It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 25 feet. (You may find it useful to reference the appropriate table: z table or t table)a. State the null and the alternative hypotheses for the test. H0: μ = 120; HA: μ ≠ 120 H0: μ ≥ 120; HA: μ < 120 H0: μ ≤ 120; HA: μ > 120b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)Find the p-value. 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05c. Use α = 0.01 to determine if the average breaking distance differs from 120 feet.
Answers
The alternative hypothesis is H0: μ = 120; HA: μ ≠ 120; test static is -1.9666; and p-value is between 0.025 and 0.05.
a. The null and alternative hypotheses for the test are:
H0: μ = 120; HA: μ ≠ 120
b. To calculate the value of the test statistic, use the following formula:
test statistic (z) = (sample average - population mean) / (population standard deviation / √sample size)
z = (112 - 120) / (25 / √38)
z = (-8) / (25 / 6.1644)
z = -8 / 4.0675
z = -1.9666 (rounded to 4 decimal places)
Now, find the p-value using the z-table:
Since the alternative hypothesis is a two-tailed test (μ ≠ 120), we need to find the two-tailed p-value.
From the z-table, the area to the left of -1.9666 is approximately 0.0247.
Since it's a two-tailed test, we multiply the area by 2.
p-value = 2 * 0.0247 = 0.0494 (rounded to 4 decimal places)
The p-value is between 0.025 and 0.05.
c. Since the p-value (0.0494) is greater than α = 0.01, we fail to reject the null hypothesis at the 0.01 significance level. Therefore, there is not enough evidence to conclude that the average braking distance differs from 120 feet.
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Related Questions
Which are the correct measures for
Answers
Answer:
option c is the correct answer
Step-by-step explanation:
∠YXZ+117°=180°
∠YXZ=180°-117°
∠YXZ=63°
63°+36°+∠YZX=180°(sum of angles is 180)
99°+∠YZX=180
∠YZX=180-99
∠YZX=81
Number 8 pls help 50 points! Simple question
Answers
The conversion of 5 c to pints, represented as pt will give 2.5 pt.
How to convert cups to pints
The conversion rate of 1 pint to cup is at the rate of 1 pint to 2 cups. So when we have 5 cups for conversion to pints, we will have to multiply 5 cups by 1 pint and then divide the result by 2.
When this is done, the resulting figure will be 2.5 pt. In the same vein, the conversion of 2.5 pt to cup will give 5 cups. So, for the number 8 question above, we can arrive at 2.5 pt as the answer for the conversion of 5 cups to pints.
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Using a random sample of 5613 TV households, Acme Media Statistics found that 25.1 % watched the final episode of "When Will it End question mark"
a. Find the margin of error in this percent.
b. Write a statement about the percentage of TV households in the population who tuned into the final episode of "When Will it End question mark"
Answers
Answer:
± 1.13432%
between 23.966% and 26.234% households in the population who tuned into the final episode of "When Will it End question mark"
Step-by-step explanation:
Given that:
Sample size (n). = 5613
Proportion (p) = 25.1% = 0.251
Margin of Error can be obtained using :
MOE = z * √p * (1 - p) / √n
Zscore at 95% confidence interval = 1.96
1 - p = 1 - 0.251 = 0.749
Hence,
Margin of Error :
1.96 * √0.251 * 0.749 / √5613
1.96 * (0.4335885 / 74.919957)
= 0.0113432
= ± (0.0113432) * 100%
= ± 1.13432%
B.) between (25.1 - 1.134)% = 23.966% and 25.1 + 1.134)% = 26.234% households in the population who tuned into the final episode of "When Will it End question mark"
Margin of Error (MOE) is a function of the critical value. We will choose a confidential interval of 95 %.
Solution is:
a) MOE = 0,011
b) We can affirm with 95 % of confidence that the porcentage of TV households in the population watching th final episode of " When ...
would be between 25,1 - 0,011 and 25,1 + 0,011
In our question we got:
Sample size n = 5613
p = 25.1 % ( positive events expressed as porcentage )
q = 1 - p q = 1 - 0,251 q = 0,749
According to the size of the sample, and the fact that
q×n and p×n are both q×n > 10 p×n > 10
We are in condition to apply the approximation of the binomial distribution to normal distribution and use table z scores
CI = 95 % then confidence level α = 5 % α/2 = 0,025 and fom z-table we get the critical value
z(c) = 1,96
Now to find MOE
MOE = z(c)×√(p×q/n) ⇒ MOE = 1,96 × √ ( 0,251×0,749)5613
MOE = 1,96 × 0,005787
MOE = 0,011
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If Confidential Interval is 95%
hey guys whats expand 3(x + 4)
Answers
Answer:
3x + 12
Step-by-step explanation:
3(x + 4)
3x + 12
So, the expand is 3x + 12
Answer:
3x + 12
Step-by-step explanation:
You multiply the outside of the perentheses by everything inside, and 3(x) + 3(4) = 3x + 12
The table below shows the monthly balances a person had on their credit card over a five-month period.
