Answers
All the values of a 12-sided die will be represented by two 6-sided die. The probability of rolling a 7 on the 12-sided die is 1/12 and rolling a sum of 7 on the two 6-sided dice will be 1/6.
The 12-sided die which is dodecahedral consists of numbers up to 12. The 6-sided die consists of numbers up to 6. The suggestion of using two 6-sided dice instead of a 12-sided die will make a difference in the probabilities of a specific outcome.
Although, using a pair of 6-sided dice and adding their scores will represent all the values or outcomes you can get in a 12-sided die but still there will be a difference in the probabilities.
If we find the probability of rolling 7 on the 12-sided die, then it will be 1/12.
But, in the case of two 6-sided dice, we will obtain the sum of 7 in 6 outcomes which are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of outcomes, in this case, is 36.
Therefore, the probability of rolling a sum of 7 on the two 6-sided dice will be 6/36 = 1/6.
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Related Questions
Find the line's slope and a point on the line.
y-3=3(x+4)
Answers
Answer:
y=3x−9
Step-by-step explanation:
project that requires an initial investment of $2,225,000. The project’s expected cash flows are:
Year
Cash Flow
Year 1 $300,000
Year 2 –100,000
Year 3 475,000
Year 4 450,000
WACC is 8%, and the project has the same risk as the firm’s average project. Calculate this project’s modified internal rate of return (MIRR): Options:
27.46%
33.23%
-12.72%
24.57%
If Green Caterpillar Garden Supplies Inc.’s managers select projects based on the MIRR criterion, they should _____ accept or reject?
Which of the following statements about the relationship between the IRR and the MIRR is correct? options:
A typical firm’s IRR will be greater than its MIRR.
A typical firm’s IRR will be equal to its MIRR.
A typical firm’s IRR will be less than its MIRR.
Answers
The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR.
To calculate the MIRR, we need to find the future value of the positive cash flows at the end of year 4, using the reinvestment rate equal to the WACC. We can then find the discount rate that equates the present value of the initial investment with the future value of the negative cash flows and the positive future value of the positive cash flows.
Using the financial calculator or spreadsheet software, we can find that the future value of the positive cash flows is $698,711.27, and the MIRR is 27.46%.
Therefore, the MIRR is 27.46%, and based on the MIRR criterion, the project should be accepted if the required rate of return is less than 27.46%.
The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR. This is because the IRR assumes that positive cash flows are reinvested at the IRR, which may not be realistic, while the MIRR assumes that positive cash flows are reinvested at the WACC, which is usually more realistic.
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solve this please i beg i am stuck and this is the last question
Answers
Answer:
x = 8.8 cm
Step-by-step explanation:
This is a right-angled triangle, and we are given two sides, so we can use pythagoras Theoren
[tex]a^{2} +b^{2} =c^{2}[/tex]
Where 'c' is the hypotenuse (the longest side in right angled triangle and is always opposite to the 90 degree angle).
'a' and 'b' are the other two sides.
So now we have:
2.6^2 + x^2 = 9.2^2 (Solve for 'x')
x^2 = 9.2^2 - 2.6^2
x = [tex]\sqrt{9.2^{2} - 2.6^{2} }[/tex]
x = 8.8 cm (2 s.f. as other dimensions are also 2 s.f.)
Which expression is equivalent to (z + 6)(z – 6)?
Answers
Answer:
[tex]z^{2} +z-36[/tex]
Step-by-step explanation:
Multiply
The equation 7t = 24.5 models a constant rate situation. What's the value of t?
Answers
Answer:
t=3.5
Step-by-step explanation:
Divide each term in 7t=24.5 by 7 and simplify.
A cylinder has a height of 10 cm and a radius of 4 cm. If the mass of the cylinder is 500 grams, what is the density of the material it is made of?
i think the answer is 0.9 or 1?
Answers
Answer:
The volume of the cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height:
V= πr²h = π(4cm)²(10cm) = 160π cm³
The density of the material is given by the mass per unit volume:
density = mass/volume = 500g / 160π= π(4 cm)²(10 cm)
= 160π cm³
The mass and volume are related by density (ρ), which is defined as mass per unit volume:
ρ = m/V
where m is the mass and V is the volume.
