To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.
Explanation:To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.
For policy G, there is a 45% chance of no claims, in which case the reimbursement is 0. If a claim is made, the loss amount follows an exponential distribution with a mean of 5. We need to find the expected value of the reimbursement in this case. Let X be a random variable representing the loss amount. The expected reimbursement for policy G is then given by:
Expected Reimbursement for Policy G = 0.45(0) + 0.55(0.8)(E(X) - 2)
Similarly, for policy H, there is a 35% chance of no claims and a 65% chance of a claim with a loss amount following an exponential distribution with a mean of 9. Let Y be a random variable representing the loss amount. The expected reimbursement for policy H is:
Expected Reimbursement for Policy H = 0.35(0) + 0.65(0.8)(E(Y) - 2)
To find the difference between the expected reimbursements, we subtract the expected reimbursement for policy H from the expected reimbursement for policy G:
Difference = Expected Reimbursement for Policy G - Expected Reimbursement for Policy H
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Solve for the equation for all x values by completing the square x^2 - 27= 67
Answer:
The solutions for the equation [tex]x^2\:-\:27=\:67[/tex] are [tex]x=\sqrt{94},\:x=-\sqrt{94}[/tex].
Step-by-step explanation:
To find the solutions for the equation [tex]x^2\:-\:27=\:67[/tex] you must:
[tex]\mathrm{Add\:}27\mathrm{\:to\:both\:sides}\\\\x^2-27+27=67+27[/tex]
[tex]\mathrm{Simplify}\\\\x^2=94[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{94},\:x=-\sqrt{94}[/tex]
find the length of side XZ in the right triangle shown
Answer:35 meters
Step-by-step explanation:
Answer:
35 meters
Formula:
a^2+b^2=c^2
12^2+b^2=37^2
Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent. A random sample of 100 students was taken. Fifty-five of them favored Mike. At a 0.05 level of significance, it can be concluded that the proportion of the students in favor of Mike:
a.is significantly greater than 50 percent because 55 percent of the sample favored him.
b.is not significantly greater than 50 percent.
c.is significantly greater than 55 percent.
d.is not significantly different from 55 percent.
Using the z-distribution, it is found that the correct option is:
b. is not significantly greater than 50 percent.
At the null hypothesis, it is tested if the proportion is not significantly greater than 50%, that is:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if the proportion is significantly greater than 50%, that is:
[tex]H_1: p > 0.5[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: [tex]n = 100, \overline{p} = \frac{55}{100} = 0.55, p = 0.5[/tex].
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.55 - 0.5}{\sqrt{\frac{0.5(0.5)}{100}}}[/tex]
[tex]z = 1[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, using the z-distribution with a significance level of 0.05, is of [tex]z^{\ast} = 1.645[/tex].
Since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that the proportion is greater than 50%, hence, option b is correct.
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PLEASEEEEE HELPP MEEE WITH NUMBER 13!!!!!!
QUESTION: (IN BOLDED SHOWN IN THE 2 PICTURES)
Answer:
∠1 = 31°
∠2 = 43°
Step-by-step explanation:
All triangles have a sum of 180°
Since we know this, then we know that in the end, the sum of the two triangles should both have a sum of 180° each.
∠2 equals 43° because it corresponds to ∠C and corresponding angles have the same measurement.
Now we can find the measurement of ∠1 by using the big triangle.
180 - (106 + 43)
180 - (149)
31°
So, the measurement of ∠1 is 31°.
Now, let's check our work.
Big triangle:
106 + 43 + 31 = 180
Small triangle:
43 + 31 + 106 = 180
The stockholders’ equity section of Waterway Corporation consists of common stock ($10 par) $2,050,000 and retained earnings $520,000. A 10% stock dividend (20,500 shares) is declared when the market price per share is $14. Show the before-and-after effects of the dividend on the following.
(a) The components of stockholders’ equity.
(b) Shares outstanding.
(c) Par value per share.
The stockholders' equity section of Waterway Corporation consists of common stock ($10 par) $2,050,000 and retained earnings $520,000. A 10% stock dividend (20,500 shares) is declared when the market price per share is $14. The before-and-after effects of the dividend are as follows...
