which is 11. So, adding 6 to 5 gives 11.

,

The third odd number is 7. So, adding 7 to 11 gives 18. But we need to add one more to get the next odd number, which is 19. So, adding 8 to 11 gives 19.

The fourth odd number is 9. So, adding 9 to 19 gives 28. But we need to add one more to get the next odd number, which is 29. So, adding 10 to 19 gives 29.

The fifth odd number is 11. So, adding 11 to 29 gives 40. But we need to add one more to get the next odd number, which is 41. So, adding 12 to 29 gives 41.

The sixth odd number is 13. So, adding 13 to 41 gives 54. But we only need the next number in the sequence, which is 47.

Therefore, the completed sequence is 2, 5, 11, 19, 29, 41, 47.

By identifying and isolating this effect, ANOVA provides a powerful statistical tool for determining whether there are significant differences between the means of the treatment groups being studied.

The source of variance that is presumed to explain between treatments variance in ANOVA is the treatment effect.

This effect represents the differences between the means of the treatment groups being compared. It is the primary factor being studied in ANOVA, as it is used to determine whether there are significant differences between the means of the treatment groups.

In ANOVA, the between treatments variance is explained by the treatment effect, which represents the differences between the means of the treatment groups being compared. This effect is the primary factor being studied in ANOVA, as it is used to determine whether there are significant differences between the means of the treatment groups. By isolating this effect, ANOVA allows researchers to determine whether any observed differences between the treatment groups are statistically significant or merely due to chance.

The treatment effect is the source of variance presumed to explain between treatments variance in ANOVA. By identifying and isolating this effect, ANOVA provides a powerful statistical tool for determining whether there are significant differences between the means of the treatment groups being studied.

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The value of x is 21.88

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

angle A is 27.2°, the opposite angle is 10 and the hypotenuse is x

therefore,

sin27.2 = 10/x

x( sin27.2) = 10

x = 10/sin27.2

x = 10/0.457

x = 21.88

Therefore the value of x is 21.88

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Rolling two 8-sided dice will yield 8 outcomes that result in a sum that is a square of something.

To find the number of outcomes that result in a sum that is a square, we need to determine the possible sums and identify which of them are perfect squares.

Let's analyze the possible outcomes when rolling two 8-sided dice. Each die has 8 faces, numbered from 1 to 8. Therefore, the maximum sum we can obtain is 8 + 8 = 16.

To determine the number of outcomes that result in a square sum, we need to identify the perfect square sums between 2 and 16. The perfect squares in this range are 4, 9, and 16.

Now, let's find the outcomes that yield these square sums:

To obtain a sum of 4, we can roll (1, 3), (2, 2), or (3, 1) on the two dice. That's 3 possible outcomes.

To obtain a sum of 9, we can roll (3, 6), (4, 5), (5, 4), or (6, 3) on the two dice. That's 4 possible outcomes.

To obtain a sum of 16, we can only roll (8, 8) on the two dice. That's 1 possible outcome.

Therefore, there are a total of 3 + 4 + 1 = 8 outcomes that result in a sum that is a square.

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The volume of the cone is 7225.66 m³ and the volume of the hemisphere is 209.44 cubic feet.

From the general formula of the volume of the cone,

Volume = πr²h

in the given case,

Radius (r) = 10 m

Height (h) = 23 m

Thus, Volume = π*10²*23

Volume = 7225.66 m³

The formula for the volume of a hemisphere is:

V = (2/3) * π * r³

where π is pi (approximately 3.14159), and r is the radius of the hemisphere.

Substituting the given value of r = 10 ft, we get:

V = (2/3) * π * (10 ft)³

= (2/3) * π * 1000 ft³

= (2/3) * 314.16 ft³

≈ 209.44 ft³

Therefore, the volume of the hemisphere is approximately 209.44 cubic feet.

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The coefficient used to assess the internal consistency of a measure typically refers to Cronbach's alpha coefficient.

The coefficient used to assess the internal consistency of a measure typically refers to Cronbach's alpha coefficient. This coefficient is a statistic that quantifies the internal consistency reliability of a scale or measure, specifically for measures with multiple items or indicators that are intended to measure the same underlying construct.

The coefficient ranges between 0 and 1, with higher values indicating greater internal consistency. Cronbach's alpha measures the extent to which the items in a scale or measure correlate with each other. It assesses how well the items are measuring the same underlying construct or concept.

In other words, the coefficient represents the proportion of variance in the observed scores that can be attributed to the true score, rather than measurement error or other extraneous factors. It indicates the degree to which the items in the measure are interrelated or consistent with each other, with higher values suggesting stronger internal consistency.

Researchers often use Cronbach's alpha to assess the reliability of scales in various fields, such as psychology, education, and social sciences, to ensure that the measure is measuring the construct consistently and accurately.

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Answer:

67 mph

Step-by-step explanation

A method you'd want to remember is r = d/t, or rate equals distance divided by time.

Since the Morris family drove 368.5 miles in 5.5 hours, you'd divide the distance by 5.5.

(368.5/5.5) = 67 miles per hour.

So their average rate is 67 miles per hour.

Answer:

first one is 68,328

Step-by-step explanation:

because if one liter rounded to a gallon is 4 then you gotta multiply 94.9 times 4 then multiply that by 180 us gallons then theres your answer

The volume of the cone is V = 193.8 inches³

Given data ,

Let the volume of the cone be represented as V

Now , the height of cone h = 5.9 inches

And , diameter of cone = 11.2 inches

So , radius of cone r = 5.6 inches

where , Volume of Cone = ( 1/3 ) πr²h

V = ( 1/3 ) ( 3.14 ) ( 5.6 )² ( 5.9 )

V = 193.8 inches³

Hence , the volume is V = 193.8 inches³

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We can expect that approximately 300 of the next 720 shirts claimed should be Small size.

To estimate how many of the next 720 shirts claimed should be size small, we can use the proportion of people who have taken size small so far.

First, we need to find the total number of people who have claimed T-shirts:

110 (size small) + 154 (other sizes) = 264

The proportion of people who have taken size small so far is:

110/264 ≈ 0.4167

This means that approximately 41.67% of people have taken size small so far.

To estimate how many of the next 720 shirts claimed should be size small, we can multiply the proportion by the total number of shirts:

0.4167 × 720 ≈ 300

Therefore, we can expect that approximately 300 of the next 720 shirts claimed should be size small.

However, it's important to note that this is just an estimate based on the data so far. It's possible that the proportion of people taking size small could change for the remaining shirts, especially if the population of people claiming shirts changes (e.g. if more or fewer people who typically take size small claim shirts).

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The growth factor is the constant number by which each term in a sequence is multiplied to obtain the subsequent term.

The growth factor refers to the number by which each term in a sequence is multiplied in order to get the next term. In the case of exponential growth, this factor is typically greater than 1, while in the case of exponential decay, it is typically a fraction between 0 and 1. The growth factor is an important concept in mathematics and is used in a variety of applications, including finance, science, and engineering.
The growth factor is the constant number by which each term in a sequence is multiplied to obtain the subsequent term. In exponential growth, the growth factor is greater than 1, while in exponential decay, the growth factor is a fraction between 0 and 1.

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The missing sides of the special right triangles are listed below:

Case 1: y = √2 · 13, x = 13

Case 2: x = y = 15√2

Case 3: x = 6, y = 3√3

Case 4: x = 17√3, y = 17

Case 5: x = y = 10

Case 6: x = 50, y = 25

Case 7: x = y = 4√7

Case 8: x = 16√3, y = 8√3

Case 9: x = 11√3, y = 33

Case 10: x = 3√2, y = 2√6

Case 11: x = √10, y = 2√5

Case 12: x = 4√7, y = 8√21

Herein we find twelve cases of special right triangles whose missing sides must be determined by using the following rules:

45 - 90 - 45 Right triangle

r = √2 · x = √2 · y

30 - 60 - 90 Right triangle

x = (1 / 2) · r

y = (√3 / 2) · r = √3 · x

Where:

Case 1

y = √2 · 13

x = 13

Case 2

x = y = 15√2

Case 3

x = 3 / (1 / 2)

x = 6

y = 3√3

Case 4

x = 34 · (√3 / 2)

x = 17√3

y = 34 · (1 / 2)

y = 17

Case 5

x = y = 10

Case 6

x = 25√3 / (√3 / 2)

x = 50

y = 25√3 / √3

y = 25

Case 7

x = y = 2√14 · √2 = 2√28 = 4√7

Case 8

x = 24 / (√3 / 2)

x = 48 / √3

x = 16√3

y = 24 / √3

y = 8√3

Case 9

x = 22√3 · (1 / 2)

x = 11√3

y = 22√3 · (√3 / 2)

y = 33

Case 10

x = √18

x = 3√2

y = √6 / (1 / 2)

y = 2√6

Case 11

x = √10

y = √20

y = 2√5

Case 12

x = 4√21 / √3

x = 4√7

y = 4√21 / (1 / 2)

y = 8√21

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To determine if lab 1 is reporting lower cholesterol levels, on average, than lab 2, a paired t-test for means should be used.

This is because the physician collected pairs of blood samples from each patient and wants to compare the means of the two labs' cholesterol level measurements. The paired t-test for means is appropriate for comparing the means of two related samples, in this case, the blood samples from each patient tested by lab 1 and lab 2.

A paired t-test for means should be used to determine if lab 1 is reporting lower cholesterol levels, on average, than lab 2. This test is appropriate because the data consists of paired samples from the same patients, and the goal is to compare the means of the differences between the two labs.

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The total cost would be 14 + (1.50)s.

