Answer:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Or equivalently:
[tex]\bar X \pm ME[/tex]
For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula:
[tex]ME= \frac{Upper -Lower}{2}= \frac{7.7-3.9}{2}= 1.9[/tex]
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Or equivalently:
[tex]\bar X \pm ME[/tex]
For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula:
[tex]ME= \frac{Upper -Lower}{2}= \frac{7.7-3.9}{2}= 1.9[/tex]
In a population of 210 women, the heights of the women are normally distributed with a mean of 64.4 inches and a standard deviation of 2.9 inches. If 36 women are selected at random, find the mean mu Subscript x overbar and standard deviation sigma Subscript x overbar of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor. Round to two decimal places.
Given Information:
Population size = N = 210
Mean height of women population = μ = 64.4 in.
Standard deviation of height of women population = σ = 2.9 in.
Sample size = n = 36
Required Information:
Sample mean = μx = ?
Sample standard deviation = σx = ?
Answer:
Sample mean = μx = 64.4 in.
Sample standard deviation = σx = 0.44 in.
Step-by-step explanation:
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The mean of the sample will be same as population mean that is
μ = μx = 64.4 in
Whereas the sample standard deviation is given by
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \cdot \sqrt{\frac{N-n}{N-1} }[/tex]
Where σ is the standard deviation of height of women population, N is the population size and n is the sample size.
The term [tex]\sqrt{\frac{N-n}{N-1} }[/tex] is known as finite population correction factor and is used since the sampling is done without replacement.
[tex]\sigma_{x} = \frac{2.9}{\sqrt{36} } \cdot \sqrt{\frac{210-36}{210-1} }\\\sigma_{x} = 0.483 \cdot \sqrt{\frac{174}{209} }\\\sigma_{x} = 0.483 \cdot 0.912\\\sigma_{x} = 0.44[/tex]
Therefore, the standard deviation of sample is 0.44 in.
To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, use the formulas provided.
Explanation:To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, we use the formulas:
Mean of sample means (mu Subscript x overbar) = population mean (mu)Standard deviation of sample means (sigma Subscript x overbar) = population standard deviation (sigma) divided by the square root of the sample size (n), multiplied by the finite population correction factor (sqrt(N-n)/sqrt(N-1))In this case, the population mean (mu) = 64.4 inches, the population standard deviation (sigma) = 2.9 inches, and the sample size (n) = 36.
Using these values, we can calculate:
Mean of sample means (mu Subscript x overbar) = 64.4 inchesStandard deviation of sample means (sigma Subscript x overbar) = (2.9 inches) / sqrt(36) * sqrt(210-36) / sqrt(210-1) = 0.483 inchesLearn more about Population here:https://brainly.com/question/15889243
#SPJ3
Antonia is factoring the polynomial, which has four terms.
21x3−63x2+15x−45
3[7x3−21x2+5x−15]
3[7x2(x−3)+5(x−3)]
Which is the completely factored form of her polynomial?
21x2(x − 3)
36x2(x − 3)
3(7x2 + 5) (x − 3)
3(12x2 + 5) (x − 3)
Answer:
3(7x2 + 5) (x − 3) took the quiz :)
Step-by-step explanation:
Answer:
C- 3(7x2 + 5) (x − 3)
Step-by-step explanation:
You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ = 60.8 H a : μ ≠ 60.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 8 with mean M = 66.9 and a standard deviation of S D = 10.7 . What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = -.1228 Incorrect The p-value is... less than (or equal to) α greater than α Correct This p-value leads to a decision to... reject the null accept the null fail to reject the null Incorrect
Answer:
Step-by-step explanation:
This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 60.8
For the alternative hypothesis,
µ ≠ 60.8
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8,
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 66.9
µ = population mean = 60.8
s = samples standard deviation = 10.7
t = (66.9 - 60.8)/(10.7/√8) = 1.61
We would determine the p value using the t test calculator. It becomes
p = 0.076
Since alpha, 0.01 < than the p value, 0.076, then we would fail to reject the null hypothesis. Therefore, At a 1 % level of significance, the sample data showed that there is no significant evidence that μ ≠ 60.8
Therefore, this p-value leads to a decision to accept the null hypothesis
Ms. Burke invested $23,000 in two accounts, one yielding 4% interest and the other yielding 10%. If she received a total of $1,280 in interest at the end of the year, how much did she invest in each account?
