Using the t-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.
At the null hypothesis, it is tested if they spend on average 19 hours a week working, that is:
[tex]H_0: \mu = 19[/tex]
At the alternative hypothesis, it is tested if they spend more than 19 hours a week working, that is:
[tex]H_1: \mu > 19[/tex]
We have the standard deviation for the sample, hence, 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.Searching the problem on the internet, it is found that the values of the parameters are:
[tex]\overline{x} = 24.2, \mu = 19, s = 12.59, n = 25[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24.2 - 19}{\frac{12.59}{\sqrt{25}}}[/tex]
[tex]t = 2.07[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 25 - 1 = 24 df is of [tex]t^{\ast} = 1.71[/tex]
Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.
To learn more about the t-distribution, you can take a look at https://brainly.com/question/13873630
Solve 2/3 (3x+14)=7x+6 by first multiplying both sides of the equation by 3 before applying the distributive property
[tex]\dfrac23 (3x +14) =7x+6\\\\\\\implies 3\left[\dfrac 23 (3x+14) \right] = 3(7x+6)\\\\\\\implies 2(3x+14) = 21x +18\\\\\implies 6x + 28 =21x +18\\\\\implies 21x -6x = 28-18\\\\\implies 15x = 10\\\\\implies x = \dfrac{10}{15} = \dfrac 23[/tex]
What is the name of the intersection point? Explain.
Explanation:
The drawings you made are constructions of the perpendicular bisector. The "perpendicular" refers to the fact the second line meets the first line at a right angle (aka 90 degree angle). The "bisector" portion indicates the segment has been bisected, which is mathematical way of saying "cut in half".
The key here is the "bisector" portion. Because we've cut a segment like AB in half, this means segment AC and CB are the same length. The point C is the midpoint of AB. Point C is formed by intersecting the perpendicular bisector and the original segment. I'm referring to drawing (a), but the same idea applies to drawing (b) as well. I recommend using another letter than C for the second drawing.
Help!! Simplify the expression?
Answer:
Here is my answer I have solved hope this helps
This year, a small business had a total revenue of $41,600 . If this is 28% more than their total revenue the previous year, what was their total revenue the previous year?
Answer:
Hey will you marry me? serious question
i just really dont get it
Answer: 22.02
Step-by-step explanation:
Just add them all together.
16/48 times 6/8 solve it out for me please
Answer:
0.25
Step-by-step explanation:
You, can just use a calculator But Np
Good luck
Answer: 1/4
Step-by-step explanation:
16 6 96
_ X _ = _ = simplies down to 1/4
48 8 384
Three more than a positive number is twenty less than it’s square. What is the number ?
Answer:
the +ve no. = 2
Step-by-step explanation:
let the number be x - 3
three more than a positive number = x
acc. to condition
x^{2}x
2
- 20 = x
x^{2} - x - 20 = 0x
2
−x−20=0
x^{2} - 5x + 4x - 20 = 0x
2
−5x+4x−20=0
x(x - 5) +4(x - 5) = 0x(x−5)+4(x−5)=0
(x+4)(x-5) = 0(x+4)(x−5)=0
Case 1
x + 4 = 0x+4=0
x = -4x=−4
the Number cannot be negative because the condition given in question
Case 2
x - 5 = 0x−5=0
x = 5x=5
Hence, the positive number
= x - 3=x−3
= 5 - 3=5−3
= 2=2 hope i help you
help please its overdue
Answer:
B) 4cm
Step-by-step explanation:
Hope this helps! Pls give brainliest!
20. Write an expression: Alexis has $10 less than twice the amount that David has. If David has
x dollars, write an expression to represent the amount that Alexis has.
Answer:
2x - 10
Step-by-step explanation:
'x' = amount David has
Alexis = 2x - 10
If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?
Answer:
See below
Step-by-step explanation:
(-4,0) is the solution to x+4=0
(0,0) is the solution to x=0
(2,0) is the solution to x-2=0
Therefore, (x+4)(x-2)(x) = (x²-2x+4x-8)(x) = (x²+2x-8)(x) = x³+2x²-8x is the function that has the given zeroes
Writing a ratlo as a percentage
Manuel has ridden 8 miles of a bike course. The course is 20 miles long. What percentage of the course has Manuel ridden so far?
0
se
%
X 5
?
What’s 12.71 divided 6.2?