Explanation:(a) Before the stock dividend, the components of stockholders' equity in Waterway Corporation are common stock ($10 par) $2,050,000 and retained earnings $520,000. After the stock dividend, the common stock would increase by 20,500 shares ($10 x 20,500 = $205,000) and retained earnings would decrease by the same amount since it is used to finance the dividend. So, the new components of stockholders' equity would be common stock ($10 par) $2,255,000 and retained earnings $315,000.
(b) Before the stock dividend, the shares outstanding in Waterway Corporation are not provided in the question. After the stock dividend, the number of shares outstanding would increase by 20,500 shares.
(c) The par value per share of the common stock remains the same before and after the stock dividend, which is $10 per share.
Final answer:
A 10% stock dividend for Waterway Corporation, with a par value of $10 and a market price of $14 per share, results in an increase in common stock by $205,000, a decrease in retained earnings by the same amount, an increase of 20,500 shares, while the par value per share remains at $10.
Explanation:
When a stock dividend is declared, it affects the stockholders' equity section of a corporation. In the case of Waterway Corporation, a 10% stock dividend is declared when each share has a market price of $14. Since the par value is $10 and there are 20,500 new shares being issued, the total value at par is $205,000 (20,500 shares x $10 par value). This amount is transferred from retained earnings to common stock. No additional capital is generated since it's a stock dividend, not a cash dividend.
Here's the before-and-after effects of the dividend:
(a) Components of stockholders' equity:
Before the dividend:
Common stock: $2,050,000
Retained earnings: $520,000
After the dividend:
Common stock: $2,255,000 (original $2,050,000 + $205,000 from the stock dividend)
Retained earnings: $315,000 (original $520,000 - $205,000 transferred to common stock)
(b) Shares outstanding:
Before the dividend: Assuming each common stock's par value aligns with one share, the company has 205,000 shares ($2,050,000 / $10 par value).
After the dividend: 225,500 shares (205,000 original shares + 20,500 new shares issued)
(c) Par value per share:
The par value per share remains unchanged at $10, as the stock dividend does not affect the par value.
Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores. 88%, 73%, 97%, 76%, 90%, 80% Which measure of center would best represent Ari’s grade? the mean the median both the mean and the median neither the mean nor the median
Answer:
There is no difference. Because the mean of Ari's tests equals his median score of his six tests. mean = 84% median = 84%
Step-by-step explanation:
88%, 73%, 97%, 76%, 90%, 80%
organize by low to high
73%, 76%, 80%, 88%, 90%, 97%
The median here is (80 + 88)/2 = 84%
let us find the mean
mean = [73% + 76% + 80% + 88% + 90% + 97% ]/6
mean = 504/6 = 84%
There is no difference. Because the mean of Ari's tests equals his median score of his six tests. mean = 84% median = 84%
According to a report by Scarborough Research, the average monthly household cellular phone bill is $73. Suppose local monthly household cell phone bills are normally distributed with a standard deviation of $11.
a. What is the probability that a randomly selected monthly cell phone bill is less than $95?
Answer:
The probability that a randomly selected monthly cell phone bill is less than $95 is 0.9772
Step-by-step explanation:
The average monthly household cellular phone bill is $73.
[tex]\mu = 73[/tex]
Local monthly household cell phone bills are normally distributed with a standard deviation of $11.
[tex]\sigma = 11[/tex]
We are supposed to find the probability that a randomly selected monthly cell phone bill is less than $95 i.e.P(x<95)
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{95-73}{11}[/tex]
Z=2
Refer the z table for p value
So,p value = 0.9772
Hence the probability that a randomly selected monthly cell phone bill is less than $95 is 0.9772
What is the side length of a cube with a volume of 64 mm3?
Cube V = s3
Answer:
4mm edge 2021
Step-by-step explanation:
Compare each set of data. Determine which set shows greater variability.
