Answer:
432in²Step-by-step explanation:
Volume of a triangular based prism = [tex]Base\ area * height[/tex]
Base area = Area of the triangle = 1/2 * base of the triangle * height of the triangle
Since the triangular base has dimensions of 3" by 4" by 5", then it is a right angled triangle with base of 4in and height of 3in
Base Area = 1/2 * 3 * 4
Base Area = 6in²
Substituting the volume and the base area value in the formula to get the height of the prism we have;
210 = 6H
H = 210/6
H = 35in
Surface area of the triangular prism = bh + pH
b= base of the triangle = 4in
h- height of the triangle = 3in
p= perimeter of the triangle = 3+4+5 = 12in
H= height of the prism = 35in
Surface area of the triangular prism = 4(3)+12(35)
Surface area of the triangular prism = 12+420in
Surface area of the triangular prism = 432in²
What is the value of a share of Henley Inc. to an investor who requires a 11 percent
rate of return if Henley is expected to pay a fixed dividend of $1.10 for the next 3 years and
then the dividends will grow at a constant rate of 5% indefinitely
Answer:
Value of Henley Inc.'s share is $16.76
Step-by-step explanation:
The present value of the dividends over for the three years and the terminal value of the dividends would give us a fair share price that an investor would pay
Year 1 PV of dividends=$1.10/(1+11%)^1=$0.99
Year 2 PV of dividends=$1.10/(1+11%)^2=$0.89
Year 3 PV of dividends=$1.10/(1+11%)^3=$0.80
The terminal value formula=dividend*(1+g)/(r-g)
g is the dividend growth rate of 5%
r is the investor's required rate of return which is 11%
terminal value=$1.10*(1+5%)/(11%-5%)=$19.25
The terminal is discounted to present value using the discount factor of year 3
PV of terminal value =$19.25 /(1+11%)^3=$ 14.08
Total present values=$0.99+$0.89+$0.80+$14.08 =$16.76
A marketing study conducts 60 significance tests about means and proportions for several groups. Of them, 3 tests are statistically significant at the 0.05 level. The study's final report stresses only the tests with significant results, not mentioning the other 57 tests. What is misleading about this?
Answer:
hello your question lacks the required options attached is a picture of the complete question
One would expect about 5% of tests to be significant just by chance if the null hypothesis is true, and for 60 tests, this is 0.05(60) = 3 tests. This could explain why these tests are statistically significant.
Step-by-step explanation:
What is misleading about this is the study's final report because this marketing study was carried out with a level of significance of 5% (0.05) which means that if we carry the same study with varying sample data we will mostly like arrive at a conclusion against our null conclusion 5% of the time and this is not good for the the study because it is a type 1 error and has to be eliminated and it cannot be eliminated totally .
hence One would expect about 5% of tests to be significant just by chance if the null hypothesis is true, and for 60 tests, this is 0.05(60) = 3 tests. This could explain why these tests are statistically significant.
We are told that the marketing study conducts 60 tests and that 3 tests are statistically significant at the 0.05 level, in addition to this the study's final report emphasizes only the tests with significant results without mentioning the other 57 tests.
We can interpret it as follows:
By the 0.05 level, we mean that 5% of the tests are significant by chance when the null hypothesis is true.
Here 5% of the 60.
60 * 0.05 = 3
Therefore it only mentions 3 tests and does not mention the other 57 tests, which in itself is misleading because all 60 tests should be fully mentioned in the final report.
A certain company sends 35% of its overnight mail parcels via express delivery service 1 and the rest by express delivery service 2. Express delivery service 1 has a record of 3.0% of packages being delivered late and express delivery service 2 has a record of 2.0% of packages being delivered late. A package was delivered late. What is the probability that a late package was delivered by express delivery service 2
Answer:
55.32% probability that a late package was delivered by express delivery service 2
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Late delivery.
Event B: Service 2 was used.
