Answer: 13
Step-by-step explanation: r=V
πh=5306.6
π·10≈12.9967
A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. Determine a 68 % confidence interval for the population proportion of college seniors who plan to attend graduate school. (Enter each answer rounded to three decimal places.)
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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Can someone help me with this please ?
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5625.1 hours and a sample standard deviation of 226.1 hours.
(a) Test the hypothesis that the true mean life of a biomedical device is greater than 5500 using the P-value approach.
(b) Construct a 95% lower confidence bound on the mean.
(c) Use the confidence bound found in part (b) to test the hypothesis
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : μ = 5500
H1 : μ > 5500
The test statistic assume normal distribution :
Test statistic :
(Xbar - μ) ÷ s/sqrt(n)
(5625.1 - 5500) ÷ 226.1/sqrt(15) = 2.1429 = 2.143
Pvalue from test statistic :
The Pvalue obtained using the calculator at df = 15 - 1 = 14 is 0.025083
α = 0.05
Since ;
Pvalue < α
0.025083 < 0.05 ; Reject H0
The confidence interval :
Xbar ± Tcritical * s/sqrt(n)
Tcritical at 95% = 1.761 ;
margin of error = 1.761 * 226.1/sqrt(15) = 102.805
Lower boundary : (5625.1 - 102.805) = 5522.295
(5522.295 ; ∞)
The hypothesized mean does not occur within the constructed confidence boundary. HENCE, there is significant eveidbce to support the claim that the true mean life of a biomedical device is greater than 5500
Mr. Simpson has 5 boxes of paintbrushes in his art room. After the first week of school, he buys 3 more paintbrushes. The expression below shows the total number of paintbrushes in Mr. Simpson's art room when prepresents the number of brushes in each box. 3 + px 5 If each box contains 8 paintbrushes, how many total paintbrushes are in Mr. Simpson's art room? (Show your work or explain how you got your answer in words)
Answer:
5+3+8 or if its wrong then 5+3+8+5+3 or just one 3.
Step-by-step explanation:
A worker on an assembly line is required to take a short break every 90 to 120 minutes. The worker begins his job at 7:45 a.m. Which is not a time the worker could take his break?
Answer:
7:46 - 8:59
Step-by-step explanation:
This is their first 1-89 minutes of work, thus they are not able to go on break yet.
Kira has $2,250 sitting in a savings account that
earns 2.75% simple interest each year. If she
leaves it there untouched, how much will be in
the account after 8 years?
Answer:
2 250×96×2.75=5 940
Step-by-step explanation:
1 year=12 months
8 year's =96 Month's
first thing you need to do is to convert Years into months
You can get 6 tickets for $39 at the local movie theater. How much is each ticket?
Answer:
$6.50
Step-by-step explanation:
39 / 6 = 6.5
Answer:
$6.50
Step-by-step explanation:
Hi,
To get the cost per ticket, all you have to do is divide 39 by 6. When you do that you get, 6.5 which means each ticket costs $6.50.
I hope that helps :)
Rectangle measures 2 1/4 meters 1 7/8 meters what is its area
Plss help
Answer:
4.21875
Step-by-step explanation:
2.25*1.875 =4.21875
The area of the rectangle is 135/32 or 4 whole number 7/32 whose side measures are 2 whole 1/4 and 1 whole 7/8.
What is the area of the rectangle?It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.
The formula for finding the area of a rectangle is given by:
Area of rectangle = length × width
We have side measures of the rectangle:
[tex]\rm a = 2\frac{1}{4} \\\\\rm b = 1\frac{7}{8}[/tex]
The area of the rectangle A is given by:
[tex]\rm A = (2\frac{1}{4} )\times(1\frac{7}{8} )[/tex]
[tex]\rm A = (\frac{9}{4} )\times(\frac{15}{8} )[/tex]
[tex]\rm A = \frac{135}{32}[/tex] or
[tex]\rm A =4 \frac{7}{32}[/tex]
Thus, the area of the rectangle is 135/32 or 4 whole number 7/32 whose side measures are 2 whole 1/4 and 1 whole 7/8.
