Using the t-distribution, it is found that:
a)
The null hypothesis is [tex]H_0: \mu = 3.1[/tex]
The alternative hypothesis is [tex]H_1: \mu \neq 3.1[/tex]
b)
|t| < 2.201: Do not reject the null hypothesis.|t| > 2.201: Reject the null hypothesis.c) t = 1.853
d) Since |t| = 1.853 < 2.2, we do not reject the null hypothesis, that is, the sample data does not suggest that there is a difference between the national average and the sample mean of the senior citizens.
Item a:
At the null hypothesis, it is tested if the estimate of 3.1 cups per day is correct, that is:
[tex]H_0: \mu = 3.1[/tex]
At the alternative hypothesis, it is tested if the estimate is not correct, that is:
[tex]H_1: \mu \neq 3.1[/tex]
Item b:
This is a two-tailed test, as we are testing if the mean is different of a value, with 12 - 1 = 11 df and a significance level of 0.05, hence, the critical value is [tex]t^{\ast} = 2.2[/tex].
Then, the decision rule is:
|t| < 2.201: Do not reject the null hypothesis.|t| > 2.201: Reject the null hypothesis.Item c:
We can find 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.The values of the parameters, with the help of a calculator for the sample mean and standard deviation, are given by: [tex]\overline{x} = 3.425, \mu = 3.1, s = 0.6077, n = 12[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{3.425 - 3.1}{\frac{0.6077}{\sqrt{12}}}[/tex]
[tex]t = 1.853[/tex]
Item d:
Since |t| = 1.853 < 2.2, we do not reject the null hypothesis, that is, the sample data does not suggest that there is a difference between the national average and the sample mean of the senior citizens.
A similar problem is given at https://brainly.com/question/24826023
hlo preparation for exam help with this question?? °_*!
If p/q=q/r then prove that
p3+q3+r3=(1/p3+1/q3+1/r3)p2q2r2
Hope you could get an idea from here.
Doubt clarification - use comment section.
The equation [tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex] has been proved to be true
The equation is given as:
[tex]\frac pq = \frac qr[/tex]
Cross multiply
[tex]pr = q^2[/tex]
Rewrite as:
[tex]q^2 = pr[/tex]
Also, we have:
[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex]
Substitute [tex]q^2 = pr[/tex]
[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3[/tex]
Expand
[tex]p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3[/tex]
Simplify
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3[/tex]
Rewrite as:
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3[/tex]
Substitute [tex]pr = q^2[/tex]
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3[/tex]
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3[/tex]
Divide q^6 by q^3
[tex]p3+q3+r3=r^3 +q^3 + p^3[/tex]
Rewrite the equation as:
[tex]p3+q3+r3=p^3 +q^3 + r^3[/tex]
Hence, the equation has been proved
Read more about equations at:
https://brainly.com/question/13729904
You are baking a casserole. The recipe calls for of a cup of beans to make 5 servings. How many cups of beans would you need to make 25 servings? Enter your answer.
Answer:
5 cups
Step-by-step explanation:
m(arc DE)=105 and M(arc BC)=70 Find M
Answer:
a. 70
Step-by-step explanation:
Please help other people are saying different answers and I 'm confused
Answer:
x ≈ 35.6
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos16° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{37}[/tex] ( multiply both sides by 37 )
37 × cos16° = x , then
x ≈ 35.6 ( to the nearest tenth )
solve the following equation
Answer:
X= -1/3 or 4
Step-by-step explanation:
Answer:
x =-1/3 and x=4
Step-by-step explanation:
solve by factoring:
separate into two equations:
3x+1=0
8-2x=0
(when the products of factors equals zero, at least one factor is zero)
3x=-1
x=-1/3
-2x=-8
x=4
I need help please and explain your answer it’s number 4
Answer:
29
Step-by-step explanation:
Well "value" of 3x^2 - 7x + 9 when x = 4 is just x plugged into the expression
3 * 4^2 - 7 * 4 + 9
3 * 16 - 28 + 9
= 29
PlZ HELP
fill in the blanks
Answer:
3*(8-5)=(3*8)-(3*5)
Answer:
I think it would be 3x(8-5)=(3x6)-(3x3)
Step-by-step explanation:
This is because if you answer the left side of the equation, it would be 9:
3x(8-5)
(8-5=3)
then 3x3=9
and on the right side of the equation, if you plug in 6 and 3 + solve the equation you would get 9:
(3x6)-(3x3)
18-9
=9
so all together it would be 9=9 which is true
meaning that the numbers 6, and 3 are the numbers you use to fill in the blanks (this is only one of the possible answers, there are many more!)
