Solution :
The null and the alternate hypothesis can be stated as :
Null hypothesis
[tex]$H_0:\mu_1 \geq \mu_2$[/tex]
Alternate hypothesis
[tex]$H_a:\mu_1 \leq \mu_2$[/tex]
We known;
[tex]$\overline x_1=\frac{\sum_{i=1}^n X_i}{n_1}$[/tex]
[tex]$=\frac{43+....+75}{7}$[/tex]
= 62.286
[tex]$\overline x_2=\frac{\sum_{i=1}^n X_i}{n_2}$[/tex]
[tex]$=\frac{66+....+81}{16}$[/tex]
= 72.125
[tex]$s_1^2=\frac{\sum_{i=1}^n(X_i- \overline X_1)^2}{n_1-1}$[/tex]
[tex]$=\frac{(43-65.5)^2+....+(75-65.5)^2}{7-1}$[/tex]
= 116.571
[tex]$s_2^2=\frac{\sum_{i=1}^n(X_i- \overline X_2)^2}{n_2-1}$[/tex]
[tex]$=\frac{(66-72.13)^2+....+(81-72.13)^2}{16-1}$[/tex]
= 23.45
Therefore, calculating the test statics :
[tex]$t=\frac{\overline x_1 - \overline x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$[/tex]
[tex]$t=\frac{62.29-72.125}{\sqrt{\frac{116.571}{7}+\frac{23.45}{16}}}$[/tex]
[tex]$t=\frac{-9.839}{4.2566}$[/tex]
= -2.312
Now calculating the P-value for the test as follows :
P=T.DIST(t, df)
[tex]$df=\frac{\left(\frac{s_1^2}{n_1}+\frac{s^2_2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s^2_X}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s^2_Y}{n_2}\right)^2}$[/tex]
[tex]$df=\frac{\left(\frac{116.571}{7}+\frac{23.45}{16}\right)^2}{\frac{1}{7-1}\left(\frac{116.571}{7}\right)^2+\frac{1}{16-1}\left(\frac{23.45}{16}\right)^2}$[/tex]
[tex]$=\frac{328.2868}{46.36395}$[/tex]
[tex]$\approx 7$[/tex]
P=T.DIST(t, df)
=T.DIST(-2.31, 7)
= 0.0270
Thus, the [tex]$\text{P-value}$[/tex] of the test is P = 0.0270 is [tex]$\text{less}$[/tex] than the level of significance [tex]$\alpha= 0.05$[/tex]. Hence the researcher can reject the null hypothesis.
Conclusion: The mean launch temperature for the flights with O ring damages less than that for the flights with no O rings.
A boat is 1000 meters from the base of a cliff. If the angle of depression from the top of the cliff to the boat is 15 degrees, how tall is the cliff? Round your answer to the nearest tenth
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Answer:
267.9 m
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
In this geometry, the angle of depression is the angle of interest. The "adjacent" side of the triangle is the distance to the boat. The "opposite" side is the height of the cliff.
tan(15°) = height/(1000 m)
height = (1000 m)tan(15°)
height ≈ 267.9 m
The cliff is about 267.9 meters tall.
Solve the following inequality for z. Write your answer in simplest form.
3z – 4 > 8z + 2
Answer:
I think question is wrong
Step-by-step explanation:
3z-4>8z+2
3z-4+4>8z+2+4
3z>8z+6
[tex] \frac{3}{3} z > \frac{8z + 6}{3} \\ z > 8z + 2[/tex]
Please help it’s due by the end of tonight and I’m not sure what to do if you can’t see (sorry I took a picture of my computer it’s a bit Glitched) you can zoom in
A family buys 6 airline tickets online. The family buys travel insurance that costs $18 per ticket. The total cost is $1,056. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket.
Answer:
let x represent the number tickets
number of ticket=6
cost of the travelling insurance per ticket =$18
total cost= $1056
(x+x+x+x+x+x+18)= $1,056
6x + 18 = $1,056
A total of 255 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold? answer ASAP will give brainliest!!!
Answer:
85
Step-by-step explanation:
255 ÷ 3 = 85
85×2= 170 This is how much student tickets were sold.
255 - 170= 85
85 adult tickets were sold.
Which student evaluated the power correctly?
Aida’s Work
5 Superscript 4 = 5 times 5 times 5 times 5 = 625
Hector’s Work
5 Superscript 4 = 5 times 4 = 20
Camila’s Work
5 Superscript 4 = 5 + 5 + 5 + 5 = 20
Juan’s Work
5 Superscript 4 = 5 times 5 times 5 = 125
Answer:
A.