Set A
5, 8, 9, 10, 12, 15, 16, 20
Set B
24, 34, 37, 42, 56, 57, 65
Answer:
Which set shows greater variability? Set B
Which measure provides greater variability for the set you chose? Range
Answer:
Set B
Range
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
Neil has three partial full cans of white paint they contains 1/3 gallon 1/5 gallon 1/2 gallon of paint and how much paint does Niall have in all
Answer:
1 and 1/30 gallons of paint
Step-by-step explanation:
Simplify this complex fraction
Answer:
18
Step-by-step explanation:
6 ÷ 1/3
Change the whole number to a fraction
6/1 ÷ 1/3
Copy dot flip
6/1 * 3/1
18/1
18
Answer:
18
Step-by-step explanation:
6 ÷ 1/3
Change the whole number to a fraction
6/1 ÷ 1/3
Copy dot flip
6/1 * 3/1
18/1
18
Malaya wrote a survey question in the newspaper about changing the school colors. Ninety percent of those who responded in an e-mail said they should be changed. She concludes that 90% of the student body wants the colors changed *
What is the volume of the prism below height is 5 length is 7 width is 8
Answer:
B. 280 units cubed
Step-by-step explanation:
Multiply all of the numbers together
which is another way to write 10 minutes after 9?
Answer:
quarter past 9
Step-by-step explanation:
Answer:09:10
Step-by-step explanation:
10 minutes after 9 can be written as
09:10
On the calculator, graph several monomial functions where a = 1 and n is even. For example, y = x4, y = x6, y = x8, and so on. Trace along the functions, then check all of the statements that are true about all of these functions.
The graph opens up.
The graph passes through (0, 0).
The graph is symmetric about the y-axis.
The graph only has 1 x-intercept.
The graph only has 1 y-intercept.
Answer:
All the statement are true about these functions
Step-by-step explanation:
Given any monomial function where a=1 and n is even.
Attached is the graph of [tex]y=x^4 \:\&\: y=x^6[/tex] as a case study.
From the graphs, the following are observed.
The graph opens up since a is positive. The graph passes through (0, 0). The graph is symmetric about the y-axis. i.e whenever (a,b) is on the graph, (-a,b) is also on the graph.The graph only has 1 x-intercept which is 0.The graph only has 1 y-intercept which is 0.To graph monomial functions where a = 1 and n is even, enter the equations into a graphing calculator and observe the graph. The graph opens up, passes through the origin, and is symmetric about the y-axis.
Explanation:To graph the monomial functions where $a=1$ and $n$ is even, we can use a graphing calculator. For example, to graph $y=x^4, y=x^6$, and $y=x^8$, we can enter these equations into the graphing calculator and select an appropriate viewing window. By tracing along these functions, we can make the following observations:
The graph opens up: Since the exponent $n$ in all these functions is even, the leading coefficient $a=1$ does not change the shape of the graph. The even exponent ensures that the graph opens up, similar to the shape of the parabola $y=x^2$.The graph passes through $(0, 0)$: Plugging in $x=0$ in any of these functions will give $y=0$, indicating that the graphs pass through the origin (0,0).The graph is symmetric about the y-axis: Since these functions have an even exponent, they exhibit y-axis symmetry. If a point $(x,y)$ is on the graph, then $(-x,y)$ will also be on the graph.Based on these observations, we can conclude that all of these statements are true about the graph of the monomial functions with $a=1$ and even $n$.
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Evaluate the function. Find f(5). f(x)=2x2-1. The second 2 is a exponent
Answer:
[tex]f(x)=2x^2-1\\f(5)=2(5)^2-1\\f(5)=2(25)-1\\f(5)=50-1\\f(5)=49[/tex]
Step-by-step explanation:
Solve for x in the equation x squared + 4 x minus 4 = 8
Answer:
solution is : x = -6 and x = 2
Step-by-step explanation:
Answer:
the answer is A
Step-by-step explanation:
Which scenarios have a negative correlation? Check all that apply. the number of calories consumed and the amount of weight lost by a person the temperature outside and the number of pool guests the number of children assigned to a class and the number of desks the price of rice and the number of penguins at the South Pole the thickness of the ice on a lake and the likelihood of falling through the ice
Answer:
A. the number of calories consumed and the amount of weight lost by a person.
E. the thickness of the ice on a lake and the likelihood of falling through the ice.
Step-by-step explanation: This is the correct answer on Edge 2021, just did the assignment. Hope this helps ^-^.
