Answer:
15.87% probability that 48 or more from this sample were insured by the FHA
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]p = 0.28, n = 150[/tex]
So
[tex]\mu = E(X) = np = 150*0.28 = 42[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.28*0.72} = 5.5[/tex]
What is the probability that 48 or more from this sample were insured by the FHA?
Using continuity correction, this is [tex]P(X \geq 48 - 0.5) = P(X \geq 47.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 47.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{47.5 - 42}{5.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
1 - 0.8413 = 0.1587
15.87% probability that 48 or more from this sample were insured by the FHA
Angie bought 44 pencils and paid 66.00. She sold the pencils at a rate of 2 for $3.50
calculate her profit.
Answer:
Profit of $11.00
Step-by-step explanation:
44÷2=22
22×$3.50=$77
$77.00-$66.00=$11.00/profit
In an agricultural study, the average amount of corn yield is normally distributed with a mean of 189.3 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 180 bushels of corn per acre?
Answer:
About 786 would be expected to yield more than 180 bushels of corn per acre
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 189.3, \sigma = 23.5[/tex]
Proportion of acres with more than 180 bushels of corn per acre:
This is 1 subtracted by the pvalue of Z when X = 180. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 189.3}{23.5}[/tex]
[tex]Z = -0.4[/tex]
[tex]Z = -0.4[/tex] has a pvalue of 0.3446.
1 - 0.3446 = 0.6554
Out of 1200:
0.6554*1200 = 786.48
About 786 would be expected to yield more than 180 bushels of corn per acre
What is the answer to the series of equations
Answer:
[tex]71\frac{2}{3}[/tex]
Step-by-step explanation:
1st equation:
3 cups = 3x
3x = 75
x = 25, cup = 25
2d equation
25 + lemon* lemons= 25 + y²
25 + y² = 89
y²= 89 - 25
y²= 64
y = 8, lemon = 8
3d equation
3 circles = 3c
3c = 44
c = 44/3 = 14 2/3
4th equation
25 + 32 + 14 2/3 = 71 2/3
Answer: 427/3
Step-by-step explanation:
The 3 cups added together is equal to 75, therefore, we can establish that each cup is equal to 25.
Cup=25
With the second equation, we plug in 25 for the cup and solve for the circles.
25+ Ο×Ο= 89
Ο×Ο=64
Circle=8
For the third equation, we can find the amount for the ovals if we divide by 3.
Oval= 44/3
Now that we know the value of each picture, we can solve the fourth equation.
25+8×(44/3)=?
25+(352/3)=?
(75/3)+(352/3)=427/3
Keri deposits $100 in an account every year on the same day. She makes
no other deposits or withdrawals. The account earns an annual rate of 4%
compounded annually. How much interest does it earn on the 2nd year?*
Answer:
$20.32 or $12.16 depending on the question below!
Step-by-step explanation:
$320.32
It's a bit ambiguous, the current Principal is $100 plus 2 $ additions of $100 or the current Principal is $0 plaus 2 years of $100 contributions. In this case it's $212.16
The value of 49% of 86 should be just a little over 43.
True
- False
Answer:
False
Step-by-step explanation:
50% of 86 would be 43, 49% would be a bit lower then that.
Answer:
False, Its 42.14
Step-by-step explanation:
What is 49 percent of 86: 49 percent *86 = (49:100)*86 = (49*86):100 = 4214:100 = 42.14. Now we have: 49 percent of 86 = 42.14
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 − x 2 . What are the dimensions of such a rectangle with the greatest possible area?
Answer:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width =
Height =
Width =√10 and Height [tex]= \frac{10}{4}[/tex]
Step-by-step explanation:
Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)
are (h,k) and (-h,k).
Hence, the area of the rectangle will be (h + h) × k
Therefore, A = h²k ..... (2).
