Answer:
a. The null and alternative hypothesis can be written as:
[tex]H_0: \mu=3173\\\\H_a:\mu< 3173[/tex]
b. A Type I error is made when a true null hypothesis is rejected. In this case, it would happen if it is concluded that the actual mean outstanding credit card debt of college undergraduate is significantly less than $3173, when in fact it does not.
A Type II error is made when a false null hypothesis is failed to be rejected. In this case, the actual mean outstanding credit card debt of college undergraduate is in fact less than $3173, but the test concludes there is no enough evidence to claim that.
Step-by-step explanation:
We have a prior study of the mean outstanding credit card debt of college undergraduate that states that it was $3173 in 2010.
A researcher believes that this amount has decreased since then.
Then, he has to perform a hypothesis test where the null hypothesis states that the mean is still $3173 and an alternative hypothesis that states that the actual credit card debt is significantly smaller than $3173.
The null and alternative hypothesis can be written as:
[tex]H_0: \mu=3173\\\\H_a:\mu< 3173[/tex]
The area of the triangular section is
square units. The area of the entire figure is
Answer:
still a square units.
Step-by-step explanation:
Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordless, and the other six are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, . . . , 18 to establish the order in which they will be serviced. (Round your answers to four decimal places.)
(a) What is the probability that all the cordless phones are among the first twelve to be serviced?
(b) What is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced?
(c) What is the probability that two phones of each type are among the first six serviced?
Answer:
a) 0.0498
b) 0.1489
c) 0.1818
Step-by-step explanation:
Given:
Number of telephones = 6+6+6= 18
6 cellular, 6 cordless, and 6 corded.
a) Probability that all the cordless phones are among the first twelve to be serviced:
12 are selected from 18 telephones, possible number of ways of selection = ¹⁸C₁₂
Then 6 cordless telephones are serviced, the remaining telephones are: 12 - 6 = 6.
The possible ways of selecting thr remaining 6 telephones = ¹²C₆
Probability of servicing all cordless phones among the first twelve:
= (⁶C₆) (⁶C₁₂) / (¹⁸C₁₂)
[tex] = \frac{1 * 924}{18564} [/tex]
[tex] = 0.0498 [/tex]
b) Probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced:
Here,
One type must be serviced first
The 6 remaining to be serviced can be a combination of the remaining two types.
Since there a 3 ways to select one type to be serviced, the probability will be:
= 3 [(⁶C₁)(⁶C₅) + (⁶C₂)(⁶C₄) + (⁶C₃)(⁶C₃) + (⁶C₄)(⁶C₂) + (⁶C₅)(⁶C₁)] / ¹⁸C₁₂
[tex] = \frac{3 * [(6)(6) + (15)(15) + (20)(20) + (15)(15) + (6)(6)]}{18564}[/tex]
[tex] = \frac{2766}{18564} [/tex]
[tex] = 0.1489 [/tex]
c) probability that two phones of each type are among the first six:
(⁶C₂)³/¹⁸C₆
[tex] \frac{3375}{18564}[/tex]
[tex] =0.1818 [/tex]
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Answer:
The picture on the bottom right.
Step-by-step explanation:
There are eight compartments and seven of it is shaded and the other one five of the eight compartments are shaped.
I hope this helps :)
A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values. x y 14 46 15 49 16 37 17 42 18 37 19 31 20 25 21 23 22 20 23 15 24 12 What is the equation of the regression line?
Answer:
y= -3.7x+100.94
Step-by-step explanation:
Generally this type of problems is solved by using a calculator or a spreadsheet. Now, getting the final equation depends on the model of calculator you are using, so I will suggest you look for the instructions on your calculator's instruction manual. I'll provide indications for using excel.
So first you need to input the table on an excel sheet. You can input them just the same way they were given to you. (See attached picture)
Once you inputed them, you can highlight them and go to the insert tab. There you can pick the scattering plot option. Once the scatterplot is graphed, you can right-click on the graph and a menu should appear. Pick the option add tendency line. Choose the line option and below, you can mark the option present equation on the graph and present the value of R. And that will be it! Excel will automatically provide you with the equation of the regression line you need.
Most scientific calculators nowaday can provide you with the equation, you just need to input the data and they will return the slope and y-intercept of the line.
