Answer:
21,504
Step-by-step explanation:
This is the usual method multiplication is done "by hand."
6 × 3584 = 6 × (3000 +500 +80 +4)
= 6×3000 +6×500 +6×80 +6×4
= 18000 +3000 +480 +24
= 21000 +504
= 21,504
_____
Many of us are taught in grade school to do the multiplication right to left:
= 6×4 +6×80 +6×500 +6×3000
... writing down the digit corresponding to the place value of the product, and "carrying" any more significant digits to add to the next product.
Here, that looks like 6×4 = 24, write down 4, carry 2. 6×8 = 48, add 2 to get 50, write down 0, carry 5. 6×5 = 30, add 5 to get 35, write down 5, carry 3. 6×3 = 18, add 3 to get 21, write down 21. Then the product is 21504.
__
When doing mental calculation, or using an abacus or soroban, it often works better to do the multiplication left to right, as shown in the answer above.
A perfect square trinomial can be represented by a square model with equivalent length and width. Which polynomial can be represented by a perfect square model?
x2 – 6x + 9
x2 – 2x + 4
x2 + 5x + 10
x2 + 4x + 16
Answer:
A
Step-by-step explanation:
i got it right on the exam
Find the GCF.
6m3n and 8mn2
Answer:
[tex]2mn[/tex]
Step-by-step explanation:
[tex]6m^3n,\:8mn^2[/tex]
Find the GCD of [tex]6,\:8[/tex]:
[tex]6[/tex]
[tex]=2\cdot \:3[/tex]
[tex]8[/tex]
[tex]=2\cdot \:4[/tex]
[tex]=2\cdot \:2\cdot \:2[/tex]
So the prime factor common to 6, 8 is:
[tex]2[/tex]
So the factor common to [tex]6m^3n,\:8mn^2[/tex]:
[tex]=2mn[/tex]
5-5+x*7=14
What is x=
Match each transformation of f(x) with its description. shifts f(x) 4 units down arrowRight compresses f(x) by a factor of toward the y-axis arrowRight stretches f(x) by a factor of 4 away from the x-axis arrowRight shifts f(x) 4 units right arrowRight
The different transformations have been matched to their respective operations below.
How to Interpret Transformations?Parent function is given as: f(x) = 2x - 6
Thus, the transformations are:
When f(x) shifts 4 units down, we have;
f(x) → f(x) - 4
⇒ g(x)= 2x - 6 - 4 = 2x - 10
When it stretches f(x) by a factor of 4 away from the x-axis;
f(x) → 4*f(x)
⇒ g(x) = 4(2x - 6) = 8x - 24
When it shifts f(x) 4 units right;
f(x) → f(x - 4)
⇒ g(x) = 2(x - 4) - 6 = 2x - 14
When it compresses f(x) by a factor of 4 toward the y-axis;
f(x) → f(4x)
⇒ g(x) = 2*4x - 6 = 8x - 6
Read more about Transformations at; https://brainly.com/question/4289712
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A pizzeria offers 10 different toppings. They have pepperoni, green peppers, onion, bacon, sausage, pineapple, ham, spinach, chicken and extra cheese. a. State if this problem is a permutation or combination. Briefly explain your reasoning.
Answer:
combination
Step-by-step explanation:
We have that permutations are groupings in which the order of the objects matters. Combinations are groupings where content matters but order does not.
In this case we have a list of ingredients for the pizza, therefore the order does not matter as long as the ingredients are indicated, which means that this is an example of a combination.
a study studied the birth weights of 1,999 babies born in the United States. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1492 grams and 4976 grams. Write only a number as your answer. Round your answer to the nearest whole number.
Answer:
1899
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 3234
Standard deviation = 871
Percentage of newborns who weighed between 1492 grams and 4976 grams:
1492 = 3234 - 2*871
So 1492 is two standard deviations below the mean.
4976 = 3234 + 2*871
So 4976 is two standard deviations above the mean.
By the Empirical Rule, 95% of newborns weighed between 1492 grams and 4976 grams.
