Answer:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.
Step-by-step explanation:
Information given
We have the following data: 54 55 58 59 59 60 61 61 62 65
The sample mean and deviation can be calculated with the following formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]
[tex]\bar X=59.4[/tex] represent the sample mean
[tex]s=3.239[/tex] represent the sample standard deviation
[tex]n=10[/tex] sample size
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is higher than 55, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 55[/tex]
Alternative hypothesis:[tex]\mu > 55[/tex]
Replacing the info given we got:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing the info given we got:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55
I need HELP PLEASE HELP ME
Answer:
Graph 2
Step-by-step explanation:
You can see that all the shaded numbers are above negative 25 in that graph. Hope this helped!
What is an equation of the line that is parallel to y = 9 – 5x and passes through (0, 8)?
Answer:
y = 8 - 5x
Step-by-step explanation:
both equations shares the same gradient as they are parallel
from y= 9-5x, the gradient is -5
subst x = 0, y=8, and m= -5 into the y = mx + c to find the value of c
8 = (-5)(0) + c
c= 8
therefore the eqn is y = 8 - 5x
1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground
Completed Question
1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground .
Rule: Non-self-supporting ladders, which must lean against a wall or other support, are to be positioned at such an angle that the horizontal distance from the top support to the foot of the ladder is about the 1/4 working length of the ladder.
2. Calculate the angle that the ladder makes with the ground using a trigonometric ratio.
3. If a ladder is x feet long, how high up a wall can it safely reach?
4. Would a 51-foot ladder be long enough to climb a 50-foot wall?
Answer:
(a)See attachment
(b)75.52 degrees
(c)[tex]Height ,h=\dfrac{x\sqrt{15}}{4} $ feet[/tex]
(d) NO
Step-by-step explanation:
Part 1
Let the length of the ladder =x
Since by the given rule, Horizontal Distance =[tex]\dfrac14$ of the length of the ladder[/tex]
Horizontal Distance = [tex]\dfrac14x[/tex]
In the sketch of the problem attached below,
The length of the ladder=ACHorizontal distance =BCPart 2
From Triangle ABC
[tex]\cos C=\dfrac{BC}{AC} \\\cos C=\dfrac{x/4}{x} \\\cos C=\dfrac{1}{4}\\ C=\arccos \dfrac{1}{4}\\C \approx 75.52^\circ[/tex]
The angle that the ladder makes with the ground is 75.52 degrees.
Part 3
If the ladder is x feet long
Using Pythagoras theorem in Triangle ABC below
[tex]x^2=(x/4)^2+h^2\\h^2=x^2-\dfrac{x^2}{16}\\ h^2=\dfrac{15x^2}{16}\\h=\sqrt{\dfrac{15x^2}{16}} \\h=\dfrac{x\sqrt{15}}{4}$ feet[/tex]
Part 4
If x=51 feet
[tex]Height ,h=\dfrac{51\sqrt{15}}{4}$ = 49.38 feet[/tex]
Therefore, a 51 feet ladder would not be enough to climb a 50 feet wall as it would violate the safety rule.
Which graph represents the function f(x) = |x| – 4? On a coordinate plane, an absolute value graph has a vertex at (0, 4). On a coordinate plane, an absolute value graph has a vertex at (negative 4, 0). On a coordinate plane, an absolute value graph has a vertex at (0, negative 4). On a coordinate plane, an absolute value graph has a vertex at (4, 0).
Answer:
(0, -4)
Step-by-step explanation:
The graph that represents the function is (c) on a coordinate plane, an absolute value graph has a vertex at (0, -4)
The equation of the function is given as:
[tex]f(x) = |x| - 4[/tex]
The above function is an absolute value function shifted down by 4 units
Hence, the graph that represents the function is a graph that has its vertex at (0,-4)
Read more about absolute value graphs at:
https://brainly.com/question/2166748
PLEASE HALP ME! ( WILL MARK BRAINLIEST! Thank you! ;)
Answer: 1/20
Step-by-step explanation:
Decimal Fraction Percentage
0.05 1/20 5%
Suppose you are planning an experiment and a sample has yet been selected. For this experiment you plan on taking a SRS of 50 mice with pancreatic cancer measuring a particular hormone level. What would be the impact on a 95% confidence interval calculated from the experiment on these mice if instead of a SRS of 50 mice, a SRS of 200 mice were taken?
Answer:
The width or range of the confidence interval with sample size 200 will be about half of that of the confidence interval with sample 50.
Step-by-step explanation:
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)
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)
Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)
- For the two random samples, of sizes 50 and 200, the Central limit theorem allows us to say that the sample mean is approximately equal to the population mean as this random sample satisfies the condition of being a simple random sample and a distribution obtained from a normal distribution.
- Making the right assumption that population standard deviation is known and z-distribution is used to find the critical value
Critical value for 95% = 1.96
The critical value for both samples are the same then.
- Standard Error of the mean = σₓ = (σ/√n)
where σ = population standard deviation
n = sample size
For the two distributions
Confidence Interval = (Sample mean) ± [(Critical value) × (Standard Error of the mean)
(Sample mean)₅₀ = (Sample mean)₂₀₀
(Critical value)₅₀ = (Critical value)₂₀₀
(Standard Error of the mean)₅₀ = (σ/√50) = 0.1414σ
(Standard Error of the mean)₂₀₀ = (σ/√200) = 0.0707σ
0.1414σ = 2 × 0.0707σ
(Standard Error of the mean)₅₀ = 2 × (Standard Error of the mean)₂₀₀
(Standard Error of the mean)₅₀ > (Standard Error of the mean)₂₀₀
Hence,
(Margin of Error)₅₀ > (Margin of Error)₂₀₀
(Margin of Error)₅₀ = 2 × (Margin of Error)₂₀₀
Confidence Interval = (Sample mean) ± (Margin of error)
Hence, the width or range of the confidence interval with sample size 50 will be about two times larger than the confidence interval with sample 200.
Hope this Helps!!!
Solve for the value of x
Answer:
x = 8
Step-by-step explanation:
The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...
4 +7x = 60
7x = 56 . . . . . . subtact 4
x = 8 . . . . . . . . .divide by 7
help pls take your time..
Answer:
As [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex] and as [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]
Step-by-step explanation:
Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards minus infinity).
As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)
I need help with this one
Answer:
2 2/3
Step-by-step explanation:
.
A students received a score of 50 on his history test. The test had a mean of 69 and a standard deviation of 10. Find the z score and assess whether his score is considered unusual.
1.90; unusual
–1.90; not unusual
–1.90; unusual
1.90; not unusual
Answer:
c) The Z-score = - 1.90 unusual
Step-by-step explanation:
Explanation:-
Let 'X' be the random variable in normal distribution
Given student received a score X = 50
Mean of the Population x⁻ = 69
standard deviation of the Population 'σ' = 10
now
[tex]Z = \frac{x^{-}-mean }{S.D}[/tex]
[tex]Z = \frac{x^{-}-mean }{S.D} = \frac{50 -69}{10} = - 1.90[/tex]
The Z-score = - 1.90
Conclusion:-
The Z-score = - 1.90 unusual
Answer: The Z-score = - 1.90 unusual
Step-by-step explanation:
Which of the following is the solution to |x-1|=8
Answer:
-7,9
Step-by-step explanation:
x-1=-8
x=-7
x-1=8
x=9
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal. Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)
a) The likelihood cannot be determined
b) Yes
c) No
Answer:
Option B is correct.
It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5
Step-by-step explanation:
Complete Question
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.
170 201 199 202 173 153
Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)
A) The likelihood cannot be determined.
B) Yes
C) No
Solution
For this question, obtaining the confidence interval will give a clear solution to the problem.
Since the 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, if the range obtained contains values greater than the standard we are comparing against (199.5), then the confidence interval proves that the mean magnesium ion may be greater than 199.5.
But to obtain the confidence interval, we need the mean and standard deviation for the sample.
170, 201, 199, 202, 173, 153
Mean = (sum of variables)/(total number of variables)
Sum of variables = 170+201+199+202+173+153 = 1098
Total number of variables = 6
Mean = (1098/6) = 183
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 183
N = number of variables = 6
Σ(x - xbar)² = (170-183)² + (201-183)² + (199-183)² + (202-183)² + (173-183)² + (153-183)²
= 169 + 324 + 256 + 361 + 100 + 900
= 2110
σ = √(2110/6) = 18.75
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 183
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 mean and 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 = 6 - 1 = 5.
Significance level for 95% confidence interval
(100% - 95%)/2 = 2.5% = 0.025
t (0.025, 5) = 2.57 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 18.75
n = sample size = 6
σₓ = (18.75/√6) = 7.656
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 183 ± (2.57 × 7.656)
CI = 183 ± 19.675
95% CI = (163.325, 202.675)
95% Confidence interval = (163.3, 202.7)
It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5
Hope this Helps!!!
