Answer:
c
Step-by-step explanation:
3.66+.72+1.77+2.17=8.32×6%=8.8192 =8.82
Answer:
C Yes, the total of her purchase after sales tax is $8.82.
Step-by-step explanation:
3.66+0.72+1.77+2.17= $8.32
8.32*.06 =0.4992
0.4992+8.32= $8.82
Hope this helps!
The customers at a bank complained about long lines and the time they had to spend waiting for service. It is known that the customers at this bank had to wait 7 minutes, on average, before being served. The management made some changes to reduce the waiting time for its customers. A sample of 57 customers taken after these changes were made produced a mean waiting time of 6.5 minutes with a standard deviation of 2.1 minutes. Using this sample mean, the bank manager displayed a huge banner inside the bank mentioning that the mean waiting time for customers has been reduced by new changes. Do you think the bank manager’s claim is justifiable? Use a 10% significance level to answer this question. Use both approaches.
Answer:
[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]
Critical value
The degreed of freedom are given by:
[tex]df=n-1=57-1=56[/tex]
We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:
[tex] t_{\alpha}= -1.297[/tex]
And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes
P value
The p value for this case would be given by:
[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]
Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=6.5[/tex] represent the sample mean for tje waiting times
[tex]s=2.1[/tex] represent the sample standard deviation
[tex]n=57[/tex] sample size
[tex]\mu_o =7[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean for this case is less than 7 minutes, the system of hypothesis for this case sre:
Null hypothesis:[tex]\mu \geq 7[/tex]
Alternative hypothesis:[tex]\mu < 7[/tex]
Since we don;t know the population deviation the statistic for the t test is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
If we replace the info given we got:
[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]
Critical value
The degreed of freedom are given by:
[tex]df=n-1=57-1=56[/tex]
We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:
[tex] t_{\alpha}= -1.297[/tex]
And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes
P value
The p value for this case would be given by:
[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]
Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes
Following are the solution to the given question:
Given:
size [tex](n) = 58[/tex]
mean [tex]\mu = 7.4 \ minutes[/tex]
standard deviation [tex]\sigma = 2.3 \ minutes[/tex]
null and alternative hypotheses:
[tex]H_0 : \mu = 8 \ minutes\\\\H_a : \mu < 8 \ minutes\\\\[/tex]
Calculating the test statistic:
So, the observed value
Calculating the degrees of freedom:
[tex]\to 58 - 1 = 57[/tex]
Calculating the range of p-value:
Therefore the t is the critical value at the significance level that is 0.05 with of freedom is,
Therefore,
[tex]\to test \ statistic = -1.987 < -1.672[/tex] rejecting the null hypothesis.
Therefore, the conclusion of the manager's claim is "True".
Learn more:
brainly.com/question/22553360
Which of the following statements is false? a. When the alternative hypothesis is two-tailed, any hypothesis test is said to be a two-tailed test. b. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution. c. When the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution. d. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution and when the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution. e. None of these.
Answer:
Step-by-step explanation:
For a two tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis.
The curve is symmetrical and the rejection regions would be in the left and right tails
In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.
Therefore, the following statements are false
B. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution.
D. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution and when the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution.
Final answer:
Statement d is false because it combines parts of two separate true statements, which could be misleading. A two-tailed test is indicated by a not equals symbol in the alternative hypothesis, and the rejection region is split between the two tails of the test statistic's sampling distribution.
Explanation:
The false statement is d. While it's true that when the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution, statement d is false because it repeats the earlier part of the statement and combines it with a correct statement from option c, which can be misleading. The correct information is provided in separate statements b and c.
The alternative hypothesis indicates the type of test to be conducted. If the alternative hypothesis has a not equals symbol (≠), it indicates a two-tailed test. In a two-tailed test, the rejection region is split between the two tails of the test statistic's sampling distribution. In terms of p-value, it represents the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. A small p-value (< 0.05) typically indicates strong evidence against the null hypothesis, leading to its rejection.
