If f(x) = 3x + 2 and g(x) = x^2 + 1, which expression is equivalent to (f * g) (x)?
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[tex](f \times g)(x) = f(x) \times g(x)[/tex]
[tex](f \times g)(x) = (3x + 2)( {x}^{2} + 1) \\ [/tex]
[tex](f \times g)(x) = 3 {x}^{3} + 2 {x}^{2} + 3x + 2 \\ [/tex]
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Can somebody help me with solve this question
Answer:
f⁻¹(y) = y^(-7/17)
Step-by-step explanation:
f(x) = x^(-17/7)
To find the inverse, switch x and y, and solve for y.
x = y^(-17/7)
x^(-7/17) = y
Therefore, f⁻¹(y) = y^(-7/17).
Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers’ cars in less than 30 minutes on average. Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes. Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints. To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change. The number of minutes to complete each of the 36 oil changes is reported below.
Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers’ cars in less than 30 minutes on average. Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes. Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints. To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change. The number of minutes to complete each of the 36 oil changes is reported below.
42
29
19
11
10
27
41
27
22
26
28
32
17
15
25
35
31
22
13
31
17
37
33
25
18
24
28
21
40
19
33
30
14
23
22
10
1. Write the null and alternative hypothesis. Label each accordingly.
2. Calculate the Test Statistic and the P-value. Label each accordingly, and report the P-value to 4 decimal places.
3. Using the P-value calculated in #2, explain why you would or would not reject the null hypothesis? Answer using a complete sentence, proper grammar and correct spelling. Do NOT write a conclusion.
4. Based on your answer to #3, write a final conclusion for the test of hypotheses, and explain if the company is fulfilling its promise to “change the oil in customers’ cars in less than 30 minutes on average?” Answer using a complete sentence, proper grammar and correct spelling.
Answer:
Explained below.
Step-by-step explanation:
(1)
The hypothesis can be defined as follows:
H₀: The Speedy Oil Change will change the oil in customers’ cars in more than 30 minutes on average, i.e. μ > 30.
Hₐ: The Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average, i.e. μ ≤ 30.
(2)
Use Excel to compute the sample mean and standard deviation as follows:
[tex]\bar x=\text{AVERAGE(array)}=24.917\\\\s=\text{STDEV.S(array)}=8.683[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{24.917-30}{8.683/\sqrt{36}}=-3.51[/tex]
The degrees of freedom is:
df = n - 1
= 36 - 1
= 35
Compute the p-value as follows:
[tex]p-value=P(t_{35}<3.51)=0.0006[/tex]
(3)
The p-value = 0.0006 is very small.
The null hypothesis will be rejected at any of the commonly used significance level.
(4)
There is sufficient evidence to support the claim that the Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average.
Using the t-distribution, we have that:
1.
The null hypothesis is [tex]H_0: \mu \geq 30[/tex]
The alternative hypothesis is [tex]H_1: \mu < 30[/tex]
2. The test statistic is t = 3.51.
3. The p-value is of 0.0063.
4. Since the p-value is of less than the standard significance level of 0.05, we reject the null hypothesis, and can conclude that the company is fulfilling its promise.
Item 1:
At the null hypothesis, we test if the mean is of at least 30 minutes, that is:
[tex]H_0: \mu \geq 30[/tex]
At the alternative hypothesis, we test if the mean is of less than 30, that is:
[tex]H_1: \mu < 30[/tex]
Item 2:
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem:
[tex]\mu = 30, n = 36[/tex]Using a calculator, [tex]\overline{x} = 24.92, s = 8.68[/tex]The test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24.92 - 30}{\frac{8.68}{\sqrt{36}}}[/tex]
[tx]t = 3.51[/tex]
The test statistic is t = 3.51.
Item 3:
The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = 3.51 and 36 - 1 = 35 df.
Using a calculator, this p-value is of 0.0063.
Item 4:
Since the p-value is of less than the standard significance level of 0.05, we reject the null hypothesis, and can conclude that the company is fulfilling its promise.
