Complete the proof that ∠RTS≅∠XWY.

Answer:

Y=2

Step-by-step explanation:

If x=3 we can see that every two lines is 1 number up then the last

same for y access. Y=-2

Answer:

-2

Step-by-step explanation:

The required probability of the spinner not landing on a number divisible by 3 is 11/16.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
For spinners numbered from 1 to 16,
Total sample space = 16
Favorable event = 3, 6, 9, 12, 15
Total number of favorable events = 5
Now,
Probability of the spinner not landing on a number divisible by 3,
= 1 - 5 / 16
= 11 / 16

Thus, the spinner's needed probability of not landing on a number divisible by 3 is 11/16.

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​

Sherry used 3/8 of her sugar to make sweet tea, which is the fraction obtained by subtracting 1/2 from 7/8.

The fraction of sugar that Sherry used to make sweet tea, we need to subtract the amount of sugar she used from the total amount of sugar she had.

Sherry had $7/8$ of a cup of sugar in her kitchen, and she used $1/2$ of a cup of sugar to make sweet tea.

To find the remaining amount of sugar, we subtract $1/2$ from $7/8$:

$7/8 - 1/2$

To subtract fractions, we need a common denominator. In this case, the common denominator is 8. We can rewrite $1/2$ as $4/8$:

$7/8 - 4/8$

Now we can subtract the numerators:

$3/8$

Therefore, Sherry used $3/8$ of her sugar to make sweet tea.

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sample B is harder than sample A.To compare the hardness values of samples A and B, we need to convert them to the same scale.

Rockwell hardness scales are designated by a letter, such as B or F, and each scale has a different range and units of measurement.

To convert sample A's hardness value from the B scale to the F scale, we can use the conversion chart. According to the chart, the conversion formula from B to F scale is HRF = (HRB x 1.000) + 18. Therefore, the converted hardness value for sample A is:

HRF = (59 x 1.000) + 18 = 77 HRF

Now we can compare the hardness values of both samples, and we see that sample B has a higher hardness value of 90.5 HRF, compared to sample A's value of 77 HRF. Therefore, we can conclude that sample B is harder than sample A.

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Option A is correct answer

Answer: Option A

(A)  <4 and <12

Step-by-step explanation:

The strategies that survive iterated elimination of strictly dominated strategies are: (M,L), (B,L,R), (B,R), (M,R), and (M). The pure-strategy Nash equilibria are: (M,L) and (B,R).

To find the strategies that survive iterated elimination of strictly dominated strategies, we start by looking for any dominated strategies.

In row player's strategy, T dominates B as 2 > 1 and 4 > 3. So, we can eliminate row player's strategy B.

In column player's strategy, R dominates L as 3 > 0 and 2 > 1. So, we can eliminate column player's strategy L.

Now, the reduced game is:

C R

T 1,1 4,2

M 1,2 2,3

In this reduced game, there are no more strictly dominated strategies, so no further elimination is possible.

To find the pure-strategy Nash equilibria, we look for any cells in the game where neither player has an incentive to switch strategies.

One such equilibrium is (T, R), where row player plays strategy T and column player plays strategy R, since neither player has an incentive to switch to a different strategy.

Another equilibrium is (M, C), where row player plays strategy M and column player plays strategy C, since neither player has an incentive to switch to a different strategy.

So, the strategies that survive iterated elimination of strictly dominated strategies are T and M, and the pure-strategy Nash equilibria are (T, R) and (M, C).

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750 bats leave the barn during the time interval 0 ≤ t < 15 minutes. the expression involving one or more integrals for the total number of bats in the barn at time t for 0 ≤ t < 15 minutes is:  ∫[0,t] (-t^2 + 25t - 100) dt = [(-1/3)t^3 + (25/2)t^2 - 100t] from t = 0 to t = 15
= 375 bats

(a) To find how many bats leave the barn during the time interval 0 ≤ t < 15 minutes, we need to integrate the rate of bats leaving the barn over this time interval.

∫[0,15] (100 - 5t) dt = [100t - (5/2)t^2] from t = 0 to t = 15
= (100(15) - (5/2)(15)^2) - (100(0) - (5/2)(0)^2)
= 750 - 0 = 750 bats

Therefore, 750 bats leave the barn during the time interval 0 ≤ t < 15 minutes.

