What type of linear association does the graph show?

(A) Strong Positive

(B) Weak Positive

(C) Strong Negative

(D) Weak Negative

The area of the portion of the saddle-like surface inside the cylinder is given by (bπ\(a^4\))/4, and the leading-order term as a→0 or b→0 is 0.

The saddle-like surface equation is z = bxy, and the cylinder equation is x² + y² ≤ a².

To find the area of the portion of the saddle-like surface inside the cylinder, we need to determine the limits of integration.

Convert the cylinder equation to polar coordinates: x = rcosθ, y = rsinθ.

The limits for r will be from 0 to a (the radius of the cylinder), and the limits for θ will be from 0 to 2π (a full revolution).

Set up the double integral to calculate the area: ∫[0 to 2π] ∫[0 to a] bxy r dr dθ.

Integrate the function bxy over the region: ∫[0 to 2π] ∫[0 to a] b(r³)(cosθ)(sinθ) dr dθ.

Integrate with respect to r: ∫[0 to 2π] [(b/4)(\(a^4\))(cosθ)(sinθ)] dθ.

Evaluate the inner integral: (b/4)(\(a^4\)) ∫[0 to 2π] (cosθ)(sinθ) dθ.

Evaluate the integral of (cosθ)(sinθ): ∫(cosθ)(sinθ) dθ = (1/2)(sin²θ).

Substitute the evaluated integral into the expression: (b/4)(\(a^4\)) (1/2) ∫[0 to 2π] sin²θ dθ.

Evaluate the integral of sin²θ: ∫sin²θ dθ = (1/2)(θ - sinθcosθ).

Substitute the evaluated integral into the expression: (b/4)(\(a^4\)) (1/2) [(2π - sin(2π)cos(2π)) - (0 - sin(0)cos(0))].

Simplify the expression: (b/4)(\(a^4\)) (1/2) (2π - 0).

The final expression for the area is (bπ\(a^4\))/4.

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Answer:

He will have to pay  $35.04

Step-by-step explanation:

4.99 x 5 = 24.95

59.99 - 24.95 = 35.04

The Vamers live on a corner lot. Often, children cut across their lot to save walking distance. the walking distance that is saved by cutting across their property instead of walking around the lot is 20 feet (to the nearest integer)

information given in the question

hypotenuse = 48 feet

opposite = x

adjacent = x + 6

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

48² = x² + (x+6)²

2304 = x² + x² + 12x + 36

equating to zero

0 = x² + x² + 12x + 36 - 2304

0 = 2x² + 12x - 2268

2x² + 12x - 2268 = 0

x = 30.808  OR   -36.808

taking the positive value, x = 30.808 feet

adjacent = x + 6 = 30.808 + 6 = 36.808

The total distance

= adjacent + opposite

= 20.808 + 36.808

= 67.616

walking distance saved

= total distance - hypotenuse

= 67.616 - 48

= 19.616

= 19.62 feet (to the nearest hundredth)

= 20 feet (to the nearest integer)

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This is a table of values of three functions at selected values of x.

It is asking for h(f(-2))

Its saying, take f(-2), and take whatever you get from that and put it into h(x)

So, find f(-2).

Find x = -2, then see what f is there.

f(-2) = -1

So, find h(-1)

h(-1) = 0

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

The other root of the polynomial is 1 - √3.

The roots of a polynomial are the values of the independent variable at which the polynomial is zero.

If a polynomial has integral coefficients with 3 + i and 1 + √3  as roots, then what other roots must it have? To find the roots it has, we note that the root of a polynomial with a square root in the root also has the conjugate of the square root as a root.

So, since 1 + √3, the conjugate is also a root.

The conjugate is 1 - √3.

So, the other root is 1 - √3.

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The data provides sufficient evidence to conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B at the 0.1 level of significance. The correct answer is option (b) [μ1 − μ2 < 0, t = -7.054].

To determine if there is a significant difference between the means of the two locations, a hypothesis test can be performed.

The level of significance is given as 0.1, which means that the probability of rejecting the null hypothesis when it is true is 0.1 or less. To conduct the hypothesis test, the t-test statistic is used.

Based on the given information, location A had an average of 39 sales per day with a sample standard deviation of 8, while location B had an average of 55 sales per day with a sample standard deviation of 2.