Answer:
$17,000 at 4%$6,000 at 10%Step-by-step explanation:
Let x represent the amount invested at 10%. Then 23000-x is the amount invested at 4%, and the total interest is ...
0.10x +0.04(23000-x) = 1280
0.06x = 360 . . . . . subtract 920, simplify
x = 6000 . . . . . . . . divide by the coefficient of x
Ms Burke invested $6000 at 10% and $17000 at 4%.
In ΔBCD, the measure of ∠D=90°, CB = 25, BD = 7, and DC = 24. What is the value of the sine of ∠C to the nearest hundredth?
Answer: The value of the sine of ∠C is 0.28.
Step-by-step explanation:
Let's draw a triangle again (see the picture below).
Remember SOHCAHTOA? It's:
-sin = opposite/hypotenuse
-cos = adjacent/hypotenuse
-tan = opposite/adjacent.
We need to use sin in here.
The sin of C is [tex]\frac{7}{25}[/tex], which in a calculator, gives [tex]0.28[/tex]
A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in theater for a 2nd time. The target is to have 30 million viewers and they want more than 30% of the viewers to return to see the movie again. They show the movie to a test audience of 200 people. After the movie they asked them if they would see the movie in theaters again. Of the test audience 68 people said they would see it again.
A. Explain what the p-value is
B. What is the p-value for the test statistic.
C. What is the statistical devision when the alpha=0.05
D. Explain the managerial conclusion for this situation.
Answer: p-value = 0.1085 and we will not reject the null hypothesis.
Step-by-step explanation:
Since we have given that
Hypothesis are :
[tex]H_0:p=0.3\\\\H_1:p>0.3[/tex]
Here, n = 200
x = 68
So, [tex]\hat{p}=\dfrac{68}{200}=0.34[/tex]
So, the test statistic value would be :
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.34-0.3}{\sqrt{\dfrac{0.3\times 0.7}{200}}}\\\\z=\dfrac{0.04}{0.0324}\\\\z=1.234[/tex]
So, the value of statistic value is 1.234.
And the p-value = 0.1085 at 5% level of significance.
So, 0.1085 < 1.234,
So, we will not reject the null hypothesis.
Hence, p-value = 0.1085 and we will not reject the null hypothesis.
The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. To calculate the p-value, we compare the observed proportion to the target percentage using a one-sample proportion test. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05.
Explanation:A. The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. It represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.
B. To calculate the p-value for the test statistic in this case, we need to perform a hypothesis test. We compare the proportion of viewers who would see the movie again (68/200 = 34%) to the target percentage of 30% using a one-sample proportion test.
C. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05. This indicates strong evidence against the null hypothesis.
D. The managerial conclusion for this situation would depend on the p-value obtained. If the p-value is less than 0.05, we can conclude that there is strong evidence to suggest that more than 30% of the viewers would see the movie again. Otherwise, we cannot make a definitive conclusion.
Learn more about P-value here:https://brainly.com/question/33325466
#SPJ11
TIME REMAINING
58:25
Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to
find the area of lawn that remains.
40 ft
15 ft
Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his
claim is correct?
He is incorrect. The path will have an area of (4)(40) = 160 sq ft. The yard has an area of 600 sq ft. The area of the lawn
will be the difference of the yard and path, so it is 440 sq ft.
Mark this and return
Save and Exit
Next
Submit
Answer:
YOUR CORRECT ANSWER IS(B.)Step-by-step explanation:
Cars on Campus. Statistics students at a community college wonder whether the cars belonging to students are, on average, older than the cars belonging to faculty. They select a random sample of 18 cars in the student parking lot and find the average age to be 8.4 years with a standard deviation of 7.3 years. A random sample of 15 cars in the faculty parking lot have an average age of 4.2 years with a standard deviation of 3.8 years.
