Answer:
This is not a rigid motion.
Step-by-step explanation:
a rigid motions is the action of taking an object & moving it to a different location without changing its shape or size. in this case its a nonrigid motion because its size changed.
Answer:
No, at least one segment length is not preserved, making this a nonrigid transformation
Step-by-step explanation:
I just did this assignment
Consider the linear system of equations. y = –x + 9 y = 0.5x – 6 If the solution is (a,–1), what is a? a =
Answer:
a = 10
Step-by-step explanation:
From the solution given, x = a and y = -1
Substitute for x and y in either of the equations
y = -x + 9
-1 = -a + 9
a = 9 + 1 = 10
Answer:
Answer is 10
Step-by-step explanation:
Since the graphe cross only at one point there is only one solution for the equation.
Can I get brianliest plz.
A random sample of adult drivers was obtained where 52% were men and 46% were women. Note that everyone is not classified as a man or a women. A survey showed that 65% of the drivers rely on GPS systems. 30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected.
a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places.b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places.c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places.d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places.e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.
Answer:
a) P(G | M) = 0.577
b) P(W | G) = 0.523
c) P(M and G') = 0.220
d) P(M or G) = 0.870
e) P(G') = 0.350
Step-by-step explanation:
A random sample of adult drivers was obtained where 52% were men and 46% were women.
P(M) = 0.52
P(W) = 0.46
A survey showed that 65% of the drivers rely on GPS systems.
P(G) = 0.65
30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS.
P(M and G) = 0.30
P(W and G) = 0.34
a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places
P(G | M) = ?
Recall that conditional probability is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(G | M) = P(M and G)/P(M)
P(G | M) = 0.30/0.52
P(G | M) = 0.577
b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places.
P(W | G) = ?
Recall that conditional probability is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(W | G) = P(W and G)/P(G)
P(W | G) = 0.34/0.65
P(W | G) = 0.523
c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places.
P(M and G') = ?
Where G' means does not rely on a GPS system
P(M and G') = P(M) - P(M and G)
P(M and G') = 0.52 - 0.30
P(M and G') = 0.220
d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places.
P(M or G) = ?
Using the addition rule of probability,
∵ P(A or B) = P(A) + P(B) - P(A and B)
For the given case,
P(M or G) = P(M) + P(G) - P(M and G)
P(M or G) = 0.52 + 0.65 - 0.30
P(M or G) = 0.870
e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.
P(G') = ?
P(G') = 1 - P(G)
P(G') = 1 - 0.65
P(G') = 0.350
I NEED HELP PLEASE, THANKS! :)
As you know, a parallelogram's area is calculated by multiplying the length of it's sides, so all we are being asked to do is find the product of u and v -
[tex]( - 4i - 9j + k )( - 6i + j + 5k ),\\[/tex]
You would apply cross products in order to determine u * v. Doing so, you would get a solution of -46i + 14j - 58k.
Now we can take the magnitude of this vector -
u * v = √( - 46 )^2 + ( 14 )^2 - ( 58 )^2,
u * v = ( About ) 75.3 square units,
Solution = Option A
The most points Sidney has scored in a basketball game is 28. She is trying to tie that record in her current game. Write an equation for the number of points Sidney needs to score to tie her record, r, if she has already scored p points.
Answer:
r = 28 - p
p r
10 18
12 16
14 14
16 12
Step-by-step explanation:
We have the highest number of points Sidney has scored in a basketball game is 28.
We have to "r" the number of points that he needs to score and "p" are the points that he has already scored and the sum of these would be 28, that is, the total record.
So the equation would be
p + r = 28
we solve for "r" and we are left with:
r = 28 - p
Now, to fill the table it is missing when p = 14 and when p = 16
r = 28 - 14 = 14
r = 28 - 16 = 12
Therefore the complete table would be:
p r
10 18
12 16
14 14
16 12
Equation: r = 28 - p
Table:
p r
10 18
12 16
14 14
16 12
Step-by-step explanation:
We have the highest number of points Sidney has scored in a basketball game is 28.
We have to "r" the number of points that he needs to score and "p" are the points that he has already scored and the sum of these would be 28, that is, the total record.
So the equation would be
p + r = 28
Therefore, the complete table would be:
p r
10 18
12 16
14 14
16 12
Marvin and Ruby had the same number of stickers. After Marvin gave 12 stickers to Ruby, Ruby had 4 times as many as Marvin. How many stickers did Ruby have in the beginning?