There are other formulas you can use to find this regression by hand, but they are generally used in statistics courses.
Every weekday, Mr. Jones bikes from his home to his job. Sometimes he rides along two roads, the long route that is shown by the solid lines. Other times, he takes the shortcut shown by the dashed line.
A right triangle. The distance from the angle with measure 90 degrees to Job is 15 kilometers. From the angle to Home is a. They hypotenuse is 17 kilometers.
How many fewer kilometers does Mr. Jones bike when he takes the shortcut instead of the long route?
6 kilometers
8 kilometers
23 kilometers
32 kilometers
Mark this and return
Answer:
(A)6 kilometers
Step-by-step explanation:
First, we determine the value of a using Pythagoras Theorem.
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\17^2=a^2+15^2\\a^2=17^2-15^2\\a^2=289-225\\a^2=64\\a^2=8^2\\a=8$ km[/tex]
Therefore:
Distance along the long route = 8 + 15 =23 km
Distance along the shortcut =17 km
Difference =23-17 =6km
Therefore, Mr. Jones bikes 6km less when he takes the shortcut instead of the long route.
Answer:
a
Step-by-step explanation:
on edge
The weights of items produced by a company are normally distributed with a mean of 5 ounces and a standard deviation of 0.2 ounces. What is the minimum weight of the heaviest 9.85% of all items produced?
Answer:
The minimum weight of the heaviest 9.85% of all items produced is 5.26 ounces.
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.
In this question, we have that:
[tex]\mu = 5, \sigma = 0.2[/tex]
What is the minimum weight of the heaviest 9.85% of all items produced?
This is the 100 - 9.85 = 90.15th percentile, which is X when Z has a pvalue of 0.9015. So X when Z = 1.29.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.29 = \frac{X - 5}{0.2}[/tex]
[tex]X - 5 = 1.29*0.2[/tex]
[tex]X = 5.26[/tex]
The minimum weight of the heaviest 9.85% of all items produced is 5.26 ounces.
Find the missing value.
Hint: Use the number line to find the missing value.
–9+ = -3
I need help
I need help on question 6.
Answer: 135 degrees
Step-by-step explanation:
First you now that ABD+DBC=180 degrees
Subsitute so you get: (5x+10)+(2x-5)=180
Solve:
(5x+10)+(2x-5)=180
=> 7x+5=180
=> 7x=175
=> x= 25
Plug in 25 :
ABD= 5*25+10=135
And there is your answer
Two dice are rolled. Determine the probability of the following: rolling a 6 or doubles
Answer as an exact fraction = 5/18
Answer as an approximate decimal = 0.2778
Answer as an approximate percentage = 27.78%
============================================================
Explanation:
x = result of the first die
y = result of the second die
(x,y) paired together shows the results of both dice at the same time.
Something like (x,y) = (4,2) means we got 4 on the first die and 2 on the second die.
--------
Let's list the ways of rolling a 6
(1,5)(2,4)(3,3)(4,2)(5,1)There are 5 ways to roll a 6. Each pair listed has the property x+y = 6.
--------
List all the ways of getting doubles
(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)There are 6 ways to roll doubles. Each pair mentioned has x = y.
--------
We have 5+6 = 11 items listed above. However, there are only 10 unique pairs though because (3,3) was listed twice. So we could say 5+6-1 = 11-1 = 10.
This is out of 6*6 = 36 different ways to roll the two dice. The probability is therefore 10/36 = 5/18.
Using a calculator, 5/18 = 0.2778 = 27.78%
A standard 52-card deck of French playing cards consists of four suits: hearts, spades, clubs, and diamonds. There are 13 cards of each suit; each suit has cards of rank 2 through 10, along with an ace, king, queen, and jack. Typically, hearts and diamonds are the red suits, while spades and clubs are the black suits. Four cards are drawn from the deck, one at a time, without replacement. a) The second card drawn is from a red suit. Based on this information, what is the probability it is a heart
Answer:
P = 0.5
Step-by-step explanation:
Let's call A the event that the second card is red suit and B the event that the second card is a heart.
So, the probability that the second card is a heart given that is a red suit is calculated as:
P(B/A) = P(A∩B)/P(A)
Additionally, the probability P(A∩B) that the second card is a red suit and is a heart is equal to the probability P(B) that the second card is a heart. So,
P(B/A) = P(B)/P(A)
Then, P(A) is equal to 0.5 because half of the cards are red cards and P(B) is equal to 0.25 because a quarter of the cards are red. Finally, P(B/A) is equal to:
P(B/A) = 0.25/0.5 = 0.5
I'm having trouble finding the missing number. Please simplify the resulting fraction. Thank you in advance. : 0) 7/8 = ?/48
Answer:
42
Step-by-step explanation:
7/8 = x / 48
We need to get a common denominator
Multiply the left side by 6
7/8 *6/6 = x/48
42/48 = x/48
Since the denominators are equal, the numerators must be equal
42 =x
Answer:
42
Step-by-step explanation:
7/8=42/48
Cross products: 7(48)=8x
what is the square root of -16
Answer:
Step-by-step explanation:
[tex]\sqrt{-16}=\sqrt{16i^{2}}\\\\ =\sqrt{4^{2}*i^{2}}\\\\=4i[/tex]
How many meters make a centimeter
Answer:
There are 0.01 meters in a centimeter.
Step-by-step explanation:
cent means 100th
Hope this helps :)
There is a 0.9986 probability that a randomly selected 27-year-old male lives through the year. A life insurance company charges $174 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $90 comma 000 as a death benefit. Complete parts (a) through (c) below. a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? The value corresponding to surviving the year is $ negative 173.76. The value corresponding to not surviving the year is $ 125.76.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
There is a 0.9986 probability that a randomly selected 27-year-old male lives through the year. A life insurance company charges $174 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $90 comma 000 as a death benefit. Complete parts (a) through (c) below.
a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 27 -year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why? From the point of view of the insurance company, the expected value of the policy is
Answer:
a. The life insurance company charges $174 for insuring if the male survives
Value(survive) = -$174
The life insurance company pays $90,000 for insuring if the male does not survive.
Value(not survive) = $89,826
b. The expected value for a 27-year-old male is
E(x) = -$48
c. The expected value for the insurance company is
E(x) = $48
Step-by-step explanation:
The probability that a randomly selected 27-year-old male survives is given by
P(survive) = 0.99864
The probability that a randomly selected 27-year-old male does not survive is given by
P(not survive) = 1 - P(survive)
P(not survive) = 1 - 0.99864
P(not survive) = 0.0014
a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
If 27-year-old male survives:
The life insurance company charges $174 for insuring if the male survives
Value(survive) = -$174
If 27-year-old male does not survive:
The life insurance company pays $90,000 for insuring if the male does not survive.
Value(not survive) = $90,000 - 174
Value(not survive) = $89,826
b. If the 27-year-old male purchases the policy, what is his expected value?
The expected value for a 27-year-old male is given by
E(x) = P(survive)×Value(survive) + P(not survive)×Value(not survive)
E(x) = 0.9986×-174 + 0.0014×89,826
E(x) = -$48
The negative sign indicates that it is a loss from the perspective of the 27-year-old male.
c. Can the insurance company expect to make a profit from many such policies? Why? From the point of view of the insurance company, the expected value of the policy is
The expected value for the insurance company is given by
E(x) = 0.9986×174 + 0.0014×-89,826
E(x) = $48
The positive sign indicates that it is a profit from the perspective of the insurance company.
About 2% of the population has a particular genetic mutation. 1000 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 10
Answer:
Step-by-step explanation:
We khow that the genetic mutation affect 2 percent of the population .
Let's try to understand what does this mean :
in a group of 100 people there is possibility of finding 2 people with this genetic mutation in a group of 1000 the possibility raises to 20 people so we can deduce that each time we add a zero we add a zero in 2so :
100⇒21000⇒2010000⇒200100000⇒2000and so on
Which statement is true? Question 6 options: A) |13| = – 13 B) – |13| = 13 C) – |–13| = 13 D) |–13| = 13
Answer:
D because absolute value always makes the sign positive but if there is a negative before the absolute value, that would still stay there.
Step-by-step explanation:
An equation |-13|=13 is correct. Therefore, option D is the correct answer.
What is an absolute value?The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To find the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.
Here,
A) |13|=-13
Absolute value of positive integer is positive. So, option A is incorrect.
