Answer:
The p-value is 0.1228.
Step-by-step explanation:
Before testing the hypothesis, we need to find the sample mean and the standard deviation.
Sample of 13:
The sample mean is the sum of all values divided by 13. Using a calculator, it is: X = 28.15.
The sample standard deviation is the square root of the division of the sum of the differences squared between each value and the mean, by the number of values. Using a calculator, we get s = 4.0162.
A researcher wants to test whether the average gas mileage of this type of car is different from 30 mpg.
At the null hypothesis, we test if the average gas mileage is of 30 mpg, that is:
[tex]H_0: \mu = 30[/tex]
At the alternate hypothesis, we test if the average is different from 30, that is:
[tex]H_1: \mu \neq 30[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
30 is tested at the null hypothesis:
This means that [tex]\mu = 30[/tex]
From the sample:
[tex]X = 28.15, s = 4.0162[/tex].
Value of the test-statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{28.15 - 30}{\frac{4.0162}{\sqrt{13}}}[/tex]
[tex]t = -1.66[/tex]
P-value of the test:
The p-value of the test is the probability that the sample mean differs from 30 by at least |28.15 - 30| = 1.75, which is a two-tailed test with t = -1.66 and 13 - 1 = 12 df.
Using a t-distribution calculator, this p-value is 0.1228.
The terminal side of in standard position contains the point (20, 21) . Find the exact values of the six trigonometric functions of? Please help
Answer:
27,29
Step-by-step explanation:
J.UIV1.2.2 DUN 2 formative Jackson, Braddyn OO 10 1 Abox, shaped like a rectangular prism, is shown below. 2 in. 8 in. 10 in. What is the surface area of the box? 232 square inches 160 square inches 116 square inches O 96 square inches ?
Answer:m
Step-by-step explanation:
Help!!!
What expression shows the relationship between the value of any term and n, its position in the sequence for the
given sequence?
-5, -8, -11, -14, -17, ...
A)
2n
B)
2n + 1
C)
n+3
D)
-3n - 2
Answer:
D) -3n - 2
Step-by-step explanation:
Hope this helps
Which kind of triangle is shown?
acute scalene
right scalene
acute isosceles
right isosceles
Answer:
the answer is acute equilateral
Chloe breaks into the pantry after Albert goes to work. She finds and opens a family-pack of mixed nuts. After surfing the web, she finds that these packs claim to be 20% almond (A), 30% cashew (C), 10% macadamia (M), and 40% peanut. Chloe discovers that her bag contains 14 almonds, 28 cashews, 6 macadamias, and 52 peanuts.
a) Perform an appropriate test to determine whether this claim is true or not at a = 0.05. State all the relevant steps (listed in exercise 1).
b) What is the decision and conclusion (write a sentence) at a = 0.1?
c) Chloe is a choosy and sneaky doggie. She likes to find a p-value first and then come up with a significance level, a later so she can reject as many Hos as possible. Is her method acceptable?
Solution :
In this case we have to use [tex]$\text{chi square test}$[/tex] for the goodness of fit.
Null hypothesis is : [tex]$H_0 :$[/tex] Data follows the given distribution
Alternate hypothesis is : [tex]$H_a:$[/tex] Data do not follow the given distribution
The level of significance, [tex]$\alpha = 0.05$[/tex]
The test statistics is given by :
Chi square = [tex]$\sum\frac{(O-E)^2}{E}$[/tex]
Here O is the observed frequencies
E is the expected frequencies
So we have, N = number of the categories = 4
df = degrees o freedom = N - 1
= 4 - 1 = 3
Critical value = [tex]$7.814727764$[/tex]
Calculating the table for the test statistics are given as :
Category prop. O E [tex]$\frac{(O-E)^2}{E}$[/tex]
A 0.2 14 20 1.80
C 0.3 28 30 0.13
M 0.1 6 10 1.60
P 0.4 52 40 3.60
Total 1 100 100 7.13
The test statics = chi square = [tex]$\sum\frac{(O-E)^2}{E}$[/tex] = 7.13
[tex]$X^2$[/tex] statistics = 7.13
P-value = 0.067767248
P -value > [tex]$\alpha = 0.05$[/tex]
Therefore, we do not reject the [tex]$\text{null hypothesis}$[/tex]. There is sufficient evidence to conclude that the data follows the given distribution. So there is sufficient evidence to conclude the given claim is true.
So I dont know what equation Im supposed to do. I'm confused either it is addition or multiplication.
Please answer it. I will give brainliest if its correct..
