Answer:
Step-by-step explanation:
Yes, there is a rigid transformation that can map triangle ΔABC to triangle ΔDEC.
A rigid transformation is a transformation that preserves the size, shape, and orientation of a figure. It includes translations, rotations, and reflections. In order for triangle ΔABC to be mapped to triangle ΔDEC, the two triangles must have the same size, shape, and orientation. This can be achieved through a combination of translation, rotation, and/or reflection. For example, if triangle ΔABC is translated by a certain vector and then rotated or reflected, it can be mapped onto triangle ΔDEC.
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Find the surface area of the cylinder.
PLS PLS HELP I REALLY DONT KNOW HOW TO DO THIS PLS HELP
Answer:
[tex]60\pi[/tex]
Step-by-step explanation:
Surface area of a cylinder is
[tex]2\pi rh + 2\pi r^2[/tex]
r=3,h=7.
Plug in the values.
[tex]42\pi +18\pi =60\pi[/tex]
You are studying a population of 1,800 wrestlers whose mean weight is 225 lbs with standard deviation of 20 lbs a) What proportion/percentage weight less than 220 lbs? b) What is the probability that a random wrestler weighs more than 250 lbs? c) How many wrestlers weigh between 210 and 230 lbs?
Approximately 670 wrestlers weigh between 210 and 230 lbs.
a) To find the proportion/percentage of wrestlers that weigh less than 220 lbs, we need to standardize the weight value using the formula:
z = (x - μ) / σ
where x is the weight value, μ is the mean weight, and σ is the standard deviation.
So, for x = 220 lbs:
z = (220 - 225) / 20 = -0.25
Looking up the standard normal table or using a calculator, we find that the area/proportion to the left of z = -0.25 is 0.4013. Therefore, the proportion/percentage of wrestlers that weigh less than 220 lbs is:
0.4013 or 40.13%
b) To find the probability that a random wrestler weighs more than 250 lbs, we again need to standardize the weight value:
z = (250 - 225) / 20 = 1.25
Using the standard normal table or a calculator, we find that the area/proportion to the right of z = 1.25 is 0.1056. Therefore, the probability that a random wrestler weighs more than 250 lbs is:
0.1056 or 10.56%
c) To find the number of wrestlers that weigh between 210 and 230 lbs, we first need to standardize these weight values:
z1 = (210 - 225) / 20 = -0.75
z2 = (230 - 225) / 20 = 0.25
Next, we need to find the area/proportion between these two standardized values:
P(-0.75 < z < 0.25) = P(z < 0.25) - P(z < -0.75)
Using the standard normal table or a calculator, we find that P(z < 0.25) is 0.5987 and P(z < -0.75) is 0.2266. Therefore:
P(-0.75 < z < 0.25) = 0.5987 - 0.2266 = 0.3721
Finally, we can find the number of wrestlers by multiplying this proportion by the total population size:
0.3721 * 1800 = 669.78 or approximately 670 wrestlers
Therefore, approximately 670 wrestlers weigh between 210 and 230 lbs.
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80 volunteers take a meningitis test to help doctors see how accurate this test is at identifying whether someone has meningitis or not.
A positive result means the test has identified you as having meningitis.
Of the volunteers, only 8 people have meningitis.
The results show 2 people who have meningitis gets a negative result and 3 people who don't have meningitis get a positive result.
What was the accuracy of the test?
Find the distance between the two points rounding to the nearest tenth (if necessary). ( 8 , − 4 ) and ( − 1 , − 2 ) (8,−4) and (−1,−2)
Let help you with that.
To find the distance between two points, we can use the distance formula:
```
d = √(x2 - x1)2 + (y2 - y1)2
```
Where:
* `d` is the distance between the two points
* `x1` and `y1` are the coordinates of the first point
* `x2` and `y2` are the coordinates of the second point
In this case, the points are (8, -4) and (-1, -2):
```
d = √((8 - (-1))^2 + ((-4) - (-2))^2)
```
```
d = √(9^2 + (-2)^2)
```
```
d = √(81 + 4)
```
```
d = √85
```
```
d = 9.2 (rounded to the nearest tenth)
```
Therefore, the distance between the two points is 9.2 units.