An example of negative correlation is;the number of calories consumed and the amount of weight lost by a person.
What is a correlation?The term correlation has to do with the way in which two quantities are related. If there is a positive correlation between two quantities, they tend to have a positive slope when plotted.
Two examples of negative correlation are;
the number of calories consumed and the amount of weight lost by a person. the thickness of the ice on a lake and the likelihood of falling through the ice.Learn more about correlation:https://brainly.com/question/6563788
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a hospital did a ten year study on patients who used its services. one thousand patients were randomly selected and followed over a period of ten years to determine the average number of visits per year. by the end of the year period some of the patients had left the area. identify the problem with the pool
Option A is the correct answer. That is a nonresponse occurred.
Given that, a hospital did a 10-year study on patients who use his services. 1000 patients were randomly selected and followed over a period of 10 years to determine the average number of visits per year.
What is a poll in statistics?An opinion poll, often simply referred to as a poll or a survey, is a human research survey of public opinion from a particular sample.
Look at the explanation given below for the options:
Option A:
We understand that in the span of 10 years, 1000 patients were monitored, and among those were some individuals who had moved. These certain individuals are not responsive anymore, and can not be a source of data, and the poll would be incorrect if the hospital decided to switch out the patients in the midst of the decade. Therefore we are to assume a nonresponse occurred. (To define nonresponse, it is simply a failure to respond, which is indeed what is defined for those who had moved.)
Option B:
It is not B for the two variables have no correlation.
Option C:
It is not C for all patients were at first patrons and the problem did not explicitly state there was missing info.
Option D:
It is incorrect for it said the sample group was selected at random.
Therefore, with the process of elimination, option A would still be the correct answer.
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A hospital did a 10-year study on patients who use his services. 1000 patients were randomly selected and followed over a period of 10 years to determine the average number of visits per year. By the end of the 10 years. Some of the patients had left the area. Identify the problem with the poll.
A) A nonresponse occurred
B) The relationship between two variables implies one causes the other
C) Some of the sample data are missing
D) The conclusion is based on a voluntary response sample
Which function is not continuous
Answer:
A not continueous function
Step-by-step explanation:
has a range
The coordinates of the point on a coordinate grid are -2,6. the point is reflected across the x-axis to obtain a new point. the coordinates of the reflected point are
Answer:
(-2,-6)
Step-by-step explanation:
The rule for reflecting across the x axis is multiply the y coordinate by -1. Your x coordinate stays the same.
(x,y)---->(x,-y)
(-2,6)---> (-2,-6)
Solve similar triangles (advanced)
Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows. x 1 2 3 4 5 P(x) 0.70 0.15 0.10 0.02 (a) Find P(4). (b) Find the probability that a car has at least 3 occupants. (c) Find the probability that a car has fewer than 3 occupants. (d) Compute the mean µX. (e) Compute the standard deviation σX.
Answer:
a) P(4)=0.03
b) P(x≥3)=0.15
c) P(x<3)=0.85
d) µX=1.52
e) σX=1.69
Step-by-step explanation:
The question is incomplete:
The variable X has the following probability distribution:
x 1 2 3 4 5
P(x) 0.7 0.15 0.10 0.03 0.02
a) The probability P(x=4) can be read from the table
[tex]P(4)=0.03[/tex]
b) The probability that there are at least 3 occupants in the car is P(x≥3).
[tex]P(x\geq3)=P(3)+P(4)+P(5)\\\\P(x\geq3)=0.10+0.03+0.02\\\\P(x\geq3)=0.15[/tex]
c) The probability that a car has fewer than 3 occupants (P(x<3)) is:
[tex]P(x<3)=1-P(x\geq3)=1-0.15=0.85[/tex]
d) The mean can be calculated as:
[tex]\mu_x=\sum_{i=1}^5p_i\cdot x_i\\\\\mu_x=0.7*1+0.15*2+0.10*3+0.03*4+0.02*5\\\\\mu_x=0.7+0.30+0.30+0.12+0.10\\\\ \mu_x=1.52[/tex]
e) The standard deviation can be calculated as:
[tex]\sigma_x=\sqrt{\sum_{i=1}^5p_i(x_i-\mu_x)^2}}\\\\ \sigma_x=\sqrt{0.7(1-1.52)^2+ 0.15(2-1.52)^2+ 0.1(3-1.52)^2+ 0.03(4-1.52)^2 +0.02(5-1.52)^2}\\\\ \sigma_x=\sqrt{0.7*0.2704+0.15*0.2304+0.1*2.1904+0.03*6.1504+0.03*12.1104}\\\\\sigma_x=\sqrt{0.18928+0.06912+0.65712+0.738048+1.21104}\\\\ \sigma_x=\sqrt{2.8646}\\\\ \sigma_x=1.69[/tex]
The graph of the probability distribution of X is a bar graph. The mean of X is 1.65 and the standard deviation can be calculated using the variance formula. The probability that a car has at least 3 occupants is 0.12 and the probability that a car has fewer than 3 occupants is 0.85.
Explanation:The graph of the probability distribution of X is a bar graph where the x-axis represents the number of occupants and the y-axis represents the probability. You will have bars at x = 1, 2, 3, 4, and 5 with heights of 0.70, 0.15, 0.10, 0.02 respectively.(i) To calculate the mean of X, you multiply each possible value of X by its corresponding probability and sum them up. So, μX = 1*0.70 + 2*0.15 + 3*0.10 + 4*0.02 + 5*0 = 1.65. (ii) To calculate the standard deviation, you need to find the variance first. The variance is calculated by squaring the difference between each value of X and the mean, multiplying it by its corresponding probability, and summing them up. The standard deviation is the square root of the variance. (a) To find the probability that a car has at least 3 occupants, you need to sum up the probabilities of X being 3, 4, and 5. So, P(X≥3) = P(3) + P(4) + P(5) = 0.10 + 0.02 = 0.12. (b) To find the probability that a car has fewer than 3 occupants, you need to sum up the probabilities of X being 1 and 2. So, P(X<3) = P(1) + P(2) = 0.70 + 0.15 = 0.85.1. Which number is 0.01 less than
67.354
in a basketball game, sally was the top scorer woth 30% of the teams points. If sally scored 15 points, how many total points did the team score
Answer:
The team scored 50 points
Step-by-step explanation:
Let the points scored by team be x
We are given that sally was the top scorer woth 30% of the teams points
So, Sally scored points = [tex]30\% \times x[/tex]
Sally scored points = [tex]\frac{30}{100}x[/tex]
We are given that Sally scored 15 points
So, [tex]\frac{30}{100}x=15[/tex]
[tex]30x=1500[/tex]
[tex]x=\frac{1500}{30}[/tex]
x=50
Hence The team scored 50 points
Daniel believes that people perform better in the barbell curl, on average, if they are encouraged by a coach. Be recruited 29 subjects to participate in an experiment and randomly assigned them into two groups. Daniel gave one group verbal encouragement during the exercise and was quiet during the exercise for the other group. He recorded the total number of barbell curls each subject was able to complete before setting the bar down.
a. Explain the purpose of random assignment in this experiment. Here are boxplots that summarize the distribution of a number of barbell curls for each group.
b. Compare these distributions
c. State the hypotheses Daniel should use to test his belief about receiving encouragement during exercise. Make sure to define any parameters you use.
d. Identify the significance test Daniel should use to analyze the results of his experiment and show that the conditions for this test are met.
e. The P-value for Daniel's test is 0.107. What conclusion should Daniel make at the a=0.05 significance level?
Answer:
Step-by-step explanation:
Hello!
a)
One of the advantages of assigning the units randomly to the different treatments is to avoid selection bias. An example of selection bias would be selecting the best subjects at the barbell curl to the "encouraged" group and the worst ones to the "not encouraged" group.
Randomization also guarantees independence between the experimental units and treatment groups.
b) (see boxplots in attachment)
Encouraged group:
Box:
Q₁≅ 10
Q₂≅ 30
Q₃= 50
IQD= 50 - 10 = 40
The box seems symmetric, the distance between Q₁-Q₂ and Q₂-Q₃ is the same and the median is exactly in the middle.
Whiskers:
The left whisker is shorter than the right whisker, which is longer.
If you were to look only at the box, the distribution seems symmetrical but adding the whiskers there is a pronounced right asymmetry.
Min value ≅ 5
Max value ≅ 75
Range= 75 - 5 = 70
Not encouraged group:
Box:
Q₁≅ 10
Q₂≅ 20
Q₃= 35
IQD= 35 - 10 = 25
The box shows a little skewness to the right (the 2nd Quartile is closer to the first one than the 3rd) and is overall shorter compared to the first group.
Whiskers:
The left whisker is shorter than the right whisker, so in general, this distribution is also right-skewed.
Min value ≅ 0
Max value ≅ 60
Range= 60 - 0 = 60
Compared with the "encouraged" group, the IQD and the Range are shorter, which means that the "not encouraged" group shows less dispersion.
c) and d)
Daniel claims that people perform better in the barbell curl, on average, when being encouraged.
He divided the 29 subjects into two groups and measured their performance, then the study variables are:
X₁: Performance in the barber curl of a subject that was encouraged by his coach.
X₂: Performance in the barber curl of a subject that did not receive encouragement.
Logically, since Daniel wants to study the performance of both groups on average, you'd think that the parameters of interest will be the population means. But to study the average you need the population to have a normal distribution and looking at those boxplots, none of them is near the normal distribution and the size of both samples isn't big enough for an approximation.
The best option is to conduct a non-parametric analysis, for example, the Mann Whitney U-test and instead of comparing the population means, you'll compare the population medians: θ₁ vs. θ₂ ⇒ In the hypothesis of this test, you'll state that both samples come from the same population and if both have the same median, then each observation of the first sample x₁i will have an equal probability of being smaller or greater than each observation of the second sample x₂i (probability 0.5)
Depending of the statistics course, the hypotheses may change, I'm used at working directly with the medians, if they are equal, it will mean that the top 50% and bottom 50% of each population will be the same, which is the same as saying that P(x₁i > x₂i)= 0.5 vs. P(x₁i > x₂i)≠ 0.5
The conditions for the Mann-Whitney U-test are:
1) All observations on both groups should be independent. Check
2) The variables should be continuous or at least ordinal. Check
3) Both variables have the same distribution under the null hypothesis. Check (Looking at the boxplots, both are right-skewed)
4) Under the alternative hypothesis, the values of one of the populations exceed the other. In this case: H₁: θ₁ > θ₂
e)
H₀: θ₁ ≤ θ₂ vs. H₁: θ₁ > θ₂
Using the p-value approach, the decision rule is always the same:
If p-value ≤ α ⇒ Reject the null hypothesis.
If p-value > α ⇒ Do not reject the null hypothesis.
p-value: 0.107 > α: 0.05 ⇒ The decision is to not reject the null hypothesis.
At a 5% significance level, there is no significant evidence to reject the null hypothesis. Both samples seem to be from the same population. He can conclude that encouraging the subjects doesn't change significantly their performance in the barbell curl.
I hope you have a SUPER day!
Determine Whether The Sides Make A Right Triangle
24,18,30
Right Triangle Or Not?
Answer:
Yes
Step-by-step explanation:
Since we want to test if it is a right triangle, we can use the Pythagorean Theorem
a^2+b^2=c^2
where a and b are the legs (shortest sides) and c is the hypotenuse (longest side)
We have the sides: 24,18 and 30
24 and 18 are the shortest, therefore they are the legs. 30 is the longest, so it is the hypotenuse.
