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
I’m desperate at this point
A man borrowed Rs.8000 for one year at the rate of 15% per annum. Find
the interest
Answer:
I = 8000×1×15
--------------
100
I = 120000
----------
100
I = Rs 1200
You have a cylindrical pond that has a diameter of 24 feet and has a depth of 6 feet. If you need to fill the pond three-quarters of the way up with water and water costs $2.50 per cubic foot, how much will you need to spend to fill the pond?
Answer:
$5089.38Step-by-step explanation:
Given cylinder with:
d = 24 ft, h = 6 ftWe need to fill it up to:
h = 6 ft * 3/4 = 4.5 ftThe volume is:
V = πr²h = π(d/2)²h = π*(24/2)²*(4.5) = 2035.75 ft³ (rounded)You need to spend:
2035.75 * $2.50 = $5089.38 (rounded)Select the expression NOT equivalent to 32 + 40x.
8(5x + 4)
(8 + 5x)4
4(4 + 10x) + 16
15x + 25x +2(16)
Answer:
dsadh
Step-by-step explanation:
!!!HELP!!!
1) Which transformation can be used to map ABCD onto EFGH and to confirm that the figures are congruent?
A) ABCD can be mapped to EFGH with a translation right 4 units and down 4 units.
B) ABCD can be mapped to EFGH with a translation left 4 units and down 4 units.
C) ABCD can be mapped to EFGH with a translation left 4 units and up 4 units.
D) ABCD can be mapped to EFGH with a translation right 4 units and up 4 units.
2) Which sequence of transformations will only produce a figure similar to but not congruent to the figure ABCD?
A) ABCD is translated 2 units to the right and then reflected across the x-axis.
B) ABCD is translated 4 units left, 2 units up, and then reflected across the y-axis.
C) ABCD is rotated 180° clockwise about the origin and the translated 3 units right.
D) ABCD is dilated by a scale factor 3 and then rotated 90° clockwise about the origin.
Answer:
itsb a
Step-by-step explanation:
sorry
What is the contrapositive of the statement below?
If you are in Reykjavik, then you are in Iceland.
Answer:
If you are not in Iceland, then you are not in Reykjavik.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The contrapositive of a statement is as follows:
"Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."
So, for this one, we need to switch as well!
If you are in Reykjavik, then you are in Iceland.
If you are NOT in Iceland, then you are not in Reykjavik.
The answer would be D
i need help please!!!!
Answer:
(c) y -2 = 6/5(x -1)
Step-by-step explanation:
The equations are all in point-slope form with a slope of 6/5. The points used are (-1, -2), (-2, -1), and (1, 2). It seems point (1, 2) best matches a point on the graphed line. Choice C is the best. (In the attached graph, choice C is the red line.)
_____
Additional comment
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
__
The equation might be easier to see if the point chosen were one at a grid intersection, such as (-4, -4) or (6, 8).
please please i beg help for brainlist !!!!!!!!
Answer:
[tex]a_n=\frac{1}{2}a_{n-1}[/tex]
Step-by-step explanation:
Here, you can see every consecutive term is divided by 2. I think that's pretty obvious looking at it, but you can work it out like this if you'd like to. Divide each consecutive term by the one before it:
[tex]6\div12=\frac{1}{2}\\\\3\div6=\frac{1}{2}\\\\\frac{3}{2}\div3=\frac{1}{2}[/tex]
Each term is multiplied by 1/2 over the last, or divided by 2. In this case actually, we do want it in the form of "multiplied by 1/2", as the recursive equation is:
[tex]a_n=xa_{n-1}[/tex]
where x is the factor. Here, we're multiplying by x, so we want "multiplied by 1/2" as described above. x is 1/2, so you can write the equation:
[tex]a_n=\frac{1}{2}a_{n-1}[/tex]
You can simply interpret this as "each term is 1/2 of the term before it"
please i beg on my knees i will give brainlist!!!!!!!!!!!
Answer:
i think it's letter c. f (n) = 4n-1
Step-by-step explanation:
1x4= 4, 2x4= 8, 3x4= 16, and so on
hope this helps!! :))
For f(x)=−2x+4, find f(x) when x=−3.
What is the measure of Segment AB if Segment BD is 10?*
Answer:
10
Step-by-step explanation:
all sides of square are the same
Solve for x. 4 1/2 ≤ 1.2x
x ≥ 3 3/4
x≤3 3/4
x≥5 2/5
x≤5 2/5
Step-by-step explanation:
4 1/2 < 1.2x
4.5 < 1.2x
4.5/1.2 < x
3.75 < x
3 3/4 < x
Option 2 is the correct answer
Answer:
the second one x<3 3/4 is the answer
1/4 divided by 3 I’m behind and I really just want to get this over with :) plus math is my least favorite subject thanks to my teacher so yeah plz help:)
Answer:
XD [tex]\frac{1}{12}[/tex] is the answer.
Step-by-step explanation:
So, to divide a fraction with a whole number you'll have to multiply the denominator with the whole number.
Hopes This Helps
Easy geometry question please help
Answer:
Y-8
Step-by-step explanation:
Any point on the upper triangle ABC, for example point B, is translated 8 units down the y axis, appearing on the lower triangle A'B'C'
Madelynn makes the following statement: "Since I have 28 people that I defi-
nitely want to invite to my party, I might as well choose Party B and invite even
more people."
Was Madelynn correct to go with Party B and invite more people? Explain why or
why not.