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Which values are solutions to the inequality below?
Check all that apply.
x2 < 81
A. 6
B. 9
C. 10
D. -4
E. -9
F. -12
Answer:
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
Guys this is simple question
Who’s fault is it
So it was Easter and my water was at the table and about 7 inches away from the table, then my sister was reaching something competing with my cousin and then she spilled the water on the floor and there was my charger, and I hurried to dry the charger but when I charged it, didn’t work. So it ment it broke.
So who’s fault is it?
What is the value of x in centimeters?
Answer:
2.5 cm
Step-by-step explanation:
Since the triangles are similar, we can use ratios to solve
AC BC
-------- = ---------
FH GH
12 15
-------- = ---------
18 x
Using cross products
12x = 15*18
Divide each side by 12
12x/12 = 15*18/12
x = 2.5
Find x to the nearest tenth
Answer:
x=30.6
Step-by-step explanation:
Gabrielle is 11 years older than Mikhail. The sum of their ages is 107. What is Mikhail's age?
Answer:
Mikhail's age is 48
Step-by-step explanation:
Answer:
107-11=96
96÷2=48
so Mikhail is 48 years old
PLEASEEEEEE HELPPPPPPPPPP MEEEEEEEEEEEEEEEE
Answer:
120.2 or in other words, the answer is the last option, D
the shorter leg of a right triangle is 8 inches shorter ybsn the longer leg. the hypotenuse is 8 inches longer thsn the longer leg
Answer:
Short leg = 24inches
Long leg = 32inches
Hypotenuse = 40inches
Step-by-step explanation:
Given:
shorter leg is 8inches shorter than the longer leghypotenuse is 8inches longer than the longer leglonger leg = x inchesPythagorean Theorem:
a²+b²=c² → (x-8)²+ x² = (x+8)²
Solving for both sides:
x² - 16x+ 64 + x² = x²+ 16x + 64
More Painful Solving:
x² - 32x = 0
x(x-32) = 0
x=0 or 32
Can't use the 0 so we trash it!
x=32
add 8 to get the hypotenuse and subtract 8 to get the short leg
Jack has $37 and saves $6.50 per week. Diane has $9 and saves $8.25 per week. Define a variable, then write and solve an equation to find out how many weeks it would take for Jack and Diane to have saved the same amount of money.
Answer:
Defining variable: x = per week
Equation: 37 + 6.5x = 9 + 8.25x
Answer: 16 weeks
Step-by-step explanation:
x = per week
Jack:
37 + 6.5x
Diane:
9 + 8.25x
Equation:
37 + 6.5x = 9 + 8.25x
6.5x - 8.25x = 9 - 37
-1.75x = -28
x = 16
The number of weeks when Jack and Diane would have the same amount of money is 16 weeks.
Equations that represents the amount of money savedTotal amount of money saved = amount the person has + (amount the person saves per week x number of weeks)
Total amount of money Jack saves = $37 + ($6.50 x w)
Total amount of money Diane saves = $9 + ($8.25 x w)
Number of weeks when they would have the same amount of moneyWhen Jack and Diane would have the same amount of money, the equations that represent the total amount of money saved for both individuals would be equal.
$37 + $6.50w = $9 + $8.25w
combine similar terms
$37 - $9 = $8.25w - $6.50
$28 = 1.75w
Divide both sides of the equation by 1.75
w = 16 weeks.
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8)Which value could be the largest whole number that could equal the
length of the missing side in the picture?
Plz help I will give brainliest
Answer:
10
Step-by-step explanation:
take 6-5=1
6+5=11
These are the parameters of a triangle. If the third side length is equal to 11 then that is impossible.
