Answer:
The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not.
This means that [tex]n = 100, \pi = \frac{20}{100} = 0.2[/tex]
68% confidence level
So [tex]\alpha = 0.32[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.32}{2} = 0.84[/tex], so [tex]Z = 0.995[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 0.995\sqrt{\frac{0.2*0.8}{100}} = 0.16[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 0.995\sqrt{\frac{0.2*0.8}{100}} = 0.24[/tex]
The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
What is the p-value?The p-value is also known by the probability value. It is the probability of getting a result that is either the same or more than the actual value.
In a given data with a number n of people surveyed with a probability of success [tex]\pi[/tex] and a confidence level [tex]1-\alpha[/tex], we have the confidence interval of proportions.
[tex]\pi[/tex] ± [tex]\rm z\sqrt{\pi (1-\pi )} /n[/tex]
where z has a p-value of 1-[tex]\alpha /2[/tex]
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not.
n = 100, [tex]\pi[/tex] = 20/100 = 0.2
So, [tex]\alpha[/tex] = 0.32 where z has a p-value 1-[tex]0.32 /2 = 0.84[/tex]
z = 0.995
The lower limit of this interval
[tex]\pi -\rm z\sqrt{\pi (1-\pi )} /n\\= 0.2 - 0.995 \sqrt{0.2 \times 0.8} /100\\= 0.16[/tex]
The upper limit of this interval
[tex]\pi -\rm z\sqrt{\pi (1-\pi )} /n\\= 0.2 +0.995 \sqrt{0.2 \times 0.8} /100\\= 0.24[/tex]
Hence, The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).
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Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3
Answer:
[tex]\dfrac{-8}{x+3}[/tex]
Step-by-step explanation:
We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".
Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.
So, we can write it as follows :
[tex]\dfrac{-8}{x+3}[/tex]
Hence, this is the required solution.
13
What is the inverse of when
15
multiplying fractions?
13
A
15
15
B
13
13
C с
13
15
D
15
Answer:
Step-by-step explanation:
15x13=?
15+15+1=31
so the answer is 31
I need help with slopes!!
Answer:
The slope of this line is -4
PLEASE HELP:):):):):):):):)
Answer:
[tex]Area = 8[/tex]
Step-by-step explanation:
Given
The attached figure
Required
Determine the area
The shape is a trapezium. So, the area is:
[tex]Area = \frac{1}{2} *(Sum\ of\ parallel\ sides) * Height[/tex]
From the attached,
The height is 2
The parallel sides are: 2 and 6
So, the area is:
[tex]Area = \frac{1}{2} *(2 + 6) * 2[/tex]
[tex]Area = \frac{1}{2} *8 * 2[/tex]
[tex]Area = 8[/tex]
Hence, the area is 8 units square
1) Madison went shopping and spent $125 she paid $45 in Texas what was the sale tax rate (percent)
Answer:
170
Step-by-step explanation:
How the sales tax de-calculator works
Step 1: take the total price and divide it by one plus the tax rate.
Step 2: multiply the result from step one by the tax rate to get the dollars of tax.
Step 3: subtract the dollars of tax from step 2 from the total price.
Pre-Tax Price = TP – [(TP / (1 + r) x r]
TP = Total Price.
Find g(-6) when g(x)
= x+3/x-1
Answer: The answer would be 3/7.
Step-by-step explanation:
Find the average number of people in these cities: New York, Philadelphia, Chicago and Detroit a. 3.35 million b. 40 million. C. 4.0 million d. 33.million
Answer:
The answer is maybe going to be D which is 33 million
Step-by-step explanation:
New york is a big city
25. Which two conversions are correct?
A. 7 mm = 70 cm
B. 7 cm = 0.07 m
C. 7,000 m = 7 km
D. 0.7 cm = 70 mm
E. 7 m = 7,000 km
Answer:
The answer is B and C
Step-by-step explanation:
1 Meter is equal to 0.001 Kilometer
1 Centimeter is equal to 0.01 Meters
The unit conversions which has the true measurements are
a) 7 cm = 0.07 m
b) 7,000 m = 7 km
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the unit conversion be represented as A
Let the first measurement be p
where the value of p is
p = 7 cm
From the unit conversion , 1 m = 100 cm
So , 7 cm = 0.07 m
And , let the second measurement be q = 7,000 m
From the unit conversion , 1 km = 1,000 m
7,000 m = 7 km
Hence , the unit conversions are solved
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4. A recipe says that 2 3/5 cups of flour are needed to make 1 batch of biscuits. How many cups of flour are needed to make 2 batches of biscuits? O 43/5 O 51/5 O 26/10 O 6
Please help me I really need it
Answer:
Angle C
Step-by-step explanation:
By applying sine rule in the given triangle,
[tex]\frac{\text{sinB}}{CD}=\frac{\text{sinC}}{BD}=\frac{\text{sinD}}{BC}[/tex]
[tex]\frac{\text{sinB}}{\text{sinC}}=\frac{\text{CD}}{\text{BD}}[/tex]
Therefore, sides of the given triangle will be in the same ratio as the sine of the angles.
