!!Will mark Brainliest!! The points in the table lie on a line. What is the slope of the line?

Answer:

the answer should be B, 1/12 > 0.083

The expression 3z^2 - 27 can be simplified by factoring out the greatest common factor (GCF), which is 3:

3z^2 - 27 = 3(z^2 - 9)

Now, we can simplify the expression further by recognizing that the term inside the parentheses is the difference of squares, which can be factored as:

z^2 - 9 = (z + 3)(z - 3)

Substituting this back into our original expression, we get:

3z^2 - 27 = 3(z^2 - 9) = 3(z + 3)(z - 3)

Therefore, the simplified form of the expression 3z^2 - 27 is 3(z + 3)(z - 3).

The volume of the slice = π(64 - x²) cm³, and the exact volume of the cylinder = 128π cm³.

Explanation:

Given values: Radius of the cylinder = 8 cm height of the cylinder = 6 cmWidth of slice = 1 cmLet us find the expression for the volume of the slice used in the Riemann sum representing the total volume of the cylinder:

Volume of slice = (Area of the slice) × (Width of the slice)

Area of slice = πr² where, r is the radius of the circular slice.

The volume of slice = πr² × (Width of the slice)For a general rectangular slice of the cylinder with a width of 1 cm and radius r, we get:r = 8 - x (since the slice is taken at a distance of x from the end of the cylinder)

Width of slice = Δx = 1 cmArea of slice = π(8 - x)²Volume of slice = π(8 - x)² × (1) = π(64 - 16x + x²) cm³Let us write a definite integral that represents the exact volume of the cylinder:

To evaluate the definite integral, we will use the Riemann sum, with Δx = 0.001.Number of slices, n = (8 - 0)/0.001 = 8000Interval [a, b] = [0, 8]Height of each slice, f(xi) = π(64 - 16xi + x²)Definite integral = \(\large\int\)f(x)dx = \(\lim_{n\to\infty}\sum_{i=1}^n f(xi)Δx\)= \(\lim_{n\to\infty}\sum_{i=1}^n π(64 - 16xi + x²)Δx\)= \(\lim_{n\to\infty}\) π\(\sum_{i=1}^n\) (64 - 16xi + x²)Δx= π\(\large\int\)[64 - 16x + x²]dx= π[(64x - 8x² + (1/3)x³)]8 to 0= π[(64 × 8 - 8 × 8² + (1/3) × 8³) - (64 × 0 - 8 × 0² + (1/3) × 0³)]= 128π cm³

Hence, the volume of the slice = π(64 - x²) cm³, and the exact volume of the cylinder = 128π cm³.

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Answer:

Subtracting integers can be represented using integer tiles. For example, if we want to subtract -3 from 4, we can lay out 4 tiles on the number line and then add -3 tiles, like this:

4 3 2 1 0 -1 -2 -3

The subtraction problem can be represented as 4 + (-3). Adding the opposite of the second number, as Paul suggests, means finding the sum of 4 and -3, which is 1. So, Paul is correct that subtracting integers is equivalent to adding the opposite of the second number.

The solution of the linear equation is f = -3/4

Here we have the linear equation:

(5/6)*f - (3/4)*f + 3/4 = 1/2

And we want to solve this for the variable f. To do that, we need to isolate f.

(5/6)*f - (3/4)*f = 1/2 - 3/4

First, we move all the terms with the variable to the left side and the terms without it to the right side, then we simplify both sides:

(5/6)*f - (3/4)*f = 2/4 - 3/4

( 5/6 - 3/4)*f = -1/4

(10/12 - 6/12)*f = -1/4

(4/12)*f = -1/4

f = -(1/4)*(12/4) = -3/4

Then we conclude that the solution of the given linear equation is f = -3/4

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Answer:

\(\sf \: f = - 3\)

Step-by-step explanation:

\( \sf \frac{5f}{6} - \frac{3f}{4} + \frac{3}{4} = \frac{1}{2} \\ \)

First, make all the denominators same to solve the fractions.

\(\sf \frac{5f \times 2}{6 \times 2} - \frac{3f \times 3}{4 \times 3} + \frac{3 \times 3}{4 \times 3} = \frac{1}{2} \\ \\ \sf \frac{10f }{12} - \frac{9f }{12} + \frac{9}{12} = \frac{1}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

Combine like terms.

\( \sf \frac{(f + 9)}{12} = \frac{1}{2} \\ \)

Use cross multiplication.

\( \sf2(f + 9) = 12 \times 1 \\ \)

Now, solve the brackets.

\( \sf 2f + 18 = 12\)

Subtract 18 by both sides.

