A probability model for rolling a cube with faces numbered 1 through 6 is:
Answer:
P(a)= Your desired outcome / The number of real outcomes.
Step-by-step explanation:
Ex. Probability model for rolling a 1 on a 6 sided die -
1 (desired outcome) / 6 (Number of real outcomes)
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8 x 10^3 is how many times as large as 4 x 10^2?
8 * 10^3 is larger than 4 * 10^2
10*10*10 = 1000 * 8 = 8000
10*10= 100 * 4 = 400
An aquarium holds 11.08 cubic feet of water,and is 2.5 feet long 1.3 feet wide.what is its depth.Round your answer to the nearest whole number.
Answer:
3ft
Step-by-step explanation:
volume = l*w*h
To solve use what you know.
11.08 ft^3 = 2.5 ft * 1.3 ft * X ft
2.5 ft *1.3 ft =3.5 ft^2
11.08ft^3 / 3.5ft^2 = 3.409 ft
nearest whole number is 3 ft
which of the following options is an odd function?
Answer: The answer is C
Step-by-step explanation:
The expression 1,000(1.0215)4t represents the amount of money in an account after t years.
The interest is compounded [annually/semiannually/quarterly/monthly], and the effective annual interest rate on the account is [2.15%/4.00%/8.60%/8.88%].
What are the two correct answers that complete the sentences? Choose from the brackets above.
Answer:
The interest is compounded quarterly.
The effective annual interest rate on the account is 8.60%.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
We are given:
[tex]A(t) = 1000(1.0215)^{4t}[/tex]
Comparing to the general formula.
[tex]P = 1000[/tex]
[tex]1 + \frac{r}{n} = 1.0215[/tex]
[tex]nt = 4t[/tex]
From the last one:
[tex]n = 4[/tex]
Which means 4 compoundings per year. This means that the interest is compounded quarterly.
Interest rate:
[tex]1 + \frac{r}{n} = 1.0215[/tex]
Since n = 4.
[tex]\frac{r}{4} = 1.0215 - 1[/tex]
[tex]\frac{r}{4} = 0.0215[/tex]
[tex]r = 4*0.0215[/tex]
[tex]r = 0.0860[/tex]
So the interest rate is of 8.60%.
Answer:
the answer is quarterly and 8.88
Step-by-step explanation:
got 100 on the test
The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find:
Chapter Reference
b
Surface area of the pyramid
Answer:
228 cm²
Step-by-step explanation:
The base of the pyramid is a regular quadrilateral (a square), so there are 4 congruent lateral faces.
The total surface area is therefore:
A = 36 cm² + 4 (48 cm²)
A = 228 cm²
The chances of a tax return being audited are about 21 in 1 comma 000 if an income is less than $100,000 and 29 in 1 comma 000 if an income is $100,000 or more. Complete parts a through e. a. What is the probability that a taxpayer with income less than $100,000 will be audited? With income of $100,000 or more? Upper P (taxpayer with income less than $ 100 comma 000 is audited )equals nothing (Type an integer or a decimal.) What is the probability that a taxpayer with income of $100,000 or more will be audited? Upper P (taxpayer with income of $ 100 comma 000 or higher is audited )equals nothing (Type an integer or a decimal.) b. If five taxpayers with incomes under $100,000 are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited?
Answer:
a) p=0.021
b) p=0.029
c) Exactly one audit: P=0.0965
More than one audit: P=0.0042
Step-by-step explanation:
a) If the income is less than $100,000, there is a probability of 21 in 1,000 of being audited. This is:
[tex]p_1=\dfrac{21}{1,000}=0.021[/tex]
If the income is equal or more than $100,000, there is a probability of 29 in 1,000 of being audited. This is:
[tex]p_2=\dfrac{29}{1,000}=0.029[/tex]
b) If we have 5 taxpayers with incomes under $100,000, and we want to know the probability that exactly one will be audited, we can model this a binomial randome variable, with p=0.021 and n=5:
[tex]P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\[/tex]
There is a probability of 0.0965 that exactly one out of a sample of five taxpayers with incomes under $100,000 will be audited.
To calculate the probability that more than one will be audited, we use the same distribution:
[tex]P(x>1)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0) = \dbinom{5}{0} p^{0}q^{5}=1*1*0.8993=0.8993\\\\\\P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\\\P(x>1)=1-[P(x=0)+P(x=1)]\\\\P(x>1)=1-(0.8993+0.0965)\\\\P(x>1)=1-0.9958\\\\P(x>1)=0.0042[/tex]
There is a probability of 0.0042 that more than one out of a sample of five taxpayers with incomes under $100,000 will be audited.
find the average rate of change over the interval 7 less than or equal to X less than or equal to 10, of the function defined by the table
X. Y.
1 1
4 16
7 49
10 100
A. 8
B. 17
C. 5
D. 11
Answer:
B. 17
Step-by-step explanation:
The average rate of change is:
m_avg = (y₂ − y₁) / (x₂ − x₁)
m_avg = (100 − 49) / (10 − 7)
m_avg = 17
When 893893 male workers were asked how many hours they worked in the previous week, the mean was 45.645.6 with a standard deviation of 14.614.6. Does this suggest that the population mean work week for men exceeds 4040 hours? Answer by completing parts (a) through (d).
Answer:
a) A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
b) Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
c) [tex]t=\frac{45.6-40}{\frac{14.6}{\sqrt{893}}}=11.46[/tex]
The p value for this case would be:
[tex] p_v = P(t_{110} >11.46) \approx =0[/tex]
d) Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case exceeds 40 hours.
Step-by-step explanation:
Information provided
[tex]\bar X=45.6[/tex] represent the sample mean
[tex]s=14.6[/tex] represent the sample standard deviation
[tex]n=893[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
a. Identify the relevant and parameter variable. Choose the correct relevant variable below.
A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
b. State the null and alternative hypotheses. State the null hypothesis.
We want to verify if the population mean is higher than 40, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
c. Calculate the statistic
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{45.6-40}{\frac{14.6}{\sqrt{893}}}=11.46[/tex]
The p value for this case would be:
[tex] p_v = P(t_{110} >11.46) \approx =0[/tex]
d. Conclusion
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case exceeds 40 hours.
A camp counselor and six campers are to be seated along a picnic bench. In how many ways could this be done if the counselor occupies the seat in the middle and the camper who tends to start food fights sits next to him (either on the left or on the right)
Answer:
This can be done in 240 ways.
Step-by-step explanation:
Number of arrangments:
The possible number of arrangments of n elements is given by the following formula:
[tex]A_{n} = n![/tex]
In this question:
7 people(camp counselor and six campers).
Camp counselor in the middle.
Camper who start food fights either to his left or to his right. For each of these cases, the other 5 campers are arranged in 5 positions. Then
How many ways:
[tex]T = 2A_{5} = 2*(5!) = 240[/tex]
This can be done in 240 ways.
Please answer this correctly
To get the volume, you need the area of the sides of the square.
The total surface area is 96, with 6 sides. To get the surface area of just one side, divide 96 by 6, which gets you 16. The surface area of a single square is 16. To get one side of the square, divide that by 4 because there are 4 sides.
Now, multiply 16 by 4 to get the volume.
The volume is 64 cubed milllimeters.
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Also i hope this helped
6.
The city's water department charges $3 per month, plus 46c for every 100 gallons of water used.
Let w be the number of gallons of water, in hundreds, used in one month. Express the total monthly cost for water, in dollars, as an equation in terms of w.
cost
Last month, one homeowner used 1,600 gallons. Write 1,600 gallons in terms of hundred gallons.
hundred gallons
What is the homeowner's total cost in dollars) for water last month?
$
The homeowner received a bill for $13.36. Was the billing correct?
Yes
Or No
Answer:
cost in term of w is
c= 0.46 w+3
1600 in terms of hundred gallons is: 16 hundred
c= 0.46*16 +3 = 10.36 dollars
no
Step-by-step explanation:
The cost in terms of w is c= 0.46 w+3 and the total cost will be $10.36.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the city's water department charges $3 per month, plus 46c for every 100 gallons of water used.
The equation will be written as:-
Let w be the number of gallons of water, in hundreds, used in one month. Express the total monthly cost for water, in dollars, as an equation in terms of w.
c= 0.46 w+3
1600 in terms of hundred gallons is: 16 hundred
c= 0.46 x 16 +3 = 10.36 dollars
Therefore, the cost in terms of w is c= 0.46 w+3 and the total cost will be $10.36.
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A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey league according to their birth month. Is there evidence to suggest that hockey players' birthdates are not uniformly distributed throughout the year? Use the level of significance α= 0.05.
Birth Month Frequency
January-March 67
April-June 56
July-September 30
October-December 37
What are the null and alternative hypotheses?
