Answer:
A. Normal
B. Between 40.08 minutes and 43.92 minutes.
C. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
Question A:
By the Central Limit Theorem, a normal distribution.
Question B:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{12}{\sqrt{150}} = 1.92[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.92 = 40.08 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.92 = 43.92 minutes
Between 40.08 minutes and 43.92 minutes.
Question C:
x% confidence interval -> x% will contain the true population mean, (100-x)% wont.
So, 95% confidence interval:
About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.
Julie runs 3 miles each morning. How far does she run in feet?
(1 mile = 5,280 feet)
Answer:
15,840 feet
Step-by-step explanation:
5,280*3 = 15840
Since she runs 3 miles each morning, and 1 mile is 5,280,
then you multiply 5,280*3
How many solutions are there in the following system of equations? (
one solution, no solutions, infinitely many solutions)
- 8x + 2y = -16
4x - y = 10 PLEASW HELP
Answer:
No solutions
Step-by-step explanation:
-8x+2y = -16
4x-y = 10 [multiply by 2 so it is easier to add/subtract]
-8x+2y = -16
8x -2y = 20
0 = 4
0 and 4 cant be equal so theres no solution
Convert r=2/7sinθ−cosθ to rectangular form.
Enter your answer in slope-intercept form by filling in the blanks. Enter values so that fractions are simplified.
y=_/_x + _/_
Answer:
x²+y²=√(2/7 x-y)
is the answer, i think
The price of an item has been reduced by 45%. The original price was $63.
Use the ALEKS calculator to find the price of the item now.
se]
?
Answer:
$28.35
Step-by-step explanation:
[tex]45\% \times 63 \\ = 0.45 \times 63 \\ = 28.35[/tex]
How do you factor x^3-2x^2+3x-6
Answer:
(x - 2) (x^2 + 3)
Step-by-step explanation:
x^3-2x^2+3x-6
Factor by grouping
Answer:
Factor by grouping
Step-by-step explanation:
[tex]x^{3}-2x^{2} +3x-6[/tex]
[tex]x^{2} (x-2) + 3 (x-2)[/tex]
[tex](x^{2} +3)(x-2)[/tex]
someone please help me answer this!!
Answer:
c = 85 in is the answer.
Step-by-step explanation:
a = 36 in
b = 77 in
c = ?
According to the Pythagoras theorem,
a² + b² = c²
36² + 77² = c²
1296 + 5929 = c²
7225 = c²
c = 85 in
∴ c = 85 in is the length of the missing leg.
A bag contains 5 apples, 4 peaches, and 3 oranges. What is the probability of choosing an apple?
I need help but the green is correct but I need help with the first 2 I need to turn this in 10 mins
Answer: see work
Step-by-step explanation:
Blue:
9-5+3x4
Red:
10+6/3+8x2
Answer:
Work
Step-by-step explanation:
Blue:
9-5+6-5
Red:
4+4+5
10. What is the perimeter of the figure on the coordinate plane below?
A 32 units
B 24 units
C 22 units
D 14 units
Answer:
24 units
Step-by-step explanation:
Each line plot equals 2, so the length is 8 and the hight is 4. 8+8+4+4 = 16 + 8 = 24 units.
Solve the system of equations x - y = 12 and x + 7y = -20 by combining the
equations.
Answer:
x=16, y=-4
Step-by-step explanation:
-1(x-y=12)
x+7y=-20
-x+y=-12
x+7y=-20
8y=-32
y=-4
x-4=12
x=16
Answer:
x= 8, y= -4
Step-by-step explanation:
You can subtract one equation by another to eliminate x
(x-y)-(x+7y)=12-(-20)
-8y = 32
y= -4
Substitute y = -4 in the first equation:
x-(-4) = 12
x =8
DUE IN THREE MINUTES
i give brainliest
factor each expression:
9+21
14+28
80+56
Answer:
Step-by-step explanation:
The secret trick to factoring is the greatest common factor.