(b) To find an expression involving one or more integrals for the total number of bats in the barn at time t for 0 ≤ t < 15 minutes, we need to find the net rate of bats entering or leaving the barn at any given time t.

The net rate of bats entering or leaving the barn at time t is given by:

R(t) = E(t) - L(t) = (20t - t^2) - (100 - 5t)
= -t^2 + 25t - 100

If we integrate the net rate of bats over the time interval 0 ≤ t < 15 minutes, we can find the total number of bats in the barn at time t.

∫[0,t] (-t^2 + 25t - 100) dt = [(-1/3)t^3 + (25/2)t^2 - 100t] from t = 0 to t = 15
= [(-1/3)(15)^3 + (25/2)(15)^2 - 100(15)] - [(-1/3)(0)^3 + (25/2)(0)^2 - 100(0)]
= -937.5 + 2812.5 - 1500 = 375 bats

Therefore, the expression involving one or more integrals for the total number of bats in the barn at time t for 0 ≤ t < 15 minutes is:

∫[0,t] (-t^2 + 25t - 100) dt = [(-1/3)t^3 + (25/2)t^2 - 100t] from t = 0 to t = 15
= 375 bats
(a) To find the number of bats that leave the barn during the time interval 0 ≤ t ≤ 15 minutes, we need to integrate the function L(t) = 100 - 5t with respect to time from 0 to 15:

∫(100 - 5t) dt from 0 to 15

This will give us the total number of bats that leave the barn during that time interval.

(b) To find the total number of bats in the barn at time t for 0 ≤ t ≤ 15, we need to find the difference between the number of bats entering and leaving the barn during that time interval. We will integrate the functions E(t) and L(t) and subtract the results:

Total Bats(t) = Initial Bats + ∫(E(t) - L(t)) dt from 0 to t

Where Initial Bats = 1000, E(t) = 20t - t^2, and L(t) = 100 - 5t.

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Drawing a number line is a useful way to visualize the relationship between tons and pounds and can help make conversions easier to understand.

If we were to draw a number line that shows the relationship between tons and pounds, we would start with the fact that one ton is equivalent to 2000 pounds. We would then draw tick marks on the number line for every whole number from 0 to 10, with each tick mark representing 100 pounds. So, the tick mark at 0 would represent 0 pounds, the tick mark at 1 would represent 100 pounds, the tick mark at 2 would represent 200 pounds, and so on. The tick mark at 20 would represent 2000 pounds, or one ton.

We could then continue the number line past 20 to show larger quantities of tons and pounds, with each additional tick mark representing another ton (2000 pounds). For example, the tick mark at 30 would represent 3000 pounds, or 1.5 tons, the tick mark at 40 would represent 4000 pounds, or 2 tons, and so on.

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Answer:

8^3

Step-by-step explanation:

8*8*8 is equivalent to 8^3 which equals a total of 512 units

c. =BINOM.DIST(3, 5, 0.2, TRUE)

1. This is a binomial probability problem since we have multiple-choice questions with a fixed probability of success (1 out of 5 or 0.2) for each question.

2. The Excel function for binomial probability is BINOM.DIST().

3. We want the probability of guessing less than four answers correctly, which means we need the cumulative probability of guessing 0, 1, 2, or 3 answers correctly.

4. Therefore, we use the formula "=BINOM.DIST(3, 5, 0.2, TRUE)", where 3 is the number of successes, 5 is the number of trials (questions), 0.2 is the probability of success (1/5), and TRUE indicates that we want the cumulative probability.

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Answer:

26km/hr

Step-by-step explanation:

78 divided by 3 hours is equal to 26km/hr

The average speed during the same time interval is approximately 2.02 km/h.

(a) To find the magnitude and direction of the woman's displacement, we can use the Pythagorean theorem and trigonometry.

Given:

Distance walked north = 3.55 km

Distance walked east = 2.00 km

To find the magnitude of the displacement, we can use the Pythagorean theorem:

Magnitude of displacement = √((Distance walked north)^2 + (Distance walked east)^2)

= √((3.55 km)^2 + (2.00 km)^2)

≈ 4.10 km

The magnitude of the displacement is approximately 4.10 km.