B) -|13|=13
Absolute value of positive integer is positive.
Then, -13≠13
So, option B is incorrect.
C) -|-13|=13
Absolute value of negative integer is positive.
Then, -13≠13
So, option C is incorrect.
D) |-13|=13
Absolute value of negative integer is positive.
So, option D is incorrect.
An equation |-13|=13 is correct. Therefore, option D is the correct answer.
To learn more about an absolute value visit:
https://brainly.com/question/1301718.
#SPJ2
In 1998, Mary Meagher set the women's world swimming record for the 100-m butterfly. She swam the distance in 57.93 seconds. On average, how long did she take to swim 10 m?
Answer:
5.793 s
Step-by-step explanation:
On average she swam 1/10 the distance in 1/10 the time.
She took an average of 5.793 seconds to swim 10 m.
___
10 m is 1/10 of 100 m
Find X. Please help.
Answer:
22.62°
Step-by-step explanation:
tan x = 5/12
tan x = 0.416666667
x = arctan(0.416666667)
x = 22.61986983
x = 22.62°
If the distribution of weight of newborn babies in Maryland is normally distributed with a mean of 3.89 kilograms and a standard deviation of 0.68 kilograms, find the weights that correspond to the following Z-scores. Round your answers to the nearest tenth, if necessary. (a) z = -1.35 kilograms (b) z = 2.64 kilograms
Answer:
a) 3 kilograms
b) 5.7 kilograms
Step-by-step explanation:
Z-score:
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:
[tex]\mu = 3.89, \sigma = 0.68[/tex]
We have to find X for both values of Z.
a) z = -1.35
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.35 = \frac{X - 3.89}{0.68}[/tex]
[tex]X - 3.89 = -1.35*0.68[/tex]
[tex]X = 3[/tex]
3 kilograms
b) z = 2.64
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.64 = \frac{X - 3.89}{0.68}[/tex]
[tex]X - 3.89 = 2.64*0.68[/tex]
[tex]X = 5.7[/tex]
5.7 kilograms
Please answer this correctly
Answer:
50%
Step-by-step explanation:
There are 3 numbers that fit this rule, 4, 5, and 6. Since there are 6 number total, and 3 fit the rule, there is a 3/6 chance or 50% or rolling either of those numbers.
Answer:
50%
Step-by-step explanation:
The numbers that are 5 or greater than 3 on a dice are 4, 5, and 6.
3 numbers out of 6.
3/6 = 1/2
Convert to percentage.
1/2 × 100
= 50%
P(5 or greater than 3) = 50%
the pie chart on the left shows the mean of transport 60 people use every morning to get to work. How many people use the train to go to work
Answer:
I wanna end myself bye random stranger.
KEVIN HAS TWO PART-TIME JOBS. HE DELIVERS PIZZA FOR PEDRO'S PIZZERIA
AND MAKES $8 AN HOUR, PLUS $20 FOR DRIVING EXPENSES EACH WEEK. HE
ALSO DOES ODD JOBS FOR A LOCAL HARDWARE STORE, WHERE HE IS PAID $10
AN HOUR.
A. WRITE A SYSTEM OF EQUATIONS TO DESCRIBE THE SCENARIO WHERE H
REPRESENTS THE NUMBER OF HOURS KEVIN WORKS, AND A
REPRESENTS THE AMOUNT HE EARNS AT EACH JOB IN A WEEK. B. HOW MANY HOURS MUST KEVIN WORK AT EACH JOB SO THAT HIS EARNINGS FROM BOTH SIDES ARE THE SAME? C. WHAT WOULD HIS INCOME FROM EACH JOB BE IN THAT CASE?
Answer:
A. A = 8h + 10
A = 10h
B. 5 hours
C. $50
Step-by-step explanation:
A. https://brainly.com/question/17036764
Pizza Place: A = 8h + 10
Hardware Store: A = 10h
Since you had made a separate question for part A, I answered that.
B. Kevin's earnings is represented by A. Because we want the earnings for each job to be equal, set the two equations equal to each other. Solve for h.
8h + 10 = 10h
10 = 2h
5 = h
Kevin has to work 5 hours.
C. Plug 5 into each equation.
A = 8h + 10
A = 8(5) + 10
A = 40 + 10
A = 50
A = 10h
A = 10(5)
A = 50
Kevin will make 50 from each job.
Suppose the claim size of an auto collision insurance, X, is uniformly distributed on the interval $1,000 to $10,000. What is the percent reduction in the expected claim payment by the insurer if a policyholder has a $2,000 deductible
Answer:
35.35%
Step-by-step explanation:
If there were no deductibles, the expected claim payment would be:
[tex]E(X) = \frac{10,000 +1,000}{2} \\E(X) =\$5,500[/tex]
If the collision insurance claim is under $2,000, then the insurer would not pay anything, but if X > $2,000, then the insurer would pay X - $2,000. The new expected value is:
[tex]E_2(X)=\frac{2,000-1,000}{10,000-1,000} *0+\frac{10,000-2,000}{10,000-1,000}*\frac{(2,000-2,000)+(10,000-2,000)}{2} \\E_2(X)=\frac{8}{9}*\frac{0+8,000}{2}\\ E_2(X)=\$3,555.56[/tex]
The percentage reduction on the claim payment is:
[tex]P=(1-\frac{E_2(X)}{E(X)})*100 \\P=(1-\frac{3,555.56}{5,500})*100\\P=35.35\%[/tex]
There was a 35.35% reduction.
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F = 3yi + yj+zk
C: counterclockwise path around the boundary of the ellipse x2/4+y2/64=1
Answer:
[tex]\int \int \bigtriangledown F\ X\ dS = \int F\cdot dr[/tex] = 12π
Step-by-step explanation:
The field F is given by:
[tex]F = 3y\hat{i} + y\hat{j}+z\hat{k}[/tex] (1)
The curve C is the ellipse:
[tex]\frac{x^2}{4}+\frac{y^2}{64}=1\\\\(\frac{x}{2})^2+(\frac{y}{8})^2=1[/tex]
In order to calculate the circulation of F around the curve C, you first find the parametric equation for the given ellipse.
The general form of an ellipse equation is:
[tex](\frac{x}{a})^2+(\frac{y}{b})^2=1[/tex]
The parametric equation is:
[tex]r(t)=acost \hat{i} + bsint\hat{j}=2cost\hat{i}+8sint\hat{j}[/tex] (2)
The Stokes's theorem is given by the following identity:
[tex]\int \int \bigtriangledown F\ X\ dS = \int F\cdot dr[/tex]
The path integral is also:
[tex]\int F\cdot dr=\int F(r(t))\cdot dr(t)[/tex] (3)
For F(r(t)) and dr(t) you obtain:
[tex]F(r(t))=3(8sint)\hat{j}+(8sint)\hat{j}+(z)\hat{k}\\\\dr(t)=(-2sint\hat{i}+8cost\hat{j}+0\hat{k})dt\\\\F(r(t))\cdot dr(t)=(-48sin^2t+64cos^2t)dt[/tex]
Next, in the equation (3) you obtain:
[tex]\int_0^{2\pi} (-48sin^2t+64cos^2t)dt=\int_0^{2\pi}(-\frac{48}{2}(1-cos2t)+\frac{64}{2}(1+cos2t))dt\\\\=\int_0^{2\pi}(-24+24cos2t+32+32cos2t)dt\\\\=\int_0^{2\pi}(6+56cos2t)dt\\\\=[6t+56sin2t]_0^{2\pi}=[6(2\pi)-0]=12\pi[/tex]
The circulation of the field around C is 12π
Suppose you do an experiment where you roll a standard die twice. You decide to keep performing this experiment unless you get a sum of the rolls to be exactly 6. How many times do you feel you have to do this experiment on an average?
Answer:
7.2 times
Step-by-step explanation:
There are 36 possible outcomes when rolling a die twice and adding the results. The outcomes for which the sum is 6 are:
Sum = 6: {1,5; 2,4; 3,3; 4,2; 5,1}
Therefore there is a 5 in 36 chance that the sum will be 6.
The expected number of trials to achieve that result is given by:
[tex]E = \frac{36}{5}\\E=7.2\ times[/tex]
On average, it would take 7.2 trials to achieve a sum of 6.
What is the volume of a sphere, to the nearest cubic inch, if the radius is 7 inches? Use π = 3.14.
Answer:
[tex]V=\frac{4}{3}\pi r^{2}[/tex]
=[tex]\frac{4}{3}[/tex] x [tex]\pi[/tex] x [tex]7^3[/tex]
= 1436.755040
Volume = 1436.755040
Step-by-step explanation:
Answer:
1436.03 in³
Step-by-step explanation:
We can use the formula V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex]r³
Plug in 7 for r:
V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex](7)³
Plug in 3.14 for pi:
V = [tex]\frac{4}{3}[/tex](3.14)(343)
V = 1436.03 in³
If triangle STU congruent to triangle HIJ, then what corresponding parts are congruent?
a. <I and <U
b. TU and HI
c. <I and <S
d. US and JH
Answer: d) US and JH
Step-by-step explanation:
Place the letters underneath each other to see which positions match up
S T U
H I J
Angles: ∠S ≡ ∠H ∠T ≡ ∠I ∠U ≡ ∠J
Sides: ST ≡ HI TU ≡ IJ SU ≡ HJ
The option that is true is US and JH are congruent
which is the same as SU ≡ HJ
Pablo Picasso is making one color version of all his paintings. He uses the colors in the following order and then starts over from the begining red, blue, pink, green, and purple. What color is painting 27
Answer:
The answer is blue
Step-by-step explanation:
There are five colors. So count by fives until you hit 25.
red, blue, pink, green, and purple. 5
red, blue, pink, green, and purple. 10
red, blue, pink, green, and purple. 15
red, blue, pink, green, and purple. 20
red, blue, pink, green, and purple. 25
Then count to 27.
red, blue. 27
So it is blue.
This question is determined by using simple mathematics tricks . Therefore, the color is blue on painting 27.
Given:
The order of painting begin from the red, blue, pink, green, and purple.
We need to determined the color of 27 painting.
According to question,
There are five colors for painting, count by fives until you hit 25.
Now, count the colors,
red, blue, pink, green, and purple - 5
red, blue, pink, green, and purple - 10
red, blue, pink, green, and purple - 15
red, blue, pink, green, and purple - 20
red, blue, pink, green, and purple - 25
Now at 26 there is red and at 27 there is blue color.
Therefore, the color is blue on painting 27.
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At a carnival, contestants are asked to keep rolling a pair of dice until they roll snake eyes. The number of rolls needed has a mean of 36 rolls, with a standard deviation of 5.4 rolls. The distribution of the number of rolls needed is not assumed to be symmetric.
Between what two numbers of rolls does Chebyshev's Theorem guarantee that we will find at least 75% of the contestants?
Answer:
The two numbers of rolls are 25.2 and 46.8.
Step-by-step explanation:
The Chebyshev's theorem states that, if X is a r.v. with mean µ and standard deviation σ, then for any positive number k, we have
[tex]P (|X -\mu| < k\sigma) \geq (1-\frac{1}{k^{2}})[/tex]
Here
[tex](1-\frac{1}{k^{2}})=0.75\\\\\Rightarrow \frac{1}{k^{2}}=0.25\\\\\Rightarrow k=\sqrt{\frac{1}{0.25}}\\\\\Rightarrow k=2[/tex]
Then we know that,
[tex]|X - \mu| \geq k\sigma,\\\\ \Rightarrow \mu - k\sigma \leq X \leq \mu + k\sigma[/tex].
Here it is given that mean (µ) = 36 and standard deviation (σ) = 5.4.
Compute the two values between which at least 75% of the contestants lie as follows:
[tex]P(\mu - k\sigma \leq X \leq \mu + k\sigma)=0.75\\\\P(36 - 2\cdot\ 5.4 \leq X \leq 36 + 2\cdot\ 5.4)=0.75\\\\P(25.2\leq X\leq 46.8)=0.75[/tex]
Thus, the two numbers of rolls are 25.2 and 46.8.
In a certain city, the monthly cost of residential electric service is given by the function C = 0.08n = 14, where n is the number of kilowatt hours (kWh) used 8 cents is the cost per kWh, and 14 is a fixed charge. Find the monthly bill if 600 kWh were used. $
Answer:
b and I will be there at work and I will be there at work and I will be there at work and I will
Step-by-step explanation:
you are not going to be able to make it to the meeting tonight but I can tomorrow if you have time