Answer:
Step-by-step explanation:
Jane figures that her monthly car insurance payment of $170 is equal to 30% of the amount of her monthly auto loan payment. What is her total combined monthly expense for auto loan payment and insurance (rounded to the nearest dollar)?
Jane's total combined monthly cost for auto loan payment and insurance is $736.67 (rounded to the nearest dollar).
If Jane's monthly car insurance payment of $170 is same to 30% of her monthly car loan fee, then we are able to set up the subsequent equation:
0.3x = 170
Where x is the monthly auto loan fee. To solve for x, we will divide each facets by using 0.3:
x = 170 / 0.3 = $566.67
So, Jane's monthly auto loan charge is $566.67.
To discover her general combined monthly price for auto loan price and insurance, we simply upload her monthly car coverage charge to her monthly auto loan payment:
$566.67 + $170 = $736.67
Consequently, Jane's total combined monthly cost for auto loan payment and coverage is $736.67
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8. Based on data from the National Health Board, weights of men are normally distributed with a mean of 178 lbs, and a standard deviation of 26 lbs. Find the probability that 20 randomly selected men will have a mean weight between 170 and 185. [3]
The probability that the mean weight of 20 randomly selected men is between 170 and 185 lbs is approximately 0.7189 or approximately 72%.
To solve this problem, we need to use the formula for the sampling distribution of the mean, which states that the mean of a sample of size n drawn from a population with mean μ and standard deviation σ is normally distributed with a mean of μ and a standard deviation of σ/sqrt(n).
In this case, we have a population of men with a mean weight of 178 lbs and a standard deviation of 26 lbs. We want to know the probability that 20 randomly selected men will have a mean weight between 170 and 185 lbs.
First, we need to calculate the standard deviation of the sampling distribution of the mean. Since we are taking a sample of size 20, the standard deviation of the sampling distribution is:
σ/sqrt(n) = 26/sqrt(20) = 5.82
Next, we need to standardize the interval between 170 and 185 lbs using the formula:
z = (x - μ) / (σ/sqrt(n))
For x = 170 lbs:
z = (170 - 178) / 5.82 = -1.37
For x = 185 lbs:
z = (185 - 178) / 5.82 = 1.20
Now we can use a standard normal distribution table (or a calculator) to find the probability of the interval between -1.37 and 1.20:
P(-1.37 < z < 1.20) = 0.8042 - 0.0853 = 0.7189
Therefore, the probability that 20 randomly selected men will have a mean weight between 170 and 185 lbs is 0.7189 or approximately 72%.
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Find the linearization L(x) of the function at a. F(x) = x3 - x2 + 5, a = -3 L(x) = Fl Show My Work
[tex]L(x) = 33x + 86[/tex] represents the regression of F(x) at a = -3.
We must apply the following formula to determine the regression L(x) of the equation: [tex]F(x) = x^{3} - x^{2} + 5[/tex] at a = -3: [tex]L(x) = F'(a)(x - a) + F(a)[/tex] , where a derivative of F(x) calculated at an is denoted by F'(a).
We calculate the amount of F(-3): F(-3)
[tex]= (-3)^3 - (-3)^2 + 5[/tex]
= -27 + 9 + 5 = -13
We determine F(x)'s derivative:
[tex]F'(x) = 3x^2 - 2x[/tex]
We assess F'(-3):
[tex]F'(-3) = 3(-3)^2 - 2(-3)[/tex]
= 27 + 6 = 33
Now we can change these numbers in the L(x) formula:[tex]L(x) = -13 + 33(x + 3)[/tex]. If we condense this expression, we get: L(x) = 33x + 86
We utilise the equation [tex]L(x) = F(a) + F'(a)(x - a)[/tex], to determine the linearization of an equation at a specific point, where F(a) represents the function's value at point a and F'(a) was the function's derivative calculated at point a. We can approximate the function close to point a linearly.
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Researchers want to determine if a magician has ESP. (a) They set up a test that consists of eight trials. In each trial, a card is randomly selected (with replacement) from a standard deck of 52 cards. The magician guesses the suit of the card. The null hypothesis is that she does not have ESP, so she is just guessing randomly, and the alternative is that she is more likely to guess the suit. Suppose that she is successful for 6 out the 8 trials. What is the p-value for this test? - Define a random variable - Identify the distribution of your random variable - Write the formula for the probability explicitly - Write a R command for the probability - Use R to evaluate the probability - Round it to the nearest 0.01% (b) They take ten red cards and four black cards, shuffle them, and place them face down on the table. They ask the magician to turn over the black cards (She knows there are four black cards). The null hypothesis is that she is just turning cards over "at random," and the alternative is that she is more likely to turn over black cards. Suppose she turns over three black cards and one red card. What is the p-value for this test?
- Define a random variable
- Identify the distribution of your random variable
- Write the formula for the probability explicitly
- Write a R command for the probability - Use R to evaluate the probability
- Round it to the nearest 0.01%
(a) To answer this question, we can follow these steps:
1. Define a random variable: Let X be the number of correct suit guesses in 8 trials.
2. Identify the distribution: Since there are only two possible outcomes (correct or incorrect guess) and the trials are independent, the distribution of X is a binomial distribution with parameters n = 8 and p = 1/4 (since there are 4 suits).
3. Write the formula for the probability: P(X ≥ 6) = P(X=6) + P(X=7) + P(X=8)
4. Write an R command for the probability: `pbinom(5, size=8, prob=0.25, lower.tail=FALSE)`
5. Use R to evaluate the probability: R will return 0.0323 (approximately).
6. Round it to the nearest 0.01%: The p-value is approximately 3.23%.
(b) To answer this question, we can follow these steps:
1. Define a random variable: Let Y be the number of black cards correctly turned over in 4 attempts.
2. Identify the distribution: The distribution of Y is a hypergeometric distribution with parameters N = 14 (total cards), K = 4 (black cards), and n = 4 (attempts).
3. Write the formula for the probability: P(Y ≥ 3) = P(Y=3) + P(Y=4)
4. Write an R command for the probability: `phyper(2, 4, 10, 4, lower.tail=FALSE)`
5. Use R to evaluate the probability: R will return 0.1218 (approximately).
6. Round it to the nearest 0.01%: The p-value is approximately 12.18%.
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1) Crunchy Critters produces bags of chips. The mean weight of the chips is 16 oz
with a standard deviation of 0.3 oz. What is the probability that a bag of chips is
less than 15.4 oz? (round to nearest hundredth)
If Crunchy-Critters produces chips bags with mean weight as 16 oz, the the probability that weight of the bag is less than 15.4 oz is 0.0228.
We use the standard normal distribution to find the required probability. First, we need to standardize the value of 15.4 oz using the formula : z = (x - μ) / σ,
where x is = value we are interested in, μ is = mean weight, σ is = standard deviation, and z is the standardized score.
The mean-weight of the chips is (μ) = 16 oz,
The standard-deviation of weight (σ) is 0.3 oz,
Substituting the values we have, we get:
⇒ z = (15.4 - 16)/0.3,
⇒ z = -2, and
We know that, P(X < 15.4) = P(Z < -2) = 0.0228
Therefore, the required probability is 0.0228 or 2.28%.
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A mayor running for re-election claims that during his term, average municipal taxes have fallen by $200. A conscientious statistician wants to test this claim. He surveys 36 of his neighbors and finds that their taxes decreased (in dollars) as follows: 150, 205, 108, 188, 186, 195, 154, 169, 270, 190, 168, 185, 142, 267, 157, 218, 183, 200, 192, 250, 100, 234, 182, 231, 209, 235, 182, 173, 197, 171, 191, 150, 174, 206, 200, 171 The statistician assumes a population standard deviation of $43. Do you think the statistician should reject the mayor's claim? Why or why not?
We do not have sufficient evidence to support the mayor's claim that the average municipal taxes have fallen by $200 during his term.