Now, from equation (1) we can write k = 5 - h² ....... (3)
So, from equation (2), we can write
[tex]A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}[/tex]
For, A to be greatest ,
[tex]\frac{dA}{dh} =0 = 10h-4h^{3}[/tex]
⇒ [tex]h[10-4h^{2} ]=0[/tex]
⇒ [tex]h^{2} =\frac{10}{4} {Since, h≠ 0}[/tex]
⇒ [tex]h = ±\frac{\sqrt{10} }{2}[/tex]
Therefore, from equation (3), k = 5 - h²
⇒ [tex]k=5-\frac{10}{4} =\frac{10}{4}[/tex]
Hence,
Width = 2h =√10 and
Height = [tex]k =\frac{10}{4}.[/tex]
Solve these equations. Thanks.
Answer:
1. 3.572 x 10^(-1)
2. 3.108 x 10^(6)
3. 5.31881533 x 10^(-6)
4. 4.18676122 x 10^(-1)
Hope this helps
A county is in the shape of a rectangle that is 60 miles by 70 miles and has a population of 50,000. What is the average number of people living on each square mile of the county? Round your answer to the nearest whole number.
192
10
14
12
Answer:
The correct answer is:
12
Step-by-step explanation:
Length of county = 70 miles
breadth of county = 60 miles
area of county (rectangle) = Length × Breadth = 60 × 70 = 4,200 sqaure miles
population of county = 50,000
Therefore, to find the average number of people living on each square mile of the county, we will assume that the whole population is equally distributed in the county, hence the population per square mile is calculated thus:
Total area = 4,200 square miles
total population = 50,000
This means that:
4,200 square miles contains 50,000 people
4,200 sq. miles = 50,000 people
∴ 1 sq. mile = 50,000 ÷ 4,200 = 11.9 = 12 people (to the nearest whole number)
therefore number of people living per square mile = 12
Answer:
12
Step-by-step explanation:
Got it right on the test! <3
You bought a sachet water machine from Indie Inc. The cost of the machine was GH¢35,000. At that time, you asked for the payment to be deferred, and a contract was written. Under the contract, you could delay paying for the sachet water machine if you purchased the material for packaging the water from Indie Inc. You will then pay for the machine in a lump sum at the end of 2 years, with interest at a rate of 2% per quarter-year. According to the contract, if you ceased buying the packaging material from Indie Inc. at any time prior to 2 years, the full payment due at the end of 2 years would automatically become due. One year later, you decided to buy the packaging material elsewhere and stopped buying from Indie Inc., whereupon Indie Inc., per the contract terms, asked for the full payment that is due at the end of 2 years to be paid immediately. You were unhappy about this, so Indie Inc. offered as an alternative to accept the GH¢35,000 with interest at 10% per semiannual period for the 12 months that you had been buying the packaging material from Indie Inc. Which of the alternatives should you accept? Explain.
Answer: The answer has been attached below
Step-by-step explanation:
From the attached calculation, the amount payable in the first payment is cheaper than the amount payable for the second payment.
If both alternatives were presented to me by Indie incorporation after purchasing a sachet water machine from them, I'll choose the first method of payment.
Kindly check the attached file for the calculation which prompted the decision taken.
The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1600 and the standard deviation is $100. What is the approximate percentage of buyers who paid more than $1900? What is the approximate percentage of buyers who paid less than $1400?What is the approximate percentage of buyers who paid between $1400 and $1600?What is the approximate percentage of buyers who paid between $1500 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1900?
Answer:
(a) 0.14%
(b) 2.28%
(c) 48%
(d) 68%
(e) 34%
(f) 50%
Step-by-step explanation:
Let X be a random variable representing the prices paid for a particular model of HD television.
It is provided that X follows a normal distribution with mean, μ = $1600 and standard deviation, σ = $100.
(a)
Compute the probability of buyers who paid more than $1900 as follows:
[tex]P(X>1900)=P(\frac{X-\mu}{\sigma}>\frac{1900-1600}{100})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid more than $1900 is 0.14%.