A woman who is 5.75ft tall stands next to a lamp post that is 12ft tall. If its' shadow is 30ft long, how long is the shadow of the woman?
Answer:
The length of shadow of the woman is 14.375 ft.
Step-by-step explanation:
Here we are given that
Height of the woman = 5.75 ft
Height of the lamp post = 12 ft
Shadow of the lamp post = 30 ft
Let the angle of elevation of the light source be θ
By definition, in a right triangle, with respect to angle θ, we have;
tan(θ) = Opposite÷Adjacent
Therefore, tan(θ) = (Height of the lamp post)÷(Shadow of the lamp post)
and tan(θ) = 12 ft ÷ 30 ft = 0.4
θ = Actan(0.4) = tan⁻¹(0.4) = 21.8°
Since, angle of elevation of the light = Angle of depression of the light (alternate angles) = 21.8° we have
tan(θ) = (Height of the woman) ÷ (Length of shadow of the woman)
∴ Length of shadow of the woman = (Height of the woman) ÷ tan(θ)
Length of shadow of the woman = 5.75 ft ÷ tan(21.8) = 5.75 ft ÷ 0.4
Length of shadow of the woman = 5.75 ft ÷ 0.4 = 14.375 ft.
A store stocked 150 bundles of Charmin Extra Soft and Fluffy toilet tissue for a weekend sale. Last weekend, 72 bundles of the Charmin Extra Soft and Fluffy toilet tissue were sold. What percent of the
bundles of stocked Charmin Extra Soft and Fluffy toilet paper were sold that weekend?
Answer:
48% was sold
Step-by-step explanation:
Let the percent sold be x
x/100 * 150 = 72
(This equation basically means...what percentage of 150 bundles will give us 72 bundles remaining? and that's the answer we need)
Simplifying...
150x/100 = 72
3x/2 = 72
3x = 144
x = 48%
Which best describes the numbers satisfying the inequality x <7?
all numbers greater than 7
all numbers less than 7
all numbers greater than and including 7
all numbers less than and including
FU
O
RRET
Sa
Answer:
(B) all numbers less than 7
Step-by-step explanation:
Given the inequality:
x<7
It means that:
x cannot be equal to 7x cannot be greater than 7Therefore, x<7 consists of all numbers less than 7.
Answer:
B
Step-by-step explanation:
A local hotel wants to estimate the average age of its guests that are from out-of-state. Preliminary estimates are that standard deviation of population of guests from out-of-state is 30. How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence? a. 12 b. 11 c. 139 d. 138
Answer:
c. 139
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence?
We need a sample size of n.
n is found when [tex]M = 5, \sigma = 30[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 1.96*\frac{30}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 1.96*30[/tex]
Simplifying by 5
[tex]\sqrt{n} = 1.96*6[/tex]
[tex](\sqrt{n})^{2} = (1.96*6)^{2}[/tex]
[tex]n = 138.30[/tex]
We round up,
So the correct answer is:
c. 139
Answer:
[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]
And if we round up to the nearest integer we got n =139, and the best answer for this case is:
c. 139
Step-by-step explanation:
For this case we have this previous info:
[tex]\sigma = 30[/tex] represent the previous estimation for the population deviation
[tex]Confidence =0.95[/tex] represent the confidence level
The margin of error for the true mean is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
The desired margin of error is ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for a 95% of confidence interval given now can be founded using the normal distribution. For this case the critical value would be given by [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]
And if we round up to the nearest integer we got n =139, and the best answer for this case is:
c. 139
A schools enrollment in 2012 was 1234 now it is 1456 what does the expression look like that would help me find the percent change
Answer:
.18 % increase
Step-by-step explanation:
First you would find what the difference is between the school enrollment
you would do 1456 - 1234 = 222
Then you would divide 1234/1456 = 84.75% to see the total percentage
The increase however has a percentage of .18%
To check your work you would do .18 x 1234 = 222.12 ( round to the nearest whole number so it would just be 222) then add 1234+ 222 = 1456!