1. The null hypothesis is H0:????????=???????? H 0 : μ s = μ f . What is the alternate hypothesis? A. H????:????????≠???????? H A : μ s ≠ μ f B. H????:????????<???????? H A : μ s < μ f C. H????:????????>???????? H A : μ s > μ f
2. Calculate the test statistic. =
3. Calculate the p-value for this hypothesis test. p value =
4. Suppose that students at a nearby university decide to replicate this test. Using the information from the community college, they calculate an effect size of 0.7. Next, they obtain samples from the university student and faculty lots and, using their new sample data, conduct the same hypothesis test. They calculate a p-value of -0.0213 and an effect size of 0.487. Do their results confirm or conflict with the results at the community college? A. It contradicts the community college results because the effect size is much smaller. B. It confirms the community college results because the effect size is nearly the same. C. It contradicts the community college results because the p-value is much bigger D. It can neither confirm or contradict the community college results because we don't know the sample sizes the university students used. E. It confirms the community college results because the p-value is much smaller.
Answer:
Let the 1st group be of students and 2nd group be of faculty.
n1 = 18
\bar{x}_{1} = 8.4
s1 = 7.3
n2 = 15
\bar{x}_{2} = 4.2
s2 = 3.8
1.
H0: =
HA: >
2.
Equality of variance test:
F = s12/s22
= 53.29/14.44
= 3.69
df-num = n1-1 = 17
df-den = n2-1 = 14
p-value = 0..008 < 0.05 i.e.H0 can be rejected and hence we can say that both populations do not have the same variances.
So, test-statistic will be calculated as follows:
[ Find the solution of this part in the attachment]
3.
df = 26
p-value = 0.0217
4.
E. It confirms the community college results because the p-value is much smaller.
The blacksmith had two identical iron wires, which were used for making two chains containing 80 and 100 links accordingly. Each of the links in the shorter chain was 5 grams heavier than that in the longer one. What was the weight of each chain ?
PLEASE HELP I NEED THIS NOW!!!
Answer:
2kg is the answer
ok well let's see it's 2000 grams
What is the measure of side x in the isosceles triangle that is shown below
Answer:
x = 29 cm
Step-by-step explanation:
An isosceles triangle has two equal sides that have equal angles at the bases
Since the 80 degree angles are at the bases of the 29 cm side, the length of x must be 29 cm
Answer:
29 cm
Step-by-step explanation:
Because both angles are 80 degrees. If your angles are the same so are your sides.
What property is 1/5+1/8=1/8+1/5?
Answer: This is the Communitve Property because the equation has the same thing on both sides, but the numbers "flip flopped" or switched around.
The sun shines at a 60° angle to the ground. How long is the shadow cast
by a 20 ft tall flagpole?
Answer:
11.55 ft
Step-by-step explanation:
tan 60° = 20 / x
x = 20 / tan 60° = 20 / √3 = 11.55
The length of the shadow will be 11.55 ft. It is found by the help of the tangent formula of trigonometry.
What is the depression angle?Angle of depression is the angle formed by the horizontal and the place where your head came to a halt.
You keep your gaze level with the ground. When you need to keep an eye on anything, though, you raise your head and lower your gaze.
The given data in the problem is;
Angle of depression = 60°
Length of the shadow(x) = ?
Height of flagpole = 20 ft
From trigonometry formula of tanΘ is;
[tex]\rm tan \theta = \frac{P}{B} \\\\ tan60^0=\frac{20}{x} \\\\ x= \frac{20}{tan60^0} \\\\ x= \frac{20}{\sqrt{3} } \\\\ x=11.55 \ ft[/tex]
Hence, the length of the shadow will be 11.55 ft.
To learn more about the depression angle, refer to the link;
https://brainly.com/question/13514202
#SPJ2
how many cups are equal to 34 pint
By using multiplication, there are 68 cups is equal to 34 pints.
Given that,
Change the number 34 pint into cups.
Used the concept of measurement unit,
A measurement unit is a standard quality used to express a physical quantity. Also, it refers to the comparison between the unknown quantity with the known quantity.
Since we know that;
1 pint = 2 cups
Hence, we get;
34 pint = 34 x 2 cups
= 68 cups
Therefore, the number of cups in 34 pints is 68.