Substituting the given values, we get:
ρ = 500 g / 160π cm³
ρ ≈ 0.988 g/cm³
Therefore, the density of the material the cylinder is made of is 0.988 g/cm³.
NO LINKS!! URGENT HELP PLEASE!!!
10. Mr. and Mrs. Rainer took out a $240,000 to purchase their home. If the interest rate on the loan is 1.2% compounded bimonthly, how much interest will they have paid after 30 years?
Answers
Answer:
$103,875.41
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
P = $240,000r = 1.2% = 0.012n = 6 (bi-monthly)t = 30 yearsNote: Bi-monthly means every 2 months.
Substitute the given values into the formula and solve for A:
[tex]A=240000\left(1+\dfrac{0.012}{6}\right)^{6 \cdot 30}[/tex]
[tex]A=240000\left(1.002\right)^{180}[/tex]
[tex]A=343875.406934...[/tex]
[tex]A=343875.41[/tex]
So after 30 years, Mr. and Mrs. Rainer will have paid a total of $343,875.41, which includes both the principal and the interest.
To find the amount of interest they paid, subtract the principal:
Interest paid = $343,875.41 - $240,000 = $103,875.41
Therefore, they will have paid $103,875.41 in interest over the 30-year period.
South Pole Edition
Your Outdoor Adventures class is providing guidance to a group that is on an expedition to the South Pole. There are 5 people on the expedition.
Due to the extreme climate and conditions, each person in the group needs to consume 6000 calories per day. The table shows the three foods that will make up their total daily calories, along with the number of calories per unit and the daily needs by percentage.
(chart is in the photo i provided)
The map shows the current location of the group, as well as the location of the South Pole and the base camp. Each unit on the grid represents 5 miles. In the question that follow, you will determine whether the group has enough food to reach the South Pole and return to base camp.
Question:
The group thought there was enough food for all 5 group members to complete the trip, with each person getting the required 6000 calories per day. They discover that 2 of the crates they brought are missing.
Each crate contains
•80 biscuits
•50 packages of pemmican
•10 packages of butter and cocoa
Use the map, create a plan for the rest of the trip that includes taking as many group members as possible to the South Pole, while sending the rest of the group members directly back to base camp. Remember that each person must have 6000 calories of food per day until he or she gets back to base camp.
Answers
The group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.
How did we arrive at this assertion?According to the given chart, calculate that each crate contains a total of 48000 calories. Therefore, two missing crates result in a total loss of 96000 calories (48000 x 2).
Determining whether the group has enough food to reach the South Pole and return to base camp, calculate the total number of calories required for the entire trip. Supposing a round trip of 10 days to the South Pole and back, the total number of calories required would be:
Total Calories = (6000 calories/person x 5 people x 10 days) x 2 (round trip)
Total Calories = 600,000 calories
To cover for the lost calories, the group would need to sacrifice one member's trip to the South Pole and send them directly back to base camp. This would leave four members to continue to the South Pole, where they would have to ration their food carefully to make sure they have enough for the entire trip.
Below is a plan to ensure enough food:
Day 1-2:
All five members travel together to position (2,1) and set up camp.Each member would consume 6000 calories per day.Total calories consumed: 5 people x 6000 calories x 2 days = 60,000 caloriesDay 3-5:
Four members (let's call them A, B, C, and D) continue to the South Pole while one member (let's call them E) returns to base camp.E would need 6000 calories per day to return to base camp.Total calories consumed by E: 1 person x 6000 calories x 3 days = 18,000 caloriesA, B, C, and D would have to consume 15000 calories per day (60000 calories ÷ 4 people ÷ 2 days) to make up for the lost calories.Total calories consumed by A, B, C, and D: 4 people x 15000 calories x 3 days = 180,000 caloriesDay 6-7:
A, B, C, and D reach the South Pole and set up camp.They would need 6000 calories per day for 2 days.Total calories consumed: 4 people x 6000 calories x 2 days = 48,000 caloriesDay 8-10:
A, B, C, and D return to position (2,1) and pick up E on the way.They would need 6000 calories per day for 3 days.Total calories consumed: 5 people x 6000 calories x 3 days = 90,000 caloriesAdd up all the total calories consumed:
60,000 + 18,000 + 180,000 + 48,000 + 90,000 = 396,000 calories
This is less than the total calories required, which was 600,000 calories. Therefore, the group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.