Step 1: Hypotheses Set-Up:
H0: The average tax decrease during the mayor's term is not $200 (μ ≠ 200)
Ha: The average tax decrease during the mayor's term is $200 (μ = 200)
Step 2: The significance level α = 0.05
Step 3: Compute the test statistic:
We will use a one-sample t-test since the population standard deviation is unknown and the sample size is less than 30.
The formula for the t-test statistic is:
t = (x - μ) / (s / √n)
Where:
x = sample mean
μ = hypothesized population mean
s = sample standard deviation
n = sample size
Substituting the values, we get:
t = (186.6 - 200) / (43 / √36)
t = -1.98
Step 4: Testing Procedure:
The test is a two-tailed test since we want to determine whether the average tax decrease is significantly different from $200, not just whether it is greater or less than $200.
At a significance level of 0.05 with 35 degrees of freedom, the critical values for a two-tailed test are ±2.03.
The p-value for the test is the probability of getting a t-value as extreme or more extreme than -1.98, given the null hypothesis. From a t-distribution table, we find that the p-value is approximately 0.057.
Step 5: Decision:
Since the calculated t-value (-1.98) is less than the critical value (-2.03) and the p-value (0.057) is greater than the significance level (0.05), we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to support the mayor's claim that the average municipal taxes have fallen by $200 during his term.
Step 6: Interpretation:
At a 5% significance level, we do not have enough evidence to reject the null hypothesis that the average tax decrease is not $200.
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Find the probability that randomly selected Atlantic cod has a length that is at least 62.99 cm. 0.0002 f) is a length of 62.99 cm unusually high for a randomly selected Atlantic cod? Why or why not? yes, since the probability of having a value of length at least that high is less than or equal to 0.05 g) What length do 48% of all Atlantic cod have more than? Round your answer to two decimal places in the first box. Put the correct units in the second box. The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm. Round the probabilities to four decimal places. It is possible with rounding for a probability to be 0.0000. a) State the random variable. VX XX. the mean length of a sample of Atlantic cod b) Find the probability that a randomly selected Atlantic cod has a length of 39.08 cm or more. 0.9981 om c) Find the probability that a randomly selected Atlantic cod has a length of 59.08 cm or less. 0.9929 d) Find the probability that a randomly selected Atlantic cod has a length between 39.08 and 59.08 cm. 0.9910 ar e) Find the probability that randomly selected Atlantic cod has a length that is at least 62.99 cm. 0.0002 fils a length of 62.99 cm unusually high for a randomly selected Atlantic cod?
The probability that a randomly selected Atlantic cod has a length of 39.08 cm or more is 0.9981. The probability that a randomly selected Atlantic cod has a length of 59.08 cm or less is 0.9935. The probability that a randomly selected Atlantic cod has a length between 39.08 and 59.08 cm is 0.9914. The probability of a randomly selected Atlantic cod having a length that is at least 62.99 cm is 0.0002. 48% of all Atlantic cod have a length of more than 50.25 cm.
a) The random variable is the length of a sample of Atlantic cod, denoted by X.
b) The probability that a randomly selected Atlantic cod has a length of 39.08 cm or more can be found using the standard normal distribution table or a calculator. We first standardize the value of 39.08 using the formula
z = (x - μ) / σ, where μ is the mean length and σ is the standard deviation.
Therefore, z = [tex](\frac{39.08- 49.9}{ 3.74 } )[/tex]= -2.89.
From the standard normal distribution table, the probability of a z-score less than or equal to -2.89 is 0.0021.
Thus, the probability of a randomly selected Atlantic cod having a length of 39.08 cm or more is 1 - 0.0021 = 0.9981.
c) The probability that a randomly selected Atlantic cod has a length of 59.08 cm or less can be found using the same method as in part (b).
Standardizing the value of 59.08, we get z = [tex](\frac{59.08- 49.9}{ 3.74 } )[/tex]= 2.45.
Using the standard normal distribution table, the probability of a z-score less than or equal to 2.45 is 0.9935. Thus, the probability of a randomly selected Atlantic cod having a length of 59.08 cm or less is 0.9935.
d) The probability that a randomly selected Atlantic cod has a length between 39.08 and 59.08 cm can be found by subtracting the probability in part (b) from the probability in part (c).
