Find the slope of the line through the given points.
(-2,7) and (2,-5)

Answer:

3.542

Step-by-step explanation:

7 1/6 - 3 5/8 = (85/24) = 3(13/24) ≅ 3.5416667.

7⅙ - 3⅝ = 8524 = 3 1324 ≅ 3.5416667 (simplified) = 3.542

Answer:

`18. x=9

19. x=4

20. x=25,5

21. x=3

22. x=3,5

23. x=10

Step-by-step explanation:

The correct option is:d.9/2 pie units cubbed. The given region is obtained by rotating the curve y = x2 – 3 about the x-axis, which can be represented as:y = x² - 3

We have to rotate this curve around the y-axis. The required volume can be obtained by integrating the area of the circular cross-sections formed after rotating the curve.The radius of each circular cross-section at any value of x is equal to the perpendicular distance between the curve and the y-axis, which is x.

Thus, the area of each circular cross-section can be represented as:A = π(x²)The limits of integration can be found by equating y = x² - 3 to 0, which is:0 = x² - 3x = ± √3

Thus, the volume of the solid obtained by rotating the region bounded by y = x² - 3 and the x-axis about the y-axis is given by:V = ∫-√3^√3 π(x²) dxV = π ∫-√3^√3 (x²) dx.

By using the formula for integration, we get:V = π [(x³)/3] -√3^√3V = π [(√3³ - (-√3)³)/3]V = π (18/3)V = 6π.Therefore, the volume of the solid obtained by rotating the region bounded by y = x² - 3 and the x-axis about the y-axis is 6π units cubed. Hence, the correct option is:d.9/2 \(\pi\)units cubbed.

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Answer: The midpoint of the line segment with endpoints (5, 1) and (2, -3) is (3.5, -1).

Step-by-step explanation:

The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are:

((x1 + x2) / 2, (y1 + y2) / 2)

In this case, (x1, y1) = (5, 1) and (x2, y2) = (2, -3). Substituting these values into the formula, we get:

((5 + 2) / 2, (1 - 3) / 2) = (3.5, -1)

Therefore, the midpoint of the line segment with endpoints (5, 1) and (2, -3) is (3.5, -1). The correct answer is A. (3.5, -1).

Answer:

17,453.30 feet

Step-by-step explanation:

1 Multiply both sides by

n

−

3.2

n−3.2.

n

+

0.3

=

9

2

(

n

−

3.2

)

n+0.3=

2

9

​

(n−3.2)

2 Simplify

9

2

(

n

−

3.2

)

2

9

​

(n−3.2) to

9

(

n

−

3.2

)

2

2

9(n−3.2)

​

.

n

+

0.3

=

9

(

n

−

3.2

)

2

n+0.3=

2

9(n−3.2)

​

3 Multiply both sides by

2

2.

2

n

+

0.6

=

9

(

n

−

3.2

)

2n+0.6=9(n−3.2)

4 Expand.

2

n

+

0.6

=

9

n

−

28.8

2n+0.6=9n−28.8

5 Subtract

2

n

2n from both sides.

0.6

=

9

n

−

28.8

−

2

n

0.6=9n−28.8−2n

6 Simplify

9

n

−

28.8

−

2

n

9n−28.8−2n to

7

n

−

28.8

7n−28.8.

0.6

=

7

n

−

28.8

0.6=7n−28.8

7 Add

28.8

28.8 to both sides.

0.6

+

28.8

=

7

n

0.6+28.8=7n

8 Simplify

0.6

+

28.8

0.6+28.8 to

29.4

29.4.

29.4

=

7

n

29.4=7n

9 Divide both sides by

7

7.

29.4

7

=

n

7

29.4

​

=n

10 Simplify

29.4

7

7

29.4

​

to

4.2

4.2.

4.2

=

n

4.2=n

11 Switch sides.

n

=

4.2

n=4.2

Answer:

4.2 (to 1d.p.)