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Find all the zeros of the polynomial p(x)=x^3+x^2+8x-60
---------------------
Enter the zeros separated by commas. Enter exact values, not decimal approximations, using square roots as needed.
Answers
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
x = 3, −2+4i, −2−4i
To find the zeros of the polynomial p(x), we need to find the values of x such that p(x) = 0.
One way to do this is to use the rational root theorem, which states that if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors), then p must divide the constant term and q must divide the leading coefficient.
For the polynomial, [tex]p(x) = x^3 + x^2 + 8x - 60,[/tex] the constant term is -60 and the leading coefficient is 1.
Therefore, the possible rational roots are:
±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60
We can then use synthetic division or long division to check which of these roots are actually zeros of the polynomial.
Trying the possible roots, we find that x = 3 is a zero of the polynomial, since p(3) = 0.
Using long division or synthetic division, we can then divide p(x) by (x - 3) to get a quadratic factor:
[tex]x^3 + x^2 + 8x - 60 = (x - 3)(x^2 + 4x + 20)[/tex]
The quadratic factor [tex]x^2 + 4x + 20[/tex] has no real roots since its discriminant [tex](b^2 - 4ac)[/tex] is negative. Therefore, the zeros of the polynomial p(x) are:
x = 3 (with multiplicity 1)
x = -2 ± 4i (with multiplicity 1 each)
Therefore, the zeros of the polynomial p(x) are 3, -2 + 4i, and -2 - 4i.
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Nina wanted to test if her 6-sided die was fair. In other words, she wanted
to test if some sides get rolled more often than others. She rolled the die
60 times and recorded how often each side was rolled. Here are her
results:
Side
1 2 3
4 5 6
Observed counts 10 7 9 11 9 14
Nina wants to perform a x² goodness-of-fit test to determine if these
results give convincing evidence that her die is unfair.
What is the expected count of rolls to land showing a 3?
You may round your answer to the nearest hundredth.
Expected:
Show Calculator
Answers
Answer:
The expected count of rolls to land showing a 3 is 10.00.
Therefore, the expected probability of rolling a 3 is 1/6.
To calculate the expected count, we multiply the expected probability by the total number of rolls:
Expected count = (1/6) * 60
Expected count = 10
Therefore, the expected count of rolls to land showing a 3 is 10.
Solve for X.
X=
ABCDE
3,3,13
Answers
Answer:
10
Step-by-step explanation:
the side is 13 and 3 so the difference is 10 on that side
on the bottom side it's 3 and if it's the same it's 10
how do i find x from the equation x(x+6)=108
Answers
Answer:
x = -3 + √117
x = -3 - √117
Step-by-step explanation:
So the equation is x(x+6)=108
first you gotta simplify
x*x + x*6 = 108
x^2 + 6x = 108
x^2 + 6x - 108 = 0
using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a) with a=1, b=6 and c=-108
Your gross income is $4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in regular savings account at a 3.8% APR. What is the total amount of your emergency fund?
a)$6,516.91
b)$4,888.40
c)$4,520.00
d)$6,107.33
Answers
The total amount of the emergency fund is A) $6,516.91
First, we need to calculate the net income after deductions:
FICA: 7.65% of $4,520.00 = $345.18Federal tax withholding: 11.75% of ($4,520.00 - $345.18) = $451.96State tax withholding: 8.5% of ($four,520.00 - $345.18 - $451.96) = $297.98Net profits = $4,520.00 - $345.18 - $451.96 - $297.98 = $3,425.88Next, we need to calculate the amount of constant expenses:
Fixed prices = 30% of $3,425.88 = $1,027.76
The entire amount saved inside the emergency fund is 5 months' worth of fixed costs:
Emergency fund = $1,027.76 x 5 = $5,138.80
To calculate the quantity inside the 60-day CD
We need to multiply 75% of the emergency fund by means of the interest rate and divide with the aid of 12 to get the monthly interest:
Amount in CD = ($5,138.80 x 0.75 x 0.0525) / 12 = $160.57The amount within the everyday savings account is the remaining 25% of the emergency fund:Amount in normal savings account = $5,138.80 x 0.25 = $1,284.70Therefore, the total amount of the emergency fund is:
$5,138.80 + $160.57 + $1,284.70 = $$6,516.91
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the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes
Answers
The standard deviation of the response time is 1.53 minutes.