(b)
Compute the probability of buyers who paid less than $1400 as follows:
[tex]P(X<1400)=P(\frac{X-\mu}{\sigma}<\frac{1400-1600}{100})[/tex]
[tex]=P(Z<-2)\\=1-P(Z<2)\\=1-0.97725\\=0.02275\\\approx 0.0228[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid less than $1400 is 2.28%.
(c)
Compute the probability of buyers who paid between $1400 and $1600 as follows:
[tex]P(1400<X<1600)=P(\frac{1400-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1600-1600}{100})[/tex]
[tex]=P(-2<Z<0)\\=P(Z<0)-P(Z<-2)\\=0.50-0.0228\\=0.4772\\\approx 0.48[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1400 and $1600 is 48%.
(d)
Compute the probability of buyers who paid between $1500 and $1700 as follows:
[tex]P(1500<X<1700)=P(\frac{1500-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})[/tex]
[tex]=P(-1<Z<1)\\=P(Z<1)-P(Z<-1)\\=0.84134-0.15866\\=0.68268\\\approx 0.68[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1500 and $1700 is 68%.
(e)
Compute the probability of buyers who paid between $1600 and $1700 as follows:
[tex]P(1600<X<1700)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})[/tex]
[tex]=P(0<Z<1)\\=P(Z<1)-P(Z<0)\\=0.84134-0.50\\=0.34134\\\approx 0.34[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1600 and $1700 is 34%.
(f)
Compute the probability of buyers who paid between $1600 and $1900 as follows:
[tex]P(1600<X<1900)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1900-1600}{100})[/tex]
[tex]=P(0<Z<3)\\=P(Z<3)-P(Z<0)\\=0.99865-0.50\\=0.49865\\\approx 0.50[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1600 and $1900 is 50%.
Answer:
Step-by-step explanation:
Select the number line that matches the expression |8-1|
Answer:
B
Step-by-step explanation:
We start at point 8 and go to point 1
Given the functions f(x) = 6x + 11 and g(x) = x^2 + 6, which of the following functions represents f[g(x)] correctly?
Answer:
6x^2+47
Step-by-step explanation:
You simple have to "plug" g(x) into f(x) for x.
f(x)=6x+11
f(g(x))=6(x^2+6)+11
f(g(x))=6x^2+36+11
f(g(x))=6x^2+47
Consider reflection of JKL what line of reflection maps point L to point L at (-2,3)
It’s the y-axis for the first answer and the other one it’s a reflection of JKL what line of reflection maps point L to point L at (-2,3).
What is the line of reflection?When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed-line. The fixed-line is called the line of reflection.
What reflection will produce an image of RST?RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.
Learn more about the line of reflection at
https://brainly.com/question/8496129
#SPJ2
The driver of a car traveling along a straight, flat road applies the brakes, which produce a constant acceleration ofspace a (t )thin space equals space minus 20 space f t divided by s e c squared. If the car is traveling at 80 feet per second when the driver applies the brakes, how far does the car travel between the time the brakes are applied and the time the car comes to a stop
Answer:
x = 160 ft
Step-by-step explanation:
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is given by:
[tex] v_{f}^{2} = v_{0}^{2} + 2ax [/tex]
Where:
[tex]v_{f}[/tex]: is the final speed of the car = 0 (since it stops)
[tex]v_{0}[/tex]: is the initial speed of the car = 80 ft/s
a: is the acceleration of the car = -20 ft/s²
x: is the distance recorred by the car
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is:
[tex] x = \frac{v_{f}^{2} - v_{0}^{2}}{2a} = \frac{0 - (80 ft/s)^{2}}{2*(-20 ft/s^{2})} = 160 ft [/tex]
Therefore, the car travels 160 ft between the time the brakes are applied and the time the car comes to a stop.
I hope it helps you!
y = -x2 + 6x - 5 whats
the axis of symmetry.
Answer:
x=3
Step-by-step explanation:
graphed on desmos.com
You earn $15 every week .at this rate , how much will you earn in 5 weeks
Answer:
If you earn $15 every week then you will have earned $75 by the end of 5 weeks.
Step-by-step explanation:
If $15 is 1 week,
and you need to find how much money after 5 weeks,
you multiply by the same number on both sides
1 = 15
1*5 = 15*5
5 = 75
So after 5 weeks you get $75
How many terms are in the expression below?
3x + 4x - 3
In the expression, there are 3 terms.
3x and 4x are like terms because the variables are identical.
Also, we have a constant term which is -3.
Please answer this correctly
Answer: The first one
Step-by-step explanation:
If you take a look at the light pink squares, you can count three on the top and three on the bottom. Therefore, when looking at it from the top, you’ll see the first one.
I hope you found my answer helpful! If you did, give it a five-star rating and a thanks! I would really appreciate it!
Even a brainliest if you feel like it! ;)
Answer:
the first image will b da answer
Step-by-step explanation:
happy to help ya :)
Which point on the number line represents the product of 4 and -2.
Answer:
A: -8
Step-by-step explanation:
4 * -2 is -8, and A is on that point.
Answer:
its a I literally just did it
Step-by-step explanation:
What is another way to write the equation StartFraction 7 over 8 EndFraction x + three-fourths = negative 6?
Answer:
1/8 x + 3/4 = -6
Step-by-step explanation:
If you want to solve this as well:
1/8 x = -5 3/4
x = -42
Answer:
B
Step-by-step explanation:
Find the value of x.
Answer:
x=4
Step-by-step explanation:
Answer:
√21 or 4.58
Step-by-step explanation:
area of triangle can be found in different ways, and they are equal as:
1/2*x*(7+3)= 1/2*√(x²+3³)*√(x²+7²)
(10x)²= (x²+3³)*(x²+7²)
x²= y
100y= (y+9)(y+49)y²+58y+9*49-100y=0y²-42y +441=0y=21x²=21
x=√21 = 4.58
What’s the correct answer for this question?
Answer:
C.°
Step-by-step explanation:
According to the theorem , "Angles in the same segment are congruent"
So
m<D = 55°
One-fourth If a scale factor of 1/4 is used to make a reduction, what is the base of the reduced triangle? ______ cm
Answer:
8 cm
Step-by-step explanation:
1/4 of 32 cm is (32/4) cm = 8 cm
The base of the reduced triangle is 8 cm.
Answer:
8 cm
Step-by-step explanation:
I just got it right on edge :) ur welcome
In 2011, the industries with the most complaints to the Better Business Bureau were banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships (USA Today, April 16, 2012), The results for a sample of 200 complaints are contained in the DATAfile named B8B. Click on the datafile logo to reference the data. a. Construct a frequency distribution for the number of complaints by industry, Category Bank 26 Cable Car Cell 42 60 Collection 28 Total b. Using α = .01, conduct a hypothesis test to determine if the probability of a complaint is the same for the five industries. The test-statistic is p-value- What is your conclusion?c. Which industry has the most complaints?
Answer:
Step-by-step explanation:
Hello!
The variable of study is
X: number of complaints per industry (Categorized: Bank, Cable, Car, Cell, Collection
Considering this is a categorical variable, and the hypothesis is that all categories have the same probability, you have to apply a Chi-Square Goodness to Fit test.
Observed frequencies per category
1) Bank: 26
2) Cable: 44
3) Car: 42
4) Cell: 60
5) Collection: 28
Total= 200
Statistical hypotheses:
H₀: P₁=P₂=P₃=P₄=P₅=1/5
H₁: At least one of the proposed proportions is different.
α: 0.01
[tex]X^2= sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex]
For this test the formula for the expected frequencies is:
[tex]E_i= n * P_i[/tex]
So the expected values for each category is:
[tex]E_1= n * P_1= 200*1/5= 40[/tex]
[tex]E_2= n * P_2= 200*1/5= 40[/tex]
[tex]E_3= n * P_3= 200*1/5= 40[/tex]
[tex]E_4= n * P_4= 200*1/5= 40[/tex]
[tex]E_5= n * P_5= 200*1/5= 40[/tex]
[tex]X^2_{H_0}= \frac{(26-40)^2}{40} +\frac{(44-40)^2}{40} +\frac{(42-40)^2}{40} +\frac{(60-40)^2}{40} +\frac{(28-40)^2}{40} = 11.5[/tex]
This test is one tailed and so is its p-value, under a Chi-square with 4 degrees of freedom p-value: 0.021484.
The p-value is less than the significance level so the decision is to reject the null hypothesis.
c. The industry with most complaints is the cellular phone providers
I hope this helps!
What’s the correct answer for this?
Answer
D.
Explanation
mIH = 44
mIJ = 46
mJK = 77
ADDING THEM ALL TO FIND THE MEASURE OF m<HOK
<HOK = 44+46+77
<HOK = 167°
Explain your answer choice with sentences or record your explanation.
Which expression is equivalent to n + n - 0.18n?
A. 1.18n
B. 1.82n
C. n – 0.18
D. 2n – 0.82
Answer:
B. 1.82n
Step-by-step explanation:
Expression given: n + n - 0.18n
Adding n+n gives '2n'
then subtracting 0.18n from 2n gives= 1.82 n
Therefore,
n + n - 0.18n=0.18n
Find the exact coordinates of point E.
Answer:
is the correct answer.
Step-by-step explanation:
We are given that co-ordinates of D is (-3,8) and F is (5,2).
For finding a point E on the line segment DF dividing it in a ratio 4:1, we can use segment formula.
[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]
Where [tex](x,y)[/tex] is the co-ordinate of the point which
divides the line segment joining the points and in the ratio m:n.
As per the given values
[tex]x_{1} = -3\\x_{2} = 5\\y_{1} = 8\\y_{2} = 2[/tex]
Putting the given values in above formula :
x-co-ordinate of F:
[tex]x = \dfrac{5 \times 4 + (-3 \times 1)}{4+1}\\\Rightarrow \dfrac{17}{5}\\\Rightarrow x = 3.4[/tex]
y-co-ordinate of F:
[tex]y = \dfrac{4 \times 2 + 1 \times 8}{4+1}\\\Rightarrow \dfrac{16}{5}\\\Rightarrow y = 3.2[/tex]
So, answer is [tex]E(3.4,3.2)[/tex].
Please include work! :)
Answer:
m = 13.
Step-by-step explanation:
Recall that adding logarithmic equations, (ex: log a + log b) is the same as log (a·b). Therefore:
log 12 + log 5 = log (4m + 8)
log (12·5) = log (4m + 8)
log (60) = log (4m + 8) **Ignore 'Log' to solve for 'm'
60 = 4m + 8 **Subtract both sides by 8
52 = 4m **Divide both sides by 4
m = 13.
The telephone company charges $1.35 fir the first 3 minutes of a phone call and $0.35 for each additional minute. i talk on the phone from 4:17 pm till 4:31 pm. what will the phone call cost?
Answer:
$5.20
Step-by-step explanation:
Talked on the phone for 14 minutes .
14 - 3 = 11
11 x .35 = 3.85
3.85 + 1.35 = 5.2
Answer:
The answer is $5.20
Step-by-step explanation:
HOPE THIS HELPSSSSSS:)))))
Two dataset in descending order (8,x,4,1) and (9,y,5,2). If the median is equal, find (y-x)
Answer:
y-x = -1
Step-by-step explanation:
Given the two dataset;
(8,x,4,1) and (9,y,5,2)
Since they are already arranged in descending order;
The median for the first dataset is;
M1 = (x+4)/2
The median for the second dataset is;
M2 = (y+5)/2
The median is equal;
M1 = M2
(x+4)/2 = (y+5)/2
x+4 = y+5
Collecting the like terms;
4-5 = y-x
y-x = -1