\( \sf2f + 18 - 18 = 12 - 18 \\ \sf2f = - 6\)

Divide both sides by 2.

\( \sf \: f = - 3\)

The expected value of the sampling distribution of p is 0.9.

A sampling distribution is a statistical probability distribution derived from a larger number of samples gathered from a certain population. The sampling distribution of a given population is the distribution of frequencies of a range of possible outcomes for a population statistic.

The sample size multiplied by the population mean yields the expected value of the sample total.

The anticipated value is calculated in statistics and probability analysis by multiplying each conceivable outcome by the likelihood that each outcome will occur and then adding all of those values.

In this case, the the proportion of people who order coffee with their dinner is 0.9. This is the expected value.

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Option G is the correct one. The table represents the non proportional linear relationship with equation y = 3x - 3.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given values are,

x = 4, then y = 9

x = 5, then y = 12

x = 2, then y = 3

This is clearly not a proportional relation since 4/9 ≠ 5/12

Let y = 3x - 3

If x = 4, then y = (3 × 4) - 3 = 9

If x = 5, then y = (3 × 5) - 3 = 12

If x = 2, then y = (3 × 2) - 3 = 3

This equation holds.

Hence the true statement is option G.

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Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

The expected return on James's portfolio is 18%.

The expected return on Siebling Manufacturing Company's common stock is 8.4%.

To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.

Let's assume James invests x% in MSFT and (100 - x)% in AAPL.

The expected return on James's portfolio can be calculated as:

Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)

Substituting the given values:

Expected Return = (x * 12%) + ((100 - x) * 24%)

To find the value of x that makes James's investments equal, we set the weights equal:

x = 100 - x

Solving this equation gives us x = 50.

Now we can substitute this value back into the expected return equation:

Expected Return = (50% * 12%) + (50% * 24%)

Expected Return = 6% + 12%

Expected Return = 18%

Therefore, the expected return on James's portfolio is 18%.

To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).

The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * Market Premium

Risk-Free Rate = 2%

Market Premium = 8%

Beta = 0.8

Expected Return = 2% + 0.8 * 8%

Expected Return = 2% + 6.4%

Expected Return = 8.4%

Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.

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Answer for Part A:

Elena makes more money than Jada does. Elena makes $1.40 more than Jada does.

Explanation for Part A:

The equation for Elena tells us that she makes $8.40 per hour. Jada makes $7 an hour. Since 8.4 > 7, Elena makes more money than Jada per hour

The definite integral that represents the area of the region enclosed by the polar curve r = 1 sin θ is ∫[a, b] 1/2 r^2 dθ

To determine the definite integral that represents the area of the region, we integrate the expression 1/2 r^2 with respect to θ over the interval [a, b], where a and b are the limits of the region.

In this case, the polar curve r = 1 sin θ represents a circle with radius 1 centered at the origin. As θ varies from 0 to π, the curve traces half of the circle in the positive direction. To find the area of the region enclosed by this curve, we integrate the expression 1/2 r^2 over this interval.

The expression 1/2 r^2 represents the area of a sector of the circle with radius r and central angle θ. Integrating this expression with respect to θ gives us the total area enclosed by the curve.

By evaluating the definite integral over the interval [a, b], we can find the area of the region enclosed by the polar curve r = 1 sin θ.

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Answer:

1st take PQ - 6 cm

then take an arc of PR of 6cm , and form QR of 6cm ...

Answer: 3

Step-by-step explanation:

The required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)

For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.

The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi

\(z = 5\sqrt{3}/4 - 5/4i\)
the polar form complex numbner  can be given as
\(z = rcos\theta +rsin\theta i\)   - - - - - -(1)
where r = \(\sqrt{a^2+b^2}\)
and \(\theta=tan^-\frac{b}{a}\)

Since a = 5√3/4 and b = -5/4
\(r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}\)
r = 10/4
r = 5/2
Now,
\(\theta=tan^-\frac{b}{a}\)
\(\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30\)

Now the polar form is given by substituting the values of r and \(\theta\) in equation 1
Here,
\(z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i\)

Thus, the required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)

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To answer this problem we have to remember that the break even point occur where the revenue function and the cost function have the same value.

Then, this happens when

Pluggin the expressions of our functions and solving for x we have:

Therefore the break even point occurs when x=74000. In this points both functions have value

Answer:

(a) If r is any rational number and s is any irrational number, then r/s is rational

(b) The statement is false when r is 0

Step-by-step explanation:

Given

\(r \to\) rational number

\(s \to\) irrational number

\(\frac{r}{s} \to\) irrational number

Solving (a): The negation

To get the negation of a statement, we only need to negate the end result

In other words, the number type of r and s will remain the same, but r/s will be negated.