A local coffee house surveyed 317 customers regarding their preference of chocolate chip or cranberry walnut scones . 150 customers prefer the Cranberry Walnut Scones . 81 customers who responded were males and prefer the Chocolate Chip Scones . 172 female customers responded . Find the probability that a customer chosen at random will be a male or prefer the Chocolate Chip Scones .
1. 25.6%
2. 24.1%
3. 72.9%
4. 98.4%
Answer:
3. 72.9%
Step-by-step explanation:
Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.
So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:
P(M∪C) = P(M) + P(C) - P(M∩C)
Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:
P(M) = 145/317 = 0.4574
There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:
P(C) = 167/317 = 0.5268
Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate chip scones is:
P(M∩C) = 81/317 = 0.2555
Therefore, P(M∪C) is equal to:
P(M∪C) = 0.4574 + 0.5268 - 0.2555
P(M∪C) = 0.7287
P(M∪C) = 72.9%
Answer:
3. 72.9%
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.
There are 172 female customers and 317-172 = 145 male customers.
150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.
81 of those are male, so 167 - 81 = 86 are female.
So the total of desired outcomes is 86 + 145 = 231
Total outcomes:
317 total customers.
Probability:
231/317 = 0.729
So the correct answer is:
3. 72.9%
What’s the correct answer for this ? Two chords AB and CD intersect at E. If AE = 2cm, EB =4, and CE = 2.5 cm, find the length of ED
Answer:
ED = 3.2 cm
Step-by-step explanation:
According to chord-chord power theorem,
(AE)(EB) = (CE)(ED)
2*4 = 2.5 *ED
8/2.5 = ED
ED = 3.2 cm
(DONT REPORT OR ANSWER) pls don’t (what is -2 plus -2)
Answer:
I think it’s -4
Step-by-step explanation:
-2 plus -2 is -4
since 2 plus 2 is 4
Hope this helps ;)
Answer:
It is -4Step-by-step explanation:
It is because 2 plus 2 is 4
so -2 plus -2 is -4
hth!
e of Scores, a publication of the Educational Testing Service, the scores on the verbal portion of the GRE have mean 150 points and standard deviation 8.75 points. Assuming that these scores are (approximately) normally distributed, a. obtain and interpret the quartiles. b. find and interpret the 99th percentile.
Answer:
a) Q1= 144.10
Median = 150
Q3=155.90
b) The 99 percentile would be:[tex]a=150 +2.33*8.75=170.39[/tex]
And represent a value who accumulate 99% of the values below
Step-by-step explanation:
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(150,8.75)[/tex]
Where [tex]\mu=150[/tex] and [tex]\sigma=8.75[/tex]
Part a
Lets begin with the first quartile:
[tex]P(X>a)=0.75[/tex] (a)
[tex]P(X<a)=0.25[/tex] (b)
We can find the quantile in the normal standard distribution and we got z=-0.674.
And we can apply the z score formula and we got:
[tex]z=-0.674<\frac{a-150}{8.75}[/tex]
And if we solve for a we got
[tex]a=150 -0.674*8.75=144.10[/tex]
The median for this case is the mean [tex]Median =150[/tex]
For the third quartile we find the quantile who accumulate 0.75 of the area below and we got z=0.674 and we got:
[tex]a=150 +0.674*8.75=155.90[/tex]
Part b
We can find the quantile in the normal standard distribution who accumulate 0.99 of the area below and we got z=2.33.
And we can apply the z score formula and we got:
[tex]z=2.33<\frac{a-150}{8.75}[/tex]
And if we solve for a we got
[tex]a=150 +2.33*8.75=170.39[/tex]
And represent a value who accumulate 99% of the values below
graph the equation in a coordinate plane, x+2y=4
Hope this helps!
Stay safe, have a good day :D
The following histogram shows the exam scores for a Prealgebra class. Use this histogram to answer the questions.Prealgebra Exam ScoresScores 70.5, 75.5, 80.5, 85.5, 90.5, 95.5, 100.5Frequency 0, 4, 8, 12, 16, 20, 24Step 1 of 5:Find the number of the class containing the largest number of exam scores (1, 2, 3, 4, 5, or 6).Step 2 of 5:Find the upper class limit of the third class.Step 3 of 5:Find the class width for this histogram.Step 4 of 5:Find the number of students that took this exam.Step 5 of 5:Find the percentage of students that scored higher than 95.595.5. Round your answer to the nearest percent.