A similar problem is given at https://brainly.com/question/16194574
235 people are at a summer camp. There are 35 more boys than girls, and 70 fewer adults than girls. How many people of each group are at the camp?
Answer:
125 boys, 90 girls and 20 adults
Step-by-step explanation:
Let the number of boys be x
Let the number of girls be y
Let the number of adults be z
If there are 235 people at the summer camp, then;
x + y+ z = 235 ..... 1
If there are 35 more boys than girls, then;
x = y + 35 .... 2
If there are 70 fewer adults than girls then;
y = z - 70
z = y - 70....3
Substitute 2 and 3 into 1;
x + y+ z = 235 ..
(y+35)+y+(y-70) =235
3y -35 = 235
3y = 270
3y/3 = 270/3
y = 90
Since x = y + 35
x = 90 + 35
x = 125
Also z = y - 70
z = 90+70
z = 20
There are 125 boys, 90 girls and 20 adults
Answer:
There are 90 girls, 125 boys, and 20 adults.
Step-by-step explanation:
Let x be the number of girls. How many boys were there?
x + 35
How many adults were there?
x - 70
We know that 235 people are at RSM summer camp. Use this to make an equation.
x + (x + 35) + (x - 70) = 235
x + x + 35 + x - 70 = 235
3x - 35 = 235
3x - 35 + 35 = 235 + 35
3x = 270
3x ÷ 3 = 270 ÷ 3
x = 90
x, x + 35, x - 70
90, 125, 20
Write the LCD (Least Common Denominator I think) for each pair of fractions.
1/3, 1/5 | 2/7, 1/4 | 3/4, 3/5 | 2/9, 5/12 | 1/3, 3/7 | 1/6, 4/9
Please help. ASAP
Answer:
answer: 15, 28, 20, 36, 21, 18
1/2 + 5/2 =
I need help with this
Answer:
3
Step-by-step explanation:
1/2+5/2= 6/2= 3/1= 3
I hope this helps you and good luck!
please I need help
Answer:
6
Step-by-step explanation:
Parrelal lines, so SRQ will be 180-108=72. 72/12=6.
#12: Kara is deciding between The Lyme Point Inn and Ever After Farms for 1 point
her wedding reception. The Lyme Point Inn charges $3,000 for the venue
and $100 for each meal. Ever After Farm charges $5,400 for the venue and
$70 for each meal. Write and solve an equation to find the number of
meals at which the total cost charged by the two venues would be the
same. *
Your answer
ooo
Answer:
80 meals
Step-by-step explanation:
Set up an equation where x is the number of meals:
100x + 3000 = 70x + 5400
Solve for x:
100x + 3000 = 70x + 5400
30x + 3000 = 5400
30x = 2400
x = 80
So, at 80 meals, the cost of the 2 venues will be the same
Answer:
80 metals
Step-by-step explanation:
100x + 3000 = 70x + 5400
How to Solve for x:
100x + 3000 = 70x + 5400
30x + 3000 = 5400
30x = 2400
x = 80
So, at 80 meals, the cost of the 2 venues will be the exact same
16 correct answer out of 20 question. How many % got right?
Answer: You got 80% right
Step-by-step explanation: 100÷20=5 5×16=80
PLEASE MARK ME BRAINLIEST
80% got the right answers out of 20 questions.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The number of questions are twenty 20.
Out of this 20 questions 16 questions are correct.
We need to find the percentage of the right answers.
20x=16
Divide both sides by 20
x=16/20
x=0.8
Now to find the percentage multiply x value with 100 as it is a hundredth part.
0.8×100=80%
Hence, 80% got the right answers out of 20 questions.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ2
Brainliest...don’t need an explanation
Answer:
8
Step-by-step explanation:
Mrs teed bought 22 packs of hot dog rolls at the store for the 4th-grade picnic there were 12 rolls in each pack how many hot dog rolls did she buy remember to regroup
Answer:
Step-by-step explanation:
To find out
22 x 12 = 264 rolls
Brand A is $5 per 60 pound bag and Brand B is $12 per 150 pound bag. What Is the unit rate that brand A is selling for
Answer:
YEEYEE
Step-by-step explanation:
A camel drank 2 1/2 gallons of water in 1/4 hour. What was the average rate in gallons per hour at which the camel drank?
Answer:
10 gallons per hour
Step-by-step explanation:
1/4x4=1. 2 1/2x4=10. Hope it helps!
Determine the point estimate of the population mean and margin of error for the confidence interval with lower bound 26 and upper bound 38.
Answer
The point estimate of the mean is [tex]\= x = 32[/tex]
The margin of error is [tex]E =6[/tex]
Explanation
From the question we are told that
The lower bound of the interval is [tex]a = 26[/tex]
The upper bound of the interval is [tex]b = 38[/tex]
Generally the point estimate of the population mean is mathematically represented as
[tex]\= x = \frac{a +b}{2}[/tex]
=> [tex]\= x = \frac{26 +38}{2}[/tex]
=> [tex]\= x = 32[/tex]
Generally the margin of error is mathematically represented as
[tex]E = \frac{ b- a}{2}[/tex]
=> [tex]E = \frac{ 38- 26}{2}[/tex]
=> [tex]E =6[/tex]
Suppose the local Barons team wins every game they play with a probability of 0.75. What is the probability that the Barons would win a best-of-seven-game series (i.e., they play games until one team has won four game)?
Answer:
The probability is 0.173
Step-by-step explanation:
The probability is of winning is 0.75 = 75/100 = 3/4
This means that the probability of losing is 0.25 = 25/100 = 1/4
So if they are two win 4 games, they will lose three
We can get this probability using the Bernoulli approximation of the binomial theorem
So here, we have
P(X = 4) = 7 C 4 * 0.75^4 * 0.25^3
= 0.173034667969
which is approximately 0.1730
Clayton opens a savings account with 11 dollars he got from his grandmother
Answer:
The answer is "$3640.58"
Step-by-step explanation:
This question is incomplete, that's why we add another question in the attached file. Please find it.
P = [tex]\$ \ 1300[/tex] and effective per year is = interest rate per year = 7.2
Total [tex]\$ \ 1300[/tex] due after 8 years is P+PRT:
[tex]\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8[/tex]
[tex]\to Total \ X = \$ \ (7000-2048.8) \\\\[/tex]
[tex]= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\[/tex]
The number of dollars is X [tex]= \frac{4951.2}{1.36} = \$ \ 3640.58[/tex]
Graph the equation on the coordinate plane.
y = 4x
Naomi has earned $50 mowing lawns the past two days. She worked 3 1/2
hours yesterday and 2 3/4
hours today. If Naomi is paid the same amount for every hour she works, how much does she earn per hour to mow lawns?
Due today by 7:00pm Plz help me will mark the brainiest
Answer:
It should be -36 because there are no parentheses if it was (-6)² then it would be 36 but since there are no parentheses its like -(6²) which is -36
Answer: the answer is -36
The time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. What is the the probability it takes between 52.3 and 54.7 min. Round to 4 decimal places.
Answer:
The values is [tex]P(52.3 < X < 54.7 ) = 0.17142[/tex]
Step-by-step explanation:
From the question we are told that
The lower limit of the interval is a = 43 minutes
The upper limit of the interval is b = 57 minutes
Generally the probability distribution function of uniform distribution is mathematically represented as
[tex]F(x) = \left \{ {{\frac{1}{(b - a)}\ \ \ for \ x \ \epsilon\ | a, b | } \atop {0 } \ \ \ \ \ \ otherwise} \right.[/tex]
Generally the probability it takes between 52.3 and 54.7 min is mathematically represented as
[tex]P(52.3 < X < 54.7 ) = \int\limits^{52.4}_{54.7} {F(x)} \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = \int\limits^{52.4}_{54.7} {\frac{1}{57- 43} } \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = \int\limits^{52.4}_{54.7} {\frac{1}{14} } \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = {\frac{1}{14} } \int\limits^{52.4}_{54.7} \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = {\frac{1}{14} } [x] \ | \left 54.7} \atop {52.3}} \right.[/tex]
=> [tex]P(52.3 < X < 54.7 ) = \frac{54.7 -52.3}{14}[/tex]
=> [tex]P(52.3 < X < 54.7 ) = 0.17142[/tex]
What is the lcm of 9,18 and99
Answer:
18,11
Step-by-step explanation:
918 is the lcm 18 and 99 is the lcm 11
help please
what is 3/4×5/7 =
Answer:
15/28 simplified to 5/8 (credit to other answer.)