Answer:
20 Tickets
Step-by-step explanation:
Given
Marvin and Ruby had the same number of stickers.
Let
no. of tickets with Ruby = No. of tickets with Marvin = x
condition
Marvin gave 12 ticket to Ruby
Now\
no. of tickets with Ruby = x+12
No. of tickets with Marvin = x-12
Ruby had 4 times as many as Marvin
Thus,
no. of tickets with Ruby = 4* No. of tickets with Marvin
x+12= 4(x-12) = 4x-48
x+12 = 4x-48
adding 48 both sides
x+12 +48= 4x-48+48
x+60 = 4x
subtracting 4 from both sides
x+60 -x= 4x -x
60 = 3x
dividing both side by 3
60/3 = 3x/3
x = 20
Thus, Ruby had 20 tickets in the beginning.
Write the equation of each line in slope intercept form (If possible please show work)
Hope it make sense now :)
Joanna, a machine learning engineer is studying what programming languages are the most effective to help systems learn from data. Based on previous research, more than 50% of machine learning involves the use of Python, a programming language. She suspects this percent has increased in recent years. In the process of hypothesis testing, what set value will allow Joanna to make a conclusion about whether her sample proportion is "different enough" than the claimed population proportion?a. p-value
b. test statisticc. significance leveld. null hypothesis
Answer:
Option A
Step-by-step explanation:
The p-value will help Joanna in coming to a conclusion about her hypothesis. The p-value derived from the test statistics calculated gives an immediate accurate summary of inference information (using significance levels, confidence intervals etc) for the parameter of interest.
It is used as an alternative to rejection points; a smaller p value means there is stronger evidence leading to the rejection of the null hypothesis and vice versa.
Change each decimal or mixed decimal to a percent.
a. 0.73
b. 0.023
c. 0.176
d. 2.415
A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.
Rating (last year): 87 67 68 75 59 60 50 41 75 72
Rating (this year): 85 52 51 53 50 52 80 44 48 57
Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the rating from last year and x2 be the rating from this year and use the formula d=x2âx1 to calculate the paired differences. Round your answer to one decimal place.
Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.
Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 4 of 4: Construct the 90%90% confidence interval. Round your answers to one decimal place.
Answer:
Step 1 of 4
Point estimate for the population mean of the paired differences = -8.2
Step 2 of 4
Sample standard deviation of the paired differences = 16.116244
Step 3 of 4
Margin of Error = ±9.326419
Step 4 of 4
90% Confidence interval = (-17.5, 1.1)
Step-by-step explanation:
The ratings from last year and this year are given in table as
Rating (last year) | x1 | 87 67 68 75 59 60 50 41 75 72
Rating (this year) | x2| 85 52 51 53 50 52 80 44 48 57
Difference | x2 - x1 | -2 -15 -17 -22 -9 -8 30 3 -27 -15
Step 1 of 4
Mean = (Σx)/N = (-82/10) = -8.2 to 1 d.p.
Step 2 of 4
Standard deviation for the sample
= √{[Σ(x - xbar)²]/(N-1)} = 16.116244392951 = 16.116244 to 6 d.p.
Step 3 of 4
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = -8.2
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 10 - 1 = 9.
Significance level for 90% confidence interval
= (100% - 90%)/2 = 5% = 0.05
t (0.05, 9) = 1.83 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 16.116244
n = sample size = 10
σₓ = (16.116244/√10) = 5.0964038367
Margin of Error = (Critical value) × (standard Error of the mean) = 1.83 × 5.0964038367 = 9.3264190212 = 9.326419 to 6 d.p.
Step 4 of 4
90% Confidence Interval = (Sample mean) ± (Margin of Error)
CI = -8.2 ± (9.326419)
90% CI = (-17.5264190212, 1.1264190212)
90% Confidence interval = (-17.5, 1.1)
Hope this Helps!!!
Find the missing side and round the answer to the nearest tenth. Thanks.
Answer:
22.2
Step-by-step explanation:
The missing side is x
cos19° = 21/x switch x and cos19° x = 21/cos 19°x = 22.21≈ 22.2
Solve the equation: x(x+3)(x+3)=0
Answer:
X = 0, x = -3
Step-by-step explanation:
You have to cancel everything and -3 =3 is 0 and that would make the entire right side zero. If you have x as 0 the first 0 will multiply with everything making everything zero.
[tex]\text{Find the value of the x's}\\\\x(x+3)(x+3)=0\\\\\text{We know that the x outside of the parenthesis would equal 0}\\\\\text{In order to find the value of the other x's, we must solve by equaling}\\\text{them to 0}\\\\x+3=0\\\\\text{Subtract 3 from both sides}\\\\x=-3\\\\\text{Since there are two of them, you would have two answers as -3}\\\\\boxed{\text{x = 0, or x = -3, or x = -3}}[/tex]
The point A(-1, 4) is translated five units right and three units down. Which rule describes the translation?
0 (x,y) → (x+5.y+3)
0 (x,y) → (x+5.y-3)
0 (xy) -> (X+3.y+5)
0 (XY)= (x-3.y+5)
Answer:
(x+5,y-3)
Step-by-step explanation:
5 units to the right is positive on the x-axis
x+5
3 units down is negative on the y-axis
y-3
Answer:
B. 0 (x,y) → (x+5.y-3)
Step-by-step explanation:
good luck
If4.3 x 0.37 = 1.591, then 0.43 x 370 is 3. 4. 5.
Answer:
0.43 x 370= 159.1
Step-by-step explanation:
g Determine whether the statement is true or false. If fx(a, b) and fy(a, b) both exist, then f is differentiable at (a, b). True False Correct: Your answer is correct.
Answer:
False
Step-by-step explanation:
A function is said to be differentiable over a given region if the function is continuous and has only one value for each input.
Therefore in order to conclude that f is differentiable at (a, b), the partial derivatives must be continuous at (a, b).
It is true that the function has to be defined over a given region because without it, you cannot determine if a partial derivative is continuous or otherwise.
But the fact that the partial derivatives exist at a point is not a sufficient condition for continuity.
Given: a concave polygon Conjecture: It can be regular or irregular
Answer:
[tex]false[/tex]Step-by-step explanation:
A concave polygon can never be regular (all sides and angles must be congruent). Hope this helps..
A circuit contains two capacitors rated at 0.02 microfrads and 0.05 microfrads connected in series the circuits Source voltage is 30vac what is the circuits total capacity
Answer:
about 0.0143 microfarads
Step-by-step explanation:
The effective capacitance of capacitors in series is the reciprocal of the sum of their reciprocals:
1/(1/0.02 +1/0.05) = 1/(50+20) = 1/70 ≈ 0.0143 . . . microfarads
Lily is using dark power crystal to raise an army of zombies. Each crystal can raise 9 zombies. How many crystals does Lily need to 6,174 zombies?
Answer:
686 crystals
Step-by-step explanation:
We can use ratios to solve
1 crystal x crystals
---------------- = -------------
9 zombies 6174 zombies
Using cross products
9x = 6174
Divide each side by 9
x = 6174/9
x =686
Lindsey made an error while solving this equation. 143.5 = 2 - (7(x+3). What line has the error?
(Refer to image)
A: Step 1
B: Step 2
C: Step 3
D: Step 4
Answer:
Step 1
Step-by-step explanation:
She didn't distribute the negative while she distributed 7. It should be -7x - 21, not 7x - 21.
An online wholesaler sells buttons in bulk quantities. If you buy 50 buttons or less, they cost $1.00 each. If you buy more than 50 buttons, but less than 100 100 buttons, they cost $0.80 each. If you buy 100 or more, they cost $0.55 each. Which graph represents the cost per button based on the number of buttons purchased?
Answer:
2nd picture, rightmost graph.
Step-by-step explanation:
This is sorta like an inequality expression. If the dot is filled in, it adds an "equal to", but if it is not filled in, then it has to be either greater than or less than.
Based off that logic, you can eliminate the first picture options since they are all filled in or not, yet the problem says "if you buy 50 buttons or less" which basically means: button less than or equal to which is important. Now, onto the second picture. You can eliminate the leftmost graph since the blank dot at the fifty is supposed to be filled, since the problem said if you buy fifty or less buttons, which is supposed to cost $50, but the dark dot is filled in the wrong place.
Anyways, I hope this explanation wasn't too confusing. If so, feel free to comment back and say what stuff you didn't get.
What is the biggest whole number smaller than the perimeter of any triangle with a side of length 5.6 and a side of length 19.7? PLEASE HELP!! Also the answer is not 50. I have tried it and it is incorrect.
Answer:
39 (IT IS CORRECT!)
Step-by-step explanation:
19.7+5.6 = 25.3
19.7-5.6 = 14.1
Now add the both results: 25.3+14.1 = 39.5
The biggest whole number possible less than 39.5 is 39, so the answer is 39.