Not sure if all calculations are correct, but I hope this helps! :)
HELP ME PLZZZZ
its really hard and i cant solve it i have two more quetions to answer and thats it so plz help
Answer:
(-1, -6)
Step-by-step explanation:
The slope of a line is (-1/2) and a point on the line is (-2, 3). Find the equation for the line in slope intercept form.
Answer:
y=-1/2x+2
Step-by-step explanation:
y-y1=m(x-x1)
y-3=-1/2(x-(-2))
y-3=-1/2(x+2)
y=-1/2x-2/2+3
y=-1/2x-1+3
y=-1/2x+2
A number written in expanded form is 700,000 + 5,000 + 200 + 80 + 7. What is this number written in word form?
1 seven hundred five thousand, two hundred eighty-seven
2 seventy-five thousand, two hundred eighty-seven
3 seven hundred eighty-two thousand, five hundred seventy
4 seven hundred eighty-two thousand, five hundred seven
What is the result of 3 divided by three-fifths?
[tex]\dfrac{3}{\tfrac 35} = 3 \times \dfrac 53 = 5[/tex]
Answer:
5
Step-by-step explanation:
3 -> [tex]\frac{3}{1}[/tex]
Method is "Keep, Change, Flip"
[tex]\frac{3}{1} / \frac{3}{5} =\frac{3}{1} * \frac{5}{3} = \frac{15}{3} = 5[/tex]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
6) Error Analysis. Analyze the work below, describe the error then
determine the correct value for x.
26 = 4x - 2
24 = 4x
6 = x
Answer:
The error is that 2 should have been added to both sides, 7 = x
Step-by-step explanation:
4.Cost of 10 book is ₹800.What is the cost of 50 such books
Answer:
₹4000
Step-by-step explanation:
₹800/10 books
₹80/1 book
(₹80/1 book)*(50) = ₹4000
can someone help with this
Answer:
B and C
Step-by-step explanation:
Ms. Rowlen went Black Friday shopping and she bought a flat screen TV that originally costs $259.00. She used her super savings coupon of 45%, how much did Ms. Rowlen pay for the tv?
Answer:
142.55
Step-by-step explanation:
A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure. X = (StartFraction m Over m n EndFraction) (x 2 minus x 1) x 1 y = (StartFraction m Over m n EndFraction) (y 2 minus y 1) y 1 What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth. (11. 4, 14. 2) (7. 6, 8. 8) (5. 7, 7. 5) (10. 2, 12. 6).
The location of the treasure on the treasure map is (b) (7.6,8.8)
The ratio is given as:
[tex]m : n = 5 : 9[/tex]
The coordinates of the rock and the tree are:
[tex]Rock =(3,2)[/tex]
[tex]Tree = (16,21)[/tex]
The x and y coordinates of the location of the treasure are:
[tex](x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
So, we have:
[tex](x,y) = (\frac{5 \times 16 + 9 \times 3}{5 + 9},\frac{5 \times 21 + 9 \times 2}{5 + 9})[/tex]
[tex](x,y) = (\frac{107}{14},\frac{123}{14})[/tex]
[tex](x,y) = (7.6,8.8)[/tex]
Hence, the location of the treasure is (b) (7.6,8.8)
Read more about line segment ratios at:
https://brainly.com/question/14382744
someone answer this asap pls lots of points
Answer:
0.34
Step-by-step explanation:
64^1/2=34
10^-2=0.01
34*0.01=0.34
(4-13i)-(3+6i) how do you solve this I’ve been stuck
Answer:
1-19i
Step-by-step explanation:
i will make you brainliest
Answer:
The time in Auckland, New Zealand in the 12+ time zone: 21:00
The time in Athens, Greece in the +2 time zone: 22:00
The time in Trinidad in the -4 time zone: 05:00
The time and date in Chicago in the -6 time zone: 02:00 2016-10-19
The time and date Bangkok in the +7 time zone: 11:00 2016-10-20
The time and date in Greenwich: 06:00 2016-10-29
The time and date in Abu Dhabi in the +4 time zone: 30:00 2016-10-30
The time and date in a country in the +12 time zone: Uzbekistan 23:00 2016-11-02
The time and date in a country in the -12 time zone: Brazil 23:00 2016-11-01
The time and date in Honolulu located in the -10 time zone: 01:00 2016-11-02
When the time in Sri Lanka is 09:30 on 2017-05-02, find the time and date in Los Angeles located in the -8 time zone in the USA. 01:30 on 2017-05-02
(These are the answers i calculate i am not sure if they are fully correct)
what would the equation be??