Answer:
A) (1,456-1,234) ÷ 1,456
Which measure of central tendency is MOST EASILY affected by outliers? A) mean Eliminate B) median C) mode D) IQR
Answer: A. Mean.
Explanation:
Mean is the only measure of central tendency that is always affected by an outlier. Mean, the average is the most popular measure of central tendency.
The mean is strongly influenced by outliers because it is the average of the scores and it is not resistant.
Answer:
A) mean
Step-by-step explanation:
Mean is a measure of central tendency, it is the sum of all data divided by the number of data. Because the mean take into consideration each of the data in its calculations, it is generally affected by outliers (extremely high or low values)
Prove that if A2 = O, then 0 is the only eigenvalue of A. STEP 1: We need to show that if there exists a nonzero vector x and a real number λ such that Ax = λx, then if A2 = O, λ must be . STEP 2: Because A2 = A · A, we can write A2x as A(Ax). STEP 3: Use the fact that Ax = λx and the properties of matrix multiplication to rewrite A2x in terms of λ and x. A2x = x STEP 4: Because A2 is a zero matrix, we can conclude that λ must be .
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Four pencils are held together with a band.
Each of the pencils diameter 10mm.
Find the length of the band in this position
Give your answer in terms of π.
To find the length of the band holding four pencils together, calculate the circumference of each pencil using the formula C = 2πr, where C is the circumference and r is the radius. Multiply the circumference of each pencil by 4 to find the total length of the band.
Explanation:To find the length of the band holding four pencils together, you need to calculate the circumference of the pencils. The diameter of each pencil is given as 10 mm, so the radius is half of the diameter, which is 5 mm. The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference, π is a constant approximately equal to 3.14159, and r is the radius. Therefore, the circumference of each pencil is 2π(5 mm) = 10π mm. Since there are four pencils, the total length of the band is 10π mm x 4 = 40π mm. This is your answer in terms of π.
What’s does 200% increase mean
Answer:
from what I understand a 200% increase is tripling the number the increase is on
Please help! ASAP :)
Answer:
3.14 miles but that doesn't sound right
Step-by-step explanation:
Assuming you have to find area of the circle its
A = πr² Radius is half of diameter so half of 2 = 1
A = 3.14 x 1²
A = 3.14 x 1
A = 3.14
If you have to find area than its 3.14 it just sounds odd
Sorry if its wrong
What is the area of a regular pentagon with an apothem of 8 centimeters
Answer:
The of the pentagon is A=232.48cm²
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes, a pentagon
Now given the apothem the area can be expressed as
A=a²n tan (180/n)
where
a = the length of the apothem (in radius)
n = the number of sides= 5 for pentagon
tan is the tangent function calculated in degrees
Substituting our given data we can solve for the area A
A= 8²*5 tan (180/5)
A= 64*5 tan 36
A= 320tan 36
A= 320*0.7265
A=232.48cm²
I need help :( please help. Best answer = Brainiest,
Answer:
5
Step-by-step explanation:
let a be the other number
so one number is [tex]\frac{2}{3}a - 3[/tex]
a + [tex]\frac{2}{3}a - 3[/tex] = 17
[tex]\frac{5}{3}a - 3 = 17[/tex]
[tex]\frac{5}{3}a[/tex] = 17 + 3 = 20
a = 20 x [tex]\frac{3}{5}[/tex] = 12
[tex]\frac{2}{3}(12) - 3[/tex] = 5
Katrina is asked to simplify the expression Negative 3 a minus 4 b minus 2 (5 a minus 7 b).
She writes: Negative 3 a minus 4 b minus 2 (5 a minus 7 b) = negative 3 a minus 4 b minus 10 a + 14 b
Answer:
-13a+10b
Step-by-step explanation:
Alex has five rolls of shelf paper that is 800 cm long.She wants to use the to line the 1-meter wide shelves in her pantry. How many 1-meter wide can she line with the paper?