Thus, P(39.08 < X < 59.08) = P(X ≤ 59.08) - P(X ≤ 39.08) = 0.9935 - 0.0021 = 0.9914.
e) The probability that a randomly selected Atlantic cod has a length that is at least 62.99 cm can be found using the same method as in parts (b) and (c).
Standardizing the value of 62.99, we get z = [tex](\frac{62.99- 49.9}{ 3.74 } )[/tex] = 3.49.
Using the standard normal distribution table, the probability of a z-score less than or equal to 3.49 is 0.9998.
Thus, the probability of a randomly selected Atlantic cod having a length that is at least 62.99 cm is 1 - 0.9998 = 0.0002.
f) Yes, a length of 62.99 cm is unusually high for a randomly selected Atlantic cod because the probability of having a value of length at least that high is less than or equal to 0.05.
g) To find the length that 48% of all Atlantic cod have more than, we need to find the z-score that corresponds to a cumulative probability of 0.52 (1 - 0.48).
Using the standard normal distribution table, we find that the z-score is approximately 0.10.
Then, we use the formula z = (x - μ) / σ to solve for x, where μ = 49.9 and σ = 3.74.
Thus, x = μ + σz = 49.9 + 3.74(0.10) = 50.25 cm.
Therefore, 48% of all Atlantic cod have a length of more than 50.25 cm. The units for length are in centimeters.
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Which function is shown on the graph below?
Answer: We will see that the function is f(x) = 0.559*ln(x)
Step-by-step explanation:
What is x, if the volume of the cylinder is 768pie in^3
Answer:
48 cm
Step-by-step explanation:
The volume of an oblique(slanted) cylinder is still
[tex]\pi r^{2} \cdot h[/tex], like a "normal" cylinder. (r is radius, h or x is height)
The diameter of the cylinder is 8, so the radius would be [tex]\frac{8}{2} = 4[/tex].
The volume is therefore [tex]4^2 \pi \cdot h[/tex] , which is [tex]16 \pi h[/tex].
We know [tex]16 \pi h = 768\pi[/tex], so we divide both sides by [tex]16\pi[/tex] to isolate the variable.
[tex]\frac{768\pi}{16\pi}= 48[/tex].
So, we know that the height is 48.
Therefore, x=48. (and remember the unit!)
If the radius is supposed to be 8, then do the same thing but with r=8.
Also, I don't know if there's a typo in the title, so this is assuming the volume is [tex]786\pi[/tex]cm^3, and not [tex]768\pi[/tex]in^3.
At one time, the British advanced corporation tax system taxed British companies' foreign earnings at a higher rate than their domestic earnings. This was put in place to ______.
At one time, the British advanced corporation tax system taxed British companies' foreign earnings at a higher rate than their domestic earnings.
This was put in place to discourage multinational corporations from artificially shifting profits earned in the UK to low-tax jurisdictions. The policy was aimed at preventing companies from avoiding tax by moving profits out of the UK and into tax havens. By imposing a higher tax rate on foreign earnings, the UK government hoped to make it less attractive for companies to engage in profit-shifting practices.
The policy was controversial and faced criticism from some business groups, who argued that it placed an unfair burden on companies operating overseas. However, the government defended the policy as necessary to ensure that companies paid their fair share of tax in the countries where they operated. Eventually, the policy was replaced by a territorial tax system, which only taxes companies on their profits earned in the UK. This change was made to simplify the tax system and make it more attractive for companies to invest in the UK.
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We want to know if there is a difference between the size of the shoe between mother and daughter for which a sample of 10 pairs of mother and daughter is taken and a hypothesis test is done. If the significance is α = 0.10,
(a) what is the value of the positive critical point? Answer
b) what is the value of the negative critical point? Answer
The negative critical point is approximately -1.812.