What is the standard deviation of the response time?To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.
Z-score = z = (x - μ) / σ
For the lower bound of 10 minutes:
z = (10 - 13) / σ
For the upper bound of 16 minutes:
z = (16 - 13) / σ
As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.
Using z-scores, we set up equations:
(10 - 13) / σ = -1.96
(16 - 13) / σ = 1.96
Solving the first equation:
-3 / σ = -1.96
σ = -3 / -1.96
Solving the second equation:
3 / σ = 1.96
σ = 3 / 1.96
Dividing both sides by 1.96:
-3 / 1.96 = σ
1.53 = σ
Full question:
The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.
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Share #5000 in the ratio of #2000 to #3000 among John and chinedu what percentage of the money does each boy Receive.
Answers
Looking at the graph,would you agree that the boa constrictor population would become a problem?
Answers
Yes the boa constrictor population would become a problem, since the population of beetles in this rainforest community were to disappear, the population of poison dart frogs will most likely be affected;
The populations feed on Beetles and serve as food for poison dart frogs.
Since poison dart frogs depend on beetles for food, then, a decrease in the population of the beetles in the forest community will most likely result in a decrease in the population of the poison dart frogs.
In conclusion, we can say that the beetles serve as food for poison dart frogs.
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Can yall help me with this pls
Answers
In the given figure, after applying the vertical angle and straight line angle property, the values of x and z are 5° and 116° respectively.
Four angles are created when two lines intersect. Vertical angles are those that are opposite each other and are always congruent.
That means, z° = (12x + 56)° ---------- (1)
On a straight line, the angles add up to 180°.
That means, z° + (8x + 24)° = 180° ---------- (2)
Substituting value of z from (1) in (2),
(12x + 56) + (8x + 24) = 180
20x + 80 + 180
20x = 100
x = 5°
Substituting x = 5 in (2),
z + (8*2 + 24) = 180
z + 64 = 180
z = 116°
Therefore, x = 5° and z = 116°.
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You have narrowed your job offers down to the
following two cities:
$21,000 - Minneapolis, MN - $2,400 in Benefits - Cost
of Living Index = 106.1
$27,500-Omaha, NE - $1,200 in Benefits - Cost of
Living Index = 89.2
1) Please convert both job offers into a salary in an
average USA city. (Round your answers to the nearest
cent/two decimal places)!
2) Which job offer is better and why?
Answers
part 1. The job offers into a salary are:
The Adjusted Salary for Minneapolis, MN is $220.38
The Adjusted Salary for Omaha, NE is $322.15
part 2.
We could conclude that the job offer in Omaha, NE is better because of its the adjusted salary as it offers a higher salary in an average USA city.
How do we calculate?For Minneapolis, MN:
Adjusted Salary = (Offered Salary + Benefits) / Cost of Living Index
Adjusted Salary = ($21,000 + $2,400) / 106.1
Adjusted Salary = $23,400 / 106.1
Adjusted Salary = $220.38
For Omaha, NE:
Adjusted Salary = (Offered Salary + Benefits) / Cost of Living Index
Adjusted Salary = ($27,500 + $1,200) / 89.2
Adjusted Salary = $28,700 / 89.2
Adjusted Salary = $322.15
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is .023 a rational number
Answers
Answer:
Yes, .023 is a rational number.
Step-by-step explanation:
A rational number is defined as any number that can be expressed as a ratio of two integers, where the denominator is not zero.
To show that .023 is a rational number, we can express it as a fraction in which the numerator and denominator are integers.
We can write:
.023 = 23/1000
Both the numerator (23) and denominator (1000) are integers, so .023 is a rational number.
Solve 148x + 231y =527 231x+ 148y = 610
Answers
Answer:
(x, y) = (2, 1)
Step-by-step explanation:
You want the solution to the system of equations ...
148x +231y = 527231x +148y = 610SolutionWhen the coefficients are not nicely related, graphical methods or matrix methods are preferred, as elimination or substitution can result in messy arithmetic with large numbers.
The first attachment shows a calculator's solution using row-reduction of the augmented matrix of coefficients. It tells us the solution is ...
(x, y) = (2, 1)
Cross Multiplication methodA solution similar to the use of Cramer's rule can be found using the cross-multiplication method. For this, we rewrite the equations to general form, and make a list of the coefficients with the x-coefficients repeated at the end of the list:
148x +231y -527 = 0 ⇒ 148, 231, -527, 148231x +148y -610 = 0 ⇒ 231, 148, -610, 231Now, we form the differences of the cross products in each pair of columns:
∆ = (148)(148) -(231)(231) = -31,457
∆x = (231)(-610) -(148)(-527) = -62,914
∆y = (-527)(231) -(-610)(148) = -31,457
And the solution is ...
x = ∆x/∆ = -62,914/-31,457 = 2
y = ∆y/∆ = -31,457/-31,457 = 1
The solution is (x, y) = (2, 1).
__
Additional comment
You might consider this to be "messy arithmetic with large numbers." Yes, it looks that way, but there are actually fewer operations required here than when using the elimination method.
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A 4-digit number has the digits 0,5,9 and 3.To the nearest thousand,it rounds to 10,000. What is the number? Explain.
Answers
Answer: 9530
Step-by-step explanation: It has to be 9 in the thousands place to start of. And for it to round to 10,000, it would have to be 5 since it would round up one more thousand. And I would just say 3 because its bigger. Then 0
Please answer these papers entirely, it’s due tomorrow
Answers
The area of Curtis's triangular frame is 36 square feet. The Option C is correct.
What is the area of the triangular frame?To get area of the frame, we will use formula for the area of a triangle which is [tex]A = 1/2 * b * h[/tex]
B = length of the base
H = perpendicular distance from the base to the vertex.
Substituting the values, we get:
A = 1/2 * 12 feet * 6 feet
A = 1/2 * 72 feets
A = 36 square feet
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Please help asap!!! I will give points !!!
Answers
The value of p when q is equal to 2 is 108
What is inverse variation?Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
This means as x increases y reduces and vice versa.
If p is inversely proportional to q, then
p = k/q
p = 18 and q = 12
18 = k/12
k = 18 × 12 = 216
When q =2
p = 216/2
p = 108
therefore the value of p is 108
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Why is math important to you. (3 sentences)
Answers
Some of the reasons why math is important include:
Problem-solvingNeed in daily life Career opportunities How is math important ?Mathematics teaches us the invaluable skills of critical thinking via logical and systematical reasoning for solving complicated problems. It is, however, essential to know that mathematics is omnipresent in our day-to-day lives but we may not be conscious about it.
Our math-related actions include computing tips, shopping, allocating time for daily tasks as well as cooking meals. With a strong foundation in Mathematics, several career paths such as engineering, finance, accounting or data analysis can materialize for perspective job-visors; hence enabling them towards professional success.
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Kofi thinks of a integer number and then add 5 to it.He then multiplies the result by 3.The answer he obtains cannot be greater than 21.Find all the positive values of the number he thinks of.
Answers
The positive values of the number Kofi thinks of are 1 and 2.
Let's call the number Kofi thinks of "x".
According to the problem Kofi adds 5 to this number and then multiplies the result by 3.
We can write this as:
3(x + 5)
We know that this expression cannot be greater than 21 so we can set up an inequality:
3(x + 5) ≤ 21
Simplifying the inequality, we get:
x + 5 ≤ 7
Subtracting 5 from both sides, we get:
x ≤ 2
The possible values of the number Kofi thinks of are all the positive integers less than or equal to 2 are 1 and 2.
To check that these values work can plug them back into the expression 3(x + 5) and verify that they give a result less than or equal to 21:
If Kofi thinks of 1, then 3(1 + 5) = 18 is less than 21.
If Kofi thinks of 2 then 3(2 + 5) = 21 is equal to 21 but it satisfies the condition since the problem asks for an answer that "cannot be greater than 21".
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100 POINTS
Ann obtained the list of apartments below.
a. Use linear regression analysis to determine if there is a correlation between the square footage and the monthly rent.
b. Determine the regression equation. Round the numbers in the equation to the nearest hundredth.
c. Use your regression equation to determine the price you might expect to pay for an 810-square foot apartment.
Answers
Answer:
a) Very strong positive correlation (r = 0.99).
b) y = 299.46 + 1.74x
c) $1,709 per month
Step-by-step explanation:
Linear regression is a statistical technique used to model the relationship between a dependent variable and an independent variable by fitting a linear equation to the observed data points. It aims to find the line of best fit that minimizes the overall distance between the observed data and the predicted values based on the linear equation.
Part (a)We can use a statistical calculator to perform linear regression analysis on the given data.
The explanatory (independent) variable is the square footage (x-values).
The response (dependent) variable is monthly rent (y-values).
After entering the data into a statistical calculator we get:
a = 299.464156...b = 1.73689309...r = 0.986575728...The r-value, also known as the correlation coefficient, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges between -1 and 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.
In this case, an r-value of 0.99 suggests that there is a very strong positive linear relationship between between square footage and monthly rent. As the square footage increases, the monthly rent tends to increase as well.
This high correlation indicates that square footage is a strong predictor of monthly rent. However, it is important to note that the correlation coefficient alone does not imply causation or provide information about the underlying factors influencing the relationship.
[tex]\hrulefill[/tex]
Part (b)To determine the regression equation, substitute the found values of a and b into the regression line formula, y = a + bx.
Round the values of a and b to the nearest hundredth:
a = 299.46b = 1.74Therefore, the regression equation is:
[tex]\boxed{y = 299.46 + 1.74x}[/tex]
where:
x is the square footage.y is the monthly rent (in dollars).[tex]\hrulefill[/tex]
Part (c)To determine the monthly rent that we might expect to pay for an 810 square foot apartment, substitute x = 810 into the regression equation found in part (b), and solve for y:
[tex]\begin{aligned}y &= 299.46 + 1.74(810)\\&=299.46+1409.4\\&=1708.86\\&=1709\end{aligned}[/tex]
Therefore, we would expect to pay approximately $1,709 per month for an 810 square foot apartment.
Help me with this question please!!!
Answers
Mia's total profit for the month is given as follows:
$200.
How to obtain the profit function?The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:
P(x) = R(x) - C(x).
From the table given in this problem, the revenue and the costs are given as follows:
Revenue of $9,500.Cost of 9000 + 300 = $9,300.Hence the profit is given as follows:
9500 - 9300 = $200.
As the profit is positive, it is in fact a profit(gain) and not a loss.
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Write 382,368 in word form
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The output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.
How to determine the output level that maximize profitsTo maximize profits, we need to find the output levels of the two goods that will maximize the difference between total revenue and total cost (i.e., profit).
The profit function can be expressed as:
π = TR - TC
= 15Q1 + 18Q1^2 + 15Q2 + 18Q2^2 - 20 - 2Q1.Q2 - 393
Taking the partial derivative of the profit function with respect to Q1 and setting it equal to zero, we get:
∂π/∂Q1 = 15 + 36Q1 - 2Q2 = 0
Taking the partial derivative of the profit function with respect to Q2 and setting it equal to zero, we get:
∂π/∂Q2 = 15 + 36Q2 - 2Q1 = 0
Using Cramer's rule, we can solve for Q1 and Q2:
Q1 = (2(15) - (15)(36))/(-4) = 52.5
Q2 = (2(15) - (15)(36))/(-4) = 52.5
Therefore, the output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.
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Daniela has a three-season acting contract for a new TV show. Her pay for Season 1 iscp dollars. Then, her pay will increase by 5 percent from Season 1 to Season 2 and by 10 percent from Season 2 to Season 3. Which of the following represents Daniela's Season 3 pay in terms of p?
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1.15p is the expression which represents Daniela's Season 3 pay in terms of p
To find Daniela's Season 3 pay in terms of p, we need to calculate the pay increase for each season.
In Season 2, her pay increases by 5 percent, which means she will receive 105 percent (or 1.05) of her Season 1 pay.
In Season 3, her pay increases by 10 percent from Season 2, so she will receive 110 percent (or 1.10) of her Season 2 pay.
To express Daniela's Season 3 pay in terms of p, we multiply the Season 1 pay (p) by the pay increase factors for Season 2 and Season 3:
Season 2 pay = 1.05p
Season 3 pay = 1.10(1.05p) = (1.10)(1.05)p
Simplifying the expression, we get:
Season 3 pay = 1.155p
Therefore, 1.15p is the expression which represents Daniela's Season 3 pay in terms of p
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