1 meter = 100 cm
So a 800 cm roll can cover 8 meters
(800/100 = 8)
She has 5 rolls so 5 x 8 = 40 meters total.
Solve the system of equations:
y=2x-3
y=x2-3
Answer: x = 0 or x = 2
Step-by-step explanation:
To solve this, we must note that the two equations speaks of a single function of y. So
y = 2x - 3 = x² - 3
So from.here we can equate the two together and solve for x.
x² - 3 = 2x - 3, biw convert to a quadratic expression
x² - 2x - 3 + 3 = 0
x² - 2x = 0
Now factorize
x( x - 2 ) = 0, so solving for x
x = 0 or x = 2. .I believed getting the 2 won't be a problem
When x - 2 = 0
Then x = 2.
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
x =
Answer: x= 2/3
Step-by-step explanation: For f(x) = g(x) we should equate the two functions to get the value of x.
f(x) = g(x)
−3x + 4 = 2
-3x + 4 - 4 = 2 - 4
-3x = -2
Dividing by -3 on both sides;
(-3x)/-3 = (-2)/-3
x = 2/3
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
If f(x)=g(x), should be : -3x+4= 2
-3x + 4 = 2
-3x = -2
x= -2/-3
x = [tex]\frac{2}{3}[/tex]
Hope this helps ^-^
A substance abuse researcher wants to know whether reaction time is decreased by frequent alcohol use. He randomly selects 164 alcoholics and finds that their mean reaction time (in ms) to a stimulus equals 283. Reaction times to the stimulus in the general population are distributed normally with a mean equal to 281 and a standard deviation equal to 28. Is there sufficient evidence at the 0.01 significance level to conclude that reaction time is decreased by frequent alcohol use
Answer:
We conclude that the reaction time is increased or remains same by frequent alcohol use.
Step-by-step explanation:
We are given that a substance abuse researcher wants to know whether reaction time is decreased by frequent alcohol use. He randomly selects 164 alcoholics and finds that their mean reaction time (in ms) to a stimulus equals 283.
Reaction times to the stimulus in the general population are distributed normally with a mean equal to 281 and a standard deviation equal to 28.
Let [tex]\mu[/tex] = mean reaction time after alcohol use.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 281 {means that the reaction time is increased or remains same by frequent alcohol use}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 281 {means that the reaction time is decreased by frequent alcohol use}
The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean reaction time (in ms) = 283
[tex]\sigma[/tex] = population standard deviation = 28
n = sample of alcoholics = 164
So, test statistics = [tex]\frac{283-281}{\frac{28}{\sqrt{164}}}[/tex]
= 0.915
The value of z test statistics is 0.915.
Now, at 0.01 significance level the z table gives critical value of -2.3263 for left-tailed test. Since our test statistics is more than the critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the reaction time is increased or remains same by frequent alcohol use.
A small tie shop finds that at a sales level of x ties per day its marginal profit is MP (x )dollars per tie, where MP (x )equals 1.85 plus 0.12 x minus 0.0024 x squared. Also, the shop will lose $65 per day at a sales level of x equals 0. Find the profit from operating the shop at a sales level of x ties per day.
Question:
A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per tie, where
MP(x) =1.85 + 0.12x - 0.0024x². Also, the shop will lose $65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.
Answer:
P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65
Step-by-step explanation:
MP(x) = 1.85 + 0.12(x) - 0.0024(x^2)
At sales level, x=0, loss = $65
P(0) = - $65
Integrating MP(x) with respect to x
P(x) = ∫MP(x) dx = ∫ 1.85 + 0.12(x) - 0.0024(x^2)
P(x) = 1.85x + 0.06x^2 - 0.0008x^3 + C
Therefore :
P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65
Correct question:
A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per tie, where
MP(x) =1.85 + 0.12x - 0.0024x². Also, the shop will lose $65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.