Month Balance
January -$50
February $25
March -$70
April -$45
May $25
What was the average monthly balance over the five-month period? Enter your answers and your explanations or work in the space provided.
Answers
Answer:
43 dollars
Step-by-step explanation:
to take the average we have to add up all the numbers and divide by 5 which is
215/5=43
if my answer helps please mark as brainliest.
Pls help I’m getting confused even though should be pretty easy.
Answers
Answer:
V = 108
Step-by-step explanation:
B = 9 x 4 = 36 Height of Triangular prism is 3 so 36 x 3 = 108
A 288-m long fence is to be cut into pieces to make three enclosures, each of which is square. How should the fence be cut up in order to minimize the total area enclosed by the fence
Answers
The 24 meters should the fence be cut up in order to minimize the total area enclosed by the fence
Given that,
The length of fence is 288 meters.
Let us take the size of the smallest square is x , middle square is y and the largest square is z.
Length of the fence is equal to sum of the perimeter of the three square.
4x + 4y + 4z = 288
4(x + y +z) = 288
x + y +z = \(\frac{288}{4}\)
x + y +z = 72 --------> equation(1)
The total area A = x² + y² + z²
Put z = 72 - x - y in A
A = x² + y² + (72 - x - y)² ---------->equation(2)
Now we have to find the x and y values to minimize A.
\(\frac{dA}{dx} = \frac{d}{dx} [x^2 + y^2 + (72 -x - y)^2]\\\)
\(\frac{dA}{dx}= 2x + 0 +2(72-x-y)(-1)\)
\(\frac{dA}{dx}= 2x - 2(72-x-y)\)
Taking \(\frac{dA}{dx}\) = 0
2x - 2(72 - x - y) = 0
x - 72 + x + y = 0
2x + y - 72 = 0
2x + y = 72 ---------> equation(3)
Now, \(\frac{dA}{dy} = \frac{d}{dy} [x^2 + y^2 + (72 -x - y)^2]\\\)
\(\frac{dA}{dy}= 0 + 2y +2(72-x-y)(-1)\)
\(\frac{dA}{dy}= 2y - 2(72-x-y)\)
Taking \(\frac{dA}{dy}\) = 0
2y - 2(72 - x - y) = 0
y - 72 + x + y = 0
x + 2y - 72 = 0
x + 2y = 72 ---------> equation(4)
Now, equation(3) ×2 and subtracted by equation(4)
4x + 2y = 144
x + 2y = 72
-------------------(subtraction)
3x = 72
x = 24
Taking x = 24 in equation(3)
2x + y = 72
2(24) + y = 72
48 + y = 72
y = 72 - 48
y = 24
Substituting y and x in equation(1)
x + y + z = 72
24 + 24 + z = 72
48 + z = 72
z = 72 - 48
z = 24
Therefore, The 24 meters should the fence be cut up in order to minimize the total area enclosed by the fence
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Yesterday, Selma read 75 pages of her book. If she reads at a pace of 2 pages per minute today, which table shows only viable solutions for the total number of pages she has read, y, after x minutes have elapsed?
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries negative 16, 6, 27, 52. The second column is labeled total pages read (y) with entries 43, 87, 129, 179.
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 19, 32, 47. The second column is labeled total pages read (y) with entries 0, 113, 139, 169.
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 11, 20.25, 58. The second column is labeled total pages read (y) with entries 75, 97, 115.5, 191.
Mark this and return
Answers
The table that shows only viable solutions for the total number of pages Selma has read after x minutes have elapsed is:
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.
Which table shows only viable solutions for the total number of pages Selma has read after x minutes have elapsedA 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.
This table corresponds to Selma reading at a pace of 2 pages per minute, and the total pages read after x minutes align with the given entries in the table.
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if $m$ workers can complete a job in $d$ days, how many days will it take $n$ workers, working at the same rate, to complete one-third of the job? express your answer as a common fraction in terms of $d$, $m$ and $n$, in alphabetical order where applicable.
Answers
The answer is (1/3)(md) / n.
Let's analyze the problem step by step.
We are given that m workers can complete a job in d days. This means that the rate at which the workers complete the job is 1 job per (md) days.
Now, we need to find how many days it will take n workers to complete one-third of the job. Since the workers are working at the same rate, the number of days required will be inversely proportional to the number of workers.
Let's assume it takes x days for n workers to complete one-third of the job. In x days, the rate at which n workers complete the job will be 1 job per (nx) days.
According to the given information, the rate at which m workers complete the job is 1 job per (m d) days. Since the rates are equal, we can set up the following equation:
1/(n x) = 1/(m d)
To find x, we can cross-multiply:
n x = m d
Now, we need to find the number of days it will take n workers to complete one-third of the job, which is equivalent to (1/3) of the job.
Therefore, we can rewrite the equation as:
n x = (1/3) (m d)
Simplifying further:
x = (1/3) (m d) / n
Thus, the number of days it will take n workers, working at the same rate, to complete one-third of the job is:
x = (1/3)(md) / n
Therefore, the answer is (1/3)(md) / n.
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The Smith Family is buying a house for $350,000 with a down payment of $70,000 for a 15-year loan, $66 per month insurance, property tax is $230 per month and HOA is $600 per year. Calculate their total monthly payment
Answers
Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.
What is the Monthly Payment?To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.
1. Mortgage Payment:
The loan amount is the house price minus the down payment:
$350,000 - $70,000 = $280,000.
To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).
We can use a mortgage calculator formula to calculate the monthly payment:
M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]
Where:
M = Monthly mortgage payment
P = Loan amount
i = Monthly interest rate
n = Number of months
The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.
i = 4% / 12 = 0.00333 (monthly interest rate)
n = 180 (loan term in months)
Plugging in the values into the formula:
M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]
Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.
2. Insurance:
The monthly insurance payment is given as $66.
3. Property Tax:
The monthly property tax payment is given as $230.
4. HOA Fees:
The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.
Now, let's add up all these expenses:
Mortgage payment: $2,014.99
Insurance: $66
Property tax: $230
HOA fees: $50
Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees
Total monthly payment = $2,014.99 + $66 + $230 + $50
Total monthly payment = $2,360.99
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A. (2,-1)
B. (3,-2)
C. (0,7)
D. (1,2)
Answers
The vertex is at the the coordinates (3,-2)
Answer: (3,-2) is the answer. I hope this helped :)
Step-by-step explanation: the center point is the vertex
(Score for Question 1: ___ of 5 points) What is the solution to the system of equations? 3x-2y=8 " 6" x-4y=12 Use any algebraic method (substitution or elimination) to justify that the given system of equations has no solution. What do you know about the two lines in this system of equations graphically?
Answers
Graphically, the two lines will appear as two distinct lines running parallel to each other, never intersecting.
What algebraic concepts are involved?Mathematical statements known as algebraic rules connect two variables and are expressed as equations. One of the algebraic constants is area = length x width. As a result of a set of factors, you can also develop your own rule.
To solve the system of equations:
3x - 2y = 8
6x - 4y = 12
We can simplify the second equation by dividing both sides by 2:
3x - 2y = 8
3x - 2y = 6
Now we can see that the two equations represent two parallel lines with the same slope (-3/2) and different y-intercepts (4 and 3).
Since the two lines are parallel, they will never intersect and therefore there is no solution to the system of equations.
Graphically, the two lines will appear as two distinct lines running parallel to each other, never intersecting.
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PLEASE HELP
5. By what would you multiply the bottom equation to eliminate y?
x + 3y = 9
2x - y = 11
-2
3
2
Answers
Answer: i believe that 2
Step-by-step explanation: i did my research and i did calculated it
I need help I will give brainliest I promise please helpppp
Answers
8% of 500 is 40.
Someone explain please
Answers
Answer:
SA = 94 ft²
Step-by-step explanation:
To find the surface area of a rectangular prism, you can use the equation:
SA = 2 ( wl + hl + hw )
SA = surface area of rectangular prism
l = length
w = width
h = height
In the image, we are given the following information:
l = 4
w = 5
h = 3
Now, let's plug in the information given to us to solve for surface area:
SA = 2 ( wl + hl + hw)
SA = 2 ( 5(4) + 3(4) + 3(5) )
SA = 2 ( 20 + 12 + 15 )
SA = 2 ( 47 )
SA = 94 ft²
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o persoana depune la banca o suma de bani. banca ofera o dobanda anuala de 2%. dupa un an in cont se afla 8160 lei. Care a fost suma depuse la banca?
Answers
Answer:
8000 lei
Step-by-step explanation:
Ni se spune la întrebarea de mai sus să găsim suma depusă în bancă.
Ni se oferă următoarele valori
R = rata = 2% = 0.02
T = Timp = 1 an
Suma totală = A = 8160 lei
Trebuie să găsim principalul (suma depusă la bancă).
Formula de utilizat este dată ca:
P (Principal) = A / (1 + rt)
P = 8160 lei / 1 + 0.02 × 1
P = 8160 lei / 1.02
P = 8000 lei
Prin urmare, suma depusă în bancă este de 8000 de lei.