Answer:
The number of the class containing the largest score can be found in frequency 24 and the class is 98 - 103
For the third class 78 - 83 ; the upper limit = 83
The class width for this histogram 5
The number of students that took the exam simply refers to the frequency is 84
The percentage of students that scored higher than 95.5 is 53%
Step-by-step explanation:
The objective of this question is to use the following histogram that shows the exam scores for a Pre-algebra class to answer the question given:
NOW;
The table given in the question can be illustrated as follows:
S/N Class Score Frequency
1 68 - 73 70.5 0
2 73 - 78 75.5 4
3 78 - 83 80.5 8
4 83 - 88 85.5 12
5 88 - 93 90.5 16
6 93 - 98 95.5 20
7 98 - 103 100.5 24
TOTAL: 84
a) The number of the class containing the largest score can be found in frequency 24 and the class is 98 - 103
b) For the third class 78 - 83 ; the upper limit = 83 ( since the upper limit is derived by addition of 5 to the last number showing in the highest value specified by the number in the class interval which is 78 ( i.e 78 + 5 = 83))
c) The class width for this histogram 5 ; since it is the difference between the upper and lower boundaries limit of the given class.
So , from above the difference in any of the class will definitely result into 5
d) The number of students that took the exam simply refers to the frequency ; which is (0+4+8+12+16+20+24) = 84
e) Lastly; the percentage of students that scored higher than 95.5 is ;
⇒[tex]\dfrac{20+24}{84} *100[/tex]
= 0.5238095 × 100
= 52.83
To the nearest percentage ;the percentage of students that scored higher than 95.5 is 53%
Answer:
1. 98-103 (6th class)
2. 88
3. 5
4. 84
5. 52%
Step-by-step explanation:
Find attached the frequency table.
The class of exam scores falls between (1, 2, 3, 4, 5, or 6).
The exam score ranged from 68-103
1) The largest number of exam scores = 24
The largest number of exam scores is in the 6th class = 98 -103
Step 2 of 5:
The upper class limit is the higher number in an interval. Third class interval is 83-88
The upper class limit of the third class 88.
Step 3 of 5:
Class width = upper class limit - lower class limit
We can use any of the class interval to find this as the answer will be the same. Using the interval between 73-78
Class width = 78 - 73
Class width for the histogram = 5
Step 4 of 5:
The total of students that took the test = sum of all the frequency
= 0+4+8+12+16+20+24 = 84
The total of students that took the test = 84
Step 5 of 5:Find the percentage of students that scored higher than 95.5
Number of student that scored higher than 95.5 = 20 + 24 = 44
Percentage of students that scored higher than 95.5 = [(Number of student that scored higher than 95.5)/(total number of students that took the test)] × 100
= (44/84) × 100 = 0.5238 × 100 = 52.38%
Percentage of students that scored higher than 95.5 = 52% (nearest percent)
What is the value of n in the equation: 8n+9= -n+5?
Answer:
n = -1
Step-by-step explanation:
So first subtract 9 to both sides
8n = -n - 9
Now you want the n on one side and the constant on the other
so add the single n to the n side
9n = -9
Divide 9 to both sides to solve for n
n = -1
Please help! Will mark brainliest ! Thank you! Please explain so I can actually understand the question too :)
Answer:
A
Step-by-step explanation:
They are congruent because of the SSS theorem. The chords are congruent because the angles are congruent (angles are congruent because they are vertical angles). Congruent central angles have congruent chords. The other two sides are congruent because they are all radii of the circle and radius are always congruent.
Answer:
A
Step-by-step explanation:
The triangles are isosceles and congruent too. ( both have 2 sides congruent as radius and the angles between them are congruent- SAS)
Section Exercise 11-8 Sales of People magazine are compared over a 5-week period at four Borders outlets in Chicago. Weekly Sales Store 1 Store 2 Store 3 Store 4 102 97 89 100 106 77 91 116 105 82 75 87 115 80 106 102 112 101 94 100 Click here for the Excel Data File Fill in the missing data. (Round your p-value to 4 decimal places, mean values to 1 decimal place, and other answers to 2 decimal places.) Treatment Mean n Std. Dev Store 1 Store 2 Store 3 Store 4 Total One-Factor ANOVA Source SS df MS F p-value Treatment Error Total (a) Based on the given hypotheses choose the correct option. H0: μ1 = μ2 = μ3 = μ4 H1: Not all the means are equal α = 0.05 Reject the null hypothesis if F > 3.24 Reject the null hypothesis if F < 3.24 (b) Determine the value of F. (Round your answer to 2 decimal places.) F-value (c) On the basis of the above-determined values, choose the correct decision from below. Fail to reject the null hypothesis. Reject the null hypothesis. (d) Determine the p-value. (Round your answer to 4 decimal places.) p-value Next Visit question mapQuestion 1 of 2 Total1 of 2 Prev
Answer:
Step-by-step explanation:
Hello!
An ANOVA was conducted to analyze the variable
Y: sales of "People" magazine over a 5-week period
This was studied in 4 Borders outlets in Chicago.
So this test has one factor: "Borders outlets" and four treatments: "Store 1, store 2, store 3 and store 4"
For each store you have the data for the weekly sales over a 5-week period so the sample sizes are:
n₁=n₂=n₃=n₄= 5 weeks
Store 1
∑X₁= 540; ∑X₁²= 58434
X[bar]₁= 108
S₁²= 28.50
S₁= 5.34
Store 2
∑X₂= 437; ∑X₂²= 38663
X[bar]₂= 87.40
S₂²= 117.30
S₂= 10.83
Store 3
∑X₃= 455; ∑X₃²= 41899
X[bar]₃= 91
S₃²= 123.50
S₃= 11.11
Store 4
∑X₄=505; ∑X₄²= 51429
X[bar]₄= 101
S₄²= 106
S₄= 10.30
Totals
N= n₁ + n₂ + n₃ + n₄= 4*5= 20
∑Mean= 108+87.40+91+101= 387.4
∑Variance= 28.50+117.30+123.50+106= 375.30
∑Standard deviation= 5.34+10.83+11.11+10.30= 37.58
Hypothesis test:
H₀: μ₁= μ₂= μ₃= μ₄
H₁: At least one population mean is different.
α: 0.05
The statistic for this test is
[tex]F= \frac{MS_{Treatments}}{MS_{Error}} ~~F_{k-1;N-k}[/tex]
k-1= 3 Df of the treatments, k=4 number of treatments
N-k= 16 Df of errors, N=20 total number of observations in all treatments
[tex]F_{H_0}= \frac{441.78}{93.83}= 4.71[/tex]
The critical region and p-value for this test are one-tailed to the right.
Using the critical value approach:
[tex]F_{k-1;N-k;1-\alpha }= F_{3;16;0.95}= 3.25[/tex]
The decision rule is:
If [tex]F_{H_0}[/tex] ≥ 3.25, reject the null hypothesis.
If [tex]F_{H_0}[/tex] < 3.25, do not reject the null hypothesis.
Using the p-value approach:
Little reminder: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
So under the distribution F₃,₁₆ you have to calculate the probability of the calculated [tex]F_{H_0}[/tex]:
P(F₃,₁₆≥4.71)= 1 - P(F₃,₁₆<4.71)= 1 - 0.9847 = 0.0153
p-value= 0.0153
The decision rule for this approach is
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value is less than the level of significance, so the decision is to reject the null hypothesis.
I hope this helps!
If f(x) = 5x + 7 and g(x) = sqrt(x + 6) , which statement is true? A) 9 is NOT in the domain of f g B) 9 IS in the domain of f g
Answer 9 is in the domain of f g
Step-by-step explanation:
brenna goes on a cave tour with her family.she spots a mysterious crystal that is shaped like a cube the crystal has edge lengths of 5 centimeters what is the volume of the crystal
Answer:
The volume of the crystal is [tex]V=125 \:cm^3[/tex].
Step-by-step explanation:
The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.
To find the volume of a cube recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself three times. Or as a formula
[tex]V=s^3[/tex]
where:
s is the length of any edge of the cube.
From the information given we know that the crystal has edge lengths of 5 centimeters. Therefore, the volume of the crystal is
[tex]V=5^3=125 \:cm^3[/tex].
Choose the function that is a "parent function".
Answer:
f(x)=√x
Step-by-step explanation:
A parent function is something simple with just x
Answer:
f(x)=Square Root of x (choice B or the second one down)
Step-by-step explanation:
All the other choices have either a plus 3 or minus 3. A parent function is not going to have any type of number being added or subtracted to it.
3
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The product of (3 + 2) and a complex number is (17 + 71).
The complex number is
Answer:
5-i
Step-by-step explanation:
Product=multiplication
Let the complex number=x
(3+2i)*x=17+7i
x=17+7i / 3+2i
x=(17-7i)*(3-2i)/(3+2i)*(3+2i)
=51-34i+21i+14i^2 / 9+6i+6i+4i^2
=51+13i+14i^2 / 9+12i+4i^2
= (51+14 - 13i) / 13
= (65 -13i) / 13
= 65 / 13 - 13 i / 13
= 5 - i.