Since, BD > BC > CD
Therefore, Opposite angles of these sides will be in the same ratio.
∠C > ∠D > ∠B
Largest angle of the triangle is angle C.
HELP ME ASAP!!!! I’m very confused and I need help!! Thanks!
Answer:
Reason 2)The transitive property of congruenceStep-by-step explanation:
There are several sort of "obvious" properties of equality/congruence. Keeping them sorted out can be a bit of a trick.
A = A . . . . reflexive property
A = B ⇔ B = A . . . . symmetric property (erroneously cited in the proof)
A = B, B = C ⇒ A = C . . . . transitive property (the one needed in the proof)
__
Not to confuse the issue, but there is also the "substitution property of equality" that says if X = Y, then X can be substituted for Y or vice versa. In the end, the transitive property is an application of this, where we're substituting for B in the second equation, or for A in the first equation.
The A=B=C form of Statement 1) in the proof is what gives you the clue it is the transitive property that is wanted here.
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Answer:
the answer is 7 feet
Step-by-step explanation:
28/4=7
Mr. Thorbes bought a new journal for his poetry. If the journal normally cost $22 but was on sale for 20% off, how much did Mr. Thorbes save?
Answer:
He would save $4.40
Step-by-step explanation:
And in total he would pay 17.60
Find the value of x in the parallelogram below.
Answer:
B) x = 12
Step-by-step explanation:
m∡EOU = m∡TQE
m∡EOU =180 - (39+45) = 96°
m∡TQE: 7x + 12 = 96
7x = 84
x = 12
g(x)=x^2-5x
f(x)=2x+1
Find (g-f)(x)
Answer:
(g-f)(x) = x²-7x -1
Step-by-step explanation:
hello :
g(x)=x²-5x f(x)=2x+1
(g-f)(x) =g(x) - f(x) = x²-5x- ( 2x+1 ) = x²-5x - 2x-1
(g-f)(x) = x²-7x -1
a group of students collected old newspapers for a recycling project. the data shows the mass, in kilograms, of old newspapers collected by each student.
23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55
98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.
A.) Find the range of the mass of the newspapers collected.
B.) Find the interquartile range.
Answer:
A. 107 kg
B. 49 kg
Step-by-step explanation:
PLEASE HELP ASAP GEOMETRY I AM LITERALLY DYING!! 100 POINTS REAL ANSWERS ONLY OR YOU WILL BE REPORTED AND GET NO POINTS!
Let’s design a new ferris wheel!! Create a sketch of a new Ferris wheel. This new ferris wheel must have an arc length measuring 3 25π feet. What is the equation of your new ferris wheel if the center must be at least 60 feet from the ground? Be sure to show and explain all work.
9514 1404 393
Answer:
x^2 +(y -61)^2 = 625/36
Step-by-step explanation:
The graph of the above equation is attached.
If the circumference of the wheel is 25π/3 feet, the diameter is ...
d = C/π = (25/3π)/π = 25/3 . . . feet, about 8.33 feet
The radius will be half that value, or 25/6 feet.
For a center point (h, k) and radius r, the equation of a circle is ...
(x -h)^2 +(y -k)^2 = r^2
You want the center to be more than 60 feet from the ground, so we can make it be 61 feet. The horizontal location is not specified, so we can make it zero.
This means we apparently want the equation for a circle of radius 25/6 feet with a center that is (x, y) = (0, 61). The equation of this circle is ...
x^2 +(y -61)^2 = 625/36
1/3x + 2 =4 I need it ASAP
Answer:
x=1/6 or 0.16
Step-by-step explanation:
x has to be whatever makes the equation true.
does 1/3 +2= 4 alone no does it = 4 when you do the 1/3(1/6) yes
Given that these triangles are similar, what is the perimeter of triangle PQR? Show your work.
If someone could answer fr this time that would be great.
Answer:
24
Step-by-step explanation:
I use the Pythagoras theorem.
[tex]\sqrt{a^{2} +b^{2} } =c^{2}[/tex]
[tex]4^{2}{x}6^{2} = c^{2}[/tex]
16 x 36= 576
[tex]\sqrt{576} = 24[/tex]
Directions: Tables, graphs (use grid points!), and stories are provided. For each case:
1. Find the slope
2. Find the y-intercept
3. Write an equation
4. Explain how you know the slope and y-intercept are correct. Check 2 points in your equation to show it is correct.
Linear Function Representation- Equation - Slope - Intercept
x y
0 4
2 9
4 14
6 19
8 24
Answer:
See explanations below
Step-by-step explanation:
Using the coordinate points in the table (0, 4) and (2, 9)
Slope m = y2-y1/x2-x1
m = 9-4/2-0
m = 5/2
slope = 5/2
Get the y-intercept
Substitute m = 5/2 and (0,4) into y = mx+c
4 = 5/2(0) + c
4 = 0+c
c = 4
y-intercept is 4
Get the equation
Recall that y = mx+c
y = 5/2x + 4
Using another 2 points (2,9) and (4, 14)
Slope = 14-9/4-2
Slope = 5/2
Since the slope is the same for the coordinates, hence the the equation is correct
NO SCAM LINKS.
please reply ASAP PLEASEEEE
Answer:
B
Step-by-step explanation:
triangle: solve for x
Answer:
6 root two
Step-by-step explanation:
geometric mean for leg t.