The critical values for a two-tailed hypothesis test with a significance level of α = 0.10 and 10 degrees of freedom (sample size - 1) can be found using a t-distribution table or a statistical software.
a) The positive critical point can be found by looking up the t-distribution table or using a statistical software to find the t-value that corresponds to a cumulative probability of 0.95 with 10 degrees of freedom. The value is approximately 1.812.
b) The negative critical point can be found by finding the t-value that corresponds to a cumulative probability of 0.05 with 10 degrees of freedom. Since the t-distribution is symmetric, this value is the negative of the positive critical point. Therefore, the negative critical point is approximately -1.812.
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Toni purchased 3 points, each of which reduced her APR by 0. 125%. Each point cost 1% of her loan value. Her new APR is 3. 2%, and the points cost her $8,100. What is the original APR?
The annual interest savings is the amount Toni would save each year in interest charges due to the lower APR. It would be around 0.375%
Let x be the original APR. Then the first purchase of a point reduced the APR to x - 0.125%, the second point reduced it further to x - 0.25%, and the third point reduced it to x - 0.375%. Since Toni's new APR is 3.2%, we have:
x - 0.375% = 3.2%
Solving for x, we get:
x = 3.2% + 0.375% = 3.575%
Therefore, Toni's original APR was 3.575%.
To check our answer, we can use the fact that Toni purchased 3 points at a cost of 1% each. Since her loan value is the total cost of the points ($8,100) divided by the cost per percent (1%), we have:
loan value = $8,100 / 1% = $810,000
The reduction in APR due to the 3 points is 0.375%, which is equivalent to a reduction in the annual interest rate of:
0.375% / 100% = 0.00375
The annual interest savings due to the reduction in APR is then:
$810,000 x 0.00375 = $3,037.50
The annual interest savings is the amount Toni would save each year in interest charges due to the lower APR. Dividing this by the loan value gives us the actual reduction in APR:
$3,037.50 / $810,000 = 0.00375 = 0.375%
This confirms that our answer for the original APR is correct.
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I NEED HELP ASAP
BRAINIEST WILL GET 10 POINTS!!!
PLEASE ITS DUE IN MINUTS
Answer:
1) 4 pounds / $5.48 = .73 pounds / dollar
2) 5 pounds / $4.85 = 1.03 pounds / dollar
3) $3.51 / 3 pounds = $1.17 / pound
4) $9.12 / 6 pounds = $1.52 / pound
note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. what is the probability that bo, colleen, jeff, and rohini win the first, second, third, and fourth prizes, respectively, in a drawing if 50 people enter a contest and satisfying the following conditions? (enter the value of probability in decimals. round the answer to two decimal places.) winning more than one prize is allowed.
To find the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing with 50 people, follow these steps:
1. Since winning more than one prize is allowed, the probability of Bo winning the first prize is 1/50.
2. Likewise, the probability of Colleen winning the second prize is also 1/50.
3. Similarly, the probability of Jeff winning the third prize is 1/50.
4. Finally, the probability of Rohini winning the fourth prize is 1/50.
5. Since these events are independent, we can multiply the probabilities together to find the overall probability of this specific :
Probability = (1/50) * (1/50) * (1/50) * (1/50)
6. Calculate the result:
Probability ≈ 0.00000016
7. Round the answer to two decimal places:
Probability ≈ 0.00
So, the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing with 50 people is approximately 0.00.
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carmen went on a trip of 120 miles, traveling at an average of x miles per hour. several days later she returned over the same route at a rate that was 5 miles per hour faster than her previous rate. if the time for the return trip was one-third of an hour less than the time for the outgoing trip, which equation can be used to find the value of x?
The equation that can be used to find the value of x is 120 = (x + 5) × (120/x - 1/3).
Carmen's first trip was 120 miles, and she traveled at an average of x miles per hour. We can use the formula:
distance = rate × time, which can be written as:
120 miles = x miles/hour × time
where, time is the time for outgoing.