Out of 1999:
0.95*1999 = 1899
So the answer is 1899
1. The function h is the sum of the functions f(x)=3x+5 and g(x)=2x^2 - 6x - 2. Which represents h? A.h(x) = 5x^2 - x - 2 B. h(x) = 2x^2 - 3x + 3 C. h(x) = 2x^2 - 9x + 7
D. h(x) = -3x + 3
Answer:
B. h(x) = 2x^2 - 3x + 3
Step-by-step explanation:
Given
f(x)=3x+5
g(x)=2x^2 - 6x - 2
h(x) is sum of the functions f(x) and g(x)
Thus,
h(x) = f(x) + g(x)
substituting value of f(x) and g(x) as given above we have
h(x) = 3x+5 + 2x^2 - 6x - 2
as ( 3x - 6x = -3x and 5- 2 = 3) , we have
h(x) = 2x^2 -3x + 3
Thus, correct answer is option B. h(x) = 2x^2 - 3x + 3.
100 points for brainliest
Answer:
565.71 yd²
Step-by-step explanation:
Surface area = [tex]2 \pi r (r+h)[/tex]
Area = 2 × 22/7 × 6 (6 + 9)
Area = 22 × 12/7 × 15
Area = 565.71 yd²
Answer:
565.71 yd²
Step-by-step explanation:
Surface area =
Area = 2 × 22/7 × 6 (6 + 9)
Area = 22 × 12/7 × 15
Area = 565.71 yd²
Rihanna planned a rectangular courtyard for a park and made a scale drawing using inches as the unit of measurement. She originally planned for the length of the actual courtyard to be 54 feet, but she decided to change it to 72 feet. If the length of the courtyard is 18 inches in her scale drawing, which statement about the change of scale is true?
Answer:
I think it changed from 36x to 48x
Depending on how you look at it, it could have changed from 3x to 4x or 36x to 48x.
If they said it was 18 feet instead of 18 inches, it would be 3x or 4x, but they had it as inches.
18 inches = 1.5 feet
72/1.5 = 48
54/1.5 = 36
So originally, it would have been a scale of 1 in : 36in , but it changed to 1 in : 48 in
Sorry if this was confusing.
Answer:
One inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale. Otherwise known as D
I got 100% on my quiz.
Step-by-step explanation:
Rosalyn has three different-shaped containers that contain marbles. She has 3 round containers, each holding 16 marbles.
She has 4 square containers, each holding 25 marbles. She has 2 rectangular containers, each holding 33 marbles.
How many marbles are in the containers altogether?
Answer:
42,996
Step-by-step explanation:
3*16+4*25+2*33=48+100+66=214
Prove the identity:
sin ((x))-(y)) / cos (x) sin (y) = tan (x) cot (y) - 1
Answer:
Below.
Step-by-step explanation:
sin ((x))-(y)) / cos (x) sin (y)
sin x cos y - cos x sin y
= ----------------------------------
cos x sin y
sin x cos y
= ---------------- - 1
cos x sin y
But tan x = sin x / cos x and cot y = cos y / sin y
So the above = tan x cot y - 1.
To estimate what percent of employees are at least 1 minute late for their work in the morning, a company put registers at the office entrance that could identify each employee and collect data about the time when they arrived at work. The company found that 18% of the employees are late. What is the sample and what is the population
Answer:
Population: all company employees.
Sample: arrival times of the employees during the data collection.
Step-by-step explanation:
In this case, the population is the group about which the company wants to estimate a parameter (proportion of employees who are at least 1 minute late for work). This group is all employees of the company.
The sample is comprised of the arrival times of the individuals who went to work during the data collection by the entry time recording machine. The proportion of the sample is calculated on these arrival times, with which the proportion of the population will be inferred.
The human body has a normal temperature of 98.6°F. Doctors will get worried if a sick patient has a temperature that varies from the normal by more than 3°F. Create an absolute value inequality and solve it to determine what body temperatures would be considered unhealthy.