24*3=x2
x2=72
x=root(72)
6 root two
if my answer helps please mark as brainliest.
What fraction of 2 minutes is 6
seconds?
Answer:
1/20 of 2 minutes = 6 seconds
Answer:
1/20; 0.05; 5%
Step-by-step explanation:
Well, 2 minutes is 120 seconds, 6/120 simplified is 1/20, and decimal form would be 0.05, which is 5%
State of the given functions are inverses
Answer:
1) They are not inverses
2) They are inverses
Step-by-step explanation:
We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.
1)
Let's find f[g(x)] and simplify.
[tex]f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{7}{2}-\frac{3}{4}x[/tex]
As f[g(x)] is not equal to x, these functions are not inverses.
2)
Let's find f[g(x)] and simplify.
[tex]f[g(n)]=\frac{-16+(4n+16)}{4}[/tex]
[tex]f[g(n)]=\frac{-16+4n+16}{4}[/tex]
[tex]f[g(n)]=\frac{4n}{4}[/tex]
[tex]f[g(n)]=n[/tex]
Now, we need to find the other composition function g[f(x)]
Let's find g[f(x)] and simplify.
[tex]g[f(x)]=4(\frac{-16+n}{4})+16[/tex]
[tex]g[f(x)]=-16+n+16[/tex]
[tex]g[f(x)]=n[/tex]
Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.
I hope it helps you!
1. Find the value of x in the figure below.
74°
2x
Answer:
2x-7
Step-by-step explanation:
Find the area of the trapezoid.
22.2 cm
9.86 cm
8.52 cm
[? ]cm2
Enter the exact answer. Do not round
Answer:
151.4496
Step-by-step explanation:
it has not been rounded or anything that is the exact answer
Answer: 151.45 (151.4496)
Step-by-step explanation:
Formula: A = (a+b)/2 * h
Base = 22.2
Base = 8.52
Height = 9.86
Do the following:
(22.2+8.52)/2 * 9.86 = 151.4496
To solve the equation 5sin(2x)=3cosx, you should rewrite it as___.
Answer:
A
Step-by-step explanation:
We want to solve the equation:
[tex]5\sin(2x)=3\cos(x)[/tex]
To do so, we can rewrite the equation.
Recall the double-angle identity for sine:
[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]
By substitution:
[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]
Distribute:
[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]
We can subtract 3cos(x) from both sides:
[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]
And factor:
[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]
Hence, our answer is A.
*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.
Answer:
A. cosx(10sinx-3)=0
Step-by-step explanation:
5(2sinxcosx)=3cosx
10sinxcosx-3cosx=0
cosx(10sinx-3)=0
2. Which of the following is considered an
asset?
A Savings account
B Credit card debt
C Personal loan
D Mortgage
Answer:
A
Step-by-step explanation:
All of the rest you have to pay off. A savings account is a good place to keep money safe for the future, and you can also make interest.
Jason rolls the die 14 times. What is the experimental probability that he will roll a 2
The experimental probability that Jason will roll a 2 is 3/14.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, Jason rolls the die 14 times.
From the given table,
Number of favorable outcomes = 3
Total number of outcomes = 14
So, the probability = 3/14
Therefore, the experimental probability that Jason will roll a 2 is 3/14.
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"A driving instructor is investigating whether the time a driver spends in a driverâs education course improves their score on the driverâs test. The instructor randomly selected 10 drivers from a driverâs education course and recorded the number of hours each driver attended the driverâs education course and their corresponding score on the driverâs test. Assuming all conditions for inference are met, which of the following significance tests should be used for the investigation?"
a. A chi-square test of independence
b. A two-sample t-test for a difference between means
c. A two-sample z-test for a difference between proportions
d. A linear regression t-test for slope
e. A matched pairs t-test for a mean difference
Answer:
e. A matched pairs t-test for a mean difference
Step-by-step explanation:
When the observations from two samples are paired either naturally or by design we find the differences between the two observations of each pair.Treating the differences as a random sample from a normal population with mean ud= u1-u2 and unknwn standard deviation σd we perform one sample t- test on them. This is called the paired difference t- test or a paired t- test.
Suppose 10 young recruits are given a physical training by the Army . Their weights are recorded before and after the training. These observations constitutes natural pairing .
When we eliminate the undesireable sources of variation to take observations in pairs , this is called pairing by design.