So, the negation is:

\(r \to\) rational number

\(s \to\) irrational number

\(\frac{r}{s} \to\) rational number

Solving (b): When r/s is irrational is false

Given that:

\(\frac{r}{s} \to\) irrational number

Set r to 0

So:

\(\frac{r}{s} = \frac{0}{s}\)

\(\frac{r}{s} = 0\) -- rational

Hence, the statement is false when r is 0

Answer:

Number of students who scored atleast 1700 but less Than 2100 = 17

Step-by-step explanation:

Given the data :

1,450 1,620 1,800 1,740 1,650 1,800 2,010 1,780 1,840 1,490 1,620 1,480 2,390 1,640 1,830 1,710 1,900 1,910 1,950 1,820 1,590 2,350 2,260 1,870 1,530 1,950 2,000 1,830 1,980 2,100

Class interval __ Frequency

1400 - 1599 ____ 5

1600 - 1799 ____ 7

1800 - 1999 ____12

2000 - 2199 ___ 3

2200 - 2399 ___ 3

Number of students who scored atleast 1700 but less Than 2100 = 17

Using a significance level of 0.05 a. z approximately equals 2.00 for a P-value of 0.02275 (d) z approximately equals 2.00 for a P-value of 0.02275. Since the P-value is less than 0.05, reject the null hypothesis that there is no difference in the number of sunny days between City A and City B.

To determine if City B is significantly sunnier than City A, we can use a z-test for two proportions. Using the given data, we calculate a z-value of 2.00 and a corresponding P-value of 0.02275.

Since the P-value is less than the significance level of 0.05, we reject the null hypothesis that there is no difference in the number of sunny days between City A and City B. This means that we have evidence to suggest that City B is significantly sunnier than City A based on the sample data.

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The two angles are 45 degrees.

Step-by-step explanation:

You are just halfing the 90 degree angle, so all you have to do is divide 90 by two, and you have 45.

Step-by-step explanation:

\(\huge\mathcal\pink{answer..} \\ \\ \\ \small\mathfrak\purple{d {3}= 27} \\ \\ \small\mathfrak\purple{d = \sqrt[3]{27} } \\ \\ \small\mathfrak\purple{d {}= \ \sqrt[3]{3 \times 3 \times 3} } \\ \\ \small\mathfrak\purple{d {}= 3} \\ \\ \small\mathfrak\green{hope \: it \: helps..} \\ \\ \)

Answer:

d = 3

Step-by-step explanation:

The ordered pair which is solution of 8x+16y > 32 is (-3,5) , the correct option is (b) .

In the question ,

it is given that ,

the linear inequality is 8x+16y > 32 .

to find the solution set ,

we substitute the options that are given

Option(a)

Substituting (0,2) in 8x+16y > 32 ,

we get ,

8(0) + 16(2) > 32

32 > 32 ,

false , hence it is not a solution .

Option(b)

Substituting (-3,5) in 8x+16y > 32 ,

we get ,

8(-3) + 16(5) > 32

-24 + 80 > 32

56 > 32

true , yes it is the solution .

Option(c)

Substituting (-1,1) in 8x+16y > 32 ,

we get ,

8(-1) + 16(1) > 32

-8 + 16 > 32

8 > 32

False , hence it is not a solution .

Option(d)

Substituting (4,0) in 8x+16y > 32 ,

we get ,

8(4) + 16(0) > 32

32 + 0 > 32

32 > 32

False , hence it is not a solution .

The only solution that satisfy the inequality is (-3,5) .

Therefore  , The ordered pair which is solution of 8x+16y > 32 is (-3,5) .

The given question is incomplete , the complete question is

Which ordered pair is in the solution set of 8x+16y > 32 ?

(a) (0,2)

(b) (-3,5)

(c) (-1,1)

(d) (4,0)

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Answer:

Step-by-step explanation:

We are going to use the areas given to find the lengths of the sides of each of their respective squares. For the purple square, the area is 35 units squared. Because the formula for the area is A = s * s, then we can fill in the value for the area and solve for s, the side length, of the purple square.

\(35=s^2\) and

\(s=\sqrt{35}\). That side length also serves as the height of the right triangle. Now on to the blue square on the bottom. It has an area of 50 units squared, so

\(50=s^2\) and

\(s=\sqrt{50}\). We could feasibly simplify that, but it's not necessary, really. That side serves as the base of the right triangle. Now we can use Pythagorean's Theorem to find the length of the hypotenuse of the right triangle, which also serves as the side of the big blue square. We will call the side of the big blue square x.