To learn more about multiplication visit:
brainly.com/question/10873737
#SPJ6
Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server, and finds that 365 of the messages are spam. Can you conclude that the percentage of emails that are spam is greater than 69% ? Use both =α0.01 and =α0.05 levels of significance and the P-value method with the TI-84 Plus calculator.
Complete Question:
Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server, and finds that 365 of the messages are spam. Can you conclude that greater than 69% of emails are spam? Use both a=0.01 and a=0.05 levels of significance and the -value method with the table.
(a) State the appropriate null and alternate hypotheses.
(b) Compute the -value.
(c) At the a=0.01, can you conclude that greater than 69% of emails are spam?
(d) At the a=0.05, can you conclude that greater than 69% of emails are spam?
Answer and step-by-step explanation:
a)
The required hypothesis are
H₀: [tex]\mu[/tex] = 0.69
H₁: [tex]\mu[/tex] > 0.69
additional solutions are attached in the image below
Answer:
a) No
B) Yes
Step-by-step explanation:
Calculating the p-value, we have;
z = (p-bar) -p/√(p(1-p)/n)
But p-bar = 365/500
= 0.73
Therefore,
z = 0.73 -0.69/√0.69(1-0.69)/500
= 0.04/√0.2139/500
= 0.04/√0.0004278
= 0.04/0.02068
= 1.93
p-value = p(z ≥1.93) = 0.0268
(a) Can you conclude that the percentage of emails that are spam is greater than 69% ?
No, because the p- value is greater than α. That is p-value⊃ 0.01
(b) Can you conclude that the percentage of emails that are spam is greater than 69%
Yes, since p-value ∠ 0.05
Csc^2 u -cos u sec u=cot^2 u
Step-by-step explanation:
csc²u − cos u sec u
csc²u − 1
cot²u
What is the answer of 7/8 x 1/2 equals
Answer:
[tex]\frac{7}{16}[/tex]
Step-by-step explanation:
[tex]\frac{7}{8}[/tex]×[tex]\frac{1}{2}[/tex]
Multiply straight forward:
So 7 and 1. 8 and 2.
7x1=7
8x2=16
[tex]\frac{7}{16}[/tex]
At the fair 4 employees were paid $8.75 an hour to work at a funnel cake stand. They worked 8 hours at regular pay then for 5 hours at overtime pay for extra $2.50 an hour.How much did each employee earn?
Answer:
$125.25
Step-by-step explanation:
8.75*h+11.25*e
h is hours regular pay and e is extra pay for overtime. Since its an extra $2.50 for overtime, add that to the regular pay. Put in the hours:
[tex]8.75*8+11.25*5[/tex]
Simplify by multiplying 8.75 by 8
[tex]70+11.25*5[/tex]
Simplify by multiplying 11.25 by 5
[tex]70+56.25[/tex]
Add
[tex]70+56.25=126.25[/tex]
Since it says how much did each earn, as in individually, leave it as it is (unless regular pay was $2.18 an hour, which would be a rip-off). I'm pretty sure including the number of employees was meant to throw you off.
Choose the graph of the function. g(x)=2.5x
Answer:
the graph that matches the function is
Step-by-step explanation:
The equation, y=−16x2+32x+24 , represents the height, in feet, of a firework x seconds after it is launched. What is the maximum height of the firework? Enter your answer in the box. feet
Answer:
40
Step-by-step explanation:
got 100 on quiz
The maximum height of the firework is 40 feet.
What is maximum height?
'The maximum height of the object is the highest vertical position along its trajectory.'
According to the given problem,
y = -16x²+32x+24
For maximum height,
The slope of y with respect to x has to be 0.
⇒ [tex]\frac{dy}{dx}[/tex] = 0
Now, [tex]\frac{d(-16x^{2} +32x+24)}{dx}[/tex] = -32x +32
⇒-32x + 32 = 0
⇒ 32 = 32x
⇒1 = x or x = 1 second
Therefore after 1 second, the firework reaches maximum height.