Answer:
[tex] |T- 98.6| \geq 3[/tex]
And in order to solve this we have two possibilities:
Solution 1
[tex] T -98.6 \leq -3[/tex]
And solving for T we got:
[tex] T \leq 98.6- 3[/tex]
[tex] T\leq 95.6[/tex]
Solution 2
And the other options would be:
[tex] T -98.6 \geq 3[/tex]
[tex] T \geq 101.6[/tex]
Step-by-step explanation:
For this case we can define the variable os interest T as the real temperature and we know that if we are 3 F more than the value of 98.6 we will be unhealthy so we can set up the following equation:
[tex] |T- 98.6| \geq 3[/tex]
And in order to solve this we have two possibilities:
Solution 1
[tex] T -98.6 \leq -3[/tex]
And solving for T we got:
[tex] T \leq 98.6- 3[/tex]
[tex] T\leq 95.6[/tex]
Solution 2
And the other options would be:
[tex] T -98.6 \geq 3[/tex]
[tex] T \geq 101.6[/tex]
1,664 flound ounces = gallons
Answer:
1,664 fluid ounces = 13 gallons
Step-by-step explanation:
find the sum of the equations: 1/(x-2)+3/(x+3)=4/(x^2+x-6)
Answer:
x= 7/4
Step-by-step explanation:
Find the LCM for x-2,x+3,x^2+x-6 which is (x-2) (x+3)
then multiply
b) On one rectangular coordinate system, show approximate radian values for one circle, as
well as the degree values for every 1/8 of one circle. (2 pts.)
Answer:
(See explanation below for further details)
Step-by-step explanation:
Any point in rectangular form can be described in terms of radius and angle of the circle. That is:
[tex]P = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Since circunference is divided into 8 equal parts, the point can be modelled as:
[tex]P = (r\cdot \cos \frac{2\pi\cdot n}{8}, r \cdot \sin \frac{2\pi\cdot n}{8} )[/tex]
The approximate radian and degree values for one circle are:
Radians
[tex]0 (0), \frac{\pi}{4} (0.785), \frac{\pi}{2} (1.571), \frac{3\pi}{4} (2.355), \pi (3.142), \frac{5\pi}{4} (3.925), \frac{3\pi}{2} (4.71), \frac{7\pi}{4} (5.495), 2\pi (6.280)[/tex]
Degrees
[tex]0^{\circ}, 45^{\circ}, 90^{\circ}, 135^{\circ}, 180^{\circ}, 225^{\circ}, 270^{\circ}, 315^{\circ}, 360^{\circ}[/tex]
where can we put parentheses in 19 - 3 times 5 to make it equivalent to 80
Answer:
(19-3)*5 = 80
Step-by-step explanation:
(19-3)*5 = 80
Parentheses first
16*5 = 80
80
Answer: (19 - 3) * 5 = 80
Check to see if this is right.
(19 - 3) * 5 = 80
16 * 5 = 80
80 = 80
Best of Luck!
Eighty four percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number of adults who want to live to age 100.
1) Construct a binomial distribution.
2) Graph the binomial distribution using a histogram and describe its shape. Graph the binomial distribution.
3) What is the shape of the histogram?
A. Symmetric
B. Skewed left
C. Skewed right
4) What values of the random variablex would you consider unusual?
The value(s)_____would be unusual because the associated probability (probabilities) is(are)______.
Answer:
1) Binomial distribution with n=5 and p=0.84.
2) Attached. Skewed.
3) C. Skewed right
4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.
Step-by-step explanation:
1) A binomial distribution for this case can be constructed with the parameters n=5 and p=0.84.
The probability of k adults from the sample respond Yes is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}=\dbinom{5}{k} 0.84^{k}\cdot 0.16^{5-k}[/tex]
[tex]P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=1*1*0.0001=0.0001\\\\\\P(x=1) = \dbinom{5}{1} p^{1}(1-p)^{4}=5*0.84*0.0007=0.0028\\\\\\P(x=2) = \dbinom{5}{2} p^{2}(1-p)^{3}=10*0.7056*0.0041=0.0289\\\\\\P(x=3) = \dbinom{5}{3} p^{3}(1-p)^{2}=10*0.5927*0.0256=0.1517\\\\\\P(x=4) = \dbinom{5}{4} p^{4}(1-p)^{1}=5*0.4979*0.16=0.3983\\\\\\P(x=5) = \dbinom{5}{5} p^{5}(1-p)^{0}=1*0.4182*1=0.4182\\\\\\[/tex]
2) The graph is attached.
The shape is skewed to the right. This is due to the value of p being close to 1.
The sample space is [0,1,2,3,4,5] and the biggest values have the highest probabilities.
3) The shape is skewed right.
4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.
The value k=2 can also be considered unusual as it has an associated probability of 2.8%.