Answer:
P(x) =1.85x +0.06x² - 0.0008x³ - 65
Step-by-step explanation:
Given the marginal profit function:
MP(x) =1.85 +0.12x - 0.0024x², P(0)= -65
We are to find P(x).
P(x) = ∫MP(x) dx
P(x) = ∫(1.85 + 0.12x - 0.0024x²) dx
= ∫1.85 dx+∫0.12x dx+∫(-0.0024x²)dx + C
= 1.85x + 0.06x² - 0.0008x³ + C
Initial condition at P(0) = - 65
where x(0), P(x) = -65
we have:
-65 = 1.85(0)+0.06(0)² - 0.0008x(0)³ + C
-65 = 0 + 0 - 0 + C
-65 = C
C = -65
P(x) =1.85x + 0.06x² - 0.0008x³ - 65
Consider two populations for which μ1 = 35, σ1 = 3, μ2 = 20, and σ2 = 4. Suppose that two independent random samples of sizes n1 = 47 and n2 = 54 are selected. Describe the approximate sampling distribution of x1 − x2 (center, spread, and shape). What is the shape of the distribution? The distribution would be non-normal. The distribution is approximately normal. The shape cannot be determined. What is the mean of the distribution? What is the standard deviation of the distribution?
Answer:
The distribution is approximately normal.
The mean and standard deviation are 15 and 0.98 respectively.
Step-by-step explanation:
The population of the random variables X₁ and X₂ are distributed as follows:
[tex]X_{1}\sim (\mu_{1}=35, \sigma_{1}^{2}=3^{2})\\\\X_{2}\sim (\mu_{2}=20, \sigma_{2}^{2}=4^{2})[/tex]
Two independent random samples of sizes,
[tex]n_{1}=47\\\\n_{2}=54[/tex]
are selected form the two populations.
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Both the sample selected from the two populations are quite large, i.e. [tex]n_{1}=47>30\\\\n_{2}=54>30[/tex]
So, according to the central limit theorem the sampling distribution of sample means [tex]\bar X_{1}\ \text{and}\ \bar X_{2}[/tex] can be approximated by the Normal distribution.
Then, the distribution of [tex]\bar X_{1}[/tex] is:
[tex]\bar X_{1}\sim N(35,\ 0.44)[/tex]
And the distribution of [tex]\bar X_{2}[/tex] is:
[tex]\bar X_{2}\sim N(20,\ 0.54)[/tex]
If two random variables are normally distributed then their linear function is also normally distributed.
So, the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is Normal and the shape of the distribution is bell-shaped.
The mean of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:
[tex]E(\bar X_{1}\ -\ \bar X_{2})=E(\bar X_{1})-E(\bar X_{2})\\=35-20\\=15[/tex]
The standard deviation of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:
[tex]SD(\bar X_{1}-\bar X_{2})=SD(\bar X_{1})+SD(\bar X_{2})\\=0.44+0.54\\=0.98[/tex]
*X₁ and X₂ are independent.
Thus, the mean and standard deviation are 15 and 0.98 respectively.
An office manager just got back from vacation, so she has a pile of 424 letters to read. Then, the mail carrier comes and delivers 41 more letters for her. How many letters does the office manager have now?
465
383
455
373
Answer:
465
Step-by-step explanation:
424+41=465
Dr. Vegapunk thinks that watching anime (Japanese animated shows) decreases social skills in college students. To test this, Dr. Vegapunk randomly selected 30 brooklyn college students and assigned them to watch an episode of anime everyday for a week. After the week, each of the students answered a questionnaire about their social skills. The results showed that the sample had a mean social skills score of 7.3 and a standard deviation of 2.4. A previous study showed that the overall population of brooklyn college students had a mean social skills score of 6.2, but the standard deviation was not reported. Dr. Vegapunk decides to use an alpha level of 0.05. e) what is the obtained statistic
Answer:
The test statistic = 2.51
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, Dr. Vegapunk wants to test the claim that watching anime decreases social skills in college students.
So, the null hypothesis would be that there isn't significant evidence to conclude that watching anime decreases social skills in college students. That is, watching anime does not decrease social skills in college students.
And the alternative hypothesis is that there is significant evidence to conclude that watching anime decreases social skills in college students.
If the previous known mean social skills of college students is 6.2 and the new population mean social skills of college students who watch anime is μ,
Mathematically,
The null hypothesis is represented as
H₀: μ ≥ 6.2
The alternative hypothesis is given as
Hₐ: μ < 6.2
To do this test, we will use the t-distribution because no information on the population standard deviation is known
So, we compute the t-test statistic
t = (x - μ)/σₓ
x = sample mean = 7.3
μ₀ = Standard to be compared against = 6.2
σₓ = standard error of sample mean = [σ/√n]
where n = Sample size = 30
σ = Sample standard deviation = 2.4
σₓ = (2.4/√30) = 0.4382
t = (7.3 - 6.2) ÷ 0.4382
t = 2.51
Hope this Helps!!!
Write a verbal expression for 3m-8n/13
Step-by-step explanation:
Three m minus eight n divided by thirteen
Evaluate the function. Find f(5). f(x)=4x-1
Answer:
19
Step-by-step explanation:
plug in 5 for x so f(5)=4(5)-1 = 20-1 = 19
The solution of expression f (x) = 4x - 1at x = 5 would be 19.
Given that the expression is,
f (x) = 4x - 1
Used the concept of substitution method to solve the expression.
Now, substitute x = 5 in the expression,
f (x) = 4x - 1
f (5) = 4(5) - 1
f (5) = 20 - 1
f (5) = 19
Therefore, the value of the expression is f (5) = 19.
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Which set of ordered pairs could be generated by an exponential function?
(1, 1), (2.2), (3, 3), (4-4)
• (1, 1), (2.4), (0.5) (470)
Answer:
(1, 1), (2.4), (0.5) (470)
Step-by-step explanation:
Honestly, I only know it's this one because the first one is a linear function. If you think about it on a graph, all of the points on the first one can connect with a straight line.
You are given 4 matrices M1, M2, M3, M4 and you are asked to determine the optimal schedule for the product M1 ×M2 × M3 ×M4 that minimizes the number of operations (addition/multiplication) involved. The dimensions of the four matrices are respectively 100 × 50, 50 × 200, 200 × 50, and 50 × 10. What is the best (cheapest) schedule to multiply all the matrices together and compute M1 × M2 × M3 × M4? What is the total cost for this schedule?
Answer:
Step-by-step explanation:
first method is to try out all possible combinations and pick out the best one which has the minimum operations but that would be infeasible method if the no of matrices increases
so the best method would be using the dynamic programming approach.
A1 = 100 x 50
A2 = 50 x 200
A3 = 200 x 50
A4 = 50 x 10
Table M can be filled using the following formula
Ai(m,n)
Aj(n,k)
M[i,j]=m*n*k
The matrix should be filled diagonally i.e., filled in this order
(1,1),(2,2)(3,3)(4,4)
(2,1)(3,2)(4,3)
(3,1)(4,2)
(4,1)
Table M[i, j]
1 2 3 4
4 250000 200000 100000 0
3
750000 500000 0
2 1000000 0
1
0
Table S can filled this way
Min(m[(Ai*Aj),(Ak)],m[(Ai)(Aj*Ak)])
The matrix which is divided to get the minimum calculation is selected.
Table S[i, j]
1 2 3
4
4 1 2 3
3
1 2
2 1
1
After getting the S table the element which is present in (4,1) is key for dividing.
So the matrix multiplication chain will be (A1 (A2 * A3 * A4))
Now the element in (4,2) is 2 so it is the key for dividing the chain
So the matrix multiplication chain will be (A1 (A2 ( A3 * A4 )))
Min number of multiplications: 250000
Optimal multiplication order: (A1 (A2 ( A3 * A4 )))
to get these calculations perform automatically we can use java
code:
public class MatrixMult
{
public static int[][] m;
public static int[][] s;
public static void main(String[] args)
{
int[] p = getMatrixSizes(args);
int n = p.length-1;
if (n < 2 || n > 15)
{
System.out.println("Wrong input");
System.exit(0);
}
System.out.println("######Using a recursive non Dyn. Prog. method:");
int mm = RMC(p, 1, n);
System.out.println("Min number of multiplications: " + mm + "\n");
System.out.println("######Using bottom-top Dyn. Prog. method:");
MCO(p);
System.out.println("Table of m[i][j]:");
System.out.print("j\\i|");
for (int i=1; i<=n; i++)
System.out.printf("%5d ", i);
System.out.print("\n---+");
for (int i=1; i<=6*n-1; i++)
System.out.print("-");
System.out.println();
for (int j=n; j>=1; j--)
{
System.out.print(" " + j + " |");
for (int i=1; i<=j; i++)
System.out.printf("%5d ", m[i][j]);
System.out.println();
}
System.out.println("Min number of multiplications: " + m[1][n] + "\n");
System.out.println("Table of s[i][j]:");
System.out.print("j\\i|");
for (int i=1; i<=n; i++)
System.out.printf("%2d ", i);
System.out.print("\n---+");
for (int i=1; i<=3*n-1; i++)
System.out.print("-");
System.out.println();
for (int j=n; j>=2; j--)
{
System.out.print(" " + j + " |");
for (int i=1; i<=j-1; i++)
System.out.printf("%2d ", s[i][j]);
System.out.println();
}
System.out.print("Optimal multiplication order: ");
MCM(s, 1, n);
System.out.println("\n");
System.out.println("######Using top-bottom Dyn. Prog. method:");
mm = MMC(p);
System.out.println("Min number of multiplications: " + mm);
}
public static int RMC(int[] p, int i, int j)
{
if (i == j) return(0);
int m_ij = Integer.MAX_VALUE;
for (int k=i; k<j; k++)
{
int q = RMC(p, i, k) + RMC(p, k+1, j) + p[i-1]*p[k]*p[j];
if (q < m_ij)
m_ij = q;
}
return(m_ij);
}
public static void MCO(int[] p)
{
int n = p.length-1; // # of matrices in the product
m = new int[n+1][n+1]; // create and automatically initialize array m
s = new int[n+1][n+1];
for (int l=2; l<=n; l++)
{
for (int i=1; i<=n-l+1; i++)
{
int j=i+l-1;
m[i][j] = Integer.MAX_VALUE;
for (int k=i; k<=j-1; k++)
{
int q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
if (q < m[i][j])
{
m[i][j] = q;
s[i][j] = k;
}
}
}
}
}
public static void MCM(int[][] s, int i, int j)
{
if (i == j) System.out.print("A_" + i);
else
{
System.out.print("(");
MCM(s, i, s[i][j]);
MCM(s, s[i][j]+1, j);
System.out.print(")");
}
}
public static int MMC(int[] p)
{
int n = p.length-1;
m = new int[n+1][n+1];
for (int i=0; i<=n; i++)
for (int j=i; j<=n; j++)
m[i][j] = Integer.MAX_VALUE;
return(LC(p, 1, n));
}
public static int LC(int[] p, int i, int j)
{
if (m[i][j] < Integer.MAX_VALUE) return(m[i][j]);
if (i == j) m[i][j] = 0;
else
{
for (int k=i; k<j; k++)
{
int q = LC(p, i, k) + LC(p, k+1, j) + p[i-1]*p[k]*p[j];
if (q < m[i][j])
m[i][j] = q;
}
}
return(m[i][j]);
}
public static int[] getMatrixSizes(String[] ss)
{
int k = ss.length;
if (k == 0)
{
System.out.println("No matrix dimensions entered");
System.exit(0);
}
int[] p = new int[k];
for (int i=0; i<k; i++)
{
try
{
p[i] = Integer.parseInt(ss[i]);
if (p[i] <= 0)
{
System.out.println("Illegal input number " + k);
System.exit(0);
}
}
catch(NumberFormatException e)
{
System.out.println("Illegal input token " + ss[i]);
System.exit(0);
}
}
return(p);
}
}
output:
What are the coordinates of the image of point A after the segment has been dilated by a scale factor of One-fourth with a center of dilation at the origin? On a coordinate plane, point B is at (negative 2, 4) and point A is at (4, negative 8). (–2, 1) (1, –2) (Negative one-half, 1) (1, negative one-half)
Answer:
The answer is B
Step-by-step explanation:
Just did the assignment on Egn.