The greatest common factor of 9 and 21 is 3. Thus, our expression is
3(3 + 7).
The greatest common factor of 14 and 28 is 7. Our expression is
7(2 + 4)
The greatest common factor of 80 and 56 is 8. This makes our expression
8(10 + 7).
(5x2 + 4x + 3) - (2x2 - 2x + 5)
Answer:
3x^2+6x-2
Step-by-step explanation:
(5x2 + 4x + 3) - (2x2 - 2x + 5)
5x^2+4x+3-2x^2+2x-5
3x^2+6x-2
What is the value of (5)3?
Answer:
15
Step-by-step explanation:
This is simply just 5 x 3 = 15
What is the smallest number of people you need for
the probability to be 100 percent that at least two of
them were born in the same month?
n a study to investigate whether vitamin C will prevent colds, 400 subjects are assigned at random to one of two groups. The experimental group takes a vitamin C tablet daily, while the control group takes a placebo. At the end of the experiment, the researchers calculate the difference between the percentage of subjects in the two groups who were free of colds. This difference is statistically significant (P=0.03) in favor of the vitamin C group.
Answer:
Step-by-step explanation:
The aim of this question is to see if we can infer and conclude that vitamin C has a good impact in preventing colds based on the evidence provided.
Null hypothesis: Vitamin C has no effect on preventing colds.
Alternative hypothesis: Vitamin C has a strong effect on preventing colds.
Assuming, significance level = 0.05
Since the p-value for the difference is 0.03 which is less than 0.05.
Hence, the null hypothesis is rejected (which is there is no effect of vitamin C).
As a result, it can be concluded that Vitamin C has a major impact on the prevention of colds.
1/3 divided by 7/6 can u solve it?????
Answer:
2/7
Step-by-step explanation:
when you divide a fraction by a fraction, flip the second fraction. 1/3 x 6/7 is 6/21, then you reduce it. divide 6 by 3 and 21 by 3, =2/7
Answer:
0.28571428571
Step-by-step explanation:
This is the calculated answer.
But after a lot of. technical,work the answer,ends up be 2/7
a gardener is growing tomato plants. one plant starts out 5 cm tall. it grows a constant 2 cm every week. what equation represents the height h of the plant after t weeks
a t= 5h+2
b t= 2h+5
c h=5t + 2
d h = 2t+5
Answer:
D) h=2t+5
Step-by-step explanation:
A survey of 71 families showed that:
40 have a son(s)
45 have a daughter(s)
18 had neither a son nor a daughter.
How many families had ONLY son(s)?
Answer:
108
Step-by-step explanation:
Name the ordered pair for point R
Can you post a picture please
Mr. Brown has 1/4pan of lasagna left in the refrigerator. He wants to cut the lasagna into equal slices so he can have it for dinner for 3 nights. What fraction of the whole lasagna will he eat each night?
Answer:
1/12
Step-by-step explanation:
He has a 1/4 pan left and wants to divide that into 3 equal pieces. So in night he will eat 1/3 of what he has left from the 1/4 pan. To figure out how much one slice is from an entire pan:
1/4 * 1/3 = 1/12
What is the volume of a sphere with a diameter of 22ft? Round your answer to the nearest cubic foot.
8359 cubic feet
6193 cubic feet
• 2786 cubic feet
5572 cubic feet
Answer:
D) 5,572
Step-by-step explanation:
4/3×pi×r^3
4/3×3.14×11^3
5572.453...
5572
can i please have some actual help with this?
Answer:
x = 286.01 inches
Step-by-step explanation:
Given that,
Height of the ramp, H = 20 inches
Angle of elevation, [tex]\theta=4^{\circ}[/tex]
We need to find the value of x. It can be solved using trigonometry as follow :
[tex]\tan\theta=\dfrac{P}{B}[/tex]
Where
P is perpendicular and B is base
So,
[tex]\tan(4)=\dfrac{20}{x}\\\\x=\dfrac{20}{\tan(4)}\\\\x=286.01\ in[/tex]
So, the value of x is equal to 286.01 inches.