The independent-samples t testResearch Scenario: A forensic psychologist has developed a new program that teaches empathy and positive social skills to youth offenders who are incarcerated for a violent offense. She wants to know whether this new treatment is more effective in increasing empathy than the standard treatment that these youth offenders usually receive. She sets up a treatment group that consists of 8 youth offenders incarcerated for violent offenses who will receive the new treatment. Her control group consists of 8 similar youth offenders who receive the standard treatment only. At the end of treatment, she administers the Basic Empathy Scale (BES; Jolliffe and Farrington, 2006), a 20-item questionnaire where higher scores indicate higher levels of empathy, and records the results in the table below.Using this table, enter the data into a new SPSS data file and run an independent-samples t test to test the claim that violent youth offenders who receive the new treatment will have higher BES scores than violent youth offenders who receive standard treatment. Follow the directions below the table to complete the homework.Language-Based Spatially-based 93 83 77 89 89 72 87 95 78 76 62 63 67 99 90 84 95 931. Paste SPSS output. 2. Write an APA-style Results section based on your analysis. Include your boxplot as an APA-style figure as demonstrated in the APA writing presentation. (Results = 8 pts: Graph = 5 pts)
Answer:
Step-by-step explanation:
Hello!
The researcher developed a treatment to teach social skills to youth offenders. To test if the treatment is effective in increasing empathy compared to the standard treatment she randomly selected a group of 9 offenders and applied the new treatment and to another group of 9 randomly selected youth offenders, she applied the standard treatment. (Note: the data corresponds to two samples of 9 units each, so I've used those sizes to conduct the test)
At the end of the treatment, she administers BES to measure their empathy levels. Her claim is that the offenders that received the new treatment will have higher BES scores than those who received the standard treatment.
1) Using the records obtained for both groups, she intends to conduct an independent t-test to analyze her claim.
X₁: BES results of a youth offender treated with the new treatment.
X₂: BES results of a youth offender treated with the standard treatment.
H₀: μ₁ = μ₂
H₁: μ₁ ≠ μ₂
α:0.05
test statistic
[tex]t_{H_0}= -0.32[/tex]
p-value: 0.7517
The p-value is greater than the significance level so the decision is to not reject the null hypothesis. This means that at a 5% significance level you can conclude that there is no difference between the mean BES scores of the youth offenders treated with the new treatment and the mean BES score of the youth offenders treated with the standard treatment. The new treatment doesn't increase the levels of social empathy of the youth offenders.
I hope this helps
(Box plot in attachment)
Sara is a drummer in her school is marching band she wants to make a geometrically similar model of a snare drum for her stuffed animals. To find the dimensions she should use to make a cylindrical model with a scale of 1 : 4, Sara measures the radius and height of a snare drum and multiplies each dimension by 1/2. Which statement is true?
A. A cylinder with Sara’s dimensions will be geometrically similar, and the scale factor will be 1:4
B. A cylinder with Sara’s dimensions will be geometrically similar, but the scale factor will be 1:2
C. A cylinder with Sara’s dimensions will be geometrically similar, but the scale factor will be 1:8
D. A cylinder with Sara’s dimensions will not be geometrically similar
Answer:
Option B.
Step-by-step explanation:
Let the radius of the snare drum = r
and radius of the model = R
Ratio of the dimensions of the snare drum and the model = 1 : 4
So, [tex]\frac{r}{R}=\frac{1}{4}[/tex]
Now as per question, dimensions of the snare drum is multiplied by a scale factor of [tex]\frac{1}{2}[/tex]
Radius of the snare drum = [tex]\frac{r}{2}[/tex]
Ratio of the radius of the snare drum and cylindrical model ,
[tex]\frac{\frac{r}{2}}{R} =\frac{1}{4}[/tex]
[tex]\frac{r}{2R}=\frac{1}{4}[/tex]
[tex]\frac{r}{R}=\frac{1}{2}[/tex]
Therefore, the cylinder with Sara's dimensions will be geometrically similar but the scale factor will be 1 : 2
Option B is the answer.