\(x^2=(\sqrt{35})^2+(\sqrt{50})^2\) and

\(x^2=35+50\) and

\(x^2=85\) and

\(x=\sqrt{85}\). That is the side length of the large blue square. The area for the square is s * s, and since we know the side length to be √85:

\(A=(\sqrt{85})(\sqrt{85})\) so

A = 85 units squared

The correct answer is: Yes, relation Q is a function,because there is exactly one y-value for every x-value.

To determine whether the given relation Q is a function, we need to check if each x-value is associated with a unique y-value. If there is any x-value that corresponds to multiple y-values, then the relation is not a function.

Let's examine the ordered pairs in relation Q: (3, -2), (-3, 1), (-2, -2), (1, -3).

We can see that each x-value in Q is associated with a unique y-value:

For x = 3, the y-value is -2.

For x = -3, the y-value is 1.

For x = -2, the y-value is -2.

For x = 1, the y-value is -3.

Since each x-value is paired with a unique y-value in relation Q, we can conclude that Q is a function.

In a function, every input (x-value) maps to a single output (y-value). If there were any repeated x-values with different y-values in the relation, it would indicate a violation of this rule and Q would not be a function. However, in this case, all the x-values have distinct y-values, satisfying the criteria for a function.

It's worth noting that we can also visualize this relation on a coordinate plane and check if there are any vertical lines that intersect the graph at more than one point. If there are no such lines, it confirms that the relation is a function.

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Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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It would take the three of them about 6 hours to paint the four rooms.

Let t represent the time that it would take all three of them to paint one room.

It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room.

Therefore:

(1/6 + 1/4 + 1/8)t = 1

(2/3)t = 1

t = 1.5 hours

It would take all of them 1.5 hours each to paint one room.

For 4 rooms:

Total time = 1.5 hours * 4 = 6 hours

It would take the three of them about 6 hours to paint the four rooms.

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Answer:

A= -42

B= 3

Step-by-step explanation:

There were 60 jelly beans in the unopened bag of jelly beans.

Let's work through the problem step by step to find the original number of jelly beans in the bag.

John ate three-fourths of the jelly beans.

This means that he consumed 3/4 of the total number of jelly beans, leaving 1/4 of the original amount.

Mike then ate two-thirds of the remaining jelly beans.

Since 1/4 of the original amount was left after John, Mike ate 2/3 of this remaining 1/4.

To find out how much is left, we need to calculate \((\frac{1}{4} )\times (\frac{2}{3} )\).

\((\frac{1}{4} )\times(\frac{2}{3} )=\frac{2}{12} =\frac{1}{6}\)

Mike ate 1/6 of the original amount, leaving 1/6 of the original amount.

Finally, Fred ate the ten jelly beans that were left.

We know that these ten jelly beans represent 1/6 of the original amount.

Let's calculate how many jelly beans are equal to 1/6.

\(\frac{1}{6} = 10\) jelly beans

Now, we can determine how many jelly beans are equal to 6/6 (the whole).

\(\frac{1}{6} \times6=10\times6=60\) jelly beans

Therefore, there were 60 jelly beans in the unopened bag of jelly beans.

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There are 5 elements in 32 proper subsets.

What are subsets?

If every element of set A is also an element of set B, then set B is a superset of set A, and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Here, we have

Given:  32 proper subsets.

We have to find how many elements are in 32 proper subsets.

Subsets of a set having n elements = 2^n

2ⁿ = 32

n = 5

Hence, there are 5 elements in 32 proper subsets.

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Answer:

B

Step-by-step explanation:

Cube has a square as its base.

Triangular prism has a triangle as its base.

Rectangle is not a 3-dimensional shape.

Rectangular prism has a rectangle as its base.

Therefore, the triangular prism is the only option that has a triangle as its base.

In a triangular prism, there are two triangles and three rectangles. Then the correct option is B.

A closed solid with two parallel triangular bases joined by a triangle surface is known as a triangular prism.

Some geometries are given below.

In a cube, all the faces of the cube are square.

In a triangular prism, there are two triangles and three rectangles.

All the three rectangle may or may not be same because the base of the rectangle is decided by the side length of the triangle.

The rectangle is a two-dimensional geometry. So, it is a rectangle.

In a rectangular prism, all the faces of the rectangular prism are rectangle.

Then the correct option is B.

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The statement of the given hypothesis is False.

What is hypothesis testing?

Hypothesis testing is a statistical analysis that looks at a sample to see if the findings are representative of the population. Depending on the type of data used and the goal of the research, the analyst will choose a certain approach.

Given:  A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.

">" sign implies that right-tailed test i.e., one-tailed right-sided.

Hence, the given statement is False.

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