So, a is 24, b is 18 and c is 30
24^2+18^2=30^2
Evaluate the exponents
576+324=900
Add 576 and 324
900=900
This statement is true, so this is a right triangle
Find the value of x in each of the following
a)2x-7 = 13
b)3x+4 = 25
Sorry, I'm bad at maths.
Let W be the region bounded by z=100−y^2, y=10x^2, and the plane z=0. Calculate the volume of W as a triple integral in the order dzdydx. (Give your answer in exact form. Use symbolic notation and fractions where needed.)
To calculate the volume of the region W, set up and evaluate a triple integral over the given region. Identify the bounds, write the triple integral, find the limits of integration, and evaluate the integral.
Explanation:To calculate the volume of the region W, we need to set up and evaluate a triple integral. We will integrate over the region defined by the given inequalities. Let's break it down step by step:
Step 1:Identify the bounds of the region:
From the plane z=0, we have 0 ≤ z.From the equation y = 10x^2, we have 0 ≤ y ≤ 10x^2.From the equation z = 100 - y^2, we have 0 ≤ 100 - y^2 ≤ z.Step 2:Write the triple integral:
∫∫∫ f(x,y,z) dz dy dx
Step 3:Find the limits of integration:
For dz: 0 ≤ z ≤ 100 - y^2For dy: 0 ≤ y ≤ 10x^2For dx: Find the bounds where the region is defined. This can be done by solving the equations y = 10x^2 and z = 100 - y^2 for x.Step 4:Evaluate the integral:
Integrate the function f(x,y,z) over the given limits. The function f(x,y,z) will depend on the specific problem you are trying to solve.
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The volume of the region bounded by z = 100 - y², y = 10x², and the plane z = 0, is [tex]\(\frac{40000 \sqrt{10}}{3} \)[/tex] cubic units.
To find the volume of the region W bounded by z = 100 - y², y = 10x², and the plane z = 0, we need to evaluate a triple integral in the order dz dy dx. We can start by setting up the integral:
We first identify the boundaries for z. Since z is between 0 and 100 - y², the inner integral limits are 0 to 100 - y².Next, we determine the limits for y. Given y = 10x², we see that y ranges from 0 to 100 (since 100 = 10x² implies y = 100).Finally, we find the limits for x. Solving y = 100 for x in terms of x² = 10 gives us the bounds of -√(10) to √(10).Thus, the triple integral is:
[tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \int_{0}^{100} \int_{0}^{100-y^2} dz \, dy \, dx \][/tex]
First, we integrate with respect to z:
⇒ [tex]\[ \int_{0}^{100-y^2} dz = (100-y^2) - 0 = 100 - y^2 \][/tex]
This reduces our integral to:
[tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \int_{0}^{100} (100 - y^2) \, dy \, dx \][/tex]
Next, we integrate with respect to y:
⇒ [tex]\[ \int_{0}^{100} (100 - y^2) \, dy = 100y - \frac{y^3}{3} \bigg|_{0}^{100}[/tex]
⇒ [tex]100(100) - \frac{(100)^3}{3} = 10000 - \frac{1000000}{3}[/tex]
⇒ 10000 - 333333.33 = [tex]\frac{20000}{3}[/tex]
Finally, we integrate with respect to x:
⇒ [tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \left( \frac{20000}{3} \right)[/tex] [tex]dx = \frac{20000}{3} \left[ x \right]_{-\sqrt{10}}^{\sqrt{10}}[/tex]
⇒ [tex]\frac{20000}{3} ( 2\sqrt{10})[/tex] = [tex]\frac{40000 \sqrt{10}}{3}[/tex]
Therefore, the volume of W is [tex]\(\frac{40000 \sqrt{10}}{3} \)[/tex] cubic units.
Jake drew a kite the sketch below of a kite that he wants to make.
Part A
Which of the following expression can be used to find the area of the kite?
Part B
What is the area of Jakes kite?
area= ??
a) The area of a kite is given by [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals. So the answer is [tex]\frac{1}{2} (40 \times 60)[/tex].
b) Evaluating the expression from part (a), we get the area to be [tex]\boxed{1200 \text{ cm}^{2}}[/tex]