1<x<11
So the largest value for x would be 10
Hope that helps :)
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!1111 I REALLY NEED HELP I A, BEGGIN YOU GUYS!!!!!!!!!!!!!!!!!!!!!!!!!!! ILL GIVE BRAINLIEST AND EXTRA POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
4y - 2(5 - y + 4) = 4y - 2(9 - y)
= 4y + 9*(-2) - y *(-2)
= 4y - 18 + 2y {Combine like terms 4y and 2y}
= 6y - 18
6y - 18 = 6*y - 6*3
= 6(y - 3)
6y- 18 = 2 *3y - 2*9
= 2(3y -9)
2(3y - 9) and 6(y- 3 ) are equivalent to 4y - 2(5- y +4)
Others are not equivalent
As in Example 1, suppose a die is rolled. Find each probability.
-3y-5=10 Show your work please, thank you.
Answer:
-5
Step-by-step explanation:
-3y = 10 + 5
-3y = 15
y = - 5
Answer:
hi
Step-by-step explanation:
-3y-5=10
-3y=10+5
-3y=15
y=15/ -3
y= -5
hope it helps
have a nice day
four tenths plus four ninths
Answer:
38/45
Step-by-step explanation:
4/10+4/9 Simplify.
2/5*4/9 Find a common denominator (45).
2/5*9/9=18/45
4/9*5/5=20/45
18/45+20/45=38/45
Hope this helps and have a great day C:
Santo paid $16.25 to buy 5 children tickets and 1 adult ticket. Hulda paid $24.00 to buy 4 children tickets and 3 adult tickets. If both people paid the same price per ticket what was the price of an adult ticket
Answer:
The price of an adult ticket it $5
Step-by-step explanation:
To solve this, we would find the system of equations. We would set up two equations that will represent the situation.
Let c = price per children ticket
Let a = price per adult ticket
Santo:
5c + 1a = 16.25
Hulda:
4c + 3a = 24
5c + 1a = 16.25 -> a = 16.25 - 5c
4c + 3a = 24
4c + 3(16.25 - 5c) = 24
4c + 48.75 - 15c = 24
-11c + 48.75 = 24
-48.75 -48.75
-11c = -24.75
/-11 /-11
c = 2.25
5c + a = 16.25
5(2.25) + a = 16.25
11.25 + a = 16.25
-11.25 -11.25
a = 5
a = $5 , c = $2.25
Solve the equation. 4 2/5 + k = -3 2/11
Step-by-step explanation:
[tex]\tt{}4 \frac{2}{5} + k = - 3 \frac{2}{11} [/tex]
[tex]\tt{} \frac{22}{5} + k = - \frac{35}{11} [/tex]
[tex]\tt{}k = \frac{35}{11} - \frac{22}{5} [/tex]
[tex]\tt{}k = - \frac{417}{55} [/tex]
[tex]\tt{}k = - 7 \frac{32}{55} [/tex]
You are cutting pieces of fabric for a craft project. You need three pieces that measure 6 2/3 inches, 4 1/2inches, and 3 5/8inches.
What is the total length of fabric that you need ?
Answer:
Step-by-step explanation:
14/19/24
NEED HELP ASAP PLEASE HELP I NEED HELP! :/
Answer:
130 square feet
Step-by-step explanation:
Hey I'm back anyone remembers me?
Answer:
It's so sad no one answered saying that they do.
Step-by-step explanation:
PLEASE HELP ME!! A: Given that the triangles are similar, find the length of side KL
Order the angle measures from least to greatest
help please
Answer:
m<B, m<C, m<A
Step-by-step explanation:
The length of sides and angle measures correspond. This means the angle opposite to the longest side is the largest, etc. The shortest side is AC, which is the opposite of <B, making it the smallest. Then, the same logic can be applied to <C which is the middle, and <A which is the largest. Therefore, from least to greatest the angles are m<B, m<C, m<A.
5.
Put the following fractions in order from smallest to largest: 1/4, 2/3, 4/7, 1/2
Answer:
4/7, 1/4,1/2, 2/3
Step-by-step explanation:
In a geometric sequence, the seventh term exceeds the fifth term by 1,920. Find the sum of
the first eleven terms if the common ratio of the sequence is 2. (81880)