Answer:
60 students
Step-by-step explanation:
The confidence interval of a proportion is given by:
[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]
Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.
If the confidence interval is from 0.584 to 0.816, then:
[tex]p=\frac{0.584+0.816}{2}=0.7 \\0.816-0.584=2*(1.96*\sqrt{\frac{p*(1-p)}{n}}) \\0.116=1.96*\sqrt{\frac{0.7*(1-0.7)}{n}}\\n=16.8966^2*(0.7*0.3)\\n=60\ students[/tex]
60 students were in the sample.
Final answer:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher used a random sample and calculated a 95 percent confidence interval. Using the formula for the confidence interval for proportions, we can determine that the teacher selected approximately 223 students for the survey.
Explanation:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher selected a random sample of students and surveyed them one at a time, asking them if they regularly recycle plastic bottles. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816).
To find out how many students were in the sample selected by the teacher, we need to use the formula for the confidence interval for proportions:
n = (Z^2 * p * (1-p)) / (E^2)
Where:
n is the sample size,
Z is the Z-score corresponding to the desired level of confidence (in this case, 95 percent),
p is the estimated proportion of students who recycle plastic bottles (we can use the midpoint of the confidence interval, which is (0.584 + 0.816) / 2 = 0.7),
E is the margin of error (in this case, half the width of the confidence interval, which is (0.816 - 0.584) / 2 = 0.116).
Plugging in the values, we get:
n = (1.96^2 * 0.7 * (1-0.7)) / (0.116^2)
n = 2.992 / 0.013456
n ≈ 222.38
Since the sample size must be a whole number, we round up to the nearest whole number.
Therefore, the teacher selected approximately 223 students for the survey.
A machining company needs to manufacture more than 20 fixtures in a day. The company uses five identical machines to make the fixtures. If each machine produces x fixtures, which inequality represents this situation?
A.
5x > 20
B.
5x < 20
C.
5x > 20 + 5
D.
5x < 20 + 5
(I NEED AN EXPLANATION ON HOW YOU GOT THE ANSWER
PLEASE AND thank you)
Answer:
A
Step-by-step explanation:
We know that each machine makes x fixtures and we have 5 machines. So we need to use multiplication:
5 * x = 5x
The above expression indicates how many fixtures the 5 machines can make. We want the total to be more than 20, so we need to use the greater than sign: >.
5x > 20
The answer is A.
Answer:
A. 5x > 20
Step-by-step explanation:
Total production by 5 machines: 5x
5x > 20
A mouse has made holes in opposite corners of a rectangular kitchen. The width of the kitchen is 2 meters, and the distance between the mouse's holes is 6 meters. What is the length of the kitchen? If necessary, round to the nearest tenth.
Answer:
5.7 meters
Step-by-step explanation:
The Pythagorean theorem can be used to find the second leg (b) of a triangle with diagonal (c) 6 meters and first leg (a) 2 meters.
c^2 = a^2 + b^2
6^2 = 2^2 +b^2
b^2 = 36 -4 = 32
b = √32 ≈ 5.7 . . . . meters
The kitchen is about 5.7 meters long.
The length of the kitchen, where a mouse has made holes in opposite corners with a diagonal distance of 6 meters across a width of 2 meters, is approximately 5.7 meters.
To find the length of the kitchen where a mouse has made holes in opposite corners, forming a diagonal of 6 meters across a width of 2 meters, we can use the Pythagorean theorem.
1. Understanding the problem:
- The width of the kitchen (distance between the holes along one side) is w = 2 meters.
- The diagonal distance (distance between the holes) is d = 6 meters.
2. Applying the Pythagorean theorem:
- In a rectangle, the diagonal d , the width w, and the length l form a right triangle.
- The Pythagorean theorem states [tex]\( d^2 = w^2 + l^2 \)[/tex].
3. Substitute the given values:
[tex]\[ 6^2 = 2^2 + l^2 \][/tex]
[tex]\[ 36 = 4 + l^2 \][/tex]
4. Solve for [tex]\( l^2 \)[/tex] :
[tex]\[ l^2 = 36 - 4 \][/tex]
[tex]\[ l^2 = 32 \][/tex]
5. Find l (length of the kitchen):
[tex]\[ l = \sqrt{32} \][/tex]
[tex]\[ l \approx 5.7 \text{ meters (rounded to the nearest tenth)} \][/tex]
Therefore, the length of the kitchen is approximately [tex]\( \boxed{5.7} \)[/tex]meters.
The length of the kitchen, rounded to the nearest tenth, where a mouse has made holes in opposite corners with a diagonal distance of 6 meters across a width of 2 meters, is [tex]\( \boxed{5.7} \)[/tex] meters. This solution utilizes the Pythagorean theorem to determine the missing dimension of the rectangle based on given measurements.
Michael invests $2000 in an annuity that offers an interest rate of 4%
compounded quarterly for 5 years. What is the value of Michael's investment
after 5 years?
The future value of Michael's investment after 5 years is $44,038.01.
The future value of an annuity can be determined using the following formula:
[tex]FV=PV(1+r/n)^{n}[/tex]
FV = future value
PV = present value
r = annual interest rate
n = number of periods interest held
We can also compute the future value using an online finance calculator as follows:
N (# of periods) = 20 quarters (5 years x 4)
I/Y (Interest per year) = 4%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
FV = $2,440.38
Total Interest = $440.38
Thus, the value of Michael's investment after 5 years is $2,440.38.
There are ten kids in a class. When any two meet, they shake their hands.Before the class starts, how many handshakes are there?
Answer: 45
Step-by-step explanation:
Ok, Kid 1 can meet other 9 kids, so we have 9 handshaks.
Kid 2 can also meet other 9 kids, but he already meet kid 1, so we are not counting that handshake, this means that now we have 8 handshakes.
Kid 3 can also meet 9 kids, but we already counted the handshake with kid 1 and kid 2, so here we have other 7 andshakes.
And so on, so we have a total of:
9 + 8 + 7 + 6 + 5 + 4 +3 + 2 + 1 = 45 handshakes in total.
Answer:
45 handshakes
Step-by-step explanation:
Reggie works for an accounting firm. He earns $18,000 per year plus 8% of all money he saves his clients. How much money must he save his clients to earn $2,000 per month
Answer:
He has to save his clients $75,000.
Step-by-step explanation:
$2,000 per month is 2*2,000 = $24,000
He eanrs a fixed rate of $18,000 per year. So in bonuses, he has to earn 24,000 - 18,000 = $6,000.
His bonuses are 8% of the money he saves his clients.
So this 8% must be $6,000. How much his 100%?
0.08 - $6,000
1 - $x
[tex]0.08x = 6000[/tex]
[tex]x = \frac{6000}{0.08}[/tex]
[tex]x = 75000[/tex]
He has to save his clients $75,000.
Which graph is an example of a cubic function?
Answer:
B graph 2
Step-by-step explanation:
Jon and Jim painted a fence Jon painted a quarter of the fence and Jim painted five twelfths of the fence how much of the fence did they paint
Answer: jon & jim painted 8/12 of the fence
Step-by-step explanation: first, convert. one quarter is equal to 1/4, & 1/4 of 12 (since Jim painted 5/12) is 3/12. now we know that Jon painted 3/12 of the fence & that Jim painted 5/12 of the fence (we already knew this, didn't we?). all you have to do now is add: 3/12 + 5/12 = 8/12. so, jon & jim painted 8/12 of the fence.
- hope this helps
:)
Jon and Jim painted a total of two thirds of the fence together. We found this by converting 1/4 to 3/12 and then adding it to 5/12, which gave us 8/12, or 2/3.
Explanation:The question involves understanding the addition of fractions. Jon painted a quarter of the fence which is equal to 1/4 and Jim painted five twelfths of the fence which is equal to 5/12.
To find out how much of the fence they painted together, we simply add these fractions. The lowest common multiple of 4 and 12 is 12. So, we convert 1/4 to 3/12 to make the denominators the same. Now, we have 3/12 (Jon's part) and 5/12 (Jim's part). The total part of the fence they painted together is 3/12 + 5/12 = 8/12 = 2/3.
So, Jon and Jim painted two thirds of the fence together.
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Two new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes. Drug A is to be given to 22 mice, drug B is to be given to another 22 mice, and the remaining 16 mice are to be used as controls. How many ways can the assignment of treatments to mice be made? (A single assignment involves specifying the treatment for each mouse—whether drug A, drug B, or no drug.)
Answer:
The total number of ways of assignment is 314,790,828,599,338,321,972,833,000.
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
In this case we need to determine the number of ways in which the drugs are assigned to each mouse.
It is provided that new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes.
Drug A is to be given to 22 mice.
Compute the number of ways to assign drug A to 22 mice as follows:
[tex]{60\choose 22}=\frac{60!}{22!(60-22)!}\\\\=\frac{60!}{22!\times 38!}\\\\=14154280149473100[/tex]
Now the remaining number if mice are: 60 - 22 = 38.
Compute the number of ways to assign drug B to 22 mice as follows:
[tex]{38\choose 22}=\frac{38!}{38!(38-22)!}\\\\=\frac{38!}{22!\times 16!}\\\\=22239974430[/tex]
Now the remaining number if mice are: 38 - 22 = 16.
Compute the number of ways to assign no drug to 16 mice as follows:
[tex]{16\choose 16}=\frac{16!}{16!(16-16)!}\\\\=1[/tex]
The total number of ways of assignment is:
[tex]N = {60\choose 22}\times {38\choose 22}\times {16\choose 16}\\\\=14154280149473100\times 22239974430\times 1\\\\=314,790,828,599,338,321,972,833,000[/tex]
Thus, the total number of ways of assignment is 314,790,828,599,338,321,972,833,000.
Final answer:
The number of ways to assign treatments to the mice can be found using combinations. The calculation involves selecting a certain number of mice from the total pool and dividing it by the number of ways to arrange those mice within the group. The total number of ways to assign treatments to the mice is approximately 10,682,514,784,300.
Explanation:
When assigning treatments to the mice, we have 22 mice for drug A, 22 mice for drug B, and 16 mice for the control group. The assignment of treatments can be thought of as distributing the mice among these three groups.
To find the number of ways this can be done, we can use the concept of combinations. We can think of selecting 22 mice for drug A from the total pool of 60 mice, and then selecting 22 mice for drug B from the remaining pool. The remaining 16 mice automatically go to the control group.
The number of ways to select 22 mice out of 60 is denoted as C(60,22) and is calculated using the formula C(n, r) = n! / (r!(n-r)!). Therefore, the number of ways to assign treatments to the mice is C(60,22) multiplied by the number of ways to assign the remaining 22 mice to drug B, which is C(38,22).
Using a calculator or software, we can calculate C(60,22) as approximately 95,023,780 and C(38,22) as approximately 112,385.
Therefore, the total number of ways to assign treatments to the mice is approximately 95,023,780 * 112,385 = 10,682,514,784,300.
Sarah spent $15.75 at the movies on a ticket and snacks. Then she earned $40 babysitting, and bought a book for $9.50. Sarah has $34.75 left. How much money did she start with?
Answer:
Sarah spent $15.75 at the movies on a ticket and snacks.
She earned $40 babysitting.
She bought a book for $9.50.
She has $34.75 left.
=> The amount of money she started with:
A = 34.75 + 9.5 - 40 + 15.75 = 20$
Hope this helps!
:)
PLEASE HELP
Jan writes an e-mail to a co-worker asking her to provide information about the budget for the upcoming year. Which type of routine message is she using?
A: informational
B: appreciation
C: request
D: goodwill
Suppose a team of researchers is studying the half-life of a drug in the human body (i.e. how long it takes for 1 2 of the drug to be broken down by the body). They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people. They find the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16. Find the 95% confidence interval for population half-life based on this sample. What is the length of this interval?
Answer:
95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].
Step-by-step explanation:
We are given that the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16.
They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average half-life = 7.4 hours
[tex]\sigma[/tex] = population standard deviation = [tex]\sqrt{0.16}[/tex] = 0.4 hour
n = sample of people = 50
[tex]\mu[/tex] = population mean
Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] <
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]7.4-1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] , [tex]7.4+1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] ]
= [7.29 , 7.51]
Therefore, 95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].
The length of this interval is = 7.51 - 7.29 = 0.22
What is the coefficient of x2 in this trinomial?
(x+2) (x+3)
A. 2
B. 0
C. 1
D. 3
Answer:1
Step-by-step explanation:
(x+2)(x+3)
x^2+3x+2x+6
x^2+5x+6
Therefore the coefficient of x^2 is 1
Answer:
1
Step-by-step explanation:
(x+2) (x+3)
FOIL
x^2 + 3x+2x+6
x^2 +5x+6
The coefficient of x^2 is 1
Two sides of a triangle are 7 and 11 the length of the third side x is expressed
Answer:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ... No; The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ANSWER: No; 9.
What is a solution to the equation (x-2)(x+5)=18
Answer:
x= -7 x=3
Step-by-step explanation:
(x-2)(x+5)=18
FOIL
x^2 +5x -2x-10 = 18
Subtract 18 from each side
x^2 +5x -2x-10-18 = 18-18
x^2 +3x -28 =0
Factor
What 2 numbers multiply to -28 and add to 3
7*-4 = -28
7-4 =3
(x+7) (x-3) =0
Using the zero product property
x+7 =0 x-3 =0
x= -7 x=3
What percent of 2.5 is 0.2?
Answer:
8
Step-by-step explanation:
0.2:2.5*100 =
( 0.2*100):2.5 =
20:2.5 = 8
Sam purchases five goldfish and an aquarium with a rectangular
base. The aquarium measures twenty-four inches long, eight inches
wide, and nine inches tall. Sam fills the aquarium. How many cubic
inches of water are in Sam's aquarium?
Select one
0
1.449 cubic inches
1.728 cubic inches
0
2.112 cubic inches
0
920 cubic nches
0
Answer:
1728 cubic in
Step-by-step explanation:
24 in x 8 in x 9 in = 1728 cubic in
Final answer:
The volume of water in Sam's aquarium is 1,728 cubic inches, calculated by multiplying the length (24 inches), width (8 inches), and height (9 inches) of the aquarium.
Explanation:
The volume of Sam's aquarium can be calculated using the formula for the volume of a rectangular prism, which is length × width × height. The dimensions given are 24 inches long, 8 inches wide, and 9 inches tall.
To find out how many cubic inches of water the aquarium can hold, we multiply these dimensions:
× 24 inches (length)
× 8 inches (width)
× 9 inches (height)
Thus, the volume of the aquarium is:
24 inches × 8 inches × 9 inches = 1,728 cubic inches
Using intervals of width 10, how many intervals
are needed for this graph to be drawn correctly?
O 5 or fewer
O between 6 and 10
O between 11 and 19
0 25 or more
DONE
saaled
Answer:D
Step-by-step explanation:
The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 20% of people with home-based computers have access to on-line services. Suppose that 15 people with home-based computers were randomly and independently sampled. What is the probability that at least 1 of those sampled have access to on-line services at home?
Answer:
Probability that at least 1 of those sampled have access to on-line services at home is 0.9648.
Step-by-step explanation:
We are given that current estimates suggest that 20% of people with home-based computers have access to on-line services.
Suppose that 15 people with home-based computers were randomly and independently sampled.
The above situation can be represented through binomial distribution;
[tex]P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 15 people
r = number of success = at least one
p = probability of success which in our question is % of people
who have access to on-line services at home, i.e.; p = 20%
Let X = Number of people who have access to on-line services at home
So, X ~ Binom(n = 15, p = 0.20)
Now, probability that at least 1 of those sampled have access to on-line services at home is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1- \binom{15}{0}\times 0.20^{0} \times (1-0.20)^{15-0}[/tex]
= [tex]1- (1\times 1 \times 0.80^{15})[/tex]
= 1 - 0.0352 = 0.9648
Hence, the required probability is 0.9648.
The following problem can be solved using the binomial distribution.
Binomial distributionA common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
There is 96.481% chance that at least 1 of those sampled have access to online services at home.
Given to usThe online access computer service industry is growing at an extraordinary rate. Current estimates suggest that 20% of people with home-based computers have access to online services.Suppose that 15 people with home-based computers were randomly and independently sampled. SolutionFor the values,As given, 20% of people with home-based computers have access to online services. therefore, the probability of a person having access to online services is also 20%. thus, p = 20% = 0.2We know that for any event the sum of all probability is 1. therefore, the probability of a person not having access to online services is (1-p). thus, q = (1-0.20) = 0.80It is already stated in the sentence that the sample is been done on 15 people. therefore, the sample size is n = 15.We need the probability that at least 1 of those sampled have access to online services at home, therefore, x ≥ 1.ProbabilitySubstituting the values in a binomial distribution,
[tex]P(x\geq 1) = 1- P(0)[/tex]
[tex]P(x\geq 1) = 1-\ ^{15}C_0\times [0.20^0]\times [0.80^{(15-10)}]\\\\ P(x\geq 1)=1-\ 0.032\\\\ P(x\geq 1) = 0.96481\\\\ [/tex]
Hence, there is 96.481% chance that at least 1 of those sampled have access to online services at home.
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EB. Which statement does
Statements
Rowena is proving that AD
the represent in her proof?
A
Reasons
1. given
1. AB
ED: BC
DC
2. given
2. 2 CAD * ZCEB
3. AB = ED; BC = DC
3. def. of
segments
4. AB + BC = AC
ED + DC
4. segment addition
postulate
11
11
substitution property
ED + DC
Ο ΔACDe ΔECB
AACD = AEFD
Ο ΔΑΕΒ = ΔEED
6. AC = CE
6. substitution property
7. AC = CE
7. def. of
segments
AAFB
AECB
202C
8. reflexive property
9. ASA
Answer:it’s ACD=ECB
Step-by-step explanation:
The correct option is Segment Addition Postulate.
What is similarity theorem?Similarity of triangles. The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.
Here, we have,
The segment addition postulate states that where there are two points on a line A and C and a third point B can only be located on the line segment AB if and only if the the distances between point A and point B as well as the distance between point B and point C satisfy the equation AB + BC = AC
Therefore, given that in the figure, the point B is in between point A and point C on segment AC then AB + BC
Similarly, AD = AE + ED.
The correct option is Segment Addition Postulate.
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complete question:
BE || CD 1. Given 2. ∠A ≅ ∠A 2. Reflexive Property 3. ∠ACD ≅ ∠ABE 3. Corresponding angles formed by parallel lines and a transversal are ≅. 4. ∠ADC ≅ ∠AEB 4. Corresponding angles formed by parallel lines and a transversal are ≅. 5. ΔABE ∼ ΔACD 5. AA Similarity Postulate 6. AC AB = AD AE 6. Definition of Similar Triangles 7. AC = AB + BC, AD = AE + ED 7. ??? 8. AB + BC AB = AE + ED AE 8. Substitution 9. AB AB + BC AB = AE AE + ED AE 9. Addition 10. BC AB = ED AE 10. Subtraction Fill in the missing reason for the proof. A) Transitive Property B) Subtraction Property C) SSS Similarity Theorem D) Segment Addition Postulate
A wall hanging is made of a circular piece of wood 24 inches in diameter. Angela wants to use wire to hang the wall hanging from a nail at point N. The wire will be tangent to the circle and attached at points P and Q. What is the total length of wire needed if the distance from the top of the circle (point R) to the nail is 10 inches? Round to the nearest inch.
Answer:
18 inches
OQ2 + PQ2 = OP2
PQ2 = OP2 - OQ2
= (OR + PR) SQUARE - OQ2
= (24/2 + 10 ) SQUARE - 24/12Square
= 22square - 12square
PQ = Root 340
= 18 inches...
The answer is 18 inches.
What is the total length of wire needed if the distance from the top of the circle (point R) to the nail is 10 inches?OQ2 + PQ2 = OP2
PQ2 = OP2 - OQ2
= (OR + PR) SQUARE - OQ2
= (24/2 + 10 ) SQUARE - 24/12Square
= 22² - 12²
PQ = √ 340
= 18 inches.
What is Problem Solving?
Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.