Answer:
The only problem was that now it costs more so not really
Step-by-step explanation:
I think its an opinion question
For all values of x, f(x)=2x+1 and g(x)=x^2. Solve fg(x)=gf(x). (Mathwatch)
[tex]\text{Given that,}\\\\f(x) = 2x+1,~~ g(x) = x^2\\\\\ \text{now,}\\\\f(g(x)) = g(f(x))\\\\\implies f(x^2) = g(2x+1)\\\\\implies 2x^2+1=(2x+1)^2\\\\\implies 2x^2+1= (2x)^2 +2\cdot 2x + 1\\\\\implies 2x^2 +1 = 4x^2 + 4x +1\\\\\implies 4x^2 -2x^2 +4x +1-1 =0\\\\\implies 2x^2 +4x =0\\\\\implies 2x(x+2)=0\\\\\implies 2x =0~~ \text{or}~~ x+2 =0\\\\\implies x =0 ~~~\text{or}~ x =-2\\\\\ \text{Hence,}~ x =0 ~\text{and} ~ x =-2~ \text{are the solutions.}[/tex]
priya found x=3 and x=-1 as solutions to 3x^2-6x-9=0. Is she correct sow how you know
Answer:
Step-by-step explanation:
help me find the derivative
[tex]\dfrac{d}{dx} \left(e^{x^2} \cdot x^2\right)\\\\=e^{x^2} \dfrac{d}{dx} (x^2) + x^2 \dfrac{d}{dx}\left (e^{x^2}\right)\\\\=e^{x^2} \cdot 2x + x^2 \cdot e^{x^2} \cdot \dfrac{d}{dx} (x^2)\\\\=2x e^{x^2} + 2x^3 e^{x^2}\\\\=2xe^{x^2}(1+x^2)[/tex]
Solve for b.
r=5(b + a)
help timed
Answer:
b=(r/5)-a
Step-by-step explanation:
To solve, you do the mathematics.
r=5(b+a)
r=5b+5a
5b=r-5a
b=(r/5)-a
D(3, 6), E(-4,-3), F(6, 1) and
D'(1, 6), E'(8, -3), F(-2, 1)
Answer:
d
Step-by-step explanation:
can someone explain to me what this means
Answer:
2*2*2*3*5
Step-by-step explanation:
It is saying that 120 is the same as 24*5, and that 24* 5 is the same as 5 *2*12, which is that same as 5*2*3*4, which is then the same as 5*2*3*2*2.
Answer:
2 x 2 x 2 x 3 x 5
Step-by-step explanation:
What is 2,200 yards in miles? Round to the nearest tenth of a mile.
Answer:
1.25 mi
Step-by-step explanation:
First, we want to convert a yard into feet; recall 1 yard = 3 feet.
Then we want to divide that by the number of feet in a mile 1 mile = 5280feet.
So 2200*3 =6600, then divide by 5280
6600/5280 = 1.25 mi
2200 yard is 1.25 miles
There are 1.3 miles in 2,200 yards.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
2,200 yards ____(1)
1 mile = 1760 yards _____(2)
Now,
From (1) and (2),
1 mile = 1760 yards
Multiply 2,200/1760 on both sides.
2,200/1760 x 1 mile = 2,200/1760 x 1760 yards
1.25 miles = 2,200 yards
Rounding to the nearest tenths.
1.3 miles = 2,200 yards
Thus,
There are 1.3 miles in 2,200 yards.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ5
what is 1 over 5 divided by 6?
Answer:
[tex] \frac{1}{5} \div 6 = \frac{1}{5} \times \frac{1}{6} = \frac{1}{30} [/tex]
A floor is 40 m long and 15 m broad. It is covered with tiles, each measuring 60 cm by 50 cm. Find the number of tiles required to cover the floor.
Answer:
2,000 tiles
Step-by-step explanation:
area of the floor divided by the area of one tile
area of a rectangle is length*width
so it's 40*15= 600
area of tile is 0.6m*0.5m = 0.3
600÷0.3 = 2,000 tiles
5. A quarter is tossed in the air 300 times.
About how many times would you expect the quarter to land on heads?
A 50
E 200
B 110
C 150
D 180
Answer:
C
Step-by-step explanation:
The probability of getting heads or tails is 50%.
300*50% = 150
Answer:
C. 150 times
Step-by-step explanation:
Because a coin only has tails and heads, you can say that the probability would be half. Because it was tossed 300 times, you can say: 300*0.5=150
Multiply. {}=3\dfrac{1}{2} \times 3\dfrac12=3 2 1 ×3 2 1
I assume you mean the product of mixed numbers,
3 1/2 × 3 1/2
If we write this as
(3 + 1/2) × (3 + 1/2) = (3 + 1/2)²
we can use the identity
(a + b)² = a² + 2ab + b²
so that
3 1/2 × 3 1/2 = 3² + (2 × 3 × 1/2) + (1/2)²
3 1/2 × 3 1/2 = 9 + 3 + 1/4
3 1/2 × 3 1/2 = 12 1/4
Alternatively, we can first write 3 1/2 as a mixed number:
3 + 1/2 = 6/2 + 1/2 = (6 + 1)/2 = 7/2
Then
3 1/2 × 3 1/2 = 7/2 × 7/2 = (7 × 7) / (2 × 2) = 49/4
and
49/4 = (48 + 1)/4 = ((4 × 12) + 1)/4 = 12 + 1/4
Can someone please help me solve this
Answer:
Step-by-step explanation:
It saids evaluate given the three different functions below: The graph f(x), the equation g(x) and the table h(x)
what is 2+2 i need help like rly bad i will give 100 points
Answer:
4 bestie <3
Step-by-step explanation:
Answer:
Step-by-step explanation:
4
Plz help rn got to get this done rn
Answer:
A) 32
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Sara earned 100 points in the first round of a game. She earned 20 points in each of the following rounds of the game. She ended the game with 400 points. Write and solve an equation to find the number of rounds Sara played.
20x=400-100
20x=300
x= 300/20
15 rounds she played