Line EB is a diameter which splits the circle in the middle so the arc of EB would be half the circle. The arc goes through B and continues to C making the arc longer than half the circle.
An arc that is longer than half a circle would be a major arc.
The answer is: Major Arc
please help me with this. will give brainliest due in 5 minutes
Answer:
A
Step-by-step explanation:
HELP
WILL
GIVE BRAINLIST
...
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9. If NK = 7x-1, NM = 10x - 13, and KM = 24, find NP.
Answer:
[tex]NP = 24.18[/tex]
Step-by-step explanation:
Given
[tex]NK = 7x - 1[/tex]
[tex]NM = 10x - 13[/tex]
[tex]KM = 24[/tex]
See attachment
Required
Length of NP
First, calculate the value of x
[tex]NK = NM[/tex]
So:
[tex]7x -1 = 10x - 13[/tex]
Collect like terms
[tex]10x - 7x = 13 - 1[/tex]
[tex]3x =12[/tex]
Solve for x
[tex]x = 4[/tex]
To solve for NP, we consider right triangle [tex]\triangle NKP[/tex]
Where
[tex]NK = 7x - 1[/tex]
[tex]NK = 7 * 4 - 1[/tex]
[tex]NK = 27[/tex]
[tex]KP =\frac{1}{2}KM[/tex]
[tex]KP =\frac{1}{2} * 24[/tex]
[tex]KP =12\\[/tex]
Using Pythagoras theorem, we have:
[tex]NK^2 = KP^2 + NP^2[/tex]
[tex]27^2 = 12^2 + NP^2[/tex]
[tex]729 = 144 + NP^2[/tex]
Collect like terms
[tex]NP^2 = 729 - 144[/tex]
[tex]NP^2 = 585[/tex]
Take square roots
[tex]NP = \sqrt{585[/tex]
[tex]NP = 24.18[/tex]
Mindy is making a wood desk. Pour choices of wood and the cost for different lengths are shown in the table.
Type of Wood Cost per Length Length
$4.97 1 m
Maple $0.07 1 cm
Oak
$15.99 2 m
Walnut
$0.98 1 din
Which type of wood has the LEAST expensive price per unit length? (Note: 100 cm = 10dm = 1m)
O A Ash
OB Maple
Oc Oak
ОО
D. Walnut
Answer:
Step-by-step explanation:
A
Which equations is parallel to y=4x+8?
Answer:
y=4x-8
hope this helps
have a good day :)
Step-by-step explanation:
How long will it take $10,000 to double at 11% simple interest? (Round to the nearest year)
Answer:
[tex]I =\frac{P*R*T}{100} = \frac{10000 * 11 * T}{100} = 1100T[/tex]
Given A =20000
[tex]Amount = Interest + Principal\\20000 = 1100T + 10000\\20000 - 10000 = 1100T\\\\T= \frac{10000}{1100} = \frac{100}{11} = 9.09 years[/tex]
T =9years
f(x) = 3√4x
g(x) = 2x + 3
Find ( f/g) (x). Include any restrictions on the domain
Answer:
B
Step-by-step explanation:
To find [tex](\frac{f}{g} )(x)[/tex] you can write the expression as [tex]\frac{f(x)}{g(x)}[/tex]. We can substitute the f(x) and g(x) into the expression to get: [tex]\frac{\sqrt[3]{4x} }{2x+3}[/tex]. Now we need to find the domain. The numerator is fine, and the domain is all real numbers, but in a fraction, the denominator cannot equal 0. We can write: [tex]2x + 3\neq 0[/tex] and we can solve it:
[tex]2x\neq -3[/tex]
[tex]x\neq -\frac{3}{2}[/tex]
This is the same as option B.
The required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2. Option C is correct
Given the functions
f(x) = 3√4x
g(x) = 2x + 3
We are to find the resulting function (f/g)(x)
(f/g)(x) = f(x)/g(x)
(f/g)(x) = 3√4x/2x+3
Restriction to the function occurs at the point where the denominator is zero.
2x = 3 = 0
2x = -3
x = -3/2
Hence the required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2
Learn more here: https://brainly.com/question/11187697
ASAP HELP PLEASE I WILL GIVEE 100 just help me please and ASAP
Answer:
A
Step-by-step explanation:
Write an equation for the proportional relationship shown in the table
Answer:
y =74x
Step-by-step explanation:
A proportional relationship is represented by y = kx where x is the independent variable, or input, k is the constant of proportionality, and y is the dependent variable or output.
What do we do to the values in the row for x to get the values in the row of y?
It helps to have x = 1 in this table.
74 = (k)(1)
74 = k
in how many years 1600 invested at 5% will amount to 1920
Answer:
principal=1600
rate=5%
amount=1920
time=x
interest=p*t*r/100
=1600*x*5/100
=8000x/100
80x
amount=principal +interest
1920=1600+80x
1920-1600=80x
320/80=x
4=x
therefore after 5 years 1600 amount to 1920 at the rate of 5%
Step-by-step explanation:
Ameer uses 1/4 of a bottle of shampoo to give each of his dogs a bath. He has 5 dogs all together. How many bottles of shampoo does Ameer need?
PLEASE HELP ME NOW!!!!!The television repair charge at "We Fix TVs" is $20 per hour plus a $60 flat fee charge. The television repair charge at "Electronic Depot" is $40 per
hour with no flat fee. Write a system of equations to model the charges for each repair shop.
Answer:
Step-by-step explanation:
we fix tvs
20h+60
electronic depot
40h+0
n more than 12
A) n/12
B) 12 +n
C) 22
D) 12-n
Answer:
B) 12 +n
Step-by-step explanation:
"More than" is a key word.
Whenever you see more than, you are adding.
Michelle has 3/5 pounds of sugar. She gave her neighbor some sugar. Now she has 1/2 pounds of sugar left. How much sugar did she give to her neighbor?
Answer: 1/10
Step-by-step explanation:
Answer:
1/10 pound
Step-by-step explanation:
If you set up the equation as 3/5 - 1/2, you'll have to give them a common denominator. Multiply 3/5 by 2 and multiply 1/2 by 5, and now you can rewrite this equation as 6/10 - 5/10. From here, just subtract and you'll get 1/10.
Find the length of c using the Pythagorean theorem
Answer:
13
Step-by-step explanation:
The Pythagorean theorem state
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + 12^2 = c^2
25+144 = c^2
169 = c^2
Take the square root of each side
sqrt(169) = sqrt(c^2)
13 = c
What 68784 rounded to the nearest thousandth?
Answer: 6,9000
Step-by-step explanation:
finally the value of the expression 20m²+30m+40 where m=4
Answer:
6,560
Step-by-step explanation:
yes
brainlest for answered
Answer:
Hello! answer: 4/5
Step-by-step explanation:
20 ÷ 5 = 4 25 ÷ 5 = 5 that is 4/5 therefore 4/5 is the answer because we cannot reduce any further HOPE THAT HELPS!
Answer:
[tex]\frac{20}{25} =\frac{4}{5}[/tex]
Como se escribe el numeral 300,105,020 4to grado
What is the value of x in the solution to this system of equations?
5x+2y=67x=3y−7
Question 4 options:
6
18.5
24
11
Answer:
x = 11
Step-by-step explanation:
[tex]x-3y=-7[/tex]
[tex]5x=-2y+67[/tex]
=> [tex]x=\frac{1}{5}(-2y+67)[/tex]
=> [tex]x=-\frac{2}{5}y+\frac{67}{5}[/tex]
=> [tex]-\frac{2}{5}y+\frac{67}{5}-3y=-7[/tex]
=> [tex]-\frac{17}{5}y+\frac{67}{5} =-7[/tex]
=> [tex]\frac{-17}{5}y=-\frac{102}{5}[/tex]
=> y = 6
=> [tex]x=-\frac{2}{5} .6+\frac{67}{5}[/tex]
=> x = 11
How can you tell how many solutions a quadratic equation has by looking at its graph
Answer:
2
Step-by-step explanation:
A quadratic equation has two roots . If we wanna check it from the graph , then , the number of points on which it cuts x axis .
The table shows the number of points Malik and Alexia scored while playing a video game together. Which equation relates Alexia’s score, a, to Malik’s score, m?
A. a=0.5m
B. a=1.5m
C. a= m+10
D. a=m+30
Answer:
D. a = m + 30
Step-by-step explanation:
It's not A, because that would be dividing Malik's score in half to get Alexia's score.
B only works for the first line.
C is adding 10 to Malik's score, and the difference is greater than that...it's 30 points.
7m + 3mn
when m = 3 and n = -4
Answer:
-15
Step-by-step explanation:
When m=3 and n=-4
So, put the values
7(3)+3(3)(-4)
-> -15
Answer:
-15
Step-by-step explanation:
= 7(3) + 3(3)(-4)
= 21 + 3(3×-4)
= 21 + 3(-12)
= 21 + -36
= 21-36
= -15