Hope you mark me as Brainliest!
Use the stem-and-leaf plot to list the actual data entries. What is the maximum data entry? What is the minimum data entry? Key: 2 | 6 equals 26 2 6 3 2 4 1 2 2 5 6 6 8 5 0 1 1 2 3 3 3 4 4 4 4 5 6 6 8 9 6 8 8 8 7 3 8 8 8 3
Answer:
The minimum data entry is, 26.
The maximum data entry is, 83.
Step-by-step explanation:
The stem-and-leaf plot provided is:
2 | 6
3 | 2
4 | 1 2 2 5 6 6 8
5 | 0 1 1 2 3 3 3 4 4 4 4 5 6 6 8 9
6 | 8 8 8
7 | 3 8 8
8 | 3
As it is mentioned that 2 | 6 equals 26, the data is:
S = {26, 32, 41, 42, 42, 56, 56, 68, 50, 51, 51, 52, 53, 53, 53, 54, 54, 54, 54, 55, 56, 56, 58, 59, 68, 68, 68, 73, 78, 78, 83}
The data is arranged in ascending order.
The minimum data entry is, 26.
The maximum data entry is, 83.
Which student solved the equation 107d=1733.4 correctly?
Answer:
b correct me if i am wrong probably am
Step-by-step explanation:
mBC= measure of minor arc AC true or false?
Answer:
It's minor arc AC, it's true
As a prize for winning a contest, the contestant is blindfolded and allowed to draw 3 dollar bills one at a time out of an urn. The urn contains forty $1 bills and ten $100 bills. The urn is churned before each selection so that the selection would be at random. What is the probability that none of the $100 bills are selected
Answer:
The probability that none of the $100 bills are selected is 79.6%.
Step-by-step explanation:
The urn contains forty $1 bills and ten $100 bills. This gives a total of 50 bills in the urn.
To draw 3 dollar bills one at a time out of an urn, the probability of not selecting a $100 bill, decreases with each selection.
And the probability of not selecting a $100 bill is the probability of selecting a $1 bill in the first selection = 80% (40/50 x 100).
The probability of selecting a $1 bill the second time = 79.6% (39/49).
The probability of selecting a $1 bill the third time = 79.2% (38/48).
The sum of the probabilities divided by 3 = 79.6% (238.8/3)
b) Probability arises when there is a chance that an event may occur from a set of events that could have occurred. It is based on an estimate that one event happens when all the events in the set are given no less equal chance.
A number cubed is rolled. What is the probability that a one or six will be rolled
Answer: 1/3
Step-by-step explanation: Since there are six sides to a number cube, the total number of outcomes will be 6.
Since there are 2 favorable outcomes, rolling a 1 or a 6,
the probability of rolling a 1 or a 6 is 2/6 which reduces to 1/3.
Answer:
1/3
Step-by-step explanation:
A cube by default has 6 sides, and a number cube generally is tallied from 1 - 6 (being the numbers are 1, 2, 3, 4, 5, 6).
You are solving for the probability of the numbers 1 or 6 being rolled, which are 2 numbers of the given amount. Change into a fraction form by placing part over the total amount of numbers:
2/6
Most likely, you will be told to simplify. Divide common factors from both the numerator & denominator:
(2/6)/(2/2) = 1/3
1/3 is the probability that a 1 or a 6 is rolled in a standard number cube.
~
If you shifted y=3x+6 five units to the right, what would the linear equation be? (Hopefully it's challenging and easy at the same time.)
Answer:
[tex]3x + 6 = y \\ 3x = y - 6 \\ \frac{3x}{3} = \frac{y - 6}{3} \\ x = \frac{y - 6}{3} \\ x = \frac{y}{ 3 } - 2[/tex]
Answer:
y = 3x - 9
Step-by-step explanation:
y = 3x + 6 is a linear equation.
Shift the equation 5 units to the right.
The linear equation becomes:
y = 3x - 9
n a survey from 1998, 449 teenagers were surveyed about the music that they listen to. Of these teenagers, 129 of them said that their favorite genre of music is hip-hop. In a similar survey from 2008, 176 of 509 teenagers surveyed said that their favorite genre is hip-hop. Use a two-proportion hypothesis test to determine whether the proportion of teenagers whose favorite genre of music is hip-hop has changed from 1998 to 2008. Assume that the samples are random and independent. Use α=0.01. Let the sample from 1998 correspond to sample 1 and the other to sample 2. (a) Which answer choice shows the correct null and alternative hypotheses for this test?
Answer:
We accept H₀
Step-by-step explanation:
To compare two proportion:
proportion 1. 1998
n₁ = 449
p₁ = 129/449 p₁ = 0,2873
proportion 2. 2008
n₂ = 509
p₂ = 176/509 p₂ = 0,3457
Test hypothesis
Null Hypothesis H₀ p₂ - p₁ = 0
Alternative Hypothesis Hₐ p₂ > p₁
We have a one tail test ( to the right)
As α = 0,01 we find in z-table the z score z = 2,29 ( approximation for 0,011)
To calculate z(s),
z(s) = ( p₂ - p₁ ) /√ p*q ( 1/n₁ + 1/n₂)
p = ( x₁ + x₂ ) / n₁ + n₂
p = 129 + 176 / 449 +509
p = 0,3184 and q = 1 - p q = 0,6816
1/n₁ + 1/n₂ = 1/ 449 + 1 / 509 = 0,00222 + 0,001964
1/n₁ + 1/n₂ = 0,004184
z(s) = 0,0584/ √(0,3184*0,6816)*0,004184
z(s) = 0,0584/ 0,03013
z(s) = 1,938
z(s) < z(c) 1,938 < 2,29
z(s) is in the acceptance region we accept H₀ at α = 0,01
A director of the library calculates that 10% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 899 books would be less than 11%? Round your answer to four decimal places.
Answer:
0.8413
Step-by-step explanation:
p = 0.10
σ = √(pq/n) = 0.01
z = (x − μ) / σ
z = (0.11 − 0.10) / 0.01
z = 1
P(Z < 1) = 0.8413
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
We have,
We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.
First, we need to calculate the mean and standard deviation of the binomial distribution:
Mean:
np = 899 × 0.1 = 89.9
Standard deviation:
√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427
Next, we need to standardize the sample proportion of 11% using the formula:
z = (x - μ) / σ
where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Substituting the values we have, we get:
z = (0.11 - 0.1) / 0.9427 = 0.1059
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.
Therefore,
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
Rounded to four decimal places, the answer is 0.5425.
Learn more about probability here:
https://brainly.com/question/11234923
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The table shown lists the atomic weight of the elements that begin with the letter c. What's the range of these
atomic weights?
Review My Answers
Save & EVE
No. Atomic Weight Name 48112411 2040078 98251000
Cadmium cd Calcium Ca Californium Cf Carbon Cerium Ce Cesium Cs Chlorine C Chromium Cr Cobalt Co Copper Cu Curium Cm
6 12.011 58140116 55132906 1735453 2451996 2758933 2963546 96 *247.00
A. 215.547
B. 238.989
C. 234.989
D. 134.589
The Answer is 2
34.989.I used a physics book
A researcher wishes to see if the average number of sick days a worker takes per year is less than 5. A random sample of 30 workers at a large department store had a mean of 4.8. The standard deviation of the population is 1.2 days. Is there enough evidence to support the claim at alpha = 0.01?
Answer:
No. At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average number of sick days a worker takes per year is significantly less than 5.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5\\\\H_a:\mu< 5[/tex]
The significance level is 0.01.
The sample has a size n=30.
The sample mean is M=4.8.
The standard deviation of the population is known and has a value of σ=1.2.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.2}{\sqrt{30}}=0.219[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{4.8-5}{0.219}=\dfrac{-0.2}{0.219}=-0.913[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-0.913)=0.181[/tex]
As the P-value (0.181) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.
Using the z-distribution, it is found that since the test statistic is greater then the critical value for the left-tailed test, this is not enough evidence to support the claim at [tex]\alpja = 0.01[/tex].
At the null hypothesis, it is tested if the number of sick days is of at least 5, that is:
[tex]H_0: \mu \geq 5[/tex]
At the alternative hypothesis, we test if it is less than 5, that is:
[tex]H_1: \mu < 5[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 4.8, \mu = 5, \sigma = 1.2, n = 30[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{4.8 - 5}{\frac{1.2}{\sqrt{30}}}[/tex]
[tex]z = -0.91[/tex]
The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.01 is of [tex]z^{-\ast} = -2.327[/tex].
Since the test statistic is greater then the critical value for the left-tailed test, this is not enough evidence to support the claim at [tex]\alpja = 0.01[/tex].
A similar problem is given at https://brainly.com/question/16194574