Now, we put the value of x = 1 second in the equation: y = -16x²+32x+24
⇒ -16(1)² + 32(1) +24
= -16+32+24
= 40 feet
Hence, we can conclude that after 1 second, the firework reaches a maximum height of 40 feet.
Learn more about maximum height here:
https://brainly.com/question/11535666
#SPJ2
What is the measure of angle DEG on circle O? Please help! 50 points!
Answer:
50 degrees
Step-by-step explanation:
A manufacturer of brand A jeans has daily production costs of Upper C equals 0.3 x squared minus 114 x plus 11 comma 405, where C is the total cost (in dollars) and x is the number of jeans produced. How many jeans should be produced each day in order to minimize costs? What is the minimum daily cost?
Answer:
190 Jeans
Step-by-step explanation:
The daily production cost of the jeans manufacturer is given as:
[tex]C=0.3x^2-114x+11405[/tex]
To determine the number of Jeans,x that should be produced daily to minimize cost, C. We take the derivative of C and solve for its critical points.
[tex]C'=0.6x-114\\$When C'=0\\0.6x-114=0\\0.6x=114\\x=190[/tex]
Therefore, to minimize daily cost, 190 Jeans is the number of jeans that should be produced daily.
The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function? Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
The y-intercept is the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis.
The slope(m) is:
[tex]m=\frac{rise}{run}[/tex]
"rise" is the number of units you go up(+) or down(-) from each point
"run" is the number of units you go to the right from each point
You know:
y-intercept = -6 or (0, -6)
m = 2 or [tex]\frac{2}{1}[/tex] , so from each point you go up 2 units and to the right 1 unit to get to the next point.
#1: Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
This is true
#2: Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
This isn't accurate because the slope doesn't move left.
#3: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis
#4: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis, and the slope doesn't move to the left.
Answer:
tis be A my friends
Step-by-step explanation:
Private universities claim to offer a higher quality education compared to public universities as justification for their more expensive tuition rates. The implication is that better education in the classroom leads to better employees after graduation. As a HR specialist in charge of selecting the best possible future employees from a pool of applicants, you propose giving preference to applicants with degrees from private universities. Hoping to control for the influence of academic performance on on-the-job performance, you randomly select 25 pairs of employees based on their cumulative GPA, one with a degree from a private university and another with a degree from a public university, and record their last performance evaluation score in an Excel file. The data appears as follows:
GPA Private University Alumni Public University Alumni
4.0 85 89
3.9 82 78
3.8 75 77
3.7 91 72
(a) How should this study design be described?
O True experiment
O Posttest only quasi experiment
O Non-experimental study
O Quasi experiment
Answer:quasi experiment
Step-by-step explanation:
Because it is basically for comparison usually by measuring outcomes if a program by participants and non participants
what is the value for x 3x - 2 = 16
Answer:
18
Step-by-step explanation:
I meant 6x3=18 -2=16 sorry for confusion
To find the value of x, you need to isolate/get the variable "x" by itself in the equation:
3x - 2 = 16 Add 2 on both sides
3x - 2 + 2 = 16 + 2
3x = 18 Divide 3 on both sides to get "x" by itself
[tex]\frac{3x}{3} =\frac{18}{3}[/tex]
x = 6
PROOF
3x - 2 = 16 Substitute/plug in 6 into "x" since x = 6
3(6) - 2 = 16
18 - 2 = 16
16 = 16
Find the cubic unit make sure to put cubic units after your answer
Answer:
24 cubic units
Step-by-step explanation:
4 times 2 times 3 equals 24
−6y+13+9y=8y−3 How many solutions are there? A. No solutions
B. One solution
C. Infinite solutions
Answer:
B. One solution
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
-6y + 13 + 9y = 8y - 3
Step 2: Solve for y
Combine like terms: 13 + 3y = 8y - 3[Addition Property of Equality] Add 3 on both sides: 16 + 3y = 8y[Subtraction Property of Equality] Subtract 3y on both sides: 16 = 5yRewrite: 5y = 16[Division Property of Equality] Divide 5 on both sides: y = 16/5∴ We can see by solving the equation, we get 1 solution only.
The linear equation has one solution after simplifying and isolating the variable y, which results in y = 16/5.