Step-by-step explanation:

\(\frac{n+0.3}{n-3.2\\}\)=9/2              9/2 = 4.5

Multiply both sides by (n-3.2)

n+0.3 = 4.5(n-3.2)

Now expand the brackets

n+0.3 = 4.5n - 14.625n

Now rearrange to make n the subject

n + 0.3 = 4.5n -14.625

-n             -n

4.5n - n -14.625 = 0.3

3.5n -14.625 = 0.3

 +14.625          +14.625

3.5n = 14.925

÷3.5    ÷3.5

n = 4.2

The area of the sector is 72f

The given parameters are:

Angle = f

Diameter = 24

Start by calculating the radius

r = Diameter/2

r = 24/2

r = 12

The area of the sector is

A = (θ/2) × r^2

So, we have

A = (f/2) * 12^2

Evaluate

A = 72f

Hence, the area of the sector is 72f

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A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.

In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.

Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.

Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.

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Answer:

-0.2(24)= -4.8

-100(-9.287)= -9.287

The range of the graph is [3, ∞), because it has a minimum value at y = 3

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an absolute value graph

The rule of a graph is that

Using the above as a guide, we have the following:

Domain = All real values

Range = [3, ∞), because it has a minimum value at y = 3

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Answer:

D

Step-by-step explanation:

100-33=67

67-29=38

38%

:3

Answer:

\({ \bf{consider \: points \: (5, \: 0) \: and \: (0, \: - 5)}} \\ { \tt{slope = \frac{ - 5 - 0}{0 - 5} }} \\ { \tt{m = 1}} \\ \\ { \tt{y = mx + c}} \\ 0 = ( 1 \times 5) + c \\ c = -5 \\ \\ { \bf{answer : { \tt{y = { \boxed{ 1}x + { \boxed{-5}}}}}}}\)

Answer:

\(y = [ 1 ] x + [ - 5 ]\)

Step-by-step explanation:

Let us consider 2 points through which the line passes.

\((x_1 , y _ 1 ) = ( 5 , 0 ) \ and \ (x _ 2 , y _ 2 ) = ( 0 , - 5 )\)

Step 1 : Find slope, m

       \(slope, m = \frac{y _ 2 - y_ 1 }{x_ 2 - x_ 1 } = \frac{-5 - 0}{0-5} = \frac{-5}{-5} = 1\)

Step 2 : Equation of line

         \((y - y_ 1) = m( x - x_1)\\\\( y - 0) = 1 ( x - 5)\\\\y = x - 5 \\\\y = x + ( -5)\)

        \(y = (1) x + ( -5)\)

We have ST=5x, TU=3x+32 and they're equal if T is the midpoint:

5x = 3x + 32

2x = 32

x = 16

ST = 5x = 80

So TU = 80 and SU=160

Answer: Second choice

Answer:

D. 1x9x4

Step-by-step explanation:

V= l x w x h

Answer: Robin has 50 nickels, 60 dimes, and 120 quarters.

Step-by-step explanation:

Answer:

(-13,6)

Step-by-step explanation:

Rule for rotation 90 degrees clockwise around the origin

( x , y ) --------> ( y , -x )

Explanation of rule:

Swap the x and y values

Change sign of new y value

Find Q' after a rotation 90 degrees clockwise around the origin

Given coordinates of Q

(-6,-13)

Apply rotation 90 degree clockwise rule

(-6,-13) -------> swap x and y values -------- -> (-13,-6) -------> change sign of new y value --------> (-13,6)

Q' will be at (-13,6) after a rotation 90 degrees clockwise around the origin

Answer:

40°

Step-by-step explanation:

∠AOE and ∠COD are vertical angles meaning they have the same value.

According to the geometric series. the absolute value of the common ratio must be less than 1 for the series to converge.(option a)

In the given problem, we are asked to find the common ratio and determine if the geometric series converges or diverges. The series we are dealing with is:

Σ n=1 to ∞ (-3)ⁿ⁻¹ / 5n

To find the common ratio, we need to look at the ratio of successive terms in the series. Let's take the ratio of the second term to the first:

(-3)¹ / 5(1) ÷ (-3)⁰ / 5(0) = (-3)¹ / 5

We can see that the common ratio, denoted as |r|, is |-3/5|. Since the absolute value of the common ratio is less than 1, we can conclude that the series converges.

To find the sum of the geometric series, we can use the formula:

S = a / (1 - r)

where S is the sum of the series, a is the first term, and r is the common ratio. In this case, the first term is:

a = (-3)⁰ / 5(1) = 1/5

And the common ratio we found earlier is:

r = |-3/5| = 3/5

Therefore, the sum of the geometric series is:

S = 1/5 / (1 - 3/5) = 1/5 / 2/5 = 1/2

Hence the correct option is (a).

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The range of values that represent the middle 68% of the distribution is from 75 to 95.

In a normal distribution, the middle 68% of the data falls within one standard deviation from the mean. To find the range of values that represent the middle 68% of the distribution, we can calculate the upper and lower bounds.

Given:

Mean (μ) = 85

Standard Deviation (σ) = 10

To find the upper bound:

Upper Bound = Mean + Standard Deviation

Upper Bound = 85 + 10

Upper Bound = 95

To find the lower bound:

Lower Bound = Mean - Standard Deviation

Lower Bound = 85 - 10

Lower Bound = 75

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Answer:690

Step-by-step explanation:

690

Answer:  $3,261.

Step-by-step explanation:

The answer is $3,261. Jayden would have more money in his account than Camden because his account pays a higher interest rate and is compounded continuously, which allows more frequent compounding of interest. This means that Jayden's account accumulates more interest than Camden's account over time.

Answer:

|x-15|=0

Step-by-step explanation:

Obviously.

Answer:

|x-15|=0

Step-by-step explanation:

Let's assume the amount invested at the higher interest rate (16%) is x dollars.

The amount invested at the lower interest rate (6%) would then be ($80,000 - x) dollars, as the total investment is $80,000.

The interest earned from the investment at 16% is calculated as (x * 16%) = 0.16x dollars.

The interest earned from the investment at 6% is calculated as (($80,000 - x) * 6%) = 0.06(80,000 - x) dollars.

According to the given information, the retiree receives a total interest of $8,900 per year. So we can set up the equation:

0.16x + 0.06(80,000 - x) = 8,900

Now, let's solve the equation to find the value of x:

0.16x + 0.06(80,000 - x) = 8,900

0.16x + 4,800 - 0.06x = 8,900

0.1x + 4,800 = 8,900

0.1x = 8,900 - 4,800

0.1x = 4,100

x = 4,100 / 0.1

x = 41,000

Therefore, $41,000 is being invested at the higher interest rate (16%).

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Answer:

 8.5

Step-by-step explanation:

How to Find the Mean

Add up all data values to get the sum

Count the number of values in your data set

Divide the sum by the count

The mean is the same as the average value in a data set.

Mean Formula: The mean x of a data set is the sum of all the data divided by the count n.

[RevyBreeze]

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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The measure of central tendency most likely to be affected by an outlier is the mean.

The mean is calculated by summing all the values in a dataset and dividing by the total number of values. Since the mean takes into account every value in the dataset, it is sensitive to extreme values or outliers. An outlier is a value that significantly deviates from the other values in the dataset.

When an outlier is present in the dataset, its extreme value can heavily influence the sum of all values and consequently impact the calculation of the mean. This is because the mean is directly affected by the magnitude of each value, and outliers can greatly skew the overall average. Even a single outlier can pull the mean towards its extreme value.

In contrast, other measures of central tendency, such as the median and mode, are less affected by outliers. The median represents the middle value when the dataset is ordered, so extreme values do not influence it as much. The mode represents the most frequently occurring value and is not influenced by outliers unless the outlier itself becomes the mode.

Therefore, when there is an outlier present in a dataset, the mean is the measure of central tendency that is most likely to be affected, while the median and mode provide more robust measures in such cases. It is important to consider the presence of outliers and choose the appropriate measure of central tendency accordingly.

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Answer:

8 1/2

Step-by-step explanation:

Take the decimal portion

.5

This is 5 tenths

write 5/10

Simplify

1/2

Bring the whole number back

8 1/2

Answer:

8 1/2

Step-by-step explanation: