Answers
Answer:
80-119 ⇒ 5
Because
80-99 ⇒ 3
100-119 ⇒ 2
So 2+3 = 5
Answer:
80-119: 5
Step-by-step explanation:
If you just added up, you can find all the values.
Related Questions
Check all of the points that are solutions to the system of inequalities.
x + y<4+3
y > 4
Someone please help ASAP
Answers
Answer:
B and E
Step-by-step explanation:
A: 3 + 6 < 4 + 3 and 6 > 4
9 < 7 is false so A is not the answer.
B: 1 + 5 < 4 + 3 and 5 > 4
6 < 7 and 5 > 4 are true so B is an answer.
C: 2 + (-1) < 4 + 3 and -1 > 4
-1 > 4 is false so C is not an answer.
D: 1 + 1 < 4 + 3 and 1 > 4
1 > 4 is false so D is not an answer.
E: 2 + 8 > 4 + 3 and 8 > 4
10 > 7 and 8 > 4 are both true so E is an answer.
F: -1 + 8 > 4 + 3 and 8 > 4
7 > 7 is false so F is not an answer.
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2.5 minutes. (a) Find the probability that a customer has to wait more than 4 minutes. (Round your answer to three decimal places.) (b) Find the probability that a customer is served within the first minute. (Round your answer to three decimal places.) (c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use
Answers
Answer:
a) 0.202 = 20.2% probability that a customer has to wait more than 4 minutes.
b) 0.33 = 33% probability that a customer is served within the first minute.
c) 11.5 minutes.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this question:
[tex]m = 2.5, \mu = \frac{1}{2.5} = 0.4[/tex]
(a) Find the probability that a customer has to wait more than 4 minutes.
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
[tex]P(X > 4) = e^{-0.4*4} = 0.202[/tex]
0.202 = 20.2% probability that a customer has to wait more than 4 minutes.
(b) Find the probability that a customer is served within the first minute.
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
[tex]P(X \leq 1) = 1 - e^{-0.4*1} = 0.33[/tex]
0.33 = 33% probability that a customer is served within the first minute.
(c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use
We have to find x for which:
[tex]P(X > x) = 0.01[/tex]
So
[tex]P(X > x) = e^{-0.4x}[/tex]
Then
[tex]e^{-0.4x} = 0.01[/tex]
[tex]\ln{e^{-0.4x}} = \ln{0.01}[/tex]
[tex]-0.4x = \ln{0.01}[/tex]
[tex]x = -\frac{\ln{0.01}}{0.4}[/tex]
[tex]x = 11.5[/tex]
So 11.5 minutes.
If the price of a product is p (dollars), the number of units demanded is given by the equation q-pe-3p
(a) Find the price elasticity of demand by using the differentials definition of elasticity. Fully simplify your answer.
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
Answers
Answer:
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
Step-by-step explanation:
Given that:
the number of units demanded [tex]q = pe^{-3p}[/tex]
Taking differentiations ; we have,
[tex]\dfrac{dq}{dp}=e^{-3p}+p(-3e^{-3p})[/tex]
[tex]\dfrac{dq}{dp}=(1-3)e^{-3p}[/tex]
Now; the price elasticity of demand using the differentials definition of elasticity is:
[tex]E(p) = \dfrac{dq}{dp}*\dfrac{p}{q}[/tex]
[tex]E(p) =[(1-3)e^{-3p}]*[\dfrac{p}{pe^{-3p}}][/tex]
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
The estimate of the percentage change in price is :
[tex]=\dfrac{2.10-2.00}{2.00}*100 \%[/tex]
= 5%
From (a)
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
Now at p = $2.00
E(2) = 1 - 3 (2.00)
E(2) = 1 - 6
E(2) = -5
The percentage change in q = -5 × 5%
The percentage change in q = -25%
Thus; we can conclude that the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
aisha places 6 counters into this place value chart
list all the possible numbers she could represent
Answers
Answer:
All the possible numbers she could represent using the counters are:
0.6 | 1.5 | 2.4 | 3.3 | 4.2 | 5.1 | 6
Step-by-step explanation:
Please refer to the attached diagram for this question.
We are asked to list all the possible numbers she could represent using the counters.
The possible numbers are:
When there is 0 counter in the "ones" place and 6 counters in the "tenths" place.
0.6
When there is 1 counter in the "ones" place and 5 counters in the "tenths" place.
1.5
When there are 2 counters in the "ones" place and 4 counters in the "tenths" place.
2.4
When there are 3 counters in the "ones" place and 3 counters in the "tenths" place.
3.3
When there are 4 counters in the "ones" place and 2 counters in the "tenths" place.
4.2
When there are 5 counters in the "ones" place and 1 counter in the "tenths" place.
5.1
When there are 6 counters in the "ones" place and 0 counter in the "tenths" place.
6
Therefore, all the possible numbers she could represent using the counters are:
0.6 | 1.5 | 2.4 | 3.3 | 4.2 | 5.1 | 6
There are five faculty members in a certain academic department. These individuals have 4, 6, 7, 10, and 15 years of teaching experience. Two of these individuals are randomly selected to serve on a personnel review committee. What is the probability that the chosen representatives have a total of at least 16 years of teaching experience
Answers
Answer:
3/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given 5 individuals with 4, 6, 7, 10, and 15 years of teaching experience.
Since two of these 5 individuals are randomly selected to serve on a personnel review committee, total possible outcome = 5C2 (randomly selecting 2 personnel out of 5 )
5C2 = [tex]\frac{5!}{(5-2)!2!}[/tex]
[tex]= \frac{5!}{3!2!}\\ = \frac{5*4*3!}{3!*2} \\= 10\ possible\ selections\ can\ be\ done[/tex]
To get the probability that the chosen representatives have a total of at least 16 years of teaching experience, first we need to find the two values that will give a sum of years greater that or equal to 16 years. The possible combination are as shown;
4+15 = 19years (first reps)
6+10 = 16years (second reps)
6+15 = 21years (third reps)
7+10 = 17 years (fourth reps)
7+15 = 22 years (fifth reps)
10+15 = 25 years (sixth reps)
This shows that there are 6 possible ways to choose the representatives that have a total of at least 16 years of teaching experience
Total outcome = 10
expected outcome = 6
Probability that the chosen representatives have a total of at least 16 years of teaching experience = [tex]\frac{6}{10} = \frac{3}{5}[/tex]
If you decreased the volume of a sample of gas by a factor of three while maintaining a constant pressure, how would the absolute temperature of the gas be affected? 1. It would remain the same 2. It would decrease 3. It would increase threefold
Answers
Answer:
correct option: 2 -> It would decrease.
Step-by-step explanation:
If the amount of gas is the same, the following relation needs to be constant:
[tex]Pressure * Volume / Temperature[/tex]
So, If the pressure is constant, the volume and the temperature are directly proportional (if one increases, the other also increases).
Then, an decrease of 3 times in the volume would cause an decrease of 3 times in the temperature.
So the correct option is 2.: It would decrease.
If a company's cost function is C(x) = 15x + 100. What price should the company sell each unit, x, to break even after selling 10 units.
Answers
One kind of plant has only blue flowers and white flowers. According to a genetic model, the offsprings of a certain cross have a 0.75 chance to be blue-flowering, and a 0.25 chance to be white-flowering, independently of one another. Two hundred seeds of such a cross are raised, and 142 turn out to be blue-flowering. We are interested in determining whether the data are consistent with the model or, alternatively, the chance to be blue-flowering is smaller than 0.75. For this question, find the appropriate test statistic.
Answers
Answer:
There is not enough evidence to support the claim that the chance of this cross to be blue-flowering is significantly smaller than 0.75 (P-value = 0.11).
Test statistic z=-1.225.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the chance to be blue-flowering is significantly smaller than 0.75.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.75\\\\H_a:\pi<0.75[/tex]
The significance level is 0.05.
The sample has a size n=200.
The sample proportion is p=0.71.
[tex]p=X/n=142/200=0.71[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.75*0.25}{200}}\\\\\\ \sigma_p=\sqrt{0.000938}=0.031[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.71-0.75+0.5/200}{0.031}=\dfrac{-0.038}{0.031}=-1.225[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.225)=0.11[/tex]
As the P-value (0.11) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the chance to be blue-flowering is significantly smaller than 0.75.
Who is correct? Explain. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B. Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B. Both are correct because both AC and BC are opposite ∠B. Neither is correct because neither AC nor BC is opposite ∠B.
Answers
Answer:
A. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B.
Step-by-step explanation:
edge2021
The description of Thomas is correct. AC is opposite ∠B and BC is adjacent to ∠B.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Hypotenuse of a right angled triangle is the longest side.
Opposite side with respect to an angle is the side opposite to that angle.
Adjacent side with respect to an angle is the side which is adjacent to the angle.
Given is a triangle ABC.
Here C is the right angle.
Then the side opposite to the right angle is the hypotenuse.
So AB is the hypotenuse.
Now we are describing the sides in relation to the ∠B.
Side opposite to ∠B is AC, which is the opposite side.
Side adjacent to ∠B is BC, which is the adjacent side.
This is the description of Thomas.
Hence Thomas is correct about describing the sides in relation to ∠B.
Learn more about Right angled Triangles here :
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The complete question is as follows :
Two students describe the sides of right triangle ABC in relation to ∠B. Triangle A B C is shown. Angle A C B is a right angle. Tomas : AB is the hypotenuse. AC is the opposite side. BC is the adjacent side. Iliana : AB is the hypotenuse. BC is the opposite side. AC is the adjacent side. Who is correct? Explain. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B. Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B. Both are correct because both AC and BC are opposite ∠B. Neither is correct because neither AC nor BC is opposite ∠B.
Which has the lowest value: 1/20, 1/80, or 1/100?
Answers
Answer:
1/100
Step-by-step explanation:
Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100
[tex]{f}^{4} = - 1[/tex]
O True
O False
?
Answers
Answer:
False.
Step-by-step explanation:
This statement is false, for any value of F because the power function with an even exponent is always positive or 0.
Safety by-laws state that for a ladder to be stable, the angle the base of the ladder makes with the ground should be between 70° and 80'. A safety inspector at a construction site notices a painter on a 10-m ladder that is leaning against a wall. The base of the ladder is 1.5 m away from the wall. Does the inspector have cause to be concerned? Explain.
Answers
Cos(angle) = adjacent/hypotenuse
Cos(angle) = 1.5/10
Angle = arccos(1.5/10)
Angle = 81.37 degrees
Although the angle is close, it is over the 80 degrees, so the inspector should be concerned.
on monday, it took 3 builders 5 1/2 hours to build a wall. an identical wall needs to be built on tuesday and 5 builders are available. each builder is paid £8.90 for each hour they work. work out how much each builder will be paid for the work completed on tuesday
Answers
Answer:
£29.37
Step-by-step explanation:
→ First step is to find the amount of hours it takes for 5 builders
[tex]\frac{3*\frac{11}{2} }{5} =\frac{33}{2} /5=\frac{33}{2} *\frac{1}{5} =\frac{33}{10} =3\frac{3}{10}[/tex]
→ Now we know how long 5 builder takes we need to multiply the hourly rate by their time worked
[tex]3\frac{3}{10} *8.90=\frac{33}{10} *8.90=3.3*8.90 = 29.37[/tex]
Answer:
Step-by-step explanation:
When the number of builders is increased, the hours worked will be reduced.
So, this is inverse proportion.
Number of hours worked by 5 builders = [tex]\frac{3*\frac{11}{2}}{5}\\\\[/tex]
[tex]=3*\frac{11}{2}*\frac{1}{5}\\\\=\frac{33}{10}\\\\=3\frac{1}{10}[/tex]
Amount received by each builder= 33/10 * 8.90
= £ 29.37
2/3 divided by 3/4 and for answer of 8/9. Which statement is true
Answers
Answer: true
Step-by-step explanation: reciprocal of 3/4 is 4/3
Hence, 2/3 × 4/3 = 8/9
Boys to girls ratio is 2 to 3. There are 18 girls. What is total number of students
Answers
[tex]\frac{2}{3}=\frac{boys}{18}[/tex]
3*boys=2*18
3*boys=36
boys=12
12+18=30
total number of students: 30
Answer:
30 students
Step-by-step explanation:
2:3 = x:18
X = number of boys
[tex]\frac{2}{3} = \frac{x}{18}[/tex]
multiply 18 by both sides
18 × [tex]\frac{2}{3} = X[/tex]
X = 18 × [tex]\frac{2}{3} = 12[/tex]
18 + 12 = 30
A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
(a) How much wire should be used for the square in order to maximize the total area?m
(b) How much wire should be used for the square in order to minimize the total area? m
Answers
The length of wire used for the square in order to minimize the total area is 9.42m.
We are given that;
Length of wire= 30m
Now
Let the length of the wire used for the square x. The length of the wire used for the circle is 30-x.
The perimeter of the square is 4x and the perimeter of the circle is 2πr=2π(30-x)/(2π)=15-x/π.
The area of the square is [tex]x^2/16[/tex] and
the area of the circle is π(15-x/π)2/4π=225/π-(15x)/π2+[tex]x^2[/tex]/4π.
The total area is A=x2/16+225/π-(15x)/π2+[tex]x^2[/tex]/4π.
To maximize A, we take its derivative with respect to x and set it equal to zero: d[tex]A/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]
Solving for x, we get x=120/(8+4π).
Therefore, 30-x=120/(8+4π)(3-π).
To minimize A, we take its derivative with respect to x and set it equal to zero:
[tex]dA/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]
Solving for x, we get x=120/(8+4π)(3+π).
So, 30-x=120/(8+4π)(3-π).
Therefore, by area the answer will be approximately 9.42 m.
Learn more about the area;
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What's the measure of Z1 if Z CBD = 75° and ZABC = 135°?
Answers
Answer:
60°
Step-by-step explanation:
∠ABC-∠CBD=∠1
[tex]135-75[/tex]
[tex]=60[/tex]
Answer:
Brainliest goes to me!
Step-by-step explanation:
angle abc = 135 degrees
part of it is angle 1 and the other part is angle cbd
<abc (135) = cbd (75) + <1
angle 1 = 60 degrees
Please answer this correctly
Answers
Answer:
64
Step-by-step explanation:
There are only pink and yellow sections of the circle, so every spin will land on pink or yellow.
Answer: 64
Answer:
Brianliest!
Step-by-step explanation:
since there are only the colors pink and yellow and the prediction for the number of times it will land on pink or yellow, it will have a 100% probability
64
An account with $250 balance accrues 2% annually. If no deposits or withdrawals are made, which graphs can be used to determine approximately how many years will it take for the balance to be $282?
Answers
An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made so, to take the balance to $282 requires 6.4 years and this can be determined by using the simple interest formula.
Given :
An account with a $250 balance accrues 2% annually.No deposits or withdrawals are made.Final amount = $282SImple interest formula can be used to determine the total number of years will it take for the balance to be $282.
The formula of simple interest is given by:
[tex]\rm A = P(1+rt)[/tex]
where A is the final amount, P is the initial principal balance, r is the annual interest rate and t is the time in years.
Now, put the known values in equation (1).
[tex]\rm 282 = 250(1+0.02t)[/tex]
[tex]\rm 282=250+5t[/tex]
32 = 5t
t = 6.4 years
So, 6.4 years will it take for the balance to be $282.
So, the graph correct graph is shown by option D).
For more information, refer to the link given below:
https://brainly.com/question/24432090
Answer:
D
Step-by-step explanation:
Simplify 5^2 · 5^9 1. 5^11 2. 5^18 3. 25^11 4. 25^18
Answers
Answer:
Answer choice 1
Step-by-step explanation:
[tex]5^2\cdot 5^9= \\\\5^{2+9}= \\\\5^{11}[/tex]
Therefore, the correct answer choice is choice 1. Hope this helps!
6) The average Mathematics mark for Amin, Azman and Aziz is 73. Azman's mark is 35 more than
Amin while Aziz's is twice of Amin's. What is the Mathematics mark of Amin?
Answers
Answer:
46
Step-by-step explanation:
Azman=35+amin
Aziz=3×amin
therefore;35+amin+2amin+amin/3=73
219=35+4amin
219-35=4amin
184=4amin
Amin's mark=184÷4
=46
The moon is 2.4 X 10^5 miles from Earth. Assume the speed of the fastest spacecraft is 3.6 X 10^4 miles per hour. How many hours would it take this spacecraft to fly to the moon from Earth? Write your answer in standard form, rounded to the nearest hour. The solution is
Answers
Answer: . x 10^5 miles from the earth. How long does it take light to from a source on earth to reach a reflector on the moon and then return to earth? The speed of light is 3.0 x 10^8 m/s. ... sec. to give us our final answer of 1.28 seconds (the time required for light to travel 2.4 x 105 miles). and the fastest spaceship goes 153,454 miles per hour
Step-by-step explanation:
The number of hours that should be taken to fly to the moon from Earth is 7 hours.
Given that
Distance between earth and moon is [tex]2.4 \times 10^5\ miles[/tex]The speed is [tex]3.6 \times 10^4\ miles\ per\ hour[/tex]Now we know that
[tex]Time = \frac{Distance}{Speed} \\\\= \frac{2.4 \times 10^5 }{3.6 \times 10^4} \\\\= \frac{240}{36}[/tex]
= 6.66 hours
= 7 hours
Therefore we can conclude that The number of hours that should be taken to fly to the moon from Earth is 7 hours.
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prove that
1/(sec A - tan A) =sec A + tan A
Answers
Answer:
Step-by-step explanation:
let s estimate the following
[tex](secA-tanA)(secA+tanA)=sec^2A-tan^2A=\dfrac{1}{cos^2A}-\dfrac{sin^2A}{cos^2A}=\dfrac{1-sin^2A}{cos^2A}=\dfrac{cos^2A}{cos^2A}=1[/tex]
as [tex]cos^2A+sin^2A=1[/tex]
it means that
[tex]\dfrac{1}{secA-tanA}=secA+tanA[/tex]
hope this helps
Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Data. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.
Answers
Answer:
The 99% confidence interval for the mean germination time is (12.3, 19.3).
Step-by-step explanation:
The question is incomplete:
Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.
We start calculating the sample mean M and standard deviation s:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\[/tex]
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=15.8.
The sample size is N=10.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075[/tex]
The degrees of freedom for this sample size are:
df=n-1=10-1=9
The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=3.25 \cdot 1.075=3.49[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3[/tex]
The 99% confidence interval for the mean germination time is (12.3, 19.3).
If n is an even integer such that 5≤n≤12, then what is the mean of all possible values of n?
Answers
Answer:
9
Step-by-step explanation:
5≤n≤12
List all the even integers
6,8,10,12
Then find the mean
(6+8+10+12) /4
36/4
9
The mean is 9
Evaluate the expression. 8! − 5!
Answers
Answer:
40200
Step-by-step explanation:
(8x7x6x5x4x3x2x1) - (5x4x3x2x1)
Or simply plug 8! - 5! into the calc.
Answer:
Step-by-step explanation:
40200
Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that of the respondents did not provide a response, said that their experience fell short of expectations, and of the respondents said that their experience met expectations.A. If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations?B. If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Solution:
Probability = number of favorable outcomes/number of total outcomes
From the information given,
The probability that respondents did not provide a response, P(A) is 4/100 = 0.04
The probability that a respondent said that their experience fell short of expectations, P(B) is 26/100 = 0.26
The probability that a respondent said that their experience met expectations, P(C) is 65/100 = 0.65
A) Adding all the probabilities, it becomes 0.04 + 0.26 + 0.65 = 0.95
Therefore, the probability,P(D) that a respondent said that their experience surpassed expectations is 1 - 0.95 = 0.05
B) The event of a randomly chosen respondent saying that their experience met expectations and that their experience surpassed expectations are mutually exclusive because they cannot occur together. It means that P(C) × P(D) = 0
Therefore, the probability of P(C) or P(D) is 0.65 + 0.05 = 0.7
The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows a mean age of 46 years with a standard deviation of 5 years. The width of a 98 percent confidence interval for the true mean client age is approximately:_______.
A. ± 2.492 years.
B. ± 1.711 years.
C. ± 2.326 years.
D. ± 2.797 years.
Answers
Answer:
C. ± 2.326 years.
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.01 = 0.99[/tex], so [tex]z = 2.326/tex]
Now, find the width of the interval
[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]\sigma = 5, n = 25[/tex]
So
[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]W = 2.326*\frac{5}{\sqrt{25}}[/tex]
The correct answer is:
C. ± 2.326 years.
Find the midpoint of AB when A=(1,-2) B=(1,-1)
Answers
Answer:
Midpoint Of AB = ( 1+1/2 , -2-1/2)
= (2/2 , -3/2)
= ( 1 , -1.5)
Hope this helps
Please mark Branliest.
Answer:
-2,0
Step-by-step explanation:
GIVING 20 POINTS What is the product?
Answers
Answer:
1
Step-by-step explanation:
4^3 × 4^-3
Apply the law of exponents.
4^(3+-3)
4^(0)
Any base with the exponent of 0 is equal to 1.
= 1
Answer:
1
Step-by-step explanation:
the exponents cancel out to 0, and an exponent of 0 is always 1