A certain company sends 35% of its overnight mail parcels via express delivery service 1 and the rest by express delivery service 2.
100 - 35 = 65%.
So [tex]P(B) = 0.65[/tex]
Service 2 has a record of 2.0% of packages being delivered late.
This means that [tex]P(A|B) = 0.02[/tex]
Probability of a late delivery.
35% from service 1. Of those, 3% are late.
65% from service 2. Of those, 2% are late.
So
[tex]P(A) = 0.35*0.03 + 0.65*0.02 = 0.0235[/tex]
What is the probability that a late package was delivered by express delivery service 2
[tex]P(B|A) = \frac{0.65*0.02}{0.0235} = 0.5532[/tex]
55.32% probability that a late package was delivered by express delivery service 2
An object is launched from the ground. The object’s height, in feet, can be described by the quadratic function h(t) = 80t – 16t2, where t is the time, in seconds, since the object was launched. When will the object hit the ground after it is launched? Explain how you found your answer.
Answer:
The object hits the ground 5 seconds after being launched.
Step-by-step explanation:
The height of the object in t seconds after being launched is given by the following equation:
[tex]h(t) = 80t - 16t^{2}[/tex]
When will the object hit the ground after it is launched?
This is t for which h(t) = 0.
So
[tex]80t - 16t^{2} = 0[/tex]
[tex]16t(5 - t) = 0[/tex]
Then
[tex]16t = 0[/tex]
[tex]t = 0[/tex]
This is the launch point
[tex]5 - t = 0[/tex]
[tex]t = 5[/tex]
So
The object hits the ground 5 seconds after being launched.
Answer:
The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds.
Step-by-step explanation:
This is the exact answer on edg 2020
You can afford a $850 per month mortgage payment. You've found a 30 year loan at 8% interest.
a) How big of a loan can you afford?
$
Incorrect
b) How much total money will you pay the loan company?
$
Incorrect
c) How much of that money is interest?
$
Incorrect
Answer:
a) $115,840.97
b) $306,000
c) $190,159.03
Step-by-step explanation:
Loan payment calculations can be done using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the loan duration in years.
a) Loan amountThe principal amount of the loan can be found by filling in the given values and solving for P.
850 = P(0.08/12)/(1 -(1 +0.08/12)^(-12·30))
P = 850(1 -1.0066667^-360)/0.0066667 ≈ 850×136.283494
P = 115,840.97
You could afford a loan of $115,840.97.
b) Total paidThe total amount paid is the sum of 360 payments of $850 each:
360 × $850 = $306,000
You will pay $306,000 to the loan company.
c) InterestThe amount of interest is the difference between the amount paid and the amount borrowed:
$306,000 -115,840.97 = $190,159.03
$190,159.03 of the amount paid is interest.
__
Additional comment
A variety of apps, calculators, and spreadsheets can do these calculations for you. The result from one of these calculators is attached. The PV is the Present Value of the series of 360 payments of $850 each. It is the loan amount.
Please answer this correctly
Answer:
17.7
Step-by-step explanation:
62.3-7=55.3
55.3-19.9=35.4
35.4/2 = 17.7
brainliest pzz
Answer:
The value of s is 17.7mm.
Step-by-step explanation:
Given that perimeter of a shape happens when all sides are add up together. So for this question :
[tex]perimeter = 7 + 19.9 + s + s[/tex]
[tex]perimeter = 26.9 + 2s[/tex]
Let perimeter = 62.3mm,
[tex]62.3 = 26.9 + 2s[/tex]
[tex]2s = 62.3 - 26.9[/tex]
[tex]2s = 35.4[/tex]
[tex]s = 35.4 \div 2[/tex]
[tex]s = 17.7mm[/tex]
According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed. a.) State the random variable. b.) Find the probability that a person in China has blood pressure of 135 mmHg or more. c.) Find the probability that a person in China has blood pressure of 141 mmHg or less. d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg. e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not? f.) What blood pressure do 90% of all people in China have less than?
Answer:
a) Mean blood pressure for people in China.
b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.
d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg
f) 157.44mmHg
Step-by-step explanation:
When the distribution is normal, we use 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.
If X is two standard deviations from the mean or more, it is considered unusual.
In this question:
[tex]\mu = 128, \sigma = 23[/tex]
a.) State the random variable.
Mean blood pressure for people in China.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
This is 1 subtracted by the pvalue of Z when X = 135.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 128}{23}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a pvalue of 0.6179
1 - 0.6179 = 0.3821
38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
This is the pvalue of Z when X = 141.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{141 - 128}{23}[/tex]
[tex]Z = 0.565[/tex]
[tex]Z = 0.565[/tex] has a pvalue of 0.7140
71.30% probability that a person in China has blood pressure of 141 mmHg or less.
d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So
X = 125
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 128}{23}[/tex]
[tex]Z = -0.13[/tex]
[tex]Z = -0.13[/tex] has a pvalue of 0.4483
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 128}{23}[/tex]
[tex]Z = -0.35[/tex]
[tex]Z = -0.35[/tex] has a pvalue of 0.3632
0.4483 - 0.3632 = 0.0851
8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
From b), when X = 135, Z = 0.3
Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f.) What blood pressure do 90% of all people in China have less than?
This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 128}{23}[/tex]
[tex]X - 128 = 1.28*23[/tex]
[tex]X = 157.44[/tex]
So
157.44mmHg
Find g(1) if g(x) = x 2 + 1
Answer:
2
Step-by-step explanation:
g(1) = 1² + 1 = 2
Step-by-step explanation:
it is 2
Simplify the following expression. −3√84x3
Answer:
-18root7
Step-by-step explanation:
-3root 84*3
-3root4*7*3*3
-3(2*3)root7
-18root7
A man 1.75 meters tall cast a shadow 5.25 meters long. At the same time, a flagpole casts a shadow 120 meters long. How tall is the flagpole?
Answer:
40m
Step-by-step explanation:
5.25 divided by 1.75=3
120 divided by 3=40
will give brainliest
Answer:
About 8.2 cm
Step-by-step explanation:
Assuming that a is one of the legs of this right triangle, then using the Pythagorean Theorem:
[tex]a=\sqrt{15.3^2-12.9^2}\approx 8.2[/tex]
Hope this helps!
Please answer this correctly
Answer:
[tex]10.71 yd[/tex]
Step-by-step explanation:
First let's find the radius of the quarter circle.
[tex]area =\frac{1}{4} \pi {r}^{2} \\ 7.065 = \frac{1}{4} *3.14 {r}^{2} \\ \frac{7.065}{3.14} = \frac{1}{4} * \frac{3.14 {r}^{2} }{3.14} \\ 9 = {r}^{2} \\ \sqrt{9} = r \\ 3 yd= r[/tex]
Now let's find the arc length of this quarter circle.
[tex] \frac{90}{360} \times 2\pi \: r \\ \frac{1}{4} \times 2 \times 3.14 \times 3 \\ = \frac{9.42}{4} \\ = 4.71yd \\ [/tex]
Now let's find the perimeter[tex]perimeter \\ = arc \: \: length + radius + radius \\ = 4.71 + 3 + 3 \\ = 10.71yd[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Answer:
10.71 ydStep-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
The formula of an area of a quarter circle:
[tex]A=\dfrac{1}{4}\pi r^2[/tex]
We have the area of a quarter circle:
[tex]A=7.065\ yd^2[/tex]
Substitute to the formula and solve for r :
[tex]\dfrac{1}{4}\pi r^2=7.065[/tex] multiply both sides by 4
[tex]4\cdot\dfrac{1}{4}\pi r^2=7.065\cdot4\\\\\pi r^2=28.26[/tex]
Use 3.14 for π
[tex]3.14r^2=28.26[/tex] divide both sides by 3.14
[tex]\dfrac{3.14r^2}{3.14}=\dfrac{28.26}{3.14}\\\\r^2=9\to r=\sqrt9\\\\\boxed{r=3\ yd}[/tex]
The circumference of this figure consists of an arc (quarter of a cirumference of a circle) and two radiuses.
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
The formula of a quarter of a cicrumference of a circle:
[tex]L=\dfrac{1}{4}\cdot2\pi r[/tex]
Substitute
[tex]L=\dfrac{1}{4}\cdot2\pi\cdot3=1.5\pi[/tex]
Use 3.14 for π
[tex]L=1.5(3.14)=4.71\ yd[/tex]
The perimeter of a quarter circle:
[tex]P=4.71+2(3)=4.71+6=10.71\ yd[/tex]
grogg surveyed 135 beasts at his school about thier favorite house pet. the pie chart below summarizes his resuts. if 54 of the students preferred dogs, what is the value of x
A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes. Given this information, (a) what is the percent learning rate and (b) what is the total cumulative time to produce all 17 welded assemblies
Answer:
(a). 72.9%.
(b). 13.6 hr.
Step-by-step explanation:
So, we are given the following data or parameters or information which is going to assist us in solving this question/problem;
=> "A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). "
=> The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes"
So, we will be making use of the Crawford learning curve model.
T(7) + 10 = T (17) = 30 min.
T(7) = T1(7)^b = 45.
T(17 ) = T1(17)^b = 30.
(T1) = 45/7^b = 30/17^b.
45/30 = 7^b/17^b = (7/17)^b.
1.5 = (0.41177)^b.
ln 1.5 = b ln 0.41177.
0.40547 = -0.8873 b.
b = - 0.45696.
=> 2^ -0.45696 = 0.7285.
= 72.9%.
(b). T1= 45/7^ - 045696 = 109.5 hr.
V(TT)(17) = 109.5 {(17.51^ - 0.45696 – 0.51^ - 0.45696) / (1 - 0.45696)} .
V(TT) (17) = 109.5 {(4.7317 - 0.6863) / 0.54304} .
= 815.7 min .
= 13.595 hr.
Department 1 of a two department production process shows:
Units
Beginning Work in Process 9900
Ending Work in Process 49000
Total units to be accounted for 180200
How many units were transferred out to Department 2?
131200.
180200.
170300.
49000.
Answer:
131,200 units
Step-by-step explanation:
The number of units transferred to Department 2 from Department 1 is the total units to be accounted for which is 180,200 units minus the ending work in process of 49,000 units.
The logic here is that Department 1 is to account for 180,200 units ,part of which is the ending working process while the remainder which was transferred out is the difference between the two figures
units transferred to Department 2=180,200-49,000= 131,200.00 units
Find the sum of the first 20 terms of the sequence -7, -3, 1,…
Answer:
620
Step-by-step explanation:
The formula to find the sum of the first n terms of an arithmetic sequence is n(a1 + aN)/2, where n is the number of terms, aN is the last term and a1 is the first term. We do not know the last term, though, so we must find it. The equation for this is an=a1+(n−1)d, where d is the common difference and a1 is the first term, and n is the number of terms. Therefore, the last term, an is, -7+(19)4 = 69.
Finally, we plug it into the first formula, the formula to find the sum, and we get 20*(-7+69)/2, which gives us 620 as our final answer.
I am completely stumped...
Answer:
x=25[tex]\sqrt{2}[/tex]
Step-by-step explanation:
the hypotenuse is equal to a leg times the square root of 2. which means to find the leg with the hyp given. you take [tex]\frac{50}{\sqrt{2} }[/tex] which then translates to 50 root 2/2=x therefore 25[tex]\sqrt{2}[/tex]
College Students and Drinking Habits: A public health official is studying differences in drinking habits among students at two different universities. They collect a random sample of students independently from each of the two universities and ask each student how many alcoholic drinks they consumed in the previous week. Sample Statistics:
size(n) Mean (X) SD(s)
sample1 40 6.9 2.3
sample 2 49 5.7 1.9
The official conducts a two -sample t-test to determine whether these data provide significant evidence that students at University 1 drink more than students at University 2. The test statistics is t=2.64 with a P-value 0.005. Which of the following is an appropriate conclusion?