✔ Aida’s Work
Step-by-step explanation:
E 2021
Help plz I will give brainliest
Excuse me brainly, May i have your help..? I will give you the brainiest!
Determine the equation for the line of best fit to represent the data.
scatter plot with points going down from about zero comma 4 to the right to about 7 comma zero
y equals two thirds times x plus 4
y equals negative two thirds times x plus 4
y equals negative three halves times x plus 4
y equals negative two thirds times x minus 4
what is the median of 16, 18, 18, 19, 25, 27, 28, 31, 31, and 32.
Answer:
26
Step-by-step explanation:
If the data is in order, the median is the middle value.
If there are two values in the middle, you add them together and divide by 2
So [tex]\frac{25+27}{2} =26[/tex]
For every 9 pounds of blueberries that Joey picks, she
is able to bake 6 blueberry pies. How many pounds of
blueberries does Joey use in each pie?
2. The angles of a pentagon are 6x, (2x + 20°),(3x - 20%), 2x and 14x. Find x. Please answer please please
Answer:
x=20
Step-by-step explanation:
PLEASE HELP!!! ILL GIVE BRAINLIEST !! Which is the correct answer ?
Answer:
vertical angles
Step-by-step explanation:
bc they are across from eachother
Can you help me answer this question???????
Answer:
3^12
Step-by-step explanation:
edward deposited $6,000 into a savings account 4 years ago. the simple interest rate is 3% how much money did edward earn in interest?
(SHOW FULL WORK FOR BRAINLIEST) PLEASE HELP
Answer:
$6000×3%=180 for a month
so for for years
=6000x48×3%=R8 640
Step-by-step explanation:
1 year has 12 month so you will say 4 year's × 12 Month's it will give you 48 so you Multiply by his deposited money ×Percent
formula=Deposit money×Year's×Percent
Use the remainder theorem and synthetic division to find f(k).
k= -1; f(x) = x² - 4x +5
Answer:
10
Step-by-step explanation:
i hope this helps you <3
The sum of two numbers is -25. One number is 101 less than the other. Find the numbers
Answer:
-63, 38
Step-by-step explanation:
1st number = x
2nd number = x+101
x+x+101=-25
2x=-126
x=-63
1st number = x = -63
2nd number = x+101 = 38
Answer:
x=38
y= -63
Step-by-step explanation:
x+y=-25
y=x-101
x+(x-101)= -25
2x=-25+101
2x=76
x=76/2
x=38
y=x-101
y=38-101
y= -63
Let X and Y be the following sets:
X = {5, 10, 15}
Y = {3, 6, 9, 12, 15}
Which of the following is the set
XUY?
Answer:
XuY = { 3,5,6,9,10,12,15}
which if the following equations fit this graph?
A rectangular prism has a length of 11 centimeters, a height of 18 centimeters, and a width of 11 centimeters. What is its volume, in cubic centimeters?
Answer:
2,178
Step-by-step explanation:
Multiply all the numbers together in other words do the length of the base times the width of the base then multiply the product by the height of the prism.
(11)(11)18
Which of the following have the correct solution? Check all
that apply.
0 2x + 5 = 19; x = 7
3 + x + 2 - x = 16; x = 3
X +2
= 2; x=8
5
0 6 = 2x – 8; x = 7
14 = x +5; x = 18
Step-by-step explanation:
To do this, we will substitute the x values to their corresponding equations,
1)
[tex]2x + 5 \\ = 2(7) + 5 \\ = 14 + 5 \\ = 19[/tex]
Given 2x + 15 = 19
Calculated 2x + 15 = 19
Given = Calculated, this solution is correct.
2)
[tex]3 + x + 2 -x \\ = 3 + 3 + 2 - 3 \\ = 8 - 3 \\ = 5[/tex]
Given 3 + x + 2 - x = 16
Calculated 3 + x + 2 - x = 5
Given not equal to calculated, this solution is incorrect.
3)
[tex] \frac{x + 2}{5} \\ = \frac{8 + 2}{5} \\ = \frac{10}{5} \\ = 2[/tex]
Given (x+2)/5 = 2
Calculated (x+2)/5 = 2
Given = Calculated, this solution is correct.
4)
[tex]6 = 2x - 8 \\ 2x - 8 = 6[/tex]
[tex]2x - 8 \\ = 2(7) - 8 \\ = 14 - 8 \\ = 6[/tex]
Given 2x - 8 = 6
Calculated 2x - 8 = 6
Given = Calculated, this solution is correct.
5)
[tex]14 = \frac{1}{3} x + 5 \\ \frac{1}{3} x + 5 = 14[/tex]
[tex] \frac{1}{3} x + 5 \\ = \frac{1}{3}(18) + 5 \\ = \frac{18}{3} + 5 \\ = 6 + 5 \\ = 11[/tex]
Given 1/3x + 5 = 14
Calculated 1/3x + 5 = 11
Given not equal to Calculated, this solution is not correct.
Therefore the Correct solutions are 1,3 and 4.
Find the value of x. Round to the nearest degree
Answer:
b. 44°
Step-by-step explanation:
Reference angle = x
Hypotenuse = 21
Adjacent = 15
Apply trigonometric function CAH:
[tex] Cos(x) = \frac{Adj}{Hyp} [/tex]
[tex] Cos(x) = \frac{15}{21} [/tex]
[tex] x = cos^{-1}(\frac{15}{21}) [/tex]
x = 44.4153086° ≈ 44° (nearest degree)
Answer choices
50%
60%
65%
If you put a link I will report
Answer:
50%
Step-by-step explanation:
28, 22, 16, 10,...
O Arithmetic
O Geometric
O Neither
Answer:
Arithmetic
Step-by-step explanation:
Sequences:
A sequence is called arithmetic if the difference between consecutive terms is the same.
A sequence is called geometric if the quotient between consecutive terms is the same.
In this question:
28 - 22 = 22 - 16 = 16 - 10 = ... = 6
Difference is always 6, that is, each term is the previous one subtracted by 6. So the sequence is arithmetic.
PLEASE HELP! 20 POINTS!!
Answer:
15
Step-by-step explanation:
In this problem we need to use the numbers given. So in the problem it states that k = 20 and v = 10. We can replace the letters in the equation for the numbers that it equals so the equation can make sense so 25 - 20 + 10 because k is 20 and v is 10 I simply just replaced the letters with the numbers given in the problem. Then we can just subtract 25 - 20 which is 5 and add 10 which leaves you at a final answer of 15. Hope this helped!
Help please and show the steps
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Answer:
4096∠0°
Step-by-step explanation:
The polar form of the base value is 2∠120°. Then the 12-th power is ...
(2^12)∠(12×120°) = 4096∠0° . . . . or θ = 0 radians, as you wish
_____
I prefer the simpler notation r∠θ, rather than ...
r(cos(θ) +i·sin(θ)) or r·cis(θ) or r·e^(iθ)
You might not see this notation very often in areas outside of electrical engineering.
In the school chorus,
5
20
of the students are fourth graders.
In simplest form, what fraction of the students in the school chorus are fourth graders?
Answer: 1/6
Step-by-step explanation:
If x = 2 and y = 4, what is 6x - 5y?
Answer:
-8
Step-by-step explanation:
6(2) = 12
5(4) = 20
12-20
-8
Answer:
44
Step-by-step explanation:
(6x4)+(5x4)= 44
Is Anyone know the answer????
Answer:
Angle 1 = 40
Step-by-step explanation:
Angle 1 and Angle 2 are alternate angles. So,
2x + 20 = 3x + 10
3x - 2x = 20 - 10
x = 10
Angle 1 = 2x + 20 = 2 x 10 + 20 = 40
PLEASE HELP ASAP! I WILL MARK BRAINLIEST IF YOU ARE RIGHT! The following dot plot shows the mass, in kilograms, of each of the 46 kittens adopted from an animal shelter last month. Each dot represents a different kitten.
Which of the following is a typical mass of one kitten?
Choose 1 Answer:
A: 1.8 Kilograms
B: 2.2 Kilograms
C: 3.8 Kilograms
D: 4.6 Kilograms
Answer:
1.8
Step-by-step explanation:
here u go <3
The mass of one kitten is 1.8 Kg
What is Mean?Mean, median, and mode are the measures of central tendency, used to study the various characteristics of a given set of data. A measure of central tendency describes a set of data by identifying the central position in the data set as a single value. We can think of it as a tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendencies are Mean, Median, and Mode. Choosing the best measure of central tendency depends on the type of data we have.
The arithmetic mean of a given data is the sum of all observations divided by the number of observations. For example, a cricketer's scores in five matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:
Mean = Sum of all observations/Number of observations
Mean = (12 + 34 + 45 + 50 + 24)/5
Mean = 165/5 = 33
Given:
Total kittens= 46
So,
Mean= Total mass/ number of kittens
mean= 0.8* + 1*3 + 1.2*4+ 1.4 * 6+ 1.6*8+ 1.8*8+ 2*7+ 2.2*5 + 2.4 * 2 + 2.6*1+3.8*1 / 46
=80.4/ 46
= 1.75
Learn more about mean here:
https://brainly.com/question/15323584
#SPJ2
how many square feet is in a acre