Raymond is installing a new kitchen counter top . The counter top is a rectangular piece of quartz that is 5.75 feet long and 2.47 feet wide .Round the length and width to the nearest whole number . Then estimate the perimeter of the countertop
Answer:
5.75 ft ≈ 6 ft
2.47 ft ≈ 2 ft
perimeter of the rectangular counter top = 16 ft
Step-by-step explanation:
The counter top he is installing is a rectangular piece of quartz that is 5.75 ft long and 2.47 ft wide. The length and the width can be rounded off to the nearest whole number as follows.
length = 5.75 ft to the nearest whole number will be 6 ft
width = 2.47 ft to the nearest whole number will be 2 ft
The logic in rounding off the number to the nearest whole number is that the value on the left hand side of the decimal is rounded off to an integer. If the number at the right hand side of the number is greater or equal to 5 we borrow 1 and add to the left hand side number of the decimal number.
Therefore,
Perimeter of the rectangle = 2l + 2w
perimeter of the rectangle = 2 × 6 + 2 × 2
perimeter of the rectangle = 12 + 4
perimeter of the rectangle = 16 ft
The ratio of Adriana's age to her aunt's age is 7:10. In 2 years the sum of their ages will be 123. How old is Adriana's aunt now?
Answer:
70.35Step-by-step explanation:
The sum of 7 and 10 is 17. So 123 / 17 = 7.235 (roughly)
7.235 x 10 (for Adriana's aunt's age) equals 72.35
And to double check: We can find adriana's age by doing. 7.235 x 7 = 50.645. If we add 50.645 and 72.35 we get 122.995 which is roughly 123 and the reason why it is not 123 on the dot is because 123 / 17 is roughly 7.235 the full expanded one is: 7.23529411765
You may try checking with the full number without estimating but i am sure of my answer
what is equal to 12/10
Answer:
6/5, or 1.2
Step-by-step explanation:
The right answer is 6/5
Look at the attached picture
Hope it will help you
Good luck on your assignment
A 2013 study by pediatrician investigates whether it in better to give children the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm. The pediatricians collected the data from two different random samples. The first random sample was collected from children who were given the vaccine in the thigh. The second random sample was collected from children who were given the vaccine in the arm. Pediatricians recorded whether the children had a severe reaction or not. Reference: Jackson. LA., Peterson. D., Nelson. J.C., et al. (13 00 authors). 2013. Vaccination site and risk of local reaction in children one through six years of age. Pediatrics 131:283-289 Pediatricians conducted a chi square test of independence. The chi square test statistic fix this data is 2.0609 with a P value of O 1511. What can the pediatrician conclude? A) There is a statistically significant association between vaccine location and severe reaction. B) Pediatrician, have strong evidence that the severe reaction, to vaccine depend on location of the vaccine. C) The pediatricians cannot make a conclusion The conditions, for use of the chi-square test are not met. D) There is not enough evidence to conclude that there is. an association between vaccine location and severe reaction.
Answer:
A
Step-by-step explanation:
Since chi-squared calculated value is greater than p-value, there is a relationship between vaccine location and severe reaction.
Answer:
Step-by-step explanation:
This survey is testing for an association between the vaccine location and severe reactions using the chi-square test of independence.
Null hypothesis: Vaccine location and severe reactions are independent
Alternative: Vaccine location and severe reactions are not independent
With a chi square test statistic of 2.0609 with a P value of 0.1511. Using the p- value in comparison to either α = 0.05 or 0.01, the pediatricians can fail to reject the null as the p-value is greater than 0.05 or 0.01 and can conclude that there is a statistically significant association between vaccine location and severe reaction.
This approach was appropriate because the sampling method was simple random sampling, the variables that were under study were categorical, and the expected frequency count was at least 5 in all values to be able to reach value of 283 and 289.
i’m confused on the split circle part; do i count it as a full circle?
Answer:
Below.
Step-by-step explanation:
Yes - those are 2 semicircles so their combined area = πr^2
= 3^2π
= 9π.
Yes.. You can count it as full circle.
Answer:
3.9 squre inch
Step-by-step explanation:
Two semicircles are inscribed in a square of side 6 in. Both the semicircles if combined together will form a full circle.
Area of the yellow region would be half of the areas of the difference between area of square and area of two semicircles each with radius 3 inches.