To find the direction of the displacement, we can use trigonometry. The direction can be represented as an angle north of east.

Direction = arctan((Distance walked north) / (Distance walked east))

= arctan(3.55 km / 2.00 km)

≈ 59.0°

Therefore, the direction of the displacement is approximately 59.0° north of east.

(b) To find the magnitude and direction of the woman's average velocity, we divide the displacement by the time taken.

Average velocity = Displacement / Time taken

= (4.10 km) / (2.80 hours)

≈ 1.46 km/h

The magnitude of the average velocity is approximately 1.46 km/h.

The direction remains the same as the displacement, which is approximately 59.0° north of east.

Therefore, the direction of the average velocity is approximately 59.0° north of east.

(c) The average speed is defined as the total distance traveled divided by the time taken.

Average speed = Total distance / Time taken

= (3.55 km + 2.00 km) / (2.80 hours)

≈ 2.02 km/h

Therefore, the average speed during the same time interval is approximately 2.02 km/h.

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The required sample size for the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

Given that the number of hours spent studying by students on large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours.

we want to find the size of the sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05.

Here, the margin of error is E=2 and the level of significance is α=0.05

The critical value is Zα/2=Z₀.₀₂₅

or the critical value is 1.96

Now, we will find the sample size

n=((Zα/2)×σ/E)²

n=(1.96×8.4/2)²

n=67.76

n≈68

Hence, the size of sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

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Answer:

May be minus

Step-by-step explanation:

minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32

Answer:

6

Step-by-step explanation:

2/3, 1 1/3, 2, 2 2/3, 3 1/3, 4

Answer:

Kenjii can use 13.19 kilowatt-hour.

Step-by-step explanation:

Giving the following information:

Kenji's electricity bill costs $21.56 per month plus $2.46 per kilowatt-hour.

First, we will structure the total cost formula:

Total cost= 21.56 + 2.46*x

x= kilowatt-hour

54= 21.56 + 2.46x

32.44= 2.46x

13.19= x

Kenjii can use 13.19 kilowatt-hour.

A discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.

The main difference between a discrete function and a continuous function lies in the nature of their domains and ranges. A discrete function is defined on a set of distinct, separate values, while a continuous function is defined on a continuous interval or range of values.

A discrete function can be thought of as a function that consists of isolated points. For example, let's consider a function that represents the number of students in a classroom over the years. The domain of this function would be the set of discrete values representing each year, such as {2010, 2011, 2012, ...}. The range would be the set of corresponding numbers representing the number of students in the classroom each year.

On the other hand, a continuous function is one that can take on any value within a given interval. For instance, consider a function that represents the temperature in a room over time. The domain of this function would be a continuous interval, such as [0, 24] representing the 24-hour day. The range would be the set of possible temperature values within that interval.

To summarize, a discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.
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The number of questions on the CUNY Math Assessment Test can vary depending on the specific version of the test administered. However, typically, the CUNY Math Assessment Test consists of multiple-choice questions covering a range of math topics such as algebra, geometry, and trigonometry.

While the exact number of questions can vary, it is common for the CUNY Math Assessment Test to have around 40 to 50 questions. These questions are designed to assess your mathematical knowledge and skills in order to determine your readiness for college-level math courses.

The test is typically timed, and you will have a set amount of time to complete all the questions. It is important to manage your time effectively and pace yourself throughout the test to ensure you have enough time to answer each question.

In order to prepare for the CUNY Math Assessment Test, it is recommended to review and practice a variety of math topics, including algebraic equations, functions, graphs, geometry, and basic trigonometry concepts. Familiarizing yourself with these topics and practicing similar questions can help you become more comfortable with the content and format of the test.

Remember, it's always a good idea to consult official CUNY resources or speak with an academic advisor to get the most up-to-date and accurate information regarding the specific version of the CUNY Math Assessment Test you will be taking.

Overall, the number of questions on the CUNY Math Assessment Test can vary, but typically it consists of around 40 to 50 multiple-choice questions covering various math topics.