A) The samples provide significant evidence that students at University 1 drink more than students at university 2.
B) The samples do not provide statistically significant evidence.
C) We ca not use the t-test in this case because the variables (number of drinks) are likely skewed to the right at each university.
Answer:
Option A
Step-by-step explanation:
From the outlined data, the p value calculated was given as 0.005 which is way less than 0.05, thus we will reject the null hypothesis that there is no difference in drinking habit among students at two different universities. We can then conclude that the samples provide significant evidence that students at University 1 drink more than students at university 2.
1. What shape of the distribution is best modeled by a normal curve? *
Answer:
A symmetric bell shape
Step-by-step explanation:
A normal curve has a symmetrical bell shaped curve, this can be seen when a histogram is constructed with values that are normally distributed, the resulting shape is symmetrical and has a bell shape.
What three numbers add up to 57, with the first number being 12
The answer is 12, 15, 30
An airplane climbs at an angle of 2.7" from an altitude of 4500 ft to an altitude of 5600 ft. How far does the airplane travel as it climbs as
measured along the horizontal?
Answer:
23,325 ft, about 4.42 miles
Step-by-step explanation:
The geometry of the situation can be modeled by a right triangle, where the side adjacent to the 2.7° angle of climb is the horizontal distance, and the side opposite is the vertical change in altitude. That change is ...
5600 ft -4500 ft = 1100 ft
and the angle relation is ...
tan(2.7°) = opposite/adjacent = (1100 ft)/(horizontal distance)
Multiplying this equation by (horizontal distance)/tan(2.7°) gives ...
horizontal distance = (1100 ft)/tan(2.7°) ≈ 23,325 ft
Dividing this by 5280 ft/mi gives ...
horizontal distance ≈ 4.42 mi
The airplane travels about 23,325 ft, or 4.42 miles, horizontally as it climbs.
State the name of the property illustrated.
V5+(-3) =(-3) + 5
Associative
O Distributive
O Both associative and commutative
>
O Commutative
Answer:
The answer is commutative and associative.
Step-by-step explanation:
Urn has 5 white and 7 black balls. Urn has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn is selected, whereas if the outcome is tails, then a ball from urn is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?
Answer:
Suppose that a white ball is selected, the probability that the coin landed tails = (12/37) = 0.3243
Step-by-step explanation:
Complete Question
Urn A has 5 white and 7 black balls. Urn B has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?
Solution
Let the probability of that a head turns up and urn A is selcted be P(A) = (1/2)
Probability that a tail turns up and urn B is selected = P(B) = (1/2)
Probability that a white ball is picked = P(W)
The probability that a white ball is picked given that the coin toss gives a head and urn A is selected = P(W|A) = (5/12)
The probability that a white ball is picked given that the coin toss gives a tail and urn B is selected = P(W|B) = (3/15) = (1/5)
We now require the probability that the coin lands on a tail and urn B is selected given that a white ball is picked, P(B|W)
Note that the conditional probability P(X|Y) is expressed mathematically as
P(X|Y) = P(X n Y) ÷ P(Y)
And P(X n Y) = P(X|Y) × P(Y)
Hence, the required probability
P(B|W) = P(B n W) ÷ P(W)
Although, we do not have the probabilities P(B n W) and P(W), we can calculate them
P(B n W) = P(W n B) = P(W|B) × P(B) = (1/5) × (1/2) = (1/10)
P(W) = P(W n A) + P(W n B) (Since the events A and B are mutually exclusive)
P(W n A) = P(W|A) × P(A) = (5/12) × (1/2) = (5/24)
P(W n B) = (1/10)
P(W) = (5/24) + (1/10) = (37/120)
P(B|W) = P(B n W) ÷ P(W) = (1/10) ÷ (37/120) = (12/37) = 0.3243
Hope this Helps!!!
A street is 149m long is covered in snow. City workers are using a snowplow to clear the street. The snowplow has tires that are 1.7m in diameter. How many times does a tire have to turn in traveling the length of the street
Answer:
Approximately 28 times
Step-by-step explanation:
The tires are circular in shape.
We first need to find the circumference of the tire and then divide the length of the road by that circumference.
The circumference of a circle is given as:
C = πD
where D = diameter
The diameter of the tires is 1.7 m. Its circumference is therefore:
C = π * 1.7 = 5.34 m
Therefore, the number of times that the tire has to turn in traveling the length of the street is:
149 / 5.34 = 27.9 ≅ 28
In western Kansas, the summer density of hailstorms is estimated at about 1.5 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 9 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 9-square-mile tract.(a) Explain why a Poisson probability distribution is appropriate for r.Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent.What is λ for the 9-square-mile tract of land? Round λ to the nearest tenth (b) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r≥ 4 | r ≥ 2). (Use 4 decimal places.)(c) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r < 6 | r ≥ 3). (Use 4 decimal places.)
Answer:
Step-by-step explanation:
(a) Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent
(b) The required [tex]\lambda[/tex] = 1.7 * 10/5 = 3.4
(c) P(r ≥ 4 | r ≥ 2)
= P(r ≥ 4)/P(r ≥ 2)
= {1 - P(r < 4)}/{1 - P(r < 2)}
For Poisson distribution, P(X = x)
[tex]= \frac{e^{- \lambda} \lambda ^x}{x !}[/tex]
Thus, P(r < 4) = P(r = 0) + P(r = 1) + P(r = 2) + P(r = 3)
= 0.5584
and P(r < 2) = P(r = 0) + P(r = 1) = 0.1468
Thus, P(r ≥ 4 | r ≥ 2) = (1 - 0.5584)/(1 - 0.1468)
= 0.5177
(d) P(r < 6 | r ≥ 3)
= P(3 ≤ r < 6)/P(r ≥ 3)
P(3 ≤ r < 6) = P(r = 3) + P(r = 4) + P(r = 5) = 0.5308
P(r ≥ 3) = 1 - {P(r = 0) + P(r = 1) + P(r = 2)}
= 0.6603
Thus, P(r < 6 | r ≥ 3) = 0.5308/0.6603 = 0.8309
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $113,100?
Answer:
850
Step-by-step explanation:
Current profit per year = $ 20
Number of subscribers = 3000
For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.
So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)
Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:
Total profit = Number of subscribers x Profit per each subscriber
Total profit = (3000 + x)(20 + 0.01x)
We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:
Using quadratic formula, we can solve this equation as:
x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.
Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725
I NEED HELP ASAP PLSSSSSSSS HELPPPPPP I BEG OF YOU
In 20 minutes, John can wrap____
small boxes and Hank can wrap____
small boxes. So, Hank can wrap_____
more small boxes in 20 minutes than John can.
1/4 of x is 6 please help solve This
Answer:
x = 24
Step-by-step explanation:
Of means multiply and is means equals
1/4 * x = 6
Multiply each side by 4
1/4*4 x = 6*4
x = 24
matatila female drink 1/2 litres of milk every day during this month of September how many litres is this all together
Answer:
15 litres
Step-by-step explanation:
(1/2 litre/day)(30 days) = 15 litres
__
Multiply rate by time to get quantity.
Determine where f(x) is discontinuous. Justify your answer.
f(x)=x^2+x-2/x-1
Answer:x=1
Step-by-step explanation:
Given
[tex]F(x)=\dfrac{x^2+x-2}{x-1}[/tex]
F(x) will be discontinuous at x=1 because value of f(x) is undefined at that point.
F(x) is defined for all values of x except at x=1