Explanation:When solving the given linear equation −6y + 13 + 9y = 8y − 3, the first step is to simplify and collect like terms. Begin by combining the terms with y on the left side: 3y + 13 = 8y − 3. Next, move the terms with y to one side by subtracting 3y from both sides: 13 = 5y − 3. Lastly, isolate y by adding 3 to both sides and then dividing by 5: y = rac{16}{5}. Since we have successfully isolated y and found a specific value for it, the equation has one solution.
A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Has there been improvement? (pre-post) Student 1 2 3 4 5 Pre-test 12 14 11 12 13 Post- Test 15 17 11 13 12 The test statistic equals -1.50 What would be the p-value? Group of answer choices p-value is between 0.01 and 0.025 p-value > 0.20 p-value < 0.002 p-value > 0.10
Answer:
Step-by-step explanation:
Given the sample data
Pre-test... 12 14 11 12 13
Post-Test 15 17 11 13 12
The mean of pre-test
x = ΣX / n
x = (12+14+11+12+13) / 5
x = 12.4
The standard deviation of pre-test
S.D = √Σ(X-x)² / n
S.D = √[(12-12.4)²+(14-12.4)²+(11-12.4)²+(12-12.4)²+(13-12.4)² / 5]
S.D = √(5.2 / 5)
S.D = 1.02.
The mean of post-test
x' = ΣX / n
x' = (15+17+11+13+12) / 5
x' = 13.6
The standard deviation of post-test
S.D' = √Σ(X-x)² / n
S.D' = √[(15-13.6)²+(17-13.6)²+(11-13.6)²+(13-13.6)²+(12-13.6)² / 5]
S.D = √(23.2 / 5)
S.D = 2.15
Test value
t = (sample difference − hypothesized difference) / standard error of the difference
t = [(x-x') - (μ- μ')] / (S.D / n — S.D'/n)
t = (12.4-13.6) - (μ-μ')/ (1.02/5 - 2.15/5)
-1.5 = -1.2 - (μ-μ') / -0.226
-1.5 × -0.226 = -1.2 -(μ-μ')
0.339 = -1.2 - (μ-μ')
(μ-μ') = -1.2 -0.339
μ-μ' = -1.539
Then, μ ≠ μ'
We can calculate our P-value using table.
This is a two-sided test, so the P-value is the combined area in both scores.
The p-value is 0.172
The p value > 0.1
Using the t-distribution, it is found that the p-value is of 0.086.
At the null hypothesis, it is tested if there is no improvement, that is, the subtraction of the mean of the grades on test 1 by the mean of the grades on test 2 is of at least 0, that is:
[tex]H_0: \mu_1 - \mu_2 \geq 0[/tex]
At the alternative hypothesis, it is tested if there is improvement, that is, the grades on the second test were greater than on the first, hence:
[tex]H_1: \mu_1 - \mu_2 < 0[/tex]
We can find the standard deviation for the samples, hence, the t-distribution is used.
The p-value is found using a left-tailed test, as we are testing if the variable is less than a value, with 5 + 5 - 2 = 8 df and t = -1.5, using a calculator, the p-value is of 0.086.
A similar problem is given at https://brainly.com/question/13873630
What shapes have all sides that are different lengths
Answer:
Scalene Triangles
Step-by-step explanation:
Isosceles triangles have one pair of equivalent edges, and equilateral triangles of course have all equivalent edges, it would obviously be the scalene triangles.
I am joyous to assist you at any time.
A metal rod is being carried down a corridor which is 7 feet wide.At the end of the corridor there is a right-angle turn (to the right) into a wider corridor whichis 8 feet wide. What is the length of the longest metal rod which can be carried horizontallyaround the right-angle turn
Answer:
Length of the longest metal rod which can be carried horizontally around the right-angle turn is 21.21ft
Step-by-step explanation:
Length of the longest metal rod which can be carried horizontally around the right-angle turn, can be determined at the point at where the distance between one end of rod and the 7feet corridor is same as the distance between other end of the rod and the 8feet corridor. How do I mean.