Answer:
2.05
Step-by-step explanation:
12.71/6.2=2.05
The value of the expression 12.71 ÷ 6.2 using the division property will be 2.05.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
12.71 and 6.2
Then the division of the decimal numbers 12.71 and 6.2 will be given by putting a divide sign between them. Then we have
⇒ 12.71 ÷ 6.2
⇒ 12.71 / 6.2
⇒ 2.05
The worth of the articulation 12.71 ÷ 6.2 utilizing the division property will be 2.05.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
14. A triangle has vertices at A(4,2), B(-4,-2), and
C(2, 4). If the triangle is dilated with respect to the
origin using a scale factor of 172, what will the
coordinates for the new vertices be?
A A' (2.1). B' (-2,-1), and C (1.-2)
B. A (8.4), B (-8,-4). and C (4. - 8)
C. A' (1,2), B (-1,-2), and C (-2. - 1)
D. A (-2,-1), B' (-2,-1), and C° (-1,2)
Answer:
A
Step-by-step explanation:
Each coordinate of the triangle will have to dilate by 1/2 in order for the triangle to be fully dilated. Let's check each option to see which one has the correctly dilated points.
First, we'll look at A. A(4, 2) goes to A'(2, 1)... which is looking good so far! Half of 4 is 2, and half of 2 is 1, so the right dilation was applied. Next, let's check out B. B(-4, -2) goes to B'(-2, -1), which is still looking okay. Half of -4 is -2, and half of -2 is -1. Finally, we'll check the point C. If this one is correctly dilated, option A is the right option. C(2, -4) goes to C'(1, -2), and we can now be sure that option A is correct. Half of 2 is 1, and half of -4 is -2.
So, option A is the one to select. Hopefully that's helpful! :)
If 108 is added to a number, it will be 5 times as large as it was originally. Find the number.
Answer:
27
Step-by-step explanation:
let th original number=x
x+108=5x
5x-x=108
4x=108
x=108/4=27
What is the vertical shift for the absolute value function below f(x) =9 |x+1|+2
Answer:
Slide UP 2
Step-by-step explanation:
In the equation,
f(x) = 9|x+1| + 2
There are three transformations of the parent function f(x)=|x| (this is the simplest form of this function, it's a v-shaped graph)
The 9 in front will vertically stretch the graph and make it look like a "skinny" v-shaped graph.
The +1 in close to the x inside the absolute value bars |x+1| will shift (slide) the graph to the left (it's the opposite of what you might think-- 'plus' shifts the graph left and 'minus' shifts the graph right)
The +2 at the end is the transformation you're looking for. It slides the graph as you would expect UP 2 units. If it was a minus it would shift the graph down instead.
In the art club, there are 2 seventh graders for every 3 eighth graders. At
this year's art fair, there were 7 paintings by seventh graders for every 12
paintings by eighth graders. Is the ratio of seventh graders to eighth
graders in the art club equivalent to the ratio of paintings by seventh
graders to paintings by eighth graders? *
Answer:
no
Step-by-step explanation:
2/3 does not equal 7/12.
there would need to be 8 paintings by seventh graders for every 12 by eighth graders in order to have an equivalent ratio.
A store is having a clearance sale where all prices are 30% off. The store is located in a county with a 7.5% sales tax. The final price, including sales tax, of any item in the store will be what percent of the original price? Explain your reasoning.
Ans. 450
Solve.
Add 100and you will get the ans
if you roll a fair 6-sided die 9 times, what is the probability that at least 2 of the rolls come up as a 3 or a 4?
Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
There are 9 rolls, hence [tex]n = 9[/tex].Of the six sides, 2 are 3 or 4, hence [tex]p = \frac{2}{6} = 0.3333[/tex]The desired probability is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{9,0}.(0.3333)^{0}.(0.6667)^{9} = 0.026[/tex]
[tex]P(X = 1) = C_{9,1}.(0.3333)^{1}.(0.6667)^{8} = 0.117[/tex]
Then:
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.026 + 0.117 = 0.143[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.143 = 0.857[/tex]
0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For more on the binomial distribution, you can check https://brainly.com/question/24863377
NEED HELP JUST SEND ME QUESTIONS
Graph the solution to this inequality on the number line. 1/3x−3<−1 5/6
Answer:
x < 3 1/2
Step-by-step explanation:
first solve the inequality for x
1/3 x - 3 < -1 5/6
add 3 to both sides
1/3x < 1 1/6
multiply both sides by 3
x < 3 1/2
then just graph x < 3 1/2 on a number line
Answer: Open arrow pointing left on 3.5
Step-by-step explanation: Got correct answer from test review
Chi is planning to put a path of paving stones through her flower garden. The flower garden is a square with sides of 15 feet. How many feet long will the path be? Round your answer to one decimal place.