In 2005, there were 74,250 car accidents. In 20,187 of them, the driver was a
female. Based on this, what is the probability that a female driver was
involved in an accident?
Answer:
27.19% probability that a female driver was involved in an accident
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
74,250 car accidents. Of those, in 20,187, the driver was a female.
Based on this, what is the probability that a female driver was involved in an accident?
p = 20187/74250 = 0.2719
27.19% probability that a female driver was involved in an accident
The probability that a female driver was involved in one of the car accidents in 2005 is approximately 27.2%.
To determine the probability that a female driver was involved in an accident, we use the following formula:
Probability (P) = Number of favorable outcomes / Total number of outcomesIn this case, the number of favorable outcomes is the number of accidents involving a female driver (20,187), and the total number of outcomes is the total number of car accidents (74,250).
Divide the number of accidents involving female drivers by the total number of accidents: 20,187 / 74,250Simplify the fraction to get the decimal form: P ≈ 0.272Convert the decimal to a percentage if needed: 0.272 × 100 = 27.2%Therefore, the probability that a female driver was involved in an accident is approximately 27.2%.
find lim x →0 f(2+h)-f(2)/h if f(x)=x^3
Answer:
The value of the limit is 12.
Step-by-step explanation:
Small typing mistake, the limit is of h tending to 0.
We have that:
[tex]f(x) = x^{3}[/tex]
Then
[tex]f(2+h) = (2+h)^{3} = 8 + 12h + 6h^{2} + h^{3}[/tex]
[tex]f(2) = 2^{3} = 8[/tex]
Calling the limit L
[tex]L = \frac{f(2+h) - f(2)}{h}[/tex]
[tex]L = \frac{8 + 12h + 6h^{2} + h^{3} - 8}{h}[/tex]
[tex]L = \frac{h^{3} + 6h^{2} + 12h}{h}[/tex]
h is the common term in the numerator, then
[tex]L = \frac{h(h^{2} + 6h + 12)}{h}[/tex]
Simplifying by h
[tex]L = h^{2} + 6h + 12[/tex]
Since h tends to 0.
[tex]L = 0^{2} + 6*0 + 12[/tex]
[tex]L = 12[/tex]
So the answer is 12.
Using the definition of a derivative, the expression lim h→0 [f(2+h)-f(2)]/h for f(x)=x^3 simplifies to 12, which is the derivative of the function at x=2.
Explanation:The limit you are trying to find is representative of the definition of a derivative at a point. In this case, the function is f(x) = x^3 and we're trying to find the derivative at x = 2. This is the definition of the derivative at a point:
lim h→0 [f(x+h) - f(x)] / h
Now, we plug in the equation for f(x):
lim h→0 [(2+h)^3 - 2^3] / h = lim h→0 [8+12h+6h^2+h^3 - 8] / h
Simplify that to get:
lim h→0 h [12+6h+h^2] / h
Then, by cancelling the h's, you have:
lim h→0 [12+6h+h^2]
As h→0, 6h and h^2 become 0, so finally, you obtain 12 as the derivative of f at x=2.
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