The length of longest metal rod will be determined when distance between the one end of rod and the 7feet corridor and the distance between other end of the rod and the 8feet corridor are both 15ft (7ft + 8ft).
See attachment for illustration.
Therefore using Pythagoras theorem we can find the length of longest metal rod that can be carried horizontally around the right angle turn
See illustration in attachment
i.e
Hyp² = opp²+adj²
Hyp = √(15²+15²)
Hyp = √450
Hyp = 21.21ft
A product with an annual demand of 1000 units has Co = $25.50 and Ch = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with μ=25 and σ=5. a.What is the recommended order quantity? b. What are the recorder point and safety stock if the firm desires at most a 2% probability of stockout on any given order cycle? c. If a manager sets the reorder point at 30, what is the probability of a stockout on any given order cycle? How many times would you expect a stockout during the year if the reorder point were used?
Answer:
a) Recommended order quantity = 79.84 = 80
b) recorder point = 35
Safety stock = 10
Safety stock cost = $0/year
ci) P(stock out/cycle) = 0.1587
cii) Number of stock outs/ year = 2
Step-by-step explanation:
The pictures attached show a clear explanation of all the processes.
Final answer:
To determine the recommended order quantity, use the EOQ formula. The reorder point and safety stock can be calculated using the normal distribution. If the reorder point is set at 30, the probability of a stockout and the expected number of stockouts can be calculated.
Explanation:
To determine the recommended order quantity, we need to consider the economic order quantity (EOQ) model. The EOQ formula is given by:
EOQ = √((2 * D * Co) / Ch)
Where:
D is the annual demand (1000 units)
Co is the ordering cost per order ($25.50)
Ch is the holding cost per unit ($8)
Plugging in the values, we get:
EOQ = √((2 * 1000 * 25.50) / 8) = 79.79 (rounded to 2 decimal places)
Therefore, the recommended order quantity is 80 units.
To calculate the reorder point, we need to consider the lead-time demand. Since the lead-time demand follows a normal probability distribution with μ=25 and σ=5, we can use the normal distribution to find the reorder point.
To calculate the recorder point and safety stock for a desired probability of stockout of 2%, we need to find the Z value corresponding to the desired probability. We can use the Z-score table or a calculator to find the Z value. For a 2% probability of stockout, the Z value is approximately -2.05 (rounded to 2 decimal places).
The reorder point is given by:
Reorder Point = μ + (Z * σ)
Where:
μ is the mean of the lead-time demand (25 units)
Z is the Z value (-2.05)
σ is the standard deviation of the lead-time demand (5 units)
Plugging in the values, we get:
Reorder Point = 25 + (-2.05 * 5) = 14.75 (rounded to 2 decimal places)
The safety stock is given by:
Safety Stock = Z * σ
Plugging in the values, we get:
Safety Stock = -2.05 * 5 = -10.25 (rounded to 2 decimal places)
Therefore, the recorder point is approximately 15 units (rounded to the nearest whole unit) and the safety stock is approximately 10 units (rounded to the nearest whole unit).
If the manager sets the reorder point at 30 units, we can use the normal distribution to find the probability of a stockout. The probability of a stockout can be calculated using the Z-score formula.
The Z value is calculated using the formula:
Z = (Reorder Point - μ) / σ
Where:
Reorder Point is the given reorder point (30 units)
μ is the mean of the lead-time demand (25 units)
σ is the standard deviation of the lead-time demand (5 units)
Plugging in the values, we get:
Z = (30 - 25) / 5 = 1 (rounded to 1 decimal place)
Looking up the Z value in the Z-score table, we find that the corresponding probability is approximately 0.8413. Therefore, the probability of a stockout on any given order cycle is approximately 0.1587 or 15.87% (rounded to 2 decimal places).
The number of times you would expect a stockout during the year can be estimated using the formula:
Number of Stockouts = (Annual Demand / EOQ) * (1 - Probability of Stockout)
Plugging in the values, we get:
Number of Stockouts = (1000 / 80) * (1 - 0.1587) = 10.69 (rounded to 2 decimal places)
Therefore, you would expect a stockout approximately 11 times during the year (rounded to the nearest whole number).