Answer:
[tex]\chi^2 = \frac{(67-47.5)^2}{47.5}+\frac{(56-47.5)^2}{47.5}+\frac{(30-47.5)^2}{47.5}+\frac{(37-47.5)^2}{47.5}=18.295[/tex]
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=4-1=3[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{3} >18.295)=0.00038[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis and we can conclude that the players' birthdates are not uniformly distributed throughout the year
Step-by-step explanation:
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference of birthdates distributed throughout the year
H1: There is a difference between birthdates distributed throughout the year
The level of significance assumed for this case is [tex]\alpha=0.05[/tex]
The statistic to check the hypothesis is given by:
[tex]\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The table given represent the observed values, we just need to calculate the expected values with the following formula [tex]E_i = \frac{total}{4}[/tex]
And replacing we got:
[tex]E_{1} =\frac{67+56+30+37}{4}=47.5[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(67-47.5)^2}{47.5}+\frac{(56-47.5)^2}{47.5}+\frac{(30-47.5)^2}{47.5}+\frac{(37-47.5)^2}{47.5}=18.295[/tex]
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=4-1=3[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{3} >18.295)=0.00038[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis and we can conclude that the players' birthdates are not uniformly distributed throughout the year
The sum of three consecutive even numbers is 66. What is the smallest of these numbers?
Answer:
20
Step-by-step explanation:
one way is guess and check method, you draw a table and try out 3 different consecutive even numbers to see which 3 add up to 66
One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value.
A. True
B. False
Answer:
The statement provided is TRUE.
Step-by-step explanation:
The four principle assumptions of the simple linear regression model are,
The linearity of the relationship between the dependent variable and the independent variable. That is, value of y, the dependent variable for each value of x the independent variable is, [tex]y = \beta_{1} + \beta_{2}x + e[/tex]. Normality of the error distribution. That is, [tex]e_{i} ~\sim N (\mu, \sigma^{2})[/tex]. Thus, the variance of random error e is [tex]Var (e) = \sigma^{2}[/tex]. Statistical independence of the errors or specifically no correlation between consecutive errors. That is, if [tex]Corr (e_{i}, e_{j}) = 0[/tex], it implies that[tex]Cov (e_{i}, e_{j}) = 0[/tex]. Homoscedasticity of the errors, i.e. constant variance.The first assumption clearly indicates that the y-values are statistically dependent upon the x-values.
Thus, the statement provided is TRUE.
Sociology graduates, upon entering the workforce are normally distributed and earn a mean salary of $30,000 with a standard deviation of $4000. Jessica is an honors sociology student. Upon graduation, she would like to take a job that starts at $40,000. What is the probability that randomly chosen salary exceeds $40,000
Answer:
0.62% probability that randomly chosen salary exceeds $40,000
Step-by-step explanation:
Problems of normally distributed distributions 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:
[tex]\mu = 30000, \sigma = 4000[/tex]
What is the probability that randomly chosen salary exceeds $40,000
This is 1 subtracted by the pvalue of Z when X = 40000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40000 - 30000}{4000}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that randomly chosen salary exceeds $40,000
what is a random variable
Answer:
Check Below.
Step-by-step explanation:
In Probability/ Statistics in simple terms it is a variable which possess the following characteristics within a sample space: 1) Their values are defined within the set of Real Numbers, i.e. it is a Quantitative variable. 2) It is possible to calculate its probability.
A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program. (a) List all possible two-course selections. (b) Comment on the likelihood that EPR 646 and EPR 679 will be selected.
Answer:
A) A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program.
The courses were not listed, but let's assume the courses are:
EPR 646,
EPR 602
EPR 679
EPR 622
EPR 684
In this case, we can see there are 5 possible courses.
Selecting them:
[tex]^5C_2 = \frac{5*4*3*2*1}{2*(5-2)!} = 10[/tex]
Therefore, there are 10 selections.
All possible two course selections:
(622,602); (622, 684); (622, 679); (622, 646); (646, 602); (646, 679)
(646,684); (602, 684); (602, 679);
(679, 684)
b) Likelihood that EPR 646 and EPR 679 will be selected
From the data abeve, EPR 646 and EPR 679 can be selected just once.
Therefore, the likelihood =
P(selecting EPR 646 and EPR 679) = [tex]\frac{num. of . times. event. occured}{total. number. of. outcome} =\frac{1}{10}[/tex]
Likelihood that EPR 646 and EPR 679 will be selected is [tex]\frac{1}{10}[/tex] = 0.1
Answer:A student entering a doctoral program in educational psychology is required to select courses from the list of courses provided as part of his or her program.
(a) List all possible -course selections.
(b) Comment on the likelihood that will be selected
Step-by-step explanation:
The local historical Society wants to preserve two buildings. The total age of the buildings is 292 years. If one building is three times as old as the other, what are the ages of the two buildings?
The newer building is years old, and the older building is years old.
Answer:
building one is 292 years old and building two is 879 years old
Step-by-step explanation:
292x3= 879
The newer building is 73 years old,
And, The older building is 219 years old.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The total age of the buildings is 292 years.
Now,
Let the newer building is = x years old,
Then, The older building is = 3x years old.
Here, The total age of the buildings is 292 years.
So, We get;
⇒ x + 3x = 292
⇒ 4x = 292
⇒ x = 73
Thus, The newer building = x years old,
= 73 years old
And, The older building = 3x years old.
= 3 × 73
= 219 years old
Therefore, The newer building is 73 years old,
And, The older building is 219 years old.
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Can someone please help me with this? What would be the measure of angle R to the nearest tenth?
Answer:
Step-by-step explanation:
There are two ways to do this.
1. You could make an accurate diagram and measure R. This works but the computer won't like it. However you will know if you are correct. An answer ± 2 degrees would tell you that you are likely correct.
2. The second way is to find <C. Similarity guarantees that <C and <R are equal. The adjacent side to angle C is the second longest line. The second longest line in PQR is the adjacent side of <R.
Naturally we will use the second method, but you ought to try the first method. It's cumbersome but it will teach you how to read the values of triangles to make clear the trig functions.
Tan(C) = opposite over adjacent
Tan(C) = 7 / 9
Tan(C) = .77777777...
<C = tan-1(0.7777777...)
<C = 37.87
<C = 37.9
Exercise #1: The amount of money in Nicole's bank account can be represented by the function f(x) = 32.50x + 200,
where f(x) is the amount of money in dollars after x days. State the meaning of the slope and y-intercept of this function in
the given context
Any help would be great
the little boxes on the bottom with the numbers in it are the answers. plz do all three if u can
Answer:
is this correct? hope it works
Answer:
The difference of a number and 4 is 11
=> That number is 11 + 4 = 15
The quotient of a number and 13 is 78
=> The number is 13 x 78 = 1014
6.5 more than a number is 19.1
=> The number is 19.1 - 6.5 = 12.6
Hope this helps!
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Amy's car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas she needs, in liters, to fill the gas tank.
Answer:
10 gallons
Step-by-step explanation:
Amy's car's maximum capacity to hold gas = 19 gallons
present amount of gas = 9 gallons
As the car's capacity is 19 gallons and present amount in tank is 9 gallons, so we can fill it as much as so that the amount in tank becomes 19 gallons.
let assume she fills x gallons
then x gallons and 9 gallons present earlier should be equal to 19 gallon, as the tank can not hold more than that.
lets write it mathematically
x + 9 = 19
subtracting 9 from both side
x + 9 - 9 = 19 - 9
=> x = 10
Thus, 10 gallons of gas is needed to fill the gas tank.
Please Help, Math Problem.....
Answer:
Answer is given below with explanations.
Step-by-step explanation:
Given that triangle ABC is similar to triangle PQR
Then
Angle A is congruent to Angle PAngle B is congruent to Angle QAngle C is congruent to Angle RLine segment AB is congruent to Line segment PQLine segment BC is congruent to Line segment QRLine segment AC is congruent to Line segment PR .
THEN THE CORRECT OPTIONS ARE
OPTION D) AND
OPTION E)
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
A farmer has a total of 21 cows and chickens altogether The animals have 54 legs how many cows and how many chickens does the farmer have?
Answer:
The farmer has 4 cows and 15 chickens.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of cows
y is the number of chickens.
A farmer has a total of 21 cows and chickens altogether
This means that x + y = 21.
The animals have 54 legs
A cow has four legs, while a chicken has 2 legs. So
4x + 2y = 54.
From the first equation:
y = 21 - x
Replacing
4x + 2(21 - x) = 54
4x + 42 - 2x = 54
2x = 12
x = 6
y = 21 - x = 21 - 6 = 15
The farmer has 4 cows and 15 chickens.
a small book publisher knows that 15 books weigh 29 lbs. How much do 31 books weigh?
Answer:
I believe the answer would be 59.93333
How old is that dog if his sister is 12 and he is 3 years older
The dog is 15 year old in dog years.
In our eyes he's one, however in the eyes of a dog he is 15
small edit! thank you brainliest!!
Sue has 2 cats. Each cat eats of a tin of cat food each day. Sue buys 8 tins of cat food. Has Sue bought enough cat food to feed her 2 cats for 14 days? You must show how you get your answer.
Answer:
Each cat eats a tin each day. It means 2 tins are required each day for both the cats. So, for 14 days, they will need 28 tins.
Sue has bought just 8 tins, which is not enough
hii pls answer it guys plz help me
Answer:
7) 7/2 (its the only number between 3 and 4)
8) 7/10 ( its the only number between 3/5 and 4/5)
9) 5/8 (its the only number between 1/2 and 3/4)