Step-by-step explanation:
Multiply the top numbers 3*5 which equals 15 and then multiply the bottom numbers 4 and 7 for 28. Put 15 over 28.
Find the vertex of the following. f(x) = x2 - 12x + 35
If line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c?
mc =
Answer:
the slope would be the same as line b
Step-by-step explanation:
the slope would be the same as line b because they are both perpendicular to line a, meaning they both have the same slope.
Answer:
mc= 1
Step-by-step explanation:
correct on edge 2020
Help me please. Thanks
Answer:
ç sir kasi multiplication gamitinnnyan
Answer:
A
Step-by-step explanation:
Find the area of the square
Area = s^2
s = 8
Area = 64 square feet.
Find the area of 1 circle.
r = d / 2
r = 4 / 2
r = 2
Area of 1 circle = pi r^2
Area of 1 circle = 3.14 * 2^2
Area of 1 circle = 12.56
Area of 4 circles
Area of 4 circles = 4 * 12.56
Area of 4 circles = 50.24
Area of unshaded area
Area of unshaded area = area square - area 4 circles.
Area of unshaded area = 64 - 50.24
Area of unshaded area = 13.76
Which decimal makes the comparison true? 7.68 > ______ a. 8.81 b. 8.68 c. 7.86 d. 7.56
Answer:
D. 7.56
Step-by-step explanation:
First we can see it has a less than symbol meaning whatever we put has to be less than the first number.
So the only number less than 7.68 is 7.65!
Answer:
D
Step-by-step explanation:
The number we're dealing with is 7.68.
the symbol means that whatever number comes after it is less than 7.68. So, we look at the other numbers to see if they're bigger than 7.68.
8.81 is bigger than 7.68.
8.68 is bigger than 7.68.
7.86 is bigger than 7.68.
7.56 is smaller than 7.68.
which best describes how to solve a question below?
64x=37
Answer:
X=37/64
Step-by-step explanation:
64x=37
x=37/64
For the following pair of lines, identify the system by type.
equivalent
consistent
inconsistent
Answer:
The answer is C inconsistent
Step-by-step explanation:
The diagram compares the ratio of girls in the chorus to boys in the chorus . What is the ratio of girls to boys ? If there are 40 students in the chorus, how many are girls and how many are boys.
Answer:
The diagram can't be seen
Step-by-step explanation:
.... Sry.. I can't solve this one... I can't see the diagram
An average pen manufactured by the F&M Corporation lasts 400 days with a standard deviation of 40 days.
Assuming that pen life is normally distributed, what is the probability that such a pen will last at least 440
days?
Answer:
The probability that the pen will last at least 440 days is 0.1587
Step-by-step explanation:
Given that
Mean = μ = 400 days
SD = σ = 40 days
Now we have to find the probability of a data point X = 440
For that first of all we have to find the z-score of the value
z-score is found using the formula
[tex]z-score = \frac{x-Mean}{SD}[/tex]
Putting the values of x, mean and SD we will get,
[tex]z = \frac{440-400}{40} = \frac{40}{40} = 1[/tex]
At least 440 means that either 440 or greater than this, hence, we have to find area to the right of z=1
For that
[tex]P(z<1) = 0.8413\\P(z>1) = 1-P(z<1) = 1-0.8413 = 0.1587[/tex]
Hence,
The probability that the pen will last at least 440 days is 0.1587