Answer:
A'(4, 3)
Step-by-step explanation:
When a point is reflected across the line y = x, the transformation is ...
(x, y) ⇒ (y, x)
A(3, 4) ⇒ A'(4, 3)
The reflected point is (4, 3).
Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
Answer:
option 2
Step-by-step explanation:
4^2=16/8=2. 4^2=16/16=1. 2-1=1
A man starts with an initial velocity of 3.50 m/s and accelerates for a distance of 205
m over 28.7 s. What is the acceleration of the man?
Answer:
[tex] X= v_i t + \frac{1}{2}a t^2 [/tex]
And from this equation we can solve for a like this:
[tex] 205m = 3.5m/s *(28.7s) +\frac{1}{2}a (28.7s)^2[/tex]
And solving for a we got:
[tex] 104.55m = \frac{1}{2}a (28.7s)^2[/tex]
[tex] a = \frac{2*104.55m}{(28.7s)^2)}= 0.254 m/s^2[/tex]
Step-by-step explanation:
For this case we have the velocity , distance and time given:
[tex] v = 3.5 m/s, d=205m, t =28.7s[/tex]
And we know from kinematics that he velocity can be expressed like this:
[tex] v_f = v_i +a t[/tex]
We also know that the distance is given by:
[tex] X= v_i t + \frac{1}{2}a t^2 [/tex]
And from this equation we can solve for a like this:
[tex] 205m = 3.5m/s *(28.7s) +\frac{1}{2}a (28.7s)^2[/tex]
And solving for a we got:
[tex] 104.55m = \frac{1}{2}a (28.7s)^2[/tex]
[tex] a = \frac{2*104.55m}{(28.7s)^2)}= 0.254 m/s^2[/tex]
Assume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
She will receive a lot more money because she is already retired from work already and will win as bit more money
What is the area of triangle ABC?
3 square units
0 7 square units
11 square units
15 square units
[tex]the \: answer \: is \: 7 \: square \: units \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Please help! Will give Brainliest!
Steps 1-4 in attachment (#4 below)
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.
Answer:
g(x) = 2|x|g(x) = -2|x|g(x) = -2|x| -3g(x) = -2|x-1| -3Step-by-step explanation:
1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...
g(x) = 2|x|
__
2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.
g(x) = -2|x|
__
3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.
g(x) = -2|x| -3
__
4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...
g(x) = -2|x -1| -3
Each leg of a 45-45-90 triangle has a length of 6 units what is the length of its hypotenuse
Answer:
It's the option D
6 root 2 units
please help with math, it’s easy!! explantion needed!
Answer:
1
Step-by-step explanation:
The quadratic relation is a perfect square:
y = (7x +3)²
so has one zero, where the factor is zero:
7x +3 = 0
7x = -3
x = -3/7
_____
It is useful to have handy reference to the form of the square of a binomial:
(a +b)² = a² +2ab +b²
Here, your first clue is that 49x² and 9 are both perfect squares: (7x)² and (3)². It is easy to check that the middle term is twice the product of these roots:
2(7x)(3) = 42x . . . . matches the middle term
So, the given expression is equivalent to ...
y = (7x +3)²
If Aizuddin borrowed RM 6.300 from a bank which offers an interest of 8%
compounded annually, find.
(a) the future value
(b) the amount of interest charged
Answer:
(a) The formula to calculate the amount of money (A) that Aizuddin must pay the bank after n years, with the original amount of borrowed money is 6300 RM, interest of 8%, compounded annually, is described as following:
A = principal x (1 + rate)^(time in year)
A = 6300 x (1 + 8/100)^n
(b) The amount of interest charged (AC) that Aizuddin must pay after n years:
AC = A - 6300
AC = 6300 x (1 + 8/100)^n - 6300
AC = 6300 x [(1 + 8/100)^n - 1]
Hope this helps!
which of the following expressions is equal to 2X^2 +8
Answer:
The question is not clear.
Step-by-step explanation:
Normally it helps to rewrite 8 as
8 = 2 * 2 * 2 = 2³
However the question is not clear.
There are no following expressions given...
By 2X^2 +8,
do you mean 2*x² + 8, or do you mean 2*x^(2 + 8)
or did you perhaps mean 2^(x+8)
Next time, please add a picture.
Answer:
(2x-4i)(x+2i)
The height of water in a bathtub ,h, is a function of time ,t, let p represent this function height is measured in inches and time in minutes
The complete question is;
The height of water in a bathtub,h, is a function of time,t. Let P represent this function. Height is measured in inches and time in minutes.
Match each statement in function notation with a description.
A: P(0) = 0
B: P(4) = 10
C: P(10) = 4
D: P(20) = 0
1:After 20 minutes, the bathtub is empty.