We have,

If Matthew downloaded 15 songs in a month, he would have to pay an additional $1.50 per song,

So his total cost for that month would be written as an expression:

Total cost = $14 + 15($1.50)

Total cost = $14 + $22.50

Total cost = $36.50

Now,

If he downloaded s songs, his total cost would be:

Total cost = $14 + s($1.50)

Thus,

The total cost would be 14 + (1.50)s.

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Answer:

11:1

Step-by-step explanation:

Convert it into a fraction : 11 6/11

Multiply both the numerator and the denominator by 11 to get rid of the fraction part.

121/11

Simplify this by dividing both the numerator and the denominator by 11

11:1

Therefore, Andrea has 25 dimes in 37 coins, all nickels and dimes and the value of the 37 coins is $3.10.

Let's represent the number of nickels by "n" and the number of dimes by "d".

From the problem, we know that:

n + d = 37 (equation 1) ---(the total number of coins)

0.05n + 0.1d = 3.10 (equation 2) ---(the total value of the coins in dollars)

To solve for d, we can rearrange equation 1 to get:

n = 37 - d

Substitute this expression for n into equation 2 and simplify:

0.05(37-d) + 0.1d = 3.10

1.85 - 0.05d + 0.1d = 3.10

0.05d = 1.25

d = 25

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The measurement of the JL value is 6cm.

Given the measurement of the KM value = 6cm

The measurement of ML value = 4cm

The given figure is in the shape of a rectangle. In rectangle we know that the length and breadth is equal in both sides.

The property is in a rectangle the opposite sides which are parallel sides are equal. [the measurements of both sides are the same]

By using the above condition,

The measurement of JL value which is parallel to the KM value is also 6cm.

So, from the above analysis, we can conclude that the value of JL is 6cm.

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Given question is missing figure, I am attaching below,

There are 34 weekdays from May 8th to June 24th, excluding the weekend days.

There are 48 days altogether from May 8 through June 24.

We must only count the weekdays in order to leave out the weekend days (Saturday and Sunday) from this total.

There are 5 weekdays in a week because there are 7 days in a week, 2 of which are weekends.

We may divide the total number of days by 7 and then multiply the result by 5 to get the number of weekdays between May 8 and June 24:

Number of weekdays = (total number of days ÷ 7) x 5

= (48 ÷ 7) x 5

= 6.857 x 5

= 34.285

Therefore, there are 34 weekdays from May 8th to June 24th, excluding the weekend days.

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The angle D is 29 degrees, side DF is 9 and side DE is 10.3 rounded to nearest tenth.

Assuming the remaining angle of triangle to be x. Calculating the same we get:

90 + 61 + x = 180

151 + x = 180

x = 180 - 151

x = 29 degrees

Now, cos theta = base (EF)/hypotenuse (DE) (for 61 degree angle)

cos 61 = 5/hypotenuse

Hypotenuse = 5/cos 61

Hypotenuse = 10.3

Working out sin 90 degree to find DF

sin 61 = perpendicular (DF)/ hypotenuse (DE)

0.87 = Perpendicular/10.31

Perpendicular = 0.87 × 10.31

Perpendicular = 9

Hence, the remaining angle is 29 degrees and sides are 10.3 and 9.

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The critical points occur when the derivative of the function is equal to zero or undefined. The absolute maximum value of f(x) = ln(x)/x is approximately 0.3679.

Taking the derivative of f(x), we get:

f'(x) = (1/x)(1 - ln x)

Setting this equal to zero, we get:

1 - ln x = 0

ln x = 1

x = e

We also need to check for any values of x that make the derivative undefined. The derivative is undefined when x = 0.

Now we need to check the values of f(x) at these critical points and the endpoints of the domain, which is (0, infinity).

f(0) is undefined as ln 0 is undefined.

f(e) = (ln e)/e = 1/e

As x approaches infinity, f(x) approaches zero.

So the absolute maximum value of f(x) is 1/e, which occurs at x = e.

To find the absolute maximum value of the function f(x) = ln(x)/x, we need to follow these steps:

Step 1: Determine the domain of the function
The function is defined for x > 0, since ln(x) is only defined for positive values of x.

Step 2: Find the first derivative of the function
Using the quotient rule, we find the first derivative:
f'(x) = (1/x - ln(x))/x^2

Step 3: Find the critical points
To find the critical points, set the first derivative equal to zero and solve for x:
(1/x - ln(x))/x^2 = 0
1/x - ln(x) = 0
ln(x) = 1/x

Step 4: Solve the equation for x
The equation ln(x) = 1/x does not have a simple algebraic solution. However, using numerical methods (e.g. the Newton-Raphson method) or by graphing the two functions, we can find that the critical point occurs at x ≈ 3.591.

Step 5: Evaluate the function at the critical point
Now we plug this value of x into the original function to find the absolute maximum value:
f(3.591) ≈ ln(3.591)/3.591 ≈ 0.3679

Thus, the absolute maximum value of f(x) = ln(x)/x is approximately 0.3679.

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