Find the length of both of the unknown sides in the triangle shown here.
Give your answer correct to the nearest metre. [5 marks]
Answer:
[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]
And if we solve this equation for x we got:
[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]
We can cancel [tex]x^2[/tex] in both sides and we have this:
[tex] 22x -6x= 256+9-121 =144[/tex]
And then we got:
[tex] 16 x= 144[/tex]
[tex] x =\frac{144}{16}= 9[/tex]
And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.
Lenght of the smaller unknown side: 12m
Lenght of the larger unknown side: 20m
Step-by-step explanation:
For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:
[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]
And if we solve this equation for x we got:
[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]
We can cancel [tex]x^2[/tex] in both sides and we have this:
[tex] 22x -6x= 256+9-121 =144[/tex]
And then we got:
[tex] 16 x= 144[/tex]
[tex] x =\frac{144}{16}= 9[/tex]
And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.
Lenght of the smaller unknown side: 12m
Lenght of the larger unknown side: 20m
The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
Answer:
Option (2). 14 m
Step-by-step explanation:
Formula to get the area of a circle 'A' = [tex]\pi r^{2}[/tex]
where r = radius of the circle
Given in the question,
Area of the circle = 153.86 square meters
By putting the values in the formula,
153.86 = πr²
r = [tex]\sqrt{\frac{153.86}{\pi } }[/tex]
r = [tex]\sqrt{49}[/tex]
r = 7 meters
Diameter of circle = 2 × (radius of the circle)
= 2 × 7
= 14 meters
Therefore, diameter of the circle is 14 meters.
Option (2) is the answer.
Answer:
14m
Step-by-step explanation:
A teacher figures that final grades in the chemistry department are distributed as: A, 25%; B, 25%;C, 40%;D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic x^2 to determine if the grade distribution for the department is different than expected. Use α = 0.01.
Grade A B C D F
Number 36 42 60 14 8
a. 6.87
b. 0.6375
c. 5.25
d. 4.82
Answer:
[tex]E_{A} =0.25*160=40[/tex]
[tex]E_{B} =0.25*160=40[/tex]
[tex]E_{C} =0.4*160=64[/tex]
[tex]E_{D} =0.05*160=8[/tex]
[tex]E_{F} =0.05*160=8[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]
The answer would be:
c. 5.25
Step-by-step explanation:
The observed values are given by:
A: 36
B: 42
C: 60
D: 14
E: 8
Total =160
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference in the proportions for the final grades
H1: There is a difference in the proportions for the final grades
The level of significance assumed for this case is [tex]\alpha=0.01[/tex]
The statistic to check the hypothesis is given by:
[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
Now we just need to calculate the expected values with the following formula [tex]E_i = \% * total[/tex]
And the calculations are given by:
[tex]E_{A} =0.25*160=40[/tex]
[tex]E_{B} =0.25*160=40[/tex]
[tex]E_{C} =0.4*160=64[/tex]
[tex]E_{D} =0.05*160=8[/tex]
[tex]E_{F} =0.05*160=8[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]
The answer would be:
c. 5.25
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=(5-1)=4[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{4} >5.25)=0.263[/tex]
The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis
I want to buy a car for $1150.00. I earn $5.25 per hour. How many hours must work to buy the car if all my earnings go for this purchase?
Answer
About 219-220
Step-by-step explanation:
Answer: $219.047619
Step-by-step explanation: 1150.00 ÷ 5.25 = 219.047619
Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. WWW represents the volume of water Andrei uses (in liters) if he uses nnn marbles. W=32-0.05nW=32−0.05nW, equals, 32, minus, 0, point, 05, n What is the glass tank's volume?
Before Andrei adds the marbles to the glass tank, the glass tank was empty. This means that the volume of the empty tank is when n = 0 and the volume is 32 liters.
Given that:
[tex]W = 32 - 0.05n[/tex]
A linear function is represented as:
[tex]y = b + mx[/tex]
Where
[tex]b \to[/tex] y intercept
Literally, the y intercept is the initial value of the function.
In this function, the y intercept means the initial volume of the glass tank before filling it with marbles.
Compare [tex]y = b + mx[/tex] and [tex]W = 32 - 0.05n[/tex]
[tex]b = 32[/tex]
This means that the volume of the glass tank is 32 liters.
Read more about linear functions at:
https://brainly.com/question/21107621
Answer:
0.05
Step-by-step explanation: