The probability that all men will be interviewed first is; 1/55
How to find probability combination?To solve this question we will make use of the probability combination formula which is;
nCr = n!/(r! * (n - r)!)
Thus, since we want to find the probability that all men will be interviewed first, then we will use the formula;
3(3!)/((11C1) * (10C1) * (9C1)) = 18/990
Simplifying that fraction gives us; 1/55
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A line passes through the point (8, -1) and has a slope of
Write an equation in slope-intercept form for this line.
The equation in slope intercept form is y = - 1 / 4 x + 1
How to find the slope intercept equation?Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = - 1 / 4
it passes through (8, -1)
Hen e,
-1 = - 1 / 4 (8) + b
-1 = - 2 + b
b = -1 + 2
b = 1
Therefore,
y = - 1 / 4 x + 1
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A tennis ball can in the shape of a right circular cylinder holds four tennis balls snugly. If the radius of a tennis ball is 3.5 cm, what percentage of the can is not occupied by tennis balls?
Answer:
about 33.3%
Step-by-step explanation:
The fraction of space not occupied will be the same as the unoccupied fraction of a cylinder of the same height and diameter as a sphere.
Volume of a cylinderThe volume of a cylinder of diameter d and height d will be ...
V = πr²h = π(d/2)²(d) = (π/4)d³
Volume of a sphereThe volume of a sphere of diameter d is ...
V = 4/3πr³ = 4/3π(d/2)³ = (π/6)d³
Unoccupied spaceThe fraction of space that is occupied is ...
occupied space = (sphere volume)/(cylinder volume)
occupied space = ((π/6)d³) / ((π/4)d³) = 4/6 = 2/3
The fraction of unoccupied space is ...
unoccupied fraction = 1 -2/3 = 1/3
unoccupied fraction ≈ 33.3%
Answer:
Putangina okay
Step-by-step explanation:
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Find the area of the triangle if b = 8 inches and h = 4 inches
The area of triangle is 16 square inches.
what is Area of Triangle?Area of triangle is half times the product of base and height.
i.e., A-= 1/2 *b *h
Given:
b= 8 inches, h= 4 inches
Now, Area of triangle
= 1/2*b*h
= 1/2 * 8 *4
=1/2*32
=16.
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Write the augmented matrix of the system of equations given below. (10 points)
−2 + 2 − = −13
−3 − + = 7
− + 3 − 2 = 0
The augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
How to determine the augmented matrix?The system of equations is given as:
-2x + 2y - z = 13
-3x - y + z = 7
-x + 3y - 2z = 0
Remove the variables x, y and z
-2 2 -1 13
-3 -1 1 7
-1 3 -2 0
Express as matrix
[tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
Hence, the augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
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Complete question
Write the augmented matrix of the system of equations given below. (10 points)
-2x + 2y - z = 13
-3x - y + z = 7
-x + 3y - 2z = 0
What method of matrixes would be used for this question? ( Inverse Matrices, Cramer's Rule, Gaussian Elimination, and Gauss-Jordan Elimination)
John had $24,500 to invest. He divided the money into three different accounts. At the end of the first year he had made a total of $1,300 in interest between the three accounts. If the first account earned 4% interest on its original amount for the year, the second account earned 5.5% interest on its original amount for the year, and the third account earned 6% interest on its original amount for the year. Also, the amount of money in the first account was 4 times the amount in the second account. How much had he originally placed in each account?
Answer:
The method of matrixes that would be used for this question is Gaussian Elimination.
Step-by-step explanation:
Gaussian Elimination is a method of solving linear equations by transforming them into upper triangular form. In this case, we want to solve for the original amount of money placed in each account, which can be represented by variables x, y, and z. We can set up the equations as follows:
4x + 5.5y + 6z = 1,300
x + y + z = 24,500
4x = y
We can then use Gaussian Elimination to solve for x, y, and z.
Find f(x-4) if f(x)=-x+2. f(x-4)
Answer:
= -x+6
Step-by-step explanation:
we can simply substitute (x-4) in x place because when we say function of x , we are basically saying when we substitute a given value in the place of x we will find a given y.so for example if we have a question f(4), we can simply plug 4 to -x +2 so we will find y or f(x) = -2.
so the answer for the above question will be f(x)= -x +6.
Translate and solve: the product of
p
and
−
2.5
is
4.8
Answer:
p = 7.3
Step-by-step explanation:
Equation: p - 2.5 = 4.8
add 2.5 to both sides:
P - 2.5 + 2.5 = 4.8 + 2.5
simplify
P = 7.3
hope that helps! :)
c. Divide 45 into three parts which are in A.P. Such that the pr oduct of last two is 300.
Order the quotients of these expressions from least to greatest.
42.6 ÷ 70
42.6 ÷ 0.7
426 ÷ 70
42.6 ÷ 0.07
Given: 1.1 1.2 1.3 f(x) = 8 +4 x-8
Write down the domain and range off.
Write down the equations of the asympotes of f
Sketch the graph of f clearly showing the intercepts with the axes and the asymptotes.
Answer:
Did you mean " f(x)=8+4^{x-8} ? " The function you entered was linear, meaning there would be no asymptote.
D: (-∞, +∞)
R: (8, +∞)
Horizontal asymptote at y=8
No vertical asymptote
Work out the reciprocal of 0.0005. Give your answer in standard form. 7 Work out the reciprocal of 0.0005 . Give your answer in standard form .
Answer:
that's all I could do. hope it helps.
good day.
A landscaping company is hired to mow the grass for several large properties. The total area of the properties combined is 1,345 acres. The rate at which one person can mow is as follows:
ŷ = 1350 – 1.2x where x is the number of hours and ŷ represents the number of acres left to mow.
How many acres will be left to mow after 20 hours of work?
How many acres will be left to mow after 100 hours of work?
How many hours will it take to mow all of the lawns? (When is ŷ = 0?)
Using the given linear function, we have that:
After 20 hours, 1326 acres will be left to mow.After 100 hours, 1230 acres will be left to mow.It will take 1125 hours to mow all the lawns.What is the linear function?
The linear function for the number of acres left to mow after x hours is given as follows:
y = 1350 - 1.2x.
After 20 hours, the number acres is given as follows:
y = 1350 - 1.2(20) = 1326.
After 100 hours, the number acres is given as follows:
y = 1350 - 1.2(100) = 1230.
The time it takes to mow all the lawns is given by:
1350 - 1.2x = 0.
1.2x = 1350
x = 1350/1.2
x = 1125 hours
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What fraction of this shape is shaded?
Time
Running
Give your answer in its simplest form.
Find the product of the given polynomials
(5r+8-6r)(4+2r-7)
A.2r^2+13r-24
B.-2r^2-24r+19
C.-2r^2+19r-24
D.2r^2+19r+24
Answer:
C
Step-by-step explanation:
(5r + 8 - 6r)(4 + 2r - 7) ← collect like terms inside each parenthesis
= (8 - r)(2r - 3)
each term in the second factor is multiplied by each term in the first factor.
8(2r - 3) - r(2r - 3) ← distribute parenthesis
= 16r - 24 - 2r² + 3r ← collect like terms
= - 2r² + 19r - 24
pls help! i need an explanation and the steps that show how it’s solved too. tysm!
Answer:
true
Step-by-step explanation:
6(6(13x-2)
36(13x-2)
468x-72
please mark brainliest :D
Answer:
True
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-7\\g(x)=13x-2\\h(x)=6x\end{cases}[/tex]
[tex]h(h(g(x)))[/tex] is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function means to substitute the function g(x) in place of the x in function h(x), then substitute this in place of the x in function h(x).
Step 1
Substitute the function g(x) in place of the x in function h(x):
[tex]\begin{aligned}h(x) & = 6x\\\implies h(g(x)) & =6(g(x))\\& = 6(13x-2)\\ & = 78x-12\\\end{aligned}[/tex]
Step 2
Now substitute the above in place of the x in function h(x):
[tex]\begin{aligned}h(x) & = 6x\\\implies h \left(h(g(x))\right) & =6(h(g(x)))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]
Therefore, the statement is true.
To carry out the composite function in one step:
[tex]\begin{aligned}h(x) &=6x\\\implies h(h(g(x))) & = 6\:(h(g(x)))\\& = 6(6(g(x)))\\& = 6( 6(13x-2))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]
Taylor earned the following scores on her first ten quizzes. What would she need to earn on the eleventh test in order to have a mean score of 87? 78, 92, 98, 87, 86, 72, 92, 81, 86, 92
A mean is an arithmetic average of a set of observations. The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The score earned by Taylor in her first 10 test are 78, 92, 98, 87, 86, 72, 92, 81, 86, 92. Also, she wants the average to be 87, therefore, we can write,
(78 + 92 + 98 + 87 + 86 + 72 + 92 + 81 + 86 + 92 + x)/11 = 87
864 + x = 957
x = 93
Hence, The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
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How many three-letter "words" can be made from 7 different letters "FGHIJKL" if...
a) Repetition of letters is allowed?
b) Repetition of letters is not allowed?
Answer:
343
Step-by-step explanation:
How many three-letter ”words” can be made from 7 letters FGHIJKL” if repetition of letters (a) is allowed? (b) is not allowed? Solution: (a) If repetition is allowed each letter can be any of the 7. So number ways is 7 × 7 × 7=73 = 343
Answer: See below
Step-by-step explanation:
Given:
The letters FGHIJKL
To find:
The number of three letter words can be formed if repetition is allowed (or) if repetition is not allowed
[tex]$$(a) If repetition is allowed:Total no of three letter words can be made$$=7_{C 1} x 7_{C 1} x 7_{C 1}=7^{3}=343$$(b) If repetitions is not allowed :Total no of three letter words can be made without repetition is $$\begin{gathered}=7_{C 1} \times 6_{C 1} \times 5_{C 1} \\=7 x 6 \times 5=210\end{gathered}$$[/tex]
Problem
A [tex]prime\left trio[/tex] is a collection of three prime numbers [tex]\{p, q, r\}[/tex] in arithmetic progression, with common difference [tex]q-p=r-q[/tex]. For example, the prime trio [tex]\{3, 5, 7\}[/tex] has common difference 2.
Prove that there is no prime trio with common difference 70.
P.S. I want actual proof.
Answer:
Proof below
Step-by-step explanation:
General outlineLemma regarding remainders of non-small primes divided by 6Check [tex]p=2[/tex] and [tex]p=3[/tex] directlyProof the rest by contradictionLemmaIf [tex]p[/tex] is prime such that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then [tex]p[/tex] divided by 6 has remainder of 1 or 5.
Case 1: p/6 has remainder 0, 2, or 4.
Then there exists some natural number [tex]n[/tex] such that either [tex]p=6n[/tex], [tex]p=6n+2[/tex], or [tex]p=6n+4[/tex]. However,
if [tex]p=6n[/tex], then [tex]p=2*3n[/tex],if [tex]p=6n+2[/tex], then [tex]p=2*(3n+1)[/tex], and if [tex]p=6n+4[/tex], then [tex]p=2*(3n+2)[/tex].By definition of divisibility, [tex]p[/tex] is divisible by 2. Since [tex]p \neq2[/tex], [tex]p[/tex] cannot be prime. This contradiction implies [tex]p[/tex] cannot have a remainder of 0, 2, or 4 when divided by 6.
Case 2: p/6 has remainder 3.
Then there exists some natural number [tex]n[/tex] such that [tex]p=6n+3[/tex]. However, if [tex]p=6n+3[/tex], then [tex]p=3*(2n+1)[/tex], so [tex]p[/tex] is divisible by 3. Since [tex]p \neq 3[/tex], [tex]p[/tex] is not prime. This contradiction implies [tex]p[/tex] cannot have a remainder of 3 when divided by 6.
Therefore, if [tex]p[/tex] is a prime number such that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then when divided by 6, [tex]p[/tex] must have a remainder of 1 or 5.
Main proof of no prime trio with common difference of 70.Check p=2
Consider [tex]p=2[/tex]. Then [tex]q=2+70=72[/tex]. However, [tex]72=2*36[/tex], so [tex]q[/tex] is not prime. Hence, [tex]p \neq2[/tex].
Check p=3
Consider [tex]p=3[/tex]. Then [tex]q=3+70=73[/tex], and [tex]r=73+70=143[/tex]. However, [tex]143=11*13[/tex], so [tex]r[/tex] is not prime. Hence, [tex]p \neq 3[/tex].
So, thus far, we've proven that if there is a prime trio with a common difference of 70, that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].
Proof of the rest of primes by contradiction
By way of contradiction, assume that there does exist some prime trio [tex]\{ p,q,r \}[/tex] such that [tex]q-p=r-q=70[/tex], and [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].
Then, by the Lemma proven earlier, when [tex]p[/tex] is divided by 6, it must have a remainder of 1 or 5.
Case 1: p/6 has remainder 5
Assume that [tex]p[/tex] has remainder 5 when divided by 6. Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+5[/tex].
[tex]q=p+70\\q=(6n+5)+70\\q=6n+75\\q=3*(2n+25)[/tex]
Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), then [tex]q[/tex] is divisible by 3.
Since [tex]p[/tex] is prime, [tex]0 < p[/tex], which implies [tex]0+70 < p+70[/tex]
Since [tex]q=p+70[/tex], [tex]70 < q[/tex], so [tex]q[/tex] cannot equal 3. Since [tex]q[/tex] is divisible by 3, but [tex]q \neq 3[/tex], [tex]q[/tex] is not prime, which is a contradiction to the existence of this prime trio.
Therefore, either [tex]p[/tex] cannot have a remainder of 5 when divided by 6, or the prime trio does not exist.
Case 2: p/6 has remainder 1
Assume that [tex]p[/tex] has remainder 1 when divided by 6. Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+1[/tex].
[tex]q=p+70\\q=(6n+1)+70\\r=q+70\\r=((6n+1)+70)+70\\r=6n+141\\r=3*(2n+47)[/tex]
Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), [tex]r[/tex] is divisible by 3.
Since [tex]q[/tex] is prime, [tex]0 < q[/tex], implying [tex]0 +70 < q+70[/tex].
Since [tex]r=q+70[/tex], then [tex]70 < r[/tex]. Therefore, [tex]r\neq 3[/tex].
Since [tex]r[/tex] is divisible by 3, but [tex]r\neq 3[/tex], [tex]r[/tex] is not prime, which is a contradiction to the existence of this prime trio (with a common difference of 70). Therefore, either [tex]p[/tex] cannot have a remainder of 1 when divided by 6, or the prime trio does not exist.
Since [tex]p[/tex] was prime, by our lemma [tex]p[/tex] must have either a remainder of 1 or 5. Since both remainder possibilities resulted in a contradiction, our contradiction assumption is false, so there cannot exist a prime trio such that their common difference is 70.
What will sue pay for 18 oranges if the cost 0.49 for 6 show the process
Answer:
[tex]\huge\boxed{\sf \$ \ 1.47}[/tex]
Step-by-step explanation:
Given that,6 oranges = $0.49
Multiply 3 to both sides
6×3 oranges = $0.49 × 3
18 oranges = $1.47
[tex]\rule[226]{225}{2}[/tex]
Divide. Write the quotient in lowest terms.
Answer:
11/12
Step-by-step explanation:
2 3/4 ÷ 3
11/4 ÷ 3
11/4 × 1/3
11/12
Answer:
Hello! The answer is 11/12.
Step-by-step explanation:
Convert improper fractions:
[tex]2\frac{3}{4} \\= \frac{11}{4}[/tex]
Change 3 to its reciprocal:
[tex]\frac{1}{3}[/tex]
Multiply:
[tex]\frac{11}{4} * \frac{1}{3} \\= 11/12[/tex]
Which linear inequality is represented by the graph?
Answer:
y>2/3+3
Step-by-step explanation:
Answer:
y<2/3x+3
Step-by-step explanation:
1. Find the slope, the slope is 2/3
2. Find the y-intercept, the y intercept is 3
3. Make an linear equation out of it, y=2/3x+3
4. Dotted or solid? Its dotted which means the answer has to be greater or less than, not equal or less than or equal or greater than
5. Test you have 2 answer choices y<2/3x+3 or y>2/3x+3, input the origin (0,0)
0<2/3(0)+3, 0<3 which is true
0>2/3(0)+3 0>3 which is false
So y<2/3x+3 is the right answer. :)
A fixed deposit receipt initiallypurchased for #1,500,000 for 4years has a maturity value of #1,300,000. What is the simple interest rate per year?
Answer:
11 3/13% per annum
Step-by-step explanation:
to find rate= 100×simple interest ÷ (principal ×time)
simple interest=total amount - principal
=1,500,000-1,300,000
=200,000
=200,000 ×100÷ 1,300,000×4
=3 11/13% per annum
Which table matches the graph below
The table that matches the graph shown is the second table.
How to depict the table?It should be noted that in the graph, there's a quadratic equation. The form is given as ax² + bx + c.
When x = 0, y = 2. When x = 1, y is a number between 3 and 4. In the second table x we have y(1) = 7/2. This is in the range.
The graph is attached.
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Barn Yard Inc. is a wholesaler that stocks engine components and tests equipment for the commercial aircraft industry. A new customer has placed an order for eight high-bypass turbine engines, which increase fuel economy. The variable cost is $1.6 million per unit, and the credit price is $1.725 million each. Credit is extended for one period, and based on historical experience, payment for about one out of every 200 such orders is never collected. The required return is 1.8% per period.Suppose that customers who don’t default become repeat customers and place the same order every period forever. Further assume that repeat customers never default.
The NPV is positive, therefore, this order can be placed.
How to calculate the NPV?The calculation of probability of default will be:
= 1 / 200 = 0.005
We use NPV formula to find out whether the order should be filled or not
NPV = -Variable cost per unit +[(1-π)(price of equipment/1+percentage of return)]
= -$1.6 million +[(1-0.005)($1.725m/1.018)]
= -$1.6m + $1.6860
= 0.0860 million
As NPV is positive this order can be placed.
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What is the inverse of
F(x) =5x/3+ 5
The inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
How to determine the inverse?The function is given as:
f(x) = 5x/3 + 5
Rewrite as:
y = 5x/3 + 5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
x - 5 = 5y/3
Multiply through by 3
3x - 15 = 5y
Divide through by 5
y = 3x/5 - 3
Express as inverse function
f-1(x) = 3x/5 - 3
Hence, the inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
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if anyone knows how to answer this do so pleass
Answer:
x = 4.08
Step-by-step explanation:
As we now, from Trigonometric Identities
that [tex]tan(\alpha )=\frac{Opposite}{Adjacent}[/tex]So for our Problem , [tex]\alpha =27[/tex] , [tex]Opposite=x[/tex] , [tex]Adjacent = 8[/tex]
by substituting , then [tex]tan(27)=\frac{x}{8}[/tex]
by multiplying both sides by 8 , then [tex]x=8tan(27)=4.0762=4.08[/tex]
Word problem involving conversion between compound units...
A business based in South Africa pays a consultant in the U.S. 1,570,000 rand per year. Assume that the conversion is 1 rand to 0.074 dollars. What is the
consultant's salary in dollars per month?
First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side o
the equation.
Ratios:
1 rand
0.074 dollars
1,570,000 rand
1 yr
0.074 dollars
1 rand
1 yr
12 mo
0
0
I need help with this math problem.
Using proportions, it is found that the consultant's salary in dollars per month is of $9,681.67.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
A business based in South Africa pays a consultant in the U.S. 1,570,000 rand per year. Considering the conversion rate, his salary in dollars per year is given as follows:
S = 1570000 x 0.074 = $116,180.
Since a year has 12 months, his salary in dollars per month is given by:
Sm = $116,180/12 = $9,681.67.
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The data below represents the relationship between the number of incidences of UFO sightings in late 1930s and early 1940s. Draw a scatter plot for the data.
Year of Incidence
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
Number of Incidences (percent)
0.9
0.8
0.8
1.3
1.4
1.2
1.7
1.8
1.6
1.5
1.5
a.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
c.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5).
b.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 1.7), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
d.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
The description of graph of the data about relationship of UFO sightings in late 1930s and early 1940s will be :A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
Given:
Year of incidence percent
1936 0.9
1937 0.8
1938 0.8
1939 1.3
1940 1.4
1941 1.2
1942 1.7
1943 1.8
1944 1.6
1945 1.5
1946 1.5
We have been given the percentages of different years. The points will be (1936,0.9) , (1937,0.8) , (1938,0.8) , (1939,1.3) , (1940,1.4) , (1941,1.2) , (1942,1.7), (1943,1.8) , (1944,1.6) , (1945,1.5) , (1946,1.5).
We have to just plot the points on the graph to find scatter plot. It is called scatter plot as the points are not in line but they are scattered.
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Sandy borrows $1250 from the bank. The loan terms is 18 months with 5% annual interest. How much interest will she pay? How much will she pay back in all?
Answer:
Step-by-step explanation:
1250x0.05x1.5=93.75
93.75 is the interest
1343.75 is the total ammount.
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe some answers are correct. Thank you!
The approximate 95 % confidence interval for p is found by the formula
p^ ± Z∝/2 √p^q^/n
The sample size n can be found by the
The formula
n= (Z∝/2)² p^q^/e²
The approximate 95 % confidence interval for p is 0.165; 0.243
This indicates 95 % confidence interval level.
A sample of 6239 nonprofits should be surveyed
Solution
Part a:
Sample Proportion p^= 84/412= 0.2038 ≅ 0.204
q^ = 1-p^= 1.0 -0.204= 0.796
The degree of confidence is 95% so z∝/2= 1.96
Putting the values
p^ ± Z∝/2 √p^q^/n
0.204 ± 1.96 √0.204(0.796)/ 412
0.204 ± 0.0389
0.1650 ; 0.2429
0.165; 0.243
The approximate 95 % confidence interval for p is 0.165; 0.243
Part B
This indicates 95 % confidence interval level.
Part C
With ± 0.01 of 0.95 Confidence interval gives range 0.94 to 0.96
For 0.96 interval Z∝/2 = 2.054
For 0.94 interval Z∝/2 = 1.8808
and error e= 0.01
For solving n the formula is
n= (Z∝/2)² p^q^/e²
and e= 0.01
Putting the values
n= 1.96²(0.204)(0.796)/ 0.01²
n= 6238.1437≅ 6238.14
A sample of 6239 nonprofits should be surveyed.
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