[(15×2)+(15×2)]=60=6.0
Howie wants to get a car loan with 4% simple interest rate. If the car costs $25,000, how much would Howie need to pay back at the end of one year, including the interest?
The amount Howie will pay back at the end of one year is $26000.00
The given parameters are:
[tex]P =25000[/tex] -- the principal amount
[tex]R = 4\%[/tex] -- the interest rate
[tex]T=1[/tex] --- the duration
The amount to pay back in this duration is then calculated using:
[tex]A = P(1 + RT)[/tex]
So, we have:
[tex]A = 25000(1 + 4\% \times 1)[/tex]
[tex]A = 25000(1 + 4\% )[/tex]
Express percentage as decimal
[tex]A = 25000(1 + 0.04)[/tex]
[tex]A = 25000(1 .04)\\[/tex]
Multiply
[tex]A = 26000[/tex]
Hence, the amount to pay back is $26000.00
Read more about simple interest at:
https://brainly.com/question/1115815
Can someone help me with both questions I will mark u brilliant
1. First, he will be climbing 10,000 feet from where he is right now. 10,000 / 1,000 = 10.
-3.6 x 10 = 36 degree decrease.
25 - 36 = -11
At 12,000 feet, the temperature will be -11.
2. First, we need to do 8.80 x 7 = 61.6
61.6 / 4 = 15.4
61.6 - 15.4 = 46.2
He has $26.20 left.
Hope this helps!
Determine if the point (2,-1) is a solution of the system: 3x - y = 7 2x + 3y = 1
Answer: Yes (2,-1) is the solution for those systems.
becausee...
1. 3(2) - (-1) = 7
6 + 1 = 7
7 = 7
2. 2(2) + 3(-1) = 1
4 - 3 = 1
1 = 1
Hope this helps :)
Answer:
Yes the point (2,-1) is a solution of the system: 3x - y = 7 2x + 3y = 1
Step-by-step explanation:
(2,-1) = x = 2, y = -1
Now lets put these values in the given expressions
3x - y = 7
3 × 2 - (-1)
6 + 1
= 7 THIS EQUATION IS THE SOLUTION
2x + 3y = 1
2 × 2 + 3 × (-1)
4 - 3
= 1 THIS EQUATION IS THE SOLUTION
Which is an example of incompatible goals?
A. Your parents want to take family photos, but you already have
plans with friends that day.
B. Your teacher gives you an assignment you did not expect.
C. A friend does not agree with your opinion on a topic.
D. Your uncle enjoys fishing, but you do not believe in killing animals.
a store have a 12.7% discount on $2002 furniture. what is the new price
Answer:
$1,747.75
Step-by-step explanation:
(12.7% = 0.127)
$2,002 x 0.127 = 254.25
$2,002 - 254.25 = $1,747.75
Find the 53" term of the following arithmetic sequence.
3, 11, 19, 27, ...
Answer:
419
Step-by-step explanation:
a=3
d=11-3=8
[tex]a_{n}=a+(n-1)d\\n=53\\a_{53}=3+(53-1)*8\\=3+52*8\\=3+416\\=419[/tex]
Your school made it to the playoffs
in football and is selling t-shirts to
Celebrate their success for $10 each. The cost
to make the shirts is 5 each plus a one
time set ur fee of $20.
Answer:
I dont quite understand the question could you clarify? What are you trying to ask? how many shirts to break even? Im not quite understanding I'd be more than happy to help if you re worded the question!
Step-by-step explanation:
In class A, 17 students in a class of 25 passed an exam. In class B, 13 out of 20 passed. In class C, 7 out of 10 passed. Which class is the best class?
Answer:
class C
Step-by-step explanation:
a=(17/25)=0.68
b=(13/20)=0.65
c=(7/10)=0.7
1) Solve for x (11 - 2*) 7 = 21
ok done. Thank to me :>