Answer:
y = 4x + 8
Step-by-step explanation:
Firstly, choose 2 points ( I chose [2,11] and [4,19] ) use y2-y1/x2-x1 to find your slope of 4, next use one of the points to find your y-intercept, plug the two coordinates into your equation to get 11 = 4 (2) + b , after simplifying, your answer is y = 4x + 8
Brainliest would be appreciated. :-)
please help me with this. really need this
Answer:
(a) 1
Step-by-step explanation:
When you draw a horizontal line on the graph at y=1, you see it intersects the curve in two places. That is, there will be 2 real solutions to f(x) = 1, not 4 solutions.
If you want 4 solutions, the value of c in f(x)=c cannot be 1.
What is 5 rounded to the nearest whole number, explain why
Answer:
The answer is 10
Step-by-step explanation:
It is
4x^2+8x-12 in vertex form
Answer:
y = 4 (x + 1)² - 16
Step-by-step explanation:
Step 1: Equation at the end of step 1
(2²x²+8x)-12
Step 2:
Step 3: Pulling out like terms
Pull out like factors :
4x² + 8x - 12 = 4 • (x² + 2x - 3)
Trying to factor by splitting the middle term
Factoring x²+ 2x - 3
The first term is, x²
its coefficient is 1 .
The middle term is, +2x its coefficient is 2 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 2 .
-3 + 1 = -2
-1 + 3 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 3
x² - 1x + 3x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
Add up the last 2 terms, pulling out common factors :
3 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-1)
Which is the desired factorization
Final result :
Final result :
4 • (x + 3) • (x - 1)
Now convert to vertex form:
y = 4 (x + 1)² - 16
(1,-3) (-3,1) find the slope intercept form
Answer:
[tex]y=-x-2[/tex]
Step-by-step explanation:
1) First, find the slope between these 2 points.
(1, -3)
(-3, 1)
The change between the y-values is 4.
[tex]1--3=1+3=4[/tex]
The change between the x-values is -4.
[tex]-3-1=-4[/tex]
Slope is rise over run, and this is a rise of 4 and a run of -4, so the slope is -1.
[tex]\frac{4}{-4}=1[/tex]
If you just wanted to use the slope formula, you could do that too:
[tex]m=\frac{y2-y1}{x2-x1}\\\\m=\frac{1--3}{-3-1}\\\\m=\frac{4}{-4}\\\\m=-1[/tex]
2) Second, now you can use the slope to calculate the y-intercept.
Pick whichever point you want, and plug it into the equation along with the slope and solve for b.
(1, -3) = (x, y)
[tex]y=mx+b\\-3=(-1)(1)+b\\-3=-1+b\\-2=b\\b=-2[/tex]
The y-intercept is -2.
3) Finally, you can wire the equation in slope-intercept form.
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Plug in the values we found and you're done:
[tex]y=-x-2[/tex]
The bottom of a rectangular swimming pool has a perimeter of 62 meters. Its area is 220 square meters. What are the dimensions of the pool?
_____ meters by _____ meters
Answer:
13640cubicmeter........
Tanaka says "When you multiply an odd number and an even number together, you will
always get an odd number'.
Show that Tanaka is wrong.
Answer: Tanaka is wrong becausee...
2 x 3 = 6
Since Tanaka said "When you multiply an odd number and an even number together, you will always get an odd number." we do not need to show more examples.
Hope this helps :)
HELP ASAP PLZ
just answer the blanks
Answer:
i hope this helps!
Step-by-step explanation:
The top row contains solutions for the value of c. The bottom row contains equations that must be solved to find c. Drag each solution into the box with the matching equation.
7
20
12
9
c is 4 times as many as 5.
27 is c times as many as 3.
6 times as many as c is 72.
8 more than c is 15.
which one is it??
Solve. 34x+78=414 Enter your answer as a mixed number in simplest form in the box. x =
Answer:
The answer in mixed fraction form is [tex]9\frac{15}{17}[/tex]
Step-by-step explanation:
34x + 78 = 414=> 34x = 414 - 78=> 34x = 336=> x = 336/34=> [tex]9\frac{30}{34} = 9\frac{15}{17}[/tex]Conclusion:
Therefore, the answer in mixed fraction form is [tex]9\frac{15}{17}[/tex]
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Answer: X= 9 over 2
I think this is the right answer
sorry if it is not
1- Which comparison is NOT true?
A
3.976 > 3.97
B
1.025 < 1.25
С
9.145 > 9.14
D
0.613 > 0.631
Answer:
D
Step-by-step explanation:
Process of Elimination:
A: 3.976 is greater than 3.97
B: 1.025 is lesser than 1.25
C: 9.145 is greater than 9.14
All of the options checked are true, leaving the answer only to be D.