BRAINLIST!!!
A construction crew built 7 1/2 miles of road in 3 1/8 days.
What is the unit rate in miles per day?
Write your answer as a fraction or a mixed number in simplest form.
Answer:
If you think numbers with fractions are annoying, consider transforming the number into fractions!
Step-by-step explanation:
7 1/2 is (14+1)/2, and 3 1/8 is (24+1)/3. Not you have 15/2 miles for 25/3 days and by dividing them you get 0.9 miles a day
Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 390 grams, how long would it be until the mass of the sample reached 260 grams, to the nearest tenth of a year?
Answer:
It will take 15.029 years for element X to reach mass of 260 grams
Step-by-step explanation:
The half life period of radioactive element X is 26 years
The initial mass of radioactive element X is 260 grams
Elapsed time = half life * log (beginning amount /ending amount)/log 2
Substituting the given values, we get
Elapsed time = 26 * log (390/260)/log 2
= 15.209 years
Drag the word or expression to complete the function.
Answer:
-5 cos (2x)
Step-by-step explanation:
Reflection over x axis just means "multiply by -1" so the answer is
f(x) = 5 cos (2x)
g(x) = -5 cos (2x)
The Y-Axis on a Coordinate plane runs vertical.
Answer:
good
Step-by-step explanation:
So when you do the (,) things the x-axis would go first for example
say the x-axis=5 and the y-axis= 9 it would be (5,9)
hope this helps plz mark brainlest
Suppose that in a random selection of 100 colored candies, 21% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%. Use the 0.01 significance level to test that claim.
Answer:
The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.
Step-by-step explanation:
The candy company claims that the percentage of blue candies is equal to 29%.
This means that the null hypothesis is:
[tex]H_{0}: p = 0.29[/tex]
We want to test the hypothesis that this is true, so the alternate hypothesis is:
[tex]H_{a}: p \neq 0.29[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.29 is tested at the null hypothesis:
This means that [tex]\mu = 0.29, \sigma = \sqrt{0.29*0.71}[/tex]
Suppose that in a random selection of 100 colored candies, 21% of them are blue.
This means that [tex]n = 100, X = 0.21[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.21 - 0.29}{\frac{\sqrt{0.29*0.71}}{\sqrt{100}}}[/tex]
[tex]z = -1.76[/tex]
Pvalue of the test:
The pvalue of the test is the probability of the sample proportion differing at least 0.21 - 0.29 = 0.08 from the population proportion, which is 2 multiplied by the pvalue of Z = -1.76.
Looking at the z-table, z = -1.76 has a pvalue of 0.0392
2*0.0392 = 0.0784
The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.
Solve the Inequality Give 5 solutions of the inequality ( Show your solution).
2x -3 < 5
Answer:
Inequality Form:
x<4
1<4
3<4
-1004<4
Interval Notation:
(−∞,4)
(-1004,4)
(3,4)
(1,4)
Step-by-step explanation:
A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 ft, width 18 ft, and depth 4 ft. Suppose water is pumped out of the
pool at a rate of 216 ft per hour. If the pool starts completely full, how many hours does it take to empty the pool?
hours ( NO LINKS , LINK WILL GET YOU BANNED )
Answer:
10 hours (I am not positive)
Step-by-step explanation:
We first want to find the volume of pool which is 30 x 18 x 4 = 2160.
Then you are going to divide by 216 to find how many hours it takes to drain the whole pool. (I'm not that big of an expert)
Solve the equation:
[3 2
5 5]
[x1
x2]+
[1
2]=
[2
-3]
9514 1404 393
Answer:
(x1, x2) = (3, -4)
Step-by-step explanation:
As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.
[tex]\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{5}\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right][/tex]
Performing the multiplication of the matrix by the vector gives the solution.
x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3
y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4
Using your variables, x1, x2, the solution is ...
(x1, x2) = (3, -4)