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As per the question statement and the reference attachment attached thereby, the area of the venn diagram marked as (II) can represent the disease of Pneumonia.

As per the reference attachment attached thereby along, a chart is provided that shows the most common causes of death in three regions of united stated,

And we are required to identify the sector of the vein diagram, which can best represent the disease of Pneumonia.

From the tabular data above the venn diagram, pneumonia is a cause of death in both region A as well as in region B, and hence, the common sector of circles A and B only, can represent the disease. Since the only such sector is (II), it is our required area of the vein diagram.

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Answer:

As per the question statement and the reference attachment attached thereby, the area of the venn diagram marked as (II) can represent the disease of Pneumonia.

Step-by-step explanation:

Answer:

y-intercept = -8

Step-by-step explanation:

The y-intercept is where the line goes through the y axis. It is also the value when x = 0. From what the problem gives us, we know the y-intercept is -8 because the x value is 0

Answer:

Please check the explanation.

Step-by-step explanation:

Given the function

\(y=\frac{3}{2}x\:+3\)

FOR y=9

\(y=\frac{3}{2}x\:+3\)

putting y=9

\(9=\frac{3}{2}x+3\)

switch sides

\(\frac{3}{2}x+3=9\)

subtract 3 from both sides

\(\frac{3}{2}x+3-3=9-3\)

\(\frac{3}{2}x=6\)

\(3x=12\)

\(x=4\)

Hence,

when y=9, x=4

FOR y=6

\(y=\frac{3}{2}x\:+3\)

putting y=6

\(6=\frac{3}{2}x+3\)

switch sides

\(\frac{3}{2}x+3=6\)

subtract 3 from both sides

\(\frac{3}{2}x+3-3=6-3\)

\(\frac{3}{2}x=3\)

\(3x=6\)

\(x=2\)

Hence,

when y=6, x=2

FOR y=0

\(y=\frac{3}{2}x\:+3\)

putting y=0

\(0=\frac{3}{2}x+3\)

switch sides

\(\frac{3}{2}x+3=0\)

subtract 3 from both sides

\(\frac{3}{2}x+3-3=0-3\)

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

\(3x=-6\)

\(x=-2\)

Hence,

when y=0, x=-2

FOR y=-3

\(y=\frac{3}{2}x\:+3\)

putting y=-3

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

switch sides

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

subtract 3 from both sides

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

\(\frac{3}{2}x=-6\)

\(3x=-12\)

\(x=-4\)

Hence,

when y=-3, x=-4

Hence, the table becomes:

x                     y

9                    4

6                    2

0                    -2

-3                   -4

Answer:

Part A) = D) 13.33 m/sec

Part B) = A) Deer wins by 2.08 seconds

Step-by-step explanation:

Part A)

From the question in Part A, we know that, the White-tailed deer can run at 48 kilometers per hour for short periods. We were asked in the question, How many meters per second does the deer run?

The question gave us this (Hint: remember that there are 1,000 meters in a kilometer, 60 seconds in a minute, and 60 minutes in an hour.)

1 km = 1000 meters

48 km = x meters

Cross Multiply

= 1km × x meters = 48km × 1000 meters

x meters = 48km × 1000 meters/1 km

= 48000 meters/ hour

The speed of the dear = 48000 meters/ hour

We have to convert this to meters/ seconds

60seconds = 1 minute

60 minutes = 1 hour

Therefore, the number of seconds in one hour = 60 × 60

= 3600 seconds

Hence 48000meters/hour to meter per Seconds

= 48000meters/3600 seconds

= 13.333333333 meters/seconds

= 13.33m/s

Part B

From Part B Question, we know that Usain Bolt set a world record of 9.58 seconds for the 100 meter dash.

White-tailed deer can run at 48 kilometers per hour for short periods.

If Mr. Bolt and a white-tailed deer run a 100 meter dash at these speeds, who would win, and by how much?

Using our answer in Part A,

We know that the deer runs

48,000 meters in 3600 seconds.

The first step would be to find how many seconds it can run in an 100 meter race

Hence,

48,000 meters = 3600 seconds

100 meters = y seconds

We cross Multiply

48,000 meters × y seconds = 3600 seconds × 100 meters

y seconds = 3600 seconds × 100 meters/ 48,000 meters

y second = 7.5 seconds

This means, the deer can run a 100 meter dash in 7.5 seconds.

From the question, we know that Usain Bolt set the record of 9.58 seconds for an 100 letter dash.

The difference between both times for the Usain Bolt and the Deer = 9.58seconds - 7.5 seconds

= 2.08 seconds

Therefore the winner is the Deer , because it finishes the race is a shorter time of 7.5 seconds and wins by 2.08 seconds. Therefore, Option A) Deer wins by 2.08 seconds is correct

Therefore, You removed 5% of the wax.

To find the percentage of wax removed, we need to calculate the volume of the removed portion and divide it by the total volume of the wax pyramid.
First, we need to find the height of the pyramid. Let's call it h.
Using the formula for the volume of a pyramid:
Volume of pyramid = (1/3) * base area * height
We know the base area is 5.4 square centimeters and the volume of the entire pyramid is 108 cubic centimeters (since it's a pyramid with a square base, we can use the formula V = (1/3) * base area * height). So we can solve for h:
108 = (1/3) * 5.4 * h
h = 60
Now we can find the volume of the removed portion by using the same formula, but with a new base area and a height of 3:
Volume of removed portion = (1/3) * 5.4 * 3 = 5.4
So the percentage of wax removed is:
5.4 / 108 * 100% = 5%

Therefore, You removed 5% of the wax.

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Answer:

Exact Form:

3√5

Decimal Form:

6.70820393

Step-by-step explanation:

Answer:

Distance = 3√5 or 6.708203932,,,

Step-by-step explanation:

Find the distance between the y-values and x-values which in this case would be 6 and 3. Use the Pythagorean theorem.

\(3^2 + 6^2 = 45\)

Simplify.

\(\sqrt{45} = 3\sqrt{5}\)

Answer:

No

Step-by-step explanation:

1 ) Since there is no x, the line is horizontal and has a slope of 0.

2 ) Knowing this we can go to 4 on the y-axis and draw a horizontal line that runs both through the negative and positive sides.

Take a look at the attachment...

Hope this helps! :)

The margin of error for the confidence interval is approximately 0.014, indicating that the estimate of the proportion of dissatisfied customers could be off by approximately plus or minus 0.014. This means that we can be 95% confident that the true proportion of dissatisfied customers falls within the range of the estimated proportion ± 0.014.

(a) To find the sample size needed to achieve a margin of error of about 0.015 with a 95% confidence level, we can use the formula for sample size calculation for proportions:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = critical value (corresponding to the desired confidence level)

p = estimated proportion of the population

E = margin of error

In this case, the estimated proportion of dissatisfied customers is 0.17, and the desired margin of error is 0.015. Since we want a 95% confidence level, the critical value can be obtained from a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.

Plugging these values into the formula, we have:

n = (1.96^2 * 0.17 * (1-0.17)) / 0.015^2

n ≈ 1901.63

Therefore, the sample size needed is approximately 1902.

(b) If 25% of the sample say they are not satisfied, we can calculate the margin of error using the following formula:

MoE = Z * sqrt((p * (1-p)) / n)

Where:

MoE = margin of error

Z = critical value (corresponding to the desired confidence level)

p = proportion of the sample

n = sample size

Using the same critical value of 1.96 for a 95% confidence level and plugging in the values:

MoE = 1.96 * sqrt((0.25 * (1-0.25)) / 1902)

MoE ≈ 0.014

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The owner needs to use approximately 13 pounds of chocolate.

To determine how many pounds of chocolate should be mixed with 24 pounds of trail mix to create a mixture worth $9.84 per pound, we can use the concept of weighted averages. Let's assume x represents the number of pounds of chocolate needed.

The cost of the trail mix is $3.80 per pound, and the cost of the chocolate is $21.00 per pound. We want the resulting mixture to have an average cost of $9.84 per pound.

To find the weighted average, we can use the formula:

(x * $21.00 + 24 * $3.80) / (x + 24) = $9.84

Simplifying the equation gives:

21x + 91.20 = 9.84x + 236.16

11.16x = 144.96

x ≈ 13

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