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Help. Best answer = Brainiest
Answer:
10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation
By substituting -2 in for all the X's you have (-2)^2+2(-2)-10. After ths is simplified you have 4+(-4)-10. -4+4 =0 and 0-10= -10
What is the surface area of the cone? 17cm 10cm use 3.14 for pie
If anyone could answer this for me I would very much appreciate it
Answer:
a3 = 45
Step-by-step explanation:
a1 = 20
an = a(n-1) *3/2 where n is the term number
a2 = a(2-1) *3/2
a1 *3/2
We know a1 = 20
a2 = 20*3/2 = 30
a3 = a(3-1) *3/2
= a2 *3/2
We know a2 = 30
= 30*3/2 = 45
Suppose a simple random sample of size nequals1000 is obtained from a population whose size is Nequals1 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.44 . Complete parts (a) through (c) below. (a) Describe the sampling distribution of ModifyingAbove p with caret. A. Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0005 B. Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002 C. Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0157 (b) What is the probability of obtaining xequals460 or more individuals with the characteristic? P(xgreater than or equals460)equals nothing (Round to four decimal places as needed.) (c) What is the probability of obtaining xequals410 or fewer individuals with the characteristic? P(xless than or equals410)equals nothing (Round to four decimal places as needed.)
Question:
Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 1,000,000 and whose population proportion with a specified characteristic is p = 0.44 . Complete parts (a) through (c) below.
(a) Describe the sampling distribution of ModifyingAbove p with caret.
A.)Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002
B.)Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0005
C.)Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0157
(b) What is the probability of obtaining xequals480 or more individuals with the characteristic?
P(xgreater than or equals480)equals
nothing (Round to four decimal places as needed.)
(c) What is the probability of obtaining xequals410 or fewer individuals with the characteristic?
P(xless than or equals410)equals
nothing (Round to four decimal places as needed.)
Answer:
a) Option C.
b) 0.1021
c) 0.0280
Step-by-step explanation:
Given:
Sample size, n = 1000
p' = 0.44
a) up' = p' = 0.44
The sampling distribution will be:
[tex] \sigma _p' = \sqrt{\frac{p' (1 - p')}{n}}[/tex]
[tex] = \sqrt{\frac{0.44 (1 - 0.44)}{1000}}[/tex]
[tex] = \sqrt{\frac{0.44*0.56}{1000}} = 0.0157 [/tex]
Option C is correct.
b) The probability when x ≥ 460
[tex] P' = \frac{x}{n} = \frac{460}{1000} = 0.46[/tex]
p'(P ≥ 0.46)
[tex] 1 - P = \frac{(p' - up')}{\sigma _p'} < \frac{0.46 - 0.44}{0.0157} [/tex]
[tex] = 1-P( Z < 1.27) [/tex]
From the normal distribution table
NORMSDIST(1.27) = 0.898
1-0.8979 = 0.1021
Therefore, the probability = 0.102
c) x ≤ 410
[tex] P' = \frac{x}{n} = \frac{410}{1000} = 0.41[/tex]
p'(P ≤ 0.41)
[tex] P = \frac{(p' - up')}{\sigma _p'} < \frac{0.41 - 0.44}{0.0157} [/tex]
[tex] = P( Z < - 1.9108) [/tex]
From the normal distribution table
NORMSDIST(-1.9108) = 0.0280
Probability = 0.0280
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium population continues to grow for a while, but then stops growing and begins to decline. The size of the population at time t (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2. Find the growth rates at t equals 0 hours commat=0 hours, t equals 4 hours commat=4 hours, and t equals 8 hours.t=8 hours.
Answer:
The growth rates at t = 0 is 8⁵.
The growth rates at t = 4 is 0.
The growth rates at t = 8 is -8⁵.
Step-by-step explanation:
The expression representing the size of the population at time t hours is:
[tex]b(t)=8^{6}+8^{5}t-8^{4}t^{2}[/tex]
Differentiate b (t) with respect to t to determine the growth rate as follows:
[tex]\frac{db(t)}{dt}=\frac{d}{dt} (8^{6}+8^{5}t-8^{4}t^{2})[/tex]
[tex]=0+8^{5} (1)-8^{4}(2t)\\=8^{4}(8-2t)[/tex]
The growth rate is:
R (t) = 8⁴ (8 - 2t)
Compute the growth rates at t = 0 as follows:
[tex]R (0) = 8^{4} (8 - 2\times 0)\\=8^{4}\times 8\\=8^{5}[/tex]
Thus, the growth rates at t = 0 is 8⁵.
Compute the growth rates at t = 4 as follows:
[tex]R (4) = 8^{4} (8 - 2\times 4)\\=8^{4}\times 0\\=0[/tex]
Thus, the growth rates at t = 4 is 0.
Compute the growth rates at t = 8 as follows:
[tex]R (4) = 8^{4} (8 - 2\times 8)\\=8^{4}\times (-8)\\=-8^{5}[/tex]
Thus, the growth rates at t = 8 is -8⁵.
The growth rates at t=0 hours, t=4 hours, and t=8 hours can be calculated using the given equation.
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium Population Growth in Bacteria continues to grow for a while, but then stops growing and begins to decline.
The size of the population at time t (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2.
Find the growth rates at t equals 0 hours commat=0 hours, t equals 4 hours commat=4 hours, and t equals 8 hours.t=8 hours.
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The probable question may be:
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium population continues to grow for a while, but then stops growing and begins to decline. The size of the population at time t (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2. Find the growth rates when
t equals 0 hours commat=0 hours,
t equals 4 hours commat=4 hours,
t equals 8 hours.t=8 hours.
Carl bought a DVD that cost $24.00 plus 8.25% sales tax. How much did Carl pay for this DVD in dollars and cents?
Answer: Carl paid $25.98 for this DVD in dollars and cents.
Step-by-step explanation:
The original cost of the DVD was $24.00. If a sales tax of 8.25% was charged, it means that the original cost of the DVD would increase by 8.25%.
The value in dollar and cents of an 8.25% increment(sales tax) would be
8.25/100 × 24 = 0.0825 × 24
= $1.98
Therefore, the amount that Carl would pay for this DVD in dollars and cents is
24 + 1.98 = $25.98
4.
a) Name the highlighted arc and determine if it is a major arc, minor arc, or semicircle.
b) Find the measure of the highlighted arc.
Answer: 4.067units.
Step-by-step explanation:
(a) The highlighted arc is the major arc. That is , it covers from G to I.
(b) The length of the major arc will be
πr0°/180 where the angle substended at the center by the highlighted arc is
360° - 127° ( the angles if the arc not highlighted)
= 233°
Though this radius of the circle was not given so we are going to find the arc length without necessarily defining the radius.
Arc length = π × r × 233°
---------------
180
= 3.142 × r × 233°
------------------
180
= 4.067runits.
The arc that is highlighted is the major arc
The measure of the highlighted arc is 4.067runits.
How to solve for the arcThe formula for the length of major arc
πr0°/180
Without highlioghts the angles are
360° - 127°
= 233 degrees
Formula for lenght of arc Arc length = π × r × 233° / 180
= = 3.142 × r × 233° / 180
= 4.067runits.
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4 2/5 divided by 1 1/3
Answer:
3.3
Step-by-step explanation:
[tex] = > \frac{4 \frac{2}{5} }{1 \frac{1}{3} } \\ \\ = > \frac{ \frac{20 + 2}{5} }{ \frac{3 + 1}{3} } \\ \\ = > \frac{ \frac{22}{5} }{ \frac{4}{3} } \\ \\ = > \frac{22}{5} \times \frac{3}{4} \\ \\ = > \frac{11}{5} \times \frac{3}{2} \\ \\ = > \frac{33}{10} \\ \\ = > 3.3[/tex]
Callie is comparing the costs of two options for her college education.
Option A: Complete the first two years of schooling at a community college and then transfer to a university.
Option B: Complete all four years of schooling at the university.
Community College Financial Analysis
Costs per Year
Financial Aid Package per Year
Tuition & Fees
Scholarships & Grants
$2,900
$800
Room & Board
$1,250
University Financial Analysis
Costs per Year
Financial Aid Package per Year
Tuition & Fees
Scholarships & Grants
$9,500
$10,000
Room & Board
Work-Study
$11,500
$2,000
Which statement about the cost of the options is true?
She would save $1,000 by choosing option B.
She would save $5,650 by choosing option A.
She would save $11,200 by choosing option B.
She would save $11,300 by choosing option A.
Answer:
Callie's comparison of two options for college education
The true statement is:
She would save $11,300 by choosing option A.
Step-by-step explanation:
Cost Analyses:
Option A: Community College + University Total Expenses
Tuition & Fees $5,800 ($2,900 x 2) + $19,000 ($9,500 x 2) = $24,800
Scholarships ($1,600) ($800 x 2) + ($20,000) ($10,000 x 2)=($21,600)
Room & Board $2,500 ($1,250 x 2) + $23,000 ($11,500 x 2) = $25,500
Work-Study + ($4,000) ($2,000 x 2) = ($4,000)
Total Cost $6,700 + $18,000 = $24,700
Option B: 4 years' University
Tuition & Fees $38,000 ($9,500 x 4)
Scholarships ($40,000) ($10,000 x 4)
Room & Board $46,000 ($11,500 x 4)
Work-Study ($8,000) ($2,000 x 4)
Total Cost $36,000
Difference between the two options = $11,300 ($36,000 - $24,700
Answer: She would save $11,300 by choosing option A
Step-by-step explanation:
Community College Financial Analysis:
Tuition and fees = 2900
Scholarship and grant = 800
Rooms and board = 1250
University Financial Analysis:
Tuition and fees = 9500
Scholarship and grant = 10000
Rooms and board = 11500
Work study - 2000
Option A :
First two years at college :2 × (2900 + 1250 - 800)
2 × (3350) = $6700
2 years at university : 2 × (9500 +11500 - 2000 - 10000)
2 × 9000 = 18000
Option A total = $(18,000 + 6700) = $24,700
Option B :
4 years at university : 4 × (9500 +11500 - 2000 - 10000)
4 × 9000 = $ 36000
She would be saving $(36,000 - 24,700) = $11,300 by choosing option A
1. To evaluate the effect of a treatment, a sample (n = 16) is obtained from a population with a mean of µ = 30 and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 31.3 with a sample standard deviation of s = 3. Are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?
Answer:
We conclude that the treatment does not has a significant effect.
Step-by-step explanation:
We are given that to evaluate the effect of a treatment, a sample (n = 16) is obtained from a population with a mean of µ = 30 and a treatment is administered to the individuals in the sample.
After treatment, the sample mean is found to be M = 31.3 with a sample standard deviation of s = 3.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30 {means that the treatment does not has a significant effect}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 30 {means that the treatment has a significant effect}
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{M-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_n_-_1[/tex]
where, M = sample mean = 31.3
s = sample standard deviation = 3
n = sample size = 16
So, test statistics = [tex]\frac{31.3-30}{\frac{3}{\sqrt{16}}}[/tex] ~ [tex]t_1_5[/tex]
= 1.733
The value of t test statistics is 1.733.
Now, at 0.05 significance level the t table gives critical values of -2.131 and 2.131 at 15 degree of freedom for two-tailed test. Since our test statistics lie within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the treatment does not has a significant effect.
The data are not sufficient to conclude that the treatment has a significant effect. The calculated test statistic is less than the critical value for a two-tailed test with a significance level of α = 0.05, hence we fail to reject the null hypothesis.
Explanation:To determine if the treatment had a significant effect, we must conduct a hypothesis test. This falls under the field of statistics.
First, let's state our null hypothesis (H₀) and alternative hypothesis (H₁). H₀: µ = 30 (i.e., the treatment has no effect) and H₁: µ ≠ 30 (treatment has an effect).
Next, we find the standard error (SE) of the mean, which is s/√n = 3/√16 = 0.75.
We then calculate our test statistic, which is the difference between M (sample mean) and µ (population mean) divided by the SE: (31.3 - 30) / 0.75 = approximately 1.73.
Given a two-tailed test with a significance level of α = 0.05, the critical z-values would be -1.96 and +1.96. As our calculated test statistic falls between these two critical values (-1.96reject the null hypothesis.
Consequently, the data are not sufficient to conclude that the treatment has a significant effect.
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