For the return trip, Carmen traveled at a rate that was 5 miles per hour faster, so her speed was (x + 5) miles/hour. The time for the return trip was one-third of an hour less than the time for the outgoing trip, so we can represent the return trip time as (time - 1/3) hours. Using the distance formula again for the return trip:
120 miles = (x + 5) miles/hour × (time - 1/3) hours
Now, let's express both times in terms of x. From the first equation, we can find the time for the outgoing trip as:
time = 120 miles / x miles/hour
Substitute this expression for time in the return trip equation:
120 miles = (x + 5) miles/hour × (120/x - 1/3) hours
Now you have an equation that can be used to find the value of x:
120 = (x + 5) × (120/x - 1/3)
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5. (8 pts) Determine whether the following signals are periodic and if periodic find the fundamental period. (a) (4 pts) z(t) = 0 (b) (4 pts) [n] = 1 sin[n] + 4 cos[-] 72-
The fundamental period of [n] is N=72
(a) z(t) = 0 is a constant signal, which means it does not vary with time. A constant signal is not periodic because it does not repeat over time. Therefore, z(t) = 0 is not periodic.
(b) [n] = 1 sin[n] + 4 cos[-] 72- is a discrete-time signal, which means it is defined only at integer values of n. To determine whether it is periodic, we need to check whether there exists a positive integer N such that [n] = [n+N] for all integer values of n.
Using trigonometric identities, we can simplify [n] as follows:
[n] = 1 sin[n] + 4 cos[-] 72-
= 2 sin[36-] cos[-] 36- + 2 cos[36-] sin[n]
Next, we can rewrite [n+N] using the same trigonometric identities:
[n+N] = 2 sin[36-] cos[-] 36- + 2 cos[36-] sin[n+N]
For [n] to be periodic with period N, [n] must be equal to [n+N] for all integer values of n. This means that the two expressions above must be equal for all n, which in turn means that sin[n] must be equal to sin[n+N] and cos[n] must be equal to cos[n+N] for all n.
Since sin and cos are periodic with period 2π, this condition is satisfied if and only if N is a multiple of 72, which is the least common multiple of 36 and 72. Therefore, the fundamental period of [n] is N=72.
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Someone help!!!!!! Look at the picture below
Answer:
9
Step-by-step explanation:
i can not really tell what letters are on the picture but i think it is 9
Trapezoid A and trapezoid B as shown on the coordinate grid.
Describe three basic transformations on trapezoid A which show trapezoid B is similar to trapezoid A. In your response, be sure to identify the transformations in the order they would be performed.
Answer:
To show that trapezoid B is similar to trapezoid A, we need to perform three basic transformations in the following order:
1. Translation: Move trapezoid A to the left by 2 units and up by 2 units. This will bring point A to (-5, 3), point B to (-3, 5), point C to (3, 5), and point D to (5, 3).
2. Rotation: Rotate trapezoid A 90 degrees clockwise around the origin. This will bring point A to (3, 5), point B to (5, -3), point C to (-5, -3), and point D to (-3, 5).
3. Dilation: Enlarge the rotated trapezoid A by a scale factor of 2, using the origin as the center of dilation. This will bring point A to (6, 10), point B to (10, -6), point C to (-10, -6), and point D to (-6, 10).
After these three transformations, trapezoid A will be similar to trapezoid B.Step-by-step explanation:
What is the simplified form of (a7)3?
Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B. What is the ratio of the volume of sphere A to sphere B?
1:2
6:12
1:8
36:144
Answer:
Volume of sphere A
= (4/3)π(3^3) = 36π cubic units
Volume of sphere B
= (4/3)π((3/2)^3) = (4/3)π(27/8) = (9/2)π = 4.5π cubic units
The ratio of the volume of sphere A to sphere B is 4.5:36 = 1:8.
What is the
midpoint of AD?
y↑
10
9
8
7
6
5
4
3
2
1
1
A
O (3,6)
O (7,6)
O (6,9)
(4,3)
coordinate for the
2 3
D
4
B
C
5 6 7 8
9
10
+x
X
Answer:
6 is the middle point of AD
Let Z be a random variable with the N(0,1) distribution under a probability measure P. Let Y = 2 + H, where is a constant. (a) Find a probability measure with the property that the distribution of Z under Q is the same as the distribution of Y under P. a
The probability measure Q with the property that the distribution of Z under Q is the same as the distribution of Y under P is the Dirac delta function centered at -2: Q(Z ≤ z) = δ(z + 2)
To find the probability measure Q with the property that the distribution of Z under Q is the same as the distribution of Y under P, we can use the probability density function (PDF) approach.