2:The bathtub starts out with no water.
3:After 10 minutes, the height of the water is 4 inches.
4:The height of the water is 10 inches after 4 minutes.
Answer:
-option D is the correct answer for sentence 1.
-option A is the correct answer for sentence 2.
-option C is the correct answer for sentence 3.
-option B is the correct answer for sentence 4
Step-by-step explanation:
The height of water in a bathtub h is a function of time t.
-If t = 20 minutes, then height of water represented by P is empty so, P(20) = 0. Thus, option D is the correct option for sentence 1.
-The bath tub starts out with no water. Thus, P(0) = 0. So option A is the correct option for sentence 2.
-After 10 minutes, the height of the water is 4 inches. Thus, P(10) = 4. So, option C is the correct option for sentence 3.
- The height of the water is 10 inches after 4 minutes. Thus, P(4) = 10. So option B is the correct answer for sentence 4
Wyoming fisheries contend that the mean number of cutthroat trout caught during a full day of fly-fishing on the Snake, Buffalo, and other rivers and streams in the Jackson Hole area is 4.0. To make their yearly update, the fishery personal asked a sample of fly-fishermen to keep a count of the number caught during the day. The numbers were: 4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6. At the 0.05 significance level, can we conclude that the mean number caught is greater than 4.0?
Answer:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
Step-by-step explanation:
We have the following data given:
4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6
The sample mean and deviation from these data are:
[tex]\bar X=4.5[/tex] represent the sample mean
[tex]s=2.680[/tex] represent the sample deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =4[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to verify if the true mean is equal to 4, the system of hypothesis would be:
Null hypothesis:[tex]\mu =4[/tex]
Alternative hypothesis:[tex]\mu \neq 4[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the the info we got:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
What’s the correct answer for this question?
Answer
A. 18(3/4)π
Explanation
In the attached file
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
(a) Find the probability that at least 13 flights arrive late .
Answer:
The probability that at least 13 flights arrive late is 2.5196 [tex]\times 10^{-6}[/tex].
Step-by-step explanation:
We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.
A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = 18 Southwest flights
r = number of success = at least 13 flights arrive late
p = probability of success which in our question is probability that
flights arrive late, i.e. p = 1 - 0.80 = 20%
Let X = Number of flights that arrive late.
So, X ~ Binom(n = 18, p = 0.20)
Now, the probability that at least 13 flights arrive late is given by = P(X [tex]\geq[/tex] 13)
P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)
= [tex]\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}[/tex]
= [tex]\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}[/tex]
= 2.5196 [tex]\times 10^{-6}[/tex].
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50 Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight year period.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
Define the random variable in X and P in words.
Which distribution should you use in this problem?
Answer:
Step-by-step explanation:
a) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 451
x = 1.5/100 × 451 = 7
p = 7/451 = 0.02
q = 1 - 0.02 = 0.98
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.97 = 0.1
α/2 = 0.01/2 = 0.03
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.03 = 0.97
The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17
Therefore, the 97% confidence interval is
0.02 ± 2.17√(0.02)(0.98)/451
= 0.02 ± 0.014
b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
The distribution that should be used is the normal distribution
The perimeter of the shape is 28 cm. Find the value of radius.
Answer:
r = 4.2805cm
Step-by-step explanation:
ok first the shape its made of two slant height and and an arc of degree 70°
The total perimeter = 28cm
The formula for the total perimeter= 2l + 2πl(70/360)
Where l is the radius of the shape.
But l = 2r
So
= 2l + 1.2217l
= 3.2217l
28 = 3.2217l
l = 28/3.2217
l = 8.691
Recall that l = 2r
8.691= 2r
r = 8.691/2
r = 4.2805cm
A bird of species? A, when? diving, can travel six times as fast as a bird of species B top speed. If the total speeds for these two birds is 224 miles per hour
Answer:
Maximum speed of bird A is [tex]192\,\,\frac{mi}{h}[/tex]
Maximum speed of bird B is [tex]32\,\,\frac{mi}{h}[/tex]
Step-by-step explanation:
This is a problem with two unknowns: Max speed of bird A (we name that "A"), and max speed of bird B (we call that "B"). Now we can create two equations with these two unknowns, based on the info provided:
Equation 1): based on the phrase "bird A can travel six times as fast as bird B" we write:
[tex]A=6\,*\, B\\A=6B[/tex]
Equation 2): based on the phrase; "the total speeds for these two birds is 224 miles per hour", we write:
[tex]A+B=224\,\,\frac{mi}{h}[/tex]
Now, we use the first equation to substitute A in the second equation, ad then solve for the unknown B:
[tex]A+B=224\,\,\frac{mi}{h}\\(6B)+B=224\,\,\frac{mi}{h}\\7B=224\,\,\frac{mi}{h}\\B=\frac{224}{7} \,\,\frac{mi}{h}\\B=32\,\,\frac{mi}{h}[/tex]
Now we can solve for the other unknown "A" using the substitution equation and the value of B we just found:
[tex]A=6B\\A=6\,(32\,\,\frac{mi}{h})\\A=192\,\,\frac{mi}{h}[/tex]
Fertilizer must be mixed with water in a 1:4 ratio. If you use 3
cups of fertilizer how much water do you need?
Answer:
12
Step-by-step explanation:
1:4 = 3:12
Answer:
12 cups of water
Step-by-step explanation:
The ratio of fertilizer is 1. To get to 3 you times it by 3. Therefore to find how much water you need you'd have to do the same to the other side of the ratio, times it by three. So it would be 3:12
find the mean of x,2x,3x,4x,5x
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{No. OfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
The mean, also known as the average of x, 2x, 3x, 4x, and 5x is 3x as per the concept of Simplifying.
To find the mean of x, 2x, 3x, 4x, and 5x, we need to add up all the values and divide by the total number of values.
In this case, we have five values.
Mean = (x + 2x + 3x + 4x + 5x) / 5
Simplifying the numerator:
Mean = (15x) / 5
Mean = 3x
Therefore, the mean of x, 2x, 3x, 4x, and 5x is 3x.
The mean, also known as the average, represents the central tendency of a set of values. In this case, the mean is 3x, which indicates that on average, the values x, 2x, 3x, 4x, and 5x are three times the value of x.
To learn more about the mean;
brainly.com/question/13451489
#SPJ6
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Solution,
Radius=2 m
Area =pi r^2
= 3.142*(2)^2
=12.568 m^2
hope it helps
Good luck on your assignment
Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05 you take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02 what conclusion can be made
Options:
The supplier products have a lower mean than claimed
The supplier is more accurate than they claimed
The supplier products have a higher mean than claimed
The supplier is less accurate than they have claimed
Answer:
The supplier is less accurate than they have claimed
Step-by-step explanation:
Confidence Interval for supplier claim, CI = (20.45, 21.05)
Confidence Interval for your claim, CI = (20.48, 21.02)
Calculate the mean of the Confidence Interval for the supplier's claim:
[tex]\bar{X_s} = \frac{20.45 + 21.05}{2} \\\bar{X_s} = \frac{41.50}{2}\\\bar{X_s} = 20.75[/tex]
Calculate the mean of the Confidence Interval for your claim :
[tex]\bar{X_y} = \frac{20.48 + 21.02}{2} \\\bar{X_y} = \frac{41.50}{2}\\\bar{X_y} = 20.75[/tex]
Both the supplier and you have the equal mean
Margin of Error by the supplier = 21.05 - 20.75 = 0.30
Margin of Error by you = 21.02 - 20.75 = 0.27
Since the margin of error for the supplier is more, you can conclude that the suppler is less accurate than they have claimed.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05. You take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02. What conclusion can be made?
The supplier products have a lower mean than claimed
The supplier is more accurate than they claimed
The supplier products have a higher mean than claimed
The supplier is less accurate than they have claimed
Answer:
The margin of error reported by the supplier is greater as compared to the actual margin of error. A greater margin of error results in less accuracy.
Therefore, we can conclude that the supplier is less accurate than they have claimed.
Step-by-step explanation:
Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05.
The mean is given by
Mean = (Upper limit + Lower limit)/2
Mean = (21.05 + 20.45)/2
Mean = (41.50)/2
Mean = 20.75
The margin of error in this case is
MoE = Upper limit - Mean
MoE = 21.05 - 20.75
MoE = 0.30
You take samples and find that the 95% confidence interval of what they are sending is 20.48 to 21.02.
The mean is given by
Mean = (Upper limit + Lower limit)/2
Mean = (21.02 + 20.48)/2
Mean = (41.50)/2
Mean = 20.75
The margin of error in this case is
MoE = Upper limit - Mean
MoE = 21.02 - 20.75
MoE = 0.27
As you can notice the margin of error reported by the supplier is greater as compared to the actual margin of error. A greater margin of error results in less accuracy.
Therefore, we can conclude that the supplier is less accurate than they have claimed.
work out the value of 7^2+4^3 divided by 2^5
113/32
Step-by-step explanation:
7 squared is 49, 4 cubed is 64, 2 to the 5th power is 32.
49 plus 64 is 113 divided by 32
3.53125
Step-by-step explanation:
7^2+4^3/2^5
= 49+64/32
= 113/32
= 3.53125
The average of 12, 25 , 33 , and N is 120. Find N.