Therefore,
Area of yellow region
[tex] = \frac{1}{2} (area \: of \: square - 2 \times area \: of \: semicircle) \\ \\ = \frac{1}{2} ( {6}^{2} - 2 \times \frac{1}{2} \pi {r}^{2} ) \\ \\ = \frac{1}{2} ( {6}^{2} - 3.14 \times {3}^{2} ) \\ \\ = \frac{1}{2} ( 36 - 3.14 \times 9 ) \\ \\ = \frac{1}{2} ( 36 - 28.26 ) \\ \\ = \frac{1}{2} \times 7.74 \\ \\ = 3.87 \: {in}^{2} \\ \\ = 3.9 \: {in}^{2}[/tex]
Pls help me
(-7a2 9a3x3 :(-3ax3)] : ( 10a) -(-20a b) : (-5a²b)
Answer:
(-21a^5×b)/(2+4b)
Step by step explanation:
The question isn't complete and clear as we were not told what to determine from the expression.
Looking at the question, we can tell we are to simplify the expression.
[(-7a² × 9a³x³) :(-3ax³)] : [( 10a) -(-20a b) : (-5a²b)]
First we would work with expressions in each parenthesis (bracket).
Then we would work on the answer we derive after opening the parenthesis.
See attachment for detail
What is 0.59 in words
Answer:
fifty nine hundredths
Marc drives his car 500 miles using 20 gallons of gas. How many miles per gallon does his car get
Answer:
25 miles per gallon
Step-by-step explanation:
We want to find miles per gallon so take the miles and divide by the gallons
500 miles / 20 gallons
25 miles per gallon
Answer:
[tex]= 25 \: \: \: miles \: \: \: per \: \: \: gallon \\ [/tex]
Step-by-step explanation:
You have to find miles per gallon.
So to solve that you have to divide miles by gallon.
[tex] \frac{500}{20} \\ = 25 \: \: \: miles \: \: \: per \: \: \: gallon[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Help me with this question
Answer:
14 ft
Step-by-step explanation:
After the sides are folded up, the depth of the box is 2 ft, so the area of the square bottom is ...
(200 ft^2)/(2 ft) = 100 ft^2
The edge dimension of the bottom is then ...
√(100 ft^2) = 10 ft
Each side adds 2+2=4 ft to the bottom dimension in each direction, so the original square piece of metal was 14 ft square.
In a random sample of 49 people who work out in the morning it is found that they exercise an average of 4.1 hours per weeks with a standard deviation of 0.7 hours. In a random sample of 54 people who exercise in the afternoon or evening it is found they exercise an average of 3.7 hours with a standard deviation of 0.5 hours. Test the claim that people who exercise in the morning have a mean exercise time greater than those who work out in the afternoon or evening at a 5% level of significance. a. Identify the parameter and label all given information. b. Identify the null hypothesis and the alternative hypothesis and identify the claim. c. Find the critical value(s). d. Compute the test statistic and/or find the p-value. e. State the conclusion that addresses the original claim. Upload
Answer:
a) [tex] \mu_m -\mu_a [/tex]
[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning
[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon
[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning
[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon
[tex]n_{m}=49[/tex] sample size for the morning
[tex]n_{a}=54[/tex] sample size for the afternoon
b) Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]
Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]
c) [tex] t_{\alpha}= 1.66[/tex]
d) [tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]
The p value would be:
[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]
e) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance
Step-by-step explanation:
Part a
[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning
[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon
[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning
[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon
[tex]n_{m}=49[/tex] sample size for the morning
[tex]n_{a}=54[/tex] sample size for the afternoon
t would represent the statistic
[tex]\alpha=0.05[/tex] significance level
The parameter of interest is:
[tex] \mu_m -\mu_a [/tex]
Part b
We want to verify if the people who exercise in the morning have a mean exercise time greater than those who work out in the afternoon or evening, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]
Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]
The statistic is given by:
[tex]t=\frac{\bar X_{m}-\bar X_{a}}{\sqrt{\frac{s^2_{m}}{n_{m}}+\frac{s^2_{a}}{n_{a}}}}[/tex] (1)
Part c
Based on the significance level[tex]\alpha=0.05[/tex] and the degrees of freedom given by:
[tex] df = 49+54-2= 101[/tex]
We can find the critical value in the t distribution iwth 101 degrees of freedom who accumuate 0.05 of the area in the right and we got:
[tex] t_{\alpha}= 1.66[/tex]
Part d
[tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]
The p value would be:
[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]
Part e
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance
