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!!!
For the functions f(x)=−9x^2+9 and g(x)=8x^2+9x, find (f+g)(x) and (f+g)(−1)
Answer:
f(x) = - 9x² + 9
g(x) = 8x² + 9x
To find (f+g)(x) add g(x) to f(x)
That's
(f+g)(x) = -9x² + 9 + 8x² + 9x
Group like terms
(f+g)(x) = - 9x² + 8x² + 9x + 9
(f+g)(x) = - x² + 9x + 9To find (f + g)(- 1) substitute - 1 into (f+g)(x)
That's
(f + g)(- 1) = -(-1)² + 9(-1) + 9
= - 1 - 9 + 9
= - 1Hope this helps you
Will give brainliest answer
Answer:
9π or 28.3 units²
Step-by-step explanation:
A = πr²
A = π(3)²
A = 9π
or
A= 28.3 units²
Hope this helps. :)
Which of the following sets contains all factors of 12?
Answer:
Step-by-step explanation:
Factors of 12
2, 3 , 6 , 4, 1, 12
The graph of F(x) shown below resembles the graph of G(x) = K, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
F(x)=?
G(X) = 1x1
O A. F(X) = 3M+3
O B. F(X) --
O C. F(x) = -3M-3
O D. F(X) = 3W-3
Step-by-step explanation:
O D. F(X) = 3W-3 the answer is D
The function that represents the situation is F(x) = -x² - 3.
The correct option is A.
What is transformation on the graphs?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.
here, we have,
Let the functions f(x) and g(x) be two real functions.
And g (x) = f (x) + k, where k is real numbers.
The function can be sketched by shifting f (x), k units vertically.
The value of k can find the direction of shift:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
Given that ,
the parent function is g(x) = x².
To find the transformed function F(x):
The function's diagram is in the opposite direction.
That means the function is -x².
And the function is shifted 3 units down vertically.
From the definition the required function is,
F(x) = -x² - 3.
Therefore, F(x) = -x² - 3.
To learn more about the transformation on the graphs;
brainly.com/question/19040905
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complete question:
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
A.
F(x) = –x2 – 3
B.
F(x) = x2 – 3
C.
F(x) = –(x + 3)2
D.
F(x) = –(x – 3)2
E = { x l x is a perfect square <36}
Answer:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
Step-by-step explanation:
For this problem we have the following set:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds.
A sample of seven infants is randomly selected, and their weights at birth are recorded as:
9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds.
If Alpha = 0.05,
1. What is the critical t-value?
2. What is the decision for a statistically significant change in average weights at birth at the 5% level of significance?
Answer:
1. Critical value t=±2.447
2. The null hypothesis is failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the birth weight significantly differs from 6.6 lbs.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=6.6\\\\H_a:\mu\neq 6.6[/tex]
The significance level is 0.05.
The sample has a size n=7.
The sample mean is M=7.56.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.18.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.18}{\sqrt{7}}=0.446[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.56-6.6}{0.446}=\dfrac{0.96}{0.446}=2.152[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=7-1=6[/tex]
For a two-tailed test with 5% level of significance and 6 degrees of freedom, the critical value for t is ±2.447.
As the test statistic t=2.152 is under 2.447 and over -2.447, it falls in the acceptance region, so the effect is not significant. The null hypothesis is failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.
Sample mean and standard deviation calculations:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{7}(9+7.3+6+. . .+6.6)\\\\\\M=\dfrac{52.9}{7}\\\\\\M=7.56\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{6}((9-7.56)^2+(7.3-7.56)^2+(6-7.56)^2+. . . +(6.6-7.56)^2)}\\\\\\s=\sqrt{\dfrac{8.32}{6}}\\\\\\s=\sqrt{1.39}=1.18\\\\\\[/tex]
15. A zoo is building a glass cylindrical tank
for the small sharks. The tank is 10 feet
high and has a diameter of 16 feet. How
much water is needed to fill the tank?
(The volume of a right circular cylinder is
V = Tr?h, where r is the radius, h is the
height, and a = 3.14.)
Answer:
2009.6
Step-by-step explanation:
As we know, volume of a right cylinder is πr²h.
here, diameter is mentioned, which gives that the radius is half of the diameter.
r= 1/2*16=8 feet
height= 10 feet
π=3.14
volume= 3.14*8²*10
= 3.14*64*10
=3.14*640
= 2009.6
so, that much water is needed to fill the tank
Answer:
2,010.6192982
Step-by-step explanation:
what is the answer for 8=22x+1
Answer:
x = 22/7Step-by-step explanation:
22x + 1 = 8
Send 1 to the right side of the equation
22x = 8 - 1
22x = 7
Divide both sides by 22
x = 7/22
Hope this helps you
Less than 51% of workers got their job through networking. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H0 : p H1 : p
Use the following codes to enter the following symbols:
≥≥ enter >=
≤≤ enter <=
≠≠ enter !=
Answer:
Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Step-by-step explanation:
We are given that less than 51% of workers got their job through networking. We have to express the null and alternative hypotheses in symbolic form for this claim.
Let p = population proportion of workers who got their job through networking
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Here, the null hypothesis states that greater than or equal to 51% of workers got their job through networking.
On the other hand, the alternate hypothesis states that less than 51% of workers got their job through networking.
Hence, this is the appropriate hypothesis that can be used.
A regression line is the line that best fits the data, but this does not mean that the fit is good. In other words, there can still be a lot of variability about the regression line. Which combination describes a regression line that is a good fit for the data?
a. Larger-sq and small Se
b. Larger-sq and large Se
c. Small r-sq and small Se
d. Smallr-sq and large Se
Answer:
The following combination describes a regression line that is a good fit for the data
a. Larger R-sq and small Se
Step-by-step explanation:
In regression analysis, we measure the goodness of fit in terms of two parameters.
1. R² ( R-squared or also called the coefficient of determination)
2. SE ( Standard Error)
1. R-squared
The R-squared indicates the relative measure of the percentage of the variance with respect to the dependent variable.
R-squared is measured in percentage so it doesn't have any unit.
The greater the R-squared percentage, the better is the goodness of fit.
2. Standard Error
The SE basically indicates that on average how far the data points are from the regression line.
The unit of the standard error is the same as the dependent variable.
The lower the SE, the better is the goodness of fit.
Therefore, the correct option is (a)
a. Larger R-sq and small Se
Trish conducts an analysis which shows that the level of alcohol consumption affects reaction times more when a person is sleep-deprived than when a person is well-rested. This is an example of ______.
a. interaction
b. confounding
c. bias
d. main effect
Answer:
a. interaction
Step-by-step explanation:
In statistics, interaction occurs when the effect of one variable depends on the value of another variable.
In this case, Trish's analysis shows that the effect of alcohol consumption in a persons reaction time also depends on that person's quality of sleep, highlighting a clear case of interaction.
A survey of 132 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 66 of the 132 students responded "yes.". An approximate 98% confidence interval is (0.399, 0.601). How would the confidence interval change if the confidence level had been 90% instead of 98%
Answer:
For 90% CI = (0.428, 0.572)
For 98% CI = (0.399, 0.601)
The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
p+/-z√(p(1-p)/n)
Given that;
Proportion p = 66/132 = 0.50
Number of samples n = 132
Confidence level = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
0.50 +/- 1.645√(0.50(1-0.50)/132)
0.50 +/- 1.645√(0.001893939393)
0.50 +/- 0.071589436011
0.50 +/- 0.072
(0.428, 0.572)
The 90% confidence level estimate of the true population proportion of students who responded "yes" is (0.428, 0.572)
For 90% CI = (0.428, 0.572)
For 98% CI = (0.399, 0.601)
The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.
A trade discount of 20% amounts to $25.98.
What was the list price?
What was the net price?
Step-by-step explanation:
Net $103.92 [$25.98 ÷ 20%]
List. $129.90 [ $103.92 + $25.98]
Can someone help with this I can't fail.
Answer: B
Step-by-step explanation:
(f-g)(x) is f(x)-g(x). Since we have f(x) and g(x), we can directly subtract them.
5x-2-(2x+1) [distribute -1]
5x-2-2x-1 [combine like terms]
3x-3
This table represents a quadratic function.
where is the table that represents the quadratic function
25e +-6e7 =
What the answer
Answer:
-6511.8
Step-by-step explanation:
the table shows the time it took a group of students to complete a puzzle
Answer:
Where is the table because I dont see it up here?
6x^2-2x=20 use ac method
Answer:
Cannot be factored
Step-by-step explanation:
I’m so confused. Someone please help and if you can explain how to do it. WILL MARK BRAINLIEST
Answer:
Function
Step-by-step explanation:
A function is a relation where each x-value has only one y-value. In this problem, all the x-values have a y-value of 3. It is a function because even though they all share the same y-value, they don't have more than one y-value. It would be a relation but not a function if one x-value had two y-values.
Hope this helps. :)
The measure of angle 1 is (10 x + 8) degrees and the measure of angle 3 is (12 x minus 10) degrees. 2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4. What is the measure of angle 2 in degrees?
Answer:
Measure of angle 2 = 82°
Step-by-step explanation:
m∠1 = (10 x + 8)°
m∠3 = (12 x - 10)°
2 lines are said to intersect to form 4 angles. And the labelling of the angles was done starting from top left, clockwise: the angles are 1, 2, 3, 4.
Find attached the diagram obtained from the given information.
Vertical angles are angles opposite each other when two lines intersect. As such, they are equal to each other.
Considering our diagram
m∠1 = m∠3
m∠2 = m∠4
Sum of all four angles firmed = 360° (sum of angles at a point)
m∠1 +m∠2 + m∠3 + m∠4 = 360°
m∠1 = m∠3
(10 x + 8)°= (12 x - 10)°
10x-12x = -10-8
-2x = -18
x= 9°
Also m∠2 = m∠4, let each equal to y
(10 x + 8)°+ y + (12 x - 10)° + y = 360
10x + 12x - 10 +8 +2y = 360
Insert value of x
22(9) -2 + 2y = 360
2y = 360-196
2y = 164
y = 82°
m∠2 = m∠4 = y = 82°
Measure of angle 2 = 82°
Answer:
2 = 82°
Step-by-step explanation:
Pls help me :(((( Thank you
Step-by-step explanation:
[tex] \frac{2}{ \sqrt{9} } [/tex]
[tex] \frac{2 \times \sqrt{9} }{ \sqrt{9} \times \sqrt{9} } [/tex]
[tex] \frac{2 \sqrt{9} }{9} [/tex]
Answer:
[tex]\frac{2\sqrt{9} }{9}[/tex]
Step-by-step explanation:
[tex]\frac{2}{\sqrt{9} } \\[/tex]
[tex]\frac{2}{\sqrt{9} } * \frac{\sqrt{9} }{\sqrt{9} }[/tex]
[tex]\frac{\sqrt{9} }{\sqrt{9} }[/tex] is equal to 1, so it doesn't change the value, just helps us simplify.
[tex]\frac{2\sqrt{9} }{9}[/tex]
There are no common factors between 2 and root 9, so we are done
please help pleaseeeeeeeee
━━━━━━━☆☆━━━━━━━
▹ Answer
#3. 1.89/100
▹ Step-by-Step Explanation
1.89 → hundreths place so..
1.89/100 is the correct answer
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Human body temperatures have a mean of 98.20degrees°F and a standard deviation of 0.62degrees°F. Sally's temperature can be described by zequals=minus−1.5. What is her temperature? Round your answer to the nearest hundredth.
Answer:
Her temperature is 97.27ºF.
Step-by-step explanation:
Z-score:
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.
In this question:
[tex]\mu = 98.2, \sigma = 0.62[/tex]
Z = -1.5. What is her temperature?
Her temperature is X when Z = -1.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.5 = \frac{X - 98.2}{0.62}[/tex]
[tex]X - 98.2 = -1.5*0.62[/tex]
[tex]X = 97.27[/tex]
Her temperature is 97.27ºF.
What is the area of the sector shown in the diagram below?
A.
50 cm2
B.
11.1 cm2
C.
2.5 cm2
D.
39.3 cm2
Answer:
B
Step-by-step explanation:
Given that the sum of the first n terms of the provided series is 6560 determine the value of n (2,6,18,54....)
Answer:
n = 8
Step-by-step explanation:
The given sequence, 2, 6, 18, 54. . ., is a geometric sequence.
It has a common ratio of 3 => [tex] \frac{6}{2} = \frac{18}{6} = \frac{54}{18} = 3 [/tex]
Thus, the sum of the first n terms of a geometric sequence is given as [tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
Where,
[tex] a_1 [/tex] = first term of the series = 2
r = common ratio = 3
[tex] S_n [/tex] = sum of the first n terms = 6,560
Plug in the above values into the formula
[tex]6,560 = \frac{2(1 - 3^n)}{1 - 3}[/tex]
[tex] 6,560 = \frac{2(1 - 3^n)}{-2} [/tex]
[tex] 6,560 = \frac{1 - 3^n}{-1} [/tex]
Multiply both sides by -1
[tex] -6,560 = 1 - 3^n [/tex]
Subtract 1 from both sides
[tex] -6,560 - 1 = - 3^n [/tex]
[tex] -6,561 = - 3^n [/tex]
[tex] 6,561 = 3^n [/tex]
Evaluate
[tex] 3^8 = 3^n [/tex]
3 cancels 3
[tex] 8 = n [/tex]
The value of n = 8
Find the first four terms of the sequence defined by a(n subscript)= 1/n (separated by a comma).
Answer:
1,1/2,1/3,1/4
Step-by-step explanation:
an = 1/n
n is the term number
a1 = 1/1 =1
a2 = 1/2
a3= 1/3
a4 = 1/4
The first 4 terms are 1,1/2,1/3,1/4
A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more that $2,000 on inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. Write an equation to show the profit she will make on sneakers and sandals. P = [answer0]
Answer:
The equation that shows the profit: P = 2x + 3y
Step-by-step explanation:
The number of sneaker = x
The number of sandals = y
Cost of sneaker = 8 dollars.
Cost of sandals = 14 dollars.
Selling price of sneaker = $10
Selling price of sandals = $17
Total revenue = $10x + $17y
Total cost = $8x + $14y
Profit (P) = Total revenue - Total cost.
Profit = ($10x + $17y) – ($8x + $14y)
P = 10x +17y – 8x – 14y
P = 2x + 3y
Use the properties of logarithms to prove log81000= log210.
Answer:
Step-by-step explanation:
Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.
Starting from the Left Hand Side:
[tex]log_81000\\[/tex]= log₈ 10³= log_ 2^3 (10³)= log₂10The double cone is intersected by a vertical plane passing through the point where the tips of the cones meet. What is the shape of the cross section formed? HELP PLEASE ITS FOR PLATO
Answer:
B.
Step-by-step explanation:
The double cone is a cone on top of another cone. The bottom cone has the circular base on the bottom and the tip on top. The upper cone is upside down, and the two tips touch. Since the vertical plane goes through the tips of both cones, the cross section must have a shape that gets to a point at the middle of the height.
Answer: B. One triangle with the tip on top and an inverted triangle above it with the tips touching.
Answer:
B.
Step-by-step explanation:
answer: B. one triangle tip on top and invert above it with the top touching
If a couple plans to have 9 children, what is the probability that there will be at least one boy? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one boy in 9 children?
Answer:
It is a 9/10 chance of having at least one boy. The probability is also high enough for the couple to be very confident in having at least one boy in 9 children.
Step-by-step explanation:
I listed all of the possible combinations below
GGGGGGGGG BGGGGGGGG
BBGGGGGGG BBBGGGGGG
BBBBGGGGG BBBBBGGGG
BBBBBBGGG BBBBBBBGG
BBBBBBBBG BBBBBBBBB
Total number of combinations with at least one boy is 9/10
This is a very high percentage, which means the couple is very likely to have at least one boy.