Answer:
So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.
70+N/4 = 120
480 = 70+N
So then we subtract 70 from both sides. Then we get 410 = N.
The answer is
410 is AnswerAn artist is trying to choose 5 covers for children’s books. There are 10 different covers to choose from. How many ways can the artist choose covers? (It’s a permutation and combination kind of problem)
Answer:
252
Step-by-step explanation:
The order of the books isn't important, so we'll use combinations.
The number of ways to choose 5 books from 10 is:
₁₀C₅ = 10! / (5! (10 − 5)!)
₁₀C₅ = 10! / (5! 5!)
₁₀C₅ = 10×9×8×7×6 / (5×4×3×2×1)
₁₀C₅ = 252
On a number line, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with number a. For example b= 11/4 when a= -11/4
A) b=-a
B) -b=-a
C) b-a=0
D) b(-a)=0
Answer:
B and A
Step-by-step explanation:
So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.
Which statement could be an interpretation of the graph’s x-intercept or y-intercept?
On a coordinate plane, a line goes through points (0, 800) and (400, 0).
Answer:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
[tex] y=mx +b[/tex]
Where
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Answer:
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
Where
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
A trust fund eels is 6% simple interest divide into its members accounts every month if a member has $5000 in the funds account how much money would be in that account after three months
Answer:
$5073.37
Step-by-step explanation:
We can use the simple interest rate (appreciation) formula: A = P(1 + r)^t
Because it gives us 3 months, we need to put it in terms of years. That will give us 1/4 of a year:
A = 5000(1 + 0.06)^0.25
When you plug that into the calc, you should get 5073.37 as your final answer!
Suppose a simple random sample of size n= 11 is obtained from a population with u = 62 and a = 14.
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
(b) Assuming the normal model can be used, determine P(x < 65.8).
(c) Assuming the normal model can be used, determine P(x 2 64.2).
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) What must be true regarding the distribution of the population?
O A. Since the sample size is large enough, the population distribution does not
need to be normal.
B. The population must be normally distributed and the sample size must be large.
OC. The population must be normally distributed.
OD. There are no requirements on the shape of the distribution of the population.
Answer:
a) C. The population must be normally distributed.
b) P(x < 65.8) = 0.8159
c) P(x > 64.2) = 0.3015
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
n < 30, so the distribution of the population must be normal.
The correct answer is:
C. The population must be normally distributed.
(b) Assuming the normal model can be used, determine P(x < 65.8).
This is the pvalue of Z when X = 65.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65.8 - 62}{4.22}[/tex]
[tex]Z = 0.9[/tex]
[tex]Z = 0.9[/tex] has a pvalue of 0.8159.
So
P(x < 65.8) = 0.8159
(c) Assuming the normal model can be used, determine P(x > 64.2).
This is 1 subtracted by the pvalue of Z when X = 64.2. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.2 - 62}{4.22}[/tex]
[tex]Z = 0.52[/tex]
[tex]Z = 0.52[/tex] has a pvalue of 0.6985.
1 - 0.6985 = 0.3015
So
P(x > 64.2) = 0.3015
Please help! Correct answer only, please! The following information matrices show how many of each vehicle type sold and the bonus amount each salesperson receives for selling that type of vehicle for the car dealership for the week. Which salesperson sold the most vehicle for the week described?A. Scott B. Each sold the same number of vehicles C. Kelly D. Mark
Answer: b) Each sold the same number of vehicles
Step-by-step explanation:
This question is only asking for the quantity of vehicles (not the total amount earned) so we can disregard the second matrix and find the sum of each row in the first matrix.
Kelly: 8 + 2 + 6 = 16
Scott: 7 + 8 + 1 = 16
Mark: 10 + 4 + 2 = 16
The total number of vehicles sold by each person is the same
Results of 99% confidence intervals are consistent with results of two-sided tests with which significance level? Explain the connection. A 99% confidence interval is consistent with a two-sided test with significance level alphaequals nothing because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval ▼ contains does not contain the value in the null hypothesis.
Answer:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
Step-by-step explanation:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.
Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.
Help me plzzz with my hw
Answer:
w || n and n ⊥ m
Step-by-step explanation:
To find out which statement is true, recall the following:
1. 2 lines are said to be parallel to each other if they do not intersect at any given point and are of the same distant apart. Parallel is denoted by ||
2. 2 lines are said to be perpendicular if both lines intersect at a right angle. It is denoted by ⊥
==>From the diagram given, we can see that w and n are of the same distant apart and they do not intersect at any given point.
Also, we can see that n and m intersect at point X to at right angle.
Therefore, we can conclude that w || n and n ⊥ m