Calculating the t-test statistic using the sample means, sample standard deviations, and sample sizes, we obtain a test statistic of -7.054.

Comparing the test statistic to the critical value, we find that it falls in the rejection region.

Therefore, the correct answer is option (b) [μ1 − μ2 < 0, t = -7.054].

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Answer:

Step-by-step explanation:

I have no clue wait until 3:00

We need to prove that if p² divides ab, then p² divides a or p² divides b. Since a and b are relatively prime, p cannot divide both a and b. If p² divides ab, then it must have p in it twice.

Let p be a prime and let a and b be relatively prime integers. Now, we need to prove that if p² | ab, then p² | a or p² | b.Let's assume that p² does not divide a. Then, we can write a = p x c + r, where r is a positive integer less than p. Since a and b are relatively prime, p does not divide b. Thus, we can write pb = pxd + s, where s is a positive integer less than p. Therefore, ab = (pxc + r) (pxd + s) = p²xcd + pxr + pys + rs. Now, p² divides ab, thus, p² divides p²xcd, pxr and pys but p² does not divide rs. Thus, p² divides pxc or p² divides pxd. Hence, either p² divides a or p² divides b. Thus, we have shown that if p² | ab, then p² | a or p² | b.

It can be said that if p² divides the product of two relatively prime integers, then p² must divide either of the integers. Hence, we can prove the contrapositive of the statement: if p² does not divide a and p² does not divide b, then p² does not divide ab.

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The probability of drawing a red marble is 3/10, the probability of drawing a marble that is not red is 7/10, and the probability of drawing a black or blue marble is 6/10.

The probability of drawing a black, red, blue, or white marble is 1.

The probability of the complement of the event that the marble drawn is black or blue is 2/5.

We have,

(a)

Probability of drawing a red marble: 3/10

Probability of drawing a marble that is not red: 1 - 3/10 = 7/10

Probability of drawing a black or blue marble: 4/10 + 2/10 = 6/10

Probability of drawing a black, red, blue or white marble:

= 4/10 + 3/10 + 2/10 + 1/10

= 10/10

= 1

Probability of drawing a yellow marble:

= 0 (since there are no yellow marbles)

(b)

The event that the marble drawn is black or blue is the complement of the event that the marble drawn is not black or blue.

Therefore, the probability of the complement is the probability of drawing a marble that is not black or blue.

Probability of drawing a marble that is not black or blue

= probability of drawing a red, white, or yellow marble

= 3/10 + 1/10 + 0

= 4/10

= 2/5

Thus,

The probability of drawing a red marble is 3/10, the probability of drawing a marble that is not red is 7/10, and the probability of drawing a black or blue marble is 6/10.

The probability of drawing a black, red, blue, or white marble is 1.

The probability of the complement of the event that the marble drawn is black or blue is 2/5.

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59,425 sq mi  

When you want to round to the units place, you look at the digit in the number that is in the place to the right of that: the tenths place. Here, that digit is 7, which is more than 4. Because that digit is more than 4, 1 is added to the units place and all the digits to the right of that are dropped.  

This gives you 59,424 +1 = 59,425.    

If the tenths digit were 4 or less, no change would be made to values in the units place or to the left of that. The tenths digit and digits to the right would be dropped.  

... 59,424.3 ⇒ 59,424 . . . . . for example

Answer:

Step-by-step explanation:

240/15 is 16 projects per day

Answer:

16 projects per day

Step-by-step explanation:

Take the number of projects and divide by the number of days

240/15

16 projects per day

Answer:

\(6a - 2\)

Step-by-step explanation:

\(a - 2 + 5a\)

\(6a - 2\)

Step-by-step explanation:

It looks like you have to draw a figure and then label every side with how long it is.

This first shape is a pentagon because it has 5 sides, and for each side of the pentagon the length would be 3/5 so .6 inches.

The second shape is a square because it has 4 sides, you than would label each side as 1 ft, because when you add them all it equals 4.

The third shape is a triangle with 3 equal sides. When you divide 16.8/3 it shows thag each side of this triangle will be labeled with 5.6 meters.

Answer:

Step-by-step explanation:

the coefficient is the number that is multiplied by x² so is 17

the constant term is the one without any x ( it does not change when x changes) so is -13

Answer:

1/8

Step-by-step explanation:

7/8-3/4  = 7/8-6/8 = 1/8

please mark as brainliest!

Answer:

Step-by-step explanation:

15x² - 2x - 1 = 0

15x² - 5x + 3x - 1 = 0

5x(3x - 1) + 3x - 1 = 0

(5x + 1)(3x - 1) = 0

x = -1/5, 1/3

8x² - 10x - 3 = 0

8x² - 12x + 2x - 3 = 0

4x(2x - 3) + 2x - 3 = 0

(4x+1)(2x-3) = 0

x = -1/4 , 3/2

16x² - 8x + 3 = 0

This question has complex answers as the D = 64 - 192 < 0

So, ignore this question. It is wrong or it has complex answers.

Use the quadratic formula for it.

9x² - 6x - 2 = 0

This also needs the quadratic formula as the answer is in roots.

8x² - 2x - 3 = 0

8x² - 6x + 4x - 3 = 0

2x ( 4x - 3) + 4x - 3 = 0

(2x + 1)(4x-3) = 0

x = -1/2 , 3/4

The probability of getting two odd numbers or two even numbers is 50%, since there are an equal number of odd and even numbers.

There are 6 possible outcomes when rolling two dice:

(1,1), (1,2), (2,1), (2,2), (1,3), (3,1).

The probability of getting two odd numbers is

2/6, or 1/3.

The probability of getting two even numbers is also

2/6, or 1/3.

Therefore, the probability of getting either two odd numbers or two even numbers is 2/3.

The probability of getting two odd numbers or two even numbers is 50%. This is because there are an equal number of odd and even numbers, so each outcome is equally likely. This means that the probability of getting two odd numbers or two even numbers is the same as the probability of getting one odd number and one even number. In both cases, the probability is 50%, since each outcome is equally likely. Therefore, the probability of getting two odd numbers or two even numbers is 50% as there are an equal number of odd and even numbers. This is because all possible outcomes are equally likely, and there are an equal number of odd and even numbers, so the probability of getting either two odd numbers or two even numbers is the same.

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Answer:

no

Step-by-step explanation:

they are not

Answer:

No

Step-by-step explanation:

because the angles are not equal. If they were they would have the same numbers.

Answer:

17

Step-by-step explanation:

(9+25)/2 = 34/2 = 17

when finding a mean, you have to add all the numbers and divide the sum by the number of values given.

Answer:

C

Step-by-step explanation:

I’m pretty sure

The line whose slope will be same as that of the graph given, will be the line parallel to the given line.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a graph of a line.

For a given line to be parallel to the given line, its slope should be same as that of the line plotted. Since the graph is not given, we can make an estimate for the equation of the line parallel to the given line. The four equations given will have their slopes as mentioned -

[A] -   4x + 5y = - 10       [m] = -4/5

[B] -   4x - 5y = 0           [m] = 4/5

[C] -   5x + 4y = 24        [m] = -5/4

[D] -   5x - 4y = -8          [m] = 5/4

Now, the line whose slope will be same as that of the graph given, will be the line parallel to the given line.

Therefore, the line whose slope will be same as that of the graph given, will be the line parallel to the given line.

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Answer:

\(15,000\:\mathrm{mm^3}\)

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by \(V=s^2\cdot h\), where \(s\) is the base length and \(h\) is the height. Substituting given values, we have: \(V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}\)

The volume of a trapezoidal prism is given by \(V=\frac{b_1+b_2}{2}\cdot l\cdot h\), where \(b_1\) and \(b_2\) are bases of the trapezoid, \(l\) is the length of the height of the trapezoid and \(h\) is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (\(\frac{b_1+b_2}{2}\)) multiplied by the trapezoid's height (\(l\)).

Substituting given values, we get:

\(V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}\)

Therefore, the total volume of the composite figure is \(5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}\) (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

\(V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark\)

The percentage increase in the volume of the pyramid if the height of the pyramid were increased to 541 it and the height to base area ratio of the pyramid were kept constant is 24.20%.

From the question above, V= 1/3 Bh

where B is the area of the base and h is the height. Now we need to find the volume of the pyramid in cubic meters if the height of the pyramid is 450m and base of the pyramid is 420m.

We can find the area of the pyramid using the formula of the area of the pyramid.

Area of the pyramid = 1/2 × b × p= 1/2 × 420m × 450m= 94,500 m²

Volume of the pyramid = 1/3 × 94,500 m² × 450 m= 14,175,000 m³

Now the height of the pyramid has been increased to 541m and the height to base area ratio of the pyramid were kept constant.

We need to find the percentage increase in the volume of the pyramid.In this case, height increased by = 541 - 450 = 91 m

New volume of the pyramid = 1/3 × 94,500 m² × 541 m= 17,604,500 m³

Increase in volume of pyramid = 17,604,500 - 14,175,000= 3,429,500 m³

Percentage increase in the volume of the pyramid= Increase in volume / original volume × 100%= 3,429,500 / 14,175,000 × 100%= 24.20 %

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a) Jim's utility function is U(x,y) = xy, so Jerry has the same preferences as Jim because his utility function is U(x,y) = 1,000xy + 2,000.

b) Jim's utility function is U(x,y) = xy, so Tammy has the same indifference curves as Jim because her utility function is U(x,y) = xy(1-xy).

c) The answers to (a) and (b) differ because preferences refer to the combination of different goods that are most preferred by a person, whereas indifference curves refer to the combination of different goods that yield the same level of satisfaction.

(a) The utility function of Jim is U(x, y) = xy. To find who has the same preferences as Jim, we need to look for other utility functions that generate the same ranking of bundles as U(x, y) = xy.

One such utility function is U(x, y) = ln(x) + ln(y), which is the Cobb-Douglas utility function. Therefore, those who have the same preferences as Jim are those who have the Cobb-Douglas utility function.

(b) To find who has the same indifference curves as Jim, we need to look for other utility functions that generate the same set of indifference curves as U(x, y) = xy.

One such utility function is U(x, y) = kxy, where k is a constant. This is because the level curves of U(x, y) = kxy are given by xy = c, which are the same as the indifference curves of U(x, y) = xy. Therefore, those who have the same indifference curves as Jim are those who have a utility function of the form U(x, y) = kxy.

(c) The answers to (a) and (b) differ because there can be multiple utility functions that generate the same set of indifference curves. In other words, two different utility functions can generate the same ranking of bundles, but have different shapes of indifference curves. Therefore, having the same preferences (i.e., generating the same ranking of bundles) does not necessarily imply having the same indifference curves.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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My friend consumed 8 donuts in one sitting. 8 donuts is a lower bound on how many donuts he is physically capable of eating in one sitting option A.

An element of K that is bigger than or equal to each member of S is referred to as an upper limit or majorant of a subset S of some preordered set (K, ) in mathematics, notably in order theory. In addition, each element of K that is smaller than or equal to each element of S is characterised as a lower limit or minorant of S.

A set that has an upper (or lower) bound is referred to as being majorized (or minorized), bounded from above, or minorized by that bound. In the mathematical literature, sets that have upper (or lower, respectively) limits are referred to as being bounded above (or below).

Friend consumed 8 doughnuts. So it is

lower bound on how can eat in a sitting.

Many donuts he lower bound is the lowest quantity in a set, as in our.

example, we definitely know he can eat 8 of them. We don't know how many more can be eat (upper bound) or is it exact amount be can eat.

Hence option (a) is correct.

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The general slope intercept form equation of a line is as stated below;

where m is the slope and b is the intercept.

If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.

The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;

So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);

Remember, the point slope form equation of a line is given as;

Substituting the above values, we'll have

Let's open up the parenthesis first, we'll have;

Let's isolate y by adding 7 to both sides of the equation;

The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).

Answer:

slope

Step-by-step explanation:

y = mx + c

where m is the slope of the line

Answer:

-6x-10y

Step-by-step explanation:

Answer:

-6x - 10y

Step-by-step explanation:

because

-2(3x + 5y) can be broken into

-2 * 3x = -6y

-2 * (+ 5y) = -10y

hence -6x - 10y

note * this symbol means multiply

Answer:

2 × 3 × 3 × 5

Step-by-step explanation: