What is the slope of the line that passes through the points (1,3) and (-2,3) ?

Answer:

I think it 648.

Step-by-step explanation:

The radius AO of the circle is approximately 1.414 units when rounded to one decimal place.

To find the radius AO of the circle, we can use the properties of a regular polygon inscribed in a circle.

In a regular polygon, all sides and angles are equal. Let's consider one of the isosceles triangles formed by the center of the circle O, one of the vertices A, and the midpoint of one of the sides.

The triangle OAM is a right triangle with OA as the hypotenuse and AM as the adjacent side. The measure of angle OAM is half the central angle of the regular polygon, which is 360 degrees divided by the number of sides.

In this case, since the polygon is not specified, we cannot determine the exact central angle. However, we are given that the length of the side of the polygon is 8 units.

Using trigonometry, we can express the adjacent side AM in terms of the central angle (θ) and the radius (OA) as AM = OA × cos(θ).

Since AM is half the length of the side, we have AM = 4 units.

Substituting these values into the equation, we get 4 = OA × cos(θ).

Now, we can solve for the radius AO. Rearranging the equation, we have OA = 4 / cos(θ).

Using a calculator, we can calculate the value of cos(θ) by dividing the length of the side by 2 times the radius, which gives us 4 / (2 × OA).

Simplifying this expression, we have 2OA = 4 / (2 × OA).

Multiplying both sides by 2OA, we get 2OA^2 = 4.

Dividing both sides by 2, we have OA^2 = 2.

Taking the square root of both sides, we find OA = √2.

Using a calculator, we can evaluate this to be approximately 1.414.

Therefore, the radius AO of the circle is approximately 1.414 units when rounded to one decimal place.

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Answer:

OP = 23

Step-by-step explanation:

• The diagonals of a parallelogram bisect each other , then

OP = MP , that is

3x - 4 = 2x + 5 ( subtract 2x from both sides )

x - 4 = 5 ( add 4 to both sides )

x = 9

Then

OP = 3x - 4 = 3(9) - 4 = 27 - 4 = 23

In a triangle, The value of x is, 40°

And, The value of y is, 50°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The triangle is show in figure.

We know that;

In a triangle, the pair of two opposite sides are equal then there corresponding angles are also equal.

Now, By figure we can formulate;

⇒ x + x + 100 = 180

Solve for x;

⇒ 2x + 100 = 180

⇒ 2x = 180 - 100

⇒ 2x = 80

⇒ x = 40

Thus, The value of x = 40°

And, We get;

⇒ x° + y° + 90° = 180°

⇒ 40 + y + 90 = 180

⇒ y + 130 = 180

⇒ y = 180 - 130

⇒ y = 50°

Thus, The value of y = 50°

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The probability of exactly 16 students having jobs in the sample is 0.204 and the probability of 16 or more students having jobs in the sample is 0.334.

Let X be the number of KSU students with jobs in a random sample of 20 students. Since each student in the sample can be either employed or not employed, X follows a binomial distribution with parameters n = 20 (the sample size) and p = 0.50 (the probability of a student having a job).

To find the probability of exactly 16 students having jobs in the sample, we can use the binomial probability mass function

P(X = 16) = (20 choose 16) * 0.5^16 * 0.5^(20-16) = 0.204

To find the probability of 16 or more students having jobs in the sample, we can use the cumulative distribution function

P(X ≥ 16) = 1 - P(X < 16) = 1 - ∑(i=0 to 15) (20 choose i) * 0.5^i * 0.5^(20-i) = 0.334

Based on the sample data, it appears that the proportion of KSU students with jobs is higher than the professor's conjectured value of 0.50. However, we cannot conclusively reject the professor's conjecture based on a single sample of 20 students.

We would need to conduct a hypothesis test with appropriate statistical significance level to determine if the difference between the sample proportion and the conjectured value is statistically significant or not.

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Answer:

Juan has completed 0.7 of his assignment, which means he has not completed 0.3 of his assignment. This can also be expressed as a fraction: 3/10. Therefore, Juan has not completed 3/10 of his assignment.

Step-by-step explanation:

Answer:

d =±2sqrt(7) i

Step-by-step explanation:

d^2 = -28

Take the square root of each side

sqrt(d^2) = ±sqrt(-28)

d = ±sqrt(-28)

d = ±sqrt(-1)sqrt(28)

We know that sqrt(-1) = i

d =±i*sqrt(4)sqrt(7)

d =±i 2sqrt(7)

d =±2sqrt(7) i

The fewest number of minutes it will take Jeremy and Michael to solve 10 Rubik's cube is 16 with a speed such that Jeremy solve one in 4 minutes and Michael solves 5 in 12 minutes.

To solve the following word problem,

Time taken by Jeremy to solve one cube = 4 minutes = 240 seconds

Time taken by Michael to solve 5 cubes = 12 minutes

Time taken by Michael to solve 1 cube = \(\frac{12}{5}\) minutes = 144 seconds

Since one solves the cube alone, they do it individually,

For the first 12 minutes,  Michael solves 5 cubes and Jeremy solves 3 cubes (\(\frac{12}{3}\))

Then, to solve 2 or more cubes Michael takes 288 seconds

And if Michael and Jeremy each solve one cube it takes them 144 seconds and 240 seconds respectively.

Therefore, the second situation is responsible for solving in the least time which comes out to be 12 minutes + 4 minutes (240 seconds) is 16 minutes.

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Answer:

false the |-| mean the absolute value thus it would = the same

Answer: False

Step-by-step explanation:

This is absolute value. The absolute value of -3 is 3 because lets say you have a number line, how far is -3 to 0 ? Its 3 . Your answer would be that its equal.

It is unlikely that McDonald's is to blame for having a faulty seat in its restaurant. The company that manufactures the seat may be more likely to blame if the seat was not properly manufactured or tested.

To determine who is to blame, we need to calculate the probability of a 420-pound person causing a seat to collapse that is designed to hold an average load of 450 pounds with a standard deviation of 8 pounds.

Assuming a normal distribution, we can calculate the z-score of a 420-pound person as:

z = (420 - 450) / 8 = -3.75

Looking at a standard normal distribution table, we find that the probability of a z-score of -3.75 or lower is approximately 0.0001. This means that there is a very low chance of a 420-pound person causing a seat designed for an average load of 450 pounds to collapse.

However, it should also be noted that Mr. Smith's medical condition may have contributed to the seat's collapse, even if the judge ruled that it is not relevant to the case. Ultimately, it would be up to a court of law to determine who is to blame and whether or not Mr. Smith's claims for pain and suffering are justified.

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Answer:

Step-by-step explanation:

The function can be graphed using a graphing calculator, geometry app, or spreadsheet. One such graph is attached. Often, these tools are capable of identifying extrema and intercepts.

__

The vertex of the graph is reported as (x, y) = (2, 20). This means the maximum height is reached after 2 seconds. That maximum height is 20 meters.

__

The drop is launched from ground level at x = 0 seconds. It returns to ground level at x = 4 seconds.

Answer:

Step-by-step explanation:

Joe, do you recall this formula ?  mid-segment =  \(\frac{1}{2}\)(base1 + base2)  ?

where AD = base1  

and BC = base2

and mid-segment is EF

recall that this formula works, as long as EF is at the mid-point between the two top and bottom bases only.

The trapezoid is telling us ,  with the same length lines, that this is the case.

Then

EF =   \(\frac{1}{2}\)( x-3  +  2x -10 )

see how I got that?

EF =    \(\frac{1}{2}\)( 3x -13 )

EF =\(\frac{3}{2}\)X - \(\frac{13}{2}\)

also remember that EF = x

x  = \(\frac{3}{2}\)X - \(\frac{13}{2}\)

x  + \(\frac{13}{2}\) =  \(\frac{3}{2}\)X  - \(\frac{13}{2}\) + \(\frac{13}{2}\)

x  + \(\frac{13}{2}\) =  \(\frac{3}{2}\)X

x - x + \(\frac{13}{2}\) =  \(\frac{3}{2}\)X - x

\(\frac{13}{2}\)  =  \(\frac{1}{2}\)X

\(\frac{2}{1}\) * \(\frac{13}{2}\) = \(\frac{2}{1}\) *  \(\frac{1}{2}\)X

13 = x

EF = 13    :)

Answer:  the final balance is $5,097.18

The total compound interest is $597.18

Step-by-step explanation:

Answer:

The slope is 0.98 and the y-intercept is 1.44.

Step-by-step explanation:

The equation is a linear equation in the Slope-Intercept form y=mx+b. It’s called this because it identifies the slope m and the point on the y-axis at which the line intersects.

Answer:

There's multiple answers

Step-by-step explanation:

The value of a mixed fraction can be found multiple ways. it can be found on a pie chart, a decimal, or a smaller fraction. perhaps a mixed number.

Answer:

8

Step-by-step explanation:

Answer: (16)3/4 = 8

In general, an is a power where a is the base and n is the exponent.

Answer:

C) Marisol computed StartFraction y 2 minus x 2 Over y 1 minus x 1 EndFraction.

Step-by-step explanation:

Answer:

4/100 = x/50

Step-by-step explanation:

inches on top miles on bottom

Answer:

\(\frac{a12}{b3}\)

Step-by-step explanation:

Hope this is right and helps you!

Answer:

a^12/b^9

Step-by-step explanation:

You need to multiply the exponent -3 to every other exponent

So then you would end up with a^6b^-6/a^-6b^3

Now you need to flip the negative exponents to the other side which would be a^12/b^9

Answer:

27mph

Step-by-step explanation:

Let's assume the speed of the first car is x mph. Since the second car is traveling 6 mph slower, its speed would be (x - 6) mph.

To find out how far each car has traveled, we can use the formula: distance = speed × time.

For the first car:

Distance traveled by the first car = speed of the first car × time

d₁ = x mph × (4 hours + 20 minutes)

Since we need to work with a single unit of time, let's convert 20 minutes to hours:

20 minutes = 20/60 = 1/3 hours

Substituting the values:

d₁ = x mph × (4 + 1/3) hours

d₁ = x mph × (13/3) hours

d₁ = (13x/3) miles

For the second car:

Distance traveled by the second car = speed of the second car × time

d₂ = (x - 6) mph × (4 hours + 20 minutes)

d₂ = (x - 6) mph × (13/3) hours

d₂ = (13/3)(x - 6) miles

Since they are traveling in opposite directions, the sum of their distances is equal to the total distance between them:

d₁ + d₂ = 260 miles

Substituting the expressions for d₁ and d₂:

(13x/3) + (13/3)(x - 6) = 260

To simplify the equation, let's multiply both sides by 3 to get rid of the denominators:

13x + 13(x - 6) = 780

13x + 13x - 78 = 780

26x - 78 = 780

26x = 780 + 78

26x = 858

x = 858/26

x ≈ 33

The speed of the first car is approximately 33 mph. Substituting this value back into the equation for the speed of the second car:

Speed of the second car = x - 6 ≈ 33 - 6 ≈ 27 mph

Therefore, the first car is traveling at approximately 33 mph, and the second car is traveling at approximately 27 mph.

Answer:

\(2.28*10^7\)

Step-by-step explanation:

\((2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7\)

Answer:

228,000

Step-by-step explanation:

(2.4x10^3) x (9.5x10^3)

(2.4x100) x (9.5x100)

240x950

228,000

Answer:

No it is not because it is only once when you get the fee

Step-by-step explanation:

So if you look at it, first of all there is not multiplication going on, so there are not ratios, second when there is only once that the fee added no matter to the amount of tickets, it means no propotion

To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

We can observe that the Z-score for Alice's ERA is lower than Roger's ERA. So Alice had the better year relative to their peers as her ERA was lower than her peers comparatively, hence, she had the better year compared to Roger who had a higher ERA comparatively.

The given information is:

Number of innings pitched (n) = 9

Mean (μ) and standard deviation (σ) of males: μ = 3.756, σ = 0.592

Mean (μ) and standard deviation (σ) of females: μ = 4.688, σ = 0.748

Roger's ERA = 2.81

Alice's ERA = 2.76

To calculate the Z-score, we can use the formula given below:

Z = (X - μ) / σ, where X is the given value and μ is the mean and σ is the standard deviation.

Now let's calculate Z-scores for Roger and Alice's ERAs.

Roger had an ERA with a z-score of:

Z = (X - μ) / σ

= (2.81 - 3.756) / 0.592

= -1.58

Alice had an ERA with a z-score of:

Z = (X - μ) / σ

= (2.76 - 4.688) / 0.748

= -2.58

We can observe that the Z-score for Alice's ERA is lower than Roger's ERA. So Alice had the better year relative to their peers as her ERA was lower than her peers comparatively, hence, she had the better year compared to Roger who had a higher ERA comparatively.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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the Correct option of  coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 90° counterclockwise is A.

In arithmetic, what is a polygon?

A polygon is a closed, two-dimensional, flat or planar structure that is circumscribed by straight sides. There are no curves on its sides. Polygonal edges are another name for the sides of a polygon. A polygon's vertices (or corners) are the places where two sides converge.

To determine the coordinates of polygon A′B′C′D′, we need to rotate each vertex of polygon ABCD 90° counterclockwise.

We can do this by using the following formulas for a 90° counterclockwise rotation of a point (x, y):

x' = -y

y' = x

Using these formulas, we can find the coordinates of each vertex of polygon A′B′C′D′ as follows:

A′(0, 0): Since (0, 0) is the origin, a 90° counterclockwise rotation will still result in (0, 0).

B′(-2, 5): To rotate the point (5, 2) 90° counterclockwise, we have x' = -y = -2 and y' = x = 5. So, B′ is (-2, 5).

C′(5, 5): To rotate the point (5, -5) 90° counterclockwise, we have x' = -y = 5 and y' = x = 5. So, C′ is (5, 5).

D′(3, 0): To rotate the point (0, -3) 90° counterclockwise, we have x' = -y = 0 and y' = x = 3. So, D′ is (3, 0).

Therefore, the coordinates of polygon A′B′C′D′ are A′(0, 0), B′(-2, 5), C′(5, 5), and D′(3, 0).

So, the answer is A) A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0).

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Answer:

  1.75%

Step-by-step explanation:

The monthly interest rate is the interest amount divided by the base on which it is computed, expressed as a percentage.

  $4.96/$283.15 × 100% ≈ 1.75172% ≈ 1.75%

Simplified results are after substitute the f(x, y) = 2x - y + 5 : (a) 3 (b) 3 (c) -15 (d) 11-y (e) 2x + 1 (f) 14

a) To evaluate f(0,2), we simply substitute x = 0 and y = 2 into the expression for f(x,y):
f(0,2) = 2(0) - 2 + 5 = 3
So, f(0,2) simplifies to 3.
b) To evaluate f(-1,0), we substitute x = -1 and y = 0:
f(-1,0) = 2(-1) - 0 + 5 = 3
So, f(-1,0) simplifies to 3 as well.
c) To evaluate f(5,30), we substitute x = 5 and y = 30:
f(5,30) = 2(5) - 30 + 5 = -15
So, f(5,30) simplifies to -15.
d) To evaluate f(3,y), we substitute x = 3 and leave y as y:
f(3,y) = 2(3) - y + 5 = 11 - y
So, f(3,y) simplifies to 11 - y.
e) To evaluate f(x,4), we substitute y = 4 and leave x as x:
f(x,4) = 2x - 4 + 5 = 2x + 1
So, f(x,4) simplifies to 2x + 1.
f) To evaluate f(5,1), we substitute x = 5 and y = 1:
f(5,1) = 2(5) - 1 + 5 = 14
So, f(5,1) simplifies to 14.

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Answer:

x = 7

Step-by-step explanation:

The 2 triangles are similar ( AA postulate ), then the ratios of corresponding sides are equal, that is

\(\frac{x}{42}\) = \(\frac{6}{36}\) ( cross- multiply )

36x = 252 ( divide both sides by 36 )

x = 7

The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

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