First, we need to find the PDF of Y under P. Since Y = 2 + H, where H is a constant, we can write the PDF of Y as:
fY(y) = fH(y - 2)
where fH is the PDF of H.
Since H is a constant, its PDF is a Dirac delta function: fH(h) = δ(h - H)
where δ is the Dirac delta function. Substituting this into the expression for fY, we get:
fY(y) = δ(y - 2 - H)
Now, we need to find the PDF of Z under Q. Let FZ be the CDF of Z under Q. Then, we have:
FZ(z) = Q(Z ≤ z)
Since we want the distribution of Z under Q to be the same as the distribution of Y under P, we can equate their CDFs:
FZ(z) = P(Y ≤ z)
Substituting the expression for Y in terms of H, we get:
FZ(z) = P(2 + H ≤ z)
Solving for H, we get:
H = z - 2
Substituting this back into the expression for fY, we get:
fY(y) = δ(y - z)
Therefore, the PDF of Z under Q is: fZ(z) = fY(z - 2) = δ(z - 2 - z) = δ(-2).
This means that Z has a constant value of -2 under Q.
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What is the distance between (1, 2) and (1, -10)?
The distance between the points (1, 2) and (1, -10) is 12 square units
We have to find the distance between (1, 2) and (1, -10)
The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
=√(1-1)²+(-10-2)²
=√-12²
=√144
=12 square units
Hence, the distance between (1, 2) and (1, -10) is 12 square units
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Consider a Markov chain which at each transition either goes up 1 with probability p or down 1 with probability q = 1 - p. Argue that (q/p)^Sn , n >= 1 is a martingale.
The (q/p)^Sn, n>=1 is a martingale.
To show that (q/p)^Sn, n>=1 is a martingale, we need to show that it satisfies the three conditions of a martingale:
The expected value of (q/p)^Sn is finite for all n.
For all n, E[(q/p)^Sn+1 | Fn] = (q/p)^Sn, where Fn is the sigma-algebra generated by the first n transitions.
(q/p)^Sn is adapted to the filtration Fn.
First, we note that the expected value of (q/p)^Sn is finite for all n since q/p < 1, and thus (q/p)^n approaches zero as n approaches infinity.
Next, we consider the second condition. Let F_n be the sigma-algebra generated by the first n transitions, and let X_n = (q/p)^Sn. We need to show that E[X_n+1 | F_n] = X_n.
We can write (q/p)^(n+1) = (q/p)^n * (q/p), so we have:
E[X_n+1 | F_n] = E[(q/p)^(n+1) | F_n]
= E[(q/p)^n * (q/p) | F_n]
= (q/p)^n * E[(q/p) | F_n]
= (q/p)^n * [(q/p) * P(up) + (p/q) * P(down)]
= (q/p)^n * [(q/p) * p + (p/q) * q]
= (q/p)^n * (p + q)
= (q/p)^n * 1
= X_n
Thus, the second condition is satisfied.
Finally, we need to show that X_n is adapted to the filtration F_n. This is true since X_n only depends on the first n transitions, which are included in F_n.
Therefore, we have shown that (q/p)^Sn, n>=1 is a martingale.
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i need this asap for a test plsssss help. Which statement is true about acute triangles?
A.
a triangle that has one obtuse angle
B.
a triangle that has three acute angles
C.
a triangle with no sides that are the same length
D.
a triangle with three sides that are the same length
Answer:
B
Step by step solution:
A is an obtuse triangle
B is an acute triangle
C is a scalene triangle
D is an equilateral triangle.
Solve the inequality and graph the solution. 28<30–q
The solution of the inequality is q < -8.
We have,
38 < 30 - q
Now, solving the inequality
Subtract 30 from both of inequality as
38 - 30 < 30 - q - 30
8 < -q
Now, to make the variable q is positive then the sign of inequality change.
-8 > q
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