Answer:
the two percent of 8160 its 163.2 so its 7996.8
Step-by-step explanation:
Air is being pumped into a spherical balloon at the rate of 7 cm³/sec. What is the rate of change of the radius at the instant the volume equals 36n cm³ ? The volume of the sphere 47 [7] of radius r is ³.
Answers
the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.
The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.
We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)
7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³
36 = (4/3)r³
27 = r³
r = 3 Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)
(dr/dt) = 7 / (4π(9))
(dr/dt) = 7 / (36π)
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The surface area of a cylinder is 28π m². The distance around the base of the cylinder is 7π meters and the diameter of a base of the cylinder is 4 meters.
What is the height of the cylinder?
Enter your answer, as a simplified fraction, in the box.
m
Answers
Answer:
5
Step-by-step explanation:
diameter = 4 so radius =2
open up the cylinder so its top & bottom circle's circumference = 2πr =4π
top & bottom circle's area = πr² = 4π each, 8π for both
total surface = 28π
so lateral surface = 28π - 8π = 20π
so 20π = 4π* height
so height is 5
Please Help ASAP, end of term is the 15th and I’m super behind!!
What is the rate of change of the line in the graph below?
(Picture below)
Answers
The rate of change is 1 and the y-intercept is 1/2.
How do you find the rate of change on a line graph?
To get the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.
The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.
It is frequently referred to as rate of change when determining the slope of real-world scenarios. "Rate of change" and "slope" have the same meaning. Use the slope formula or create a slope triangle if you are asked to determine the rate of change.
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100 points, help meh! very badly need help *Sarcastic*
Answers
Answer:
2. g is the independent variable and p is the dependent variable.
Step-by-step explanation:
g is the independent variable because in the word problem it says determines so that means that p depends on g.
I hope it helps! Have a fantabulous day!
Lilac~
Answer:
"p"
Step-by-step explanation:
"p" is the dependent variable. This is because the amount of party favors (p) DEPENDS on the number of guests.
Hope this helps!
A regular square pyramid has volume of 2400 cmr- and height of 18 cm.
calculate the approximate base length of the pyramid.
Answers
To approximate the base length of a regular square pyramid with a given volume and height, we can use the formula for the volume of a pyramid and rearrange it to solve for the base length.
The volume of a pyramid is given by the formula V = (1/3) * base area * height. In the case of a regular square pyramid, the base is a square, so the base area is equal to the length of one side squared. Let's denote the base length as 'l'.
Given that the volume of the pyramid is 2400 cm^3 and the height is 18 cm, we can substitute these values into the formula:
2400 = (1/3) * l^2 * 18
To solve for the base length, we can rearrange the equation:
l^2 = (2400 * 3) / 18
l^2 = 400
Taking the square root of both sides, we get:
l = √400
l = 20 cm
Therefore, the approximate base length of the pyramid is 20 cm.
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M,
Lauren has watermelons and oranges in a ratio of 88:14. How many watermelons
does she have if she has 7 oranges?
Answers
Answer:
Lauren has 44 watermelons
Step-by-step explanation:
Let us use W to denote the number of watermelons and O to denote the number of oranges
We have
W:O = 88:14
This can be represented as a fraction:
\(\dfrac{W}{O} = \dfrac{88}{14}\)
Divide numerator and denominator of \(\dfrac{88}{14}\) by 2
\(\dfrac{88 \div 2}{14 \div 2} = \dfrac{44}{7}\\\\\\\\\mathrm{So\; \dfrac{W}{O} = \dfrac{44}{7}}\\\\\)
This means for every 7 oranges there are 44 times that number of watermelons
Since we are given that there are 7 oranges she should have 44 watermelons
Another way of looking at this is from the relation
\(\dfrac{W}{O} = \dfrac{44}{7}}\\\\\)
Putting in O = 7 we get
\(\dfrac{W}{7} = \dfrac{44}{7}\\\\\)
Since the denominators are the same the numerators must be the same i.e. W = 44
Lauren has 44 watermelons
Two containers designed to hold a water our side-by-side, both in the shape of a cylinder. Container a has A diameter of 6 feet and a height of 15 feet. Container b has a diameter of 8 feet and a height of 10 feet. Container is full of water in the water is pumped into container be until container is empty. After the pumping is complete what is the volume of the empty portion of container b, to the nearest 10th of a cubic foot
Answers
Answer:
78.5 ft3
Step-by-step explanation:
First we need to find the volume of both containers.
The volume of a cylinder is given by the equation:
Volume = pi * diameter^2 * height / 4
If cylinder A has a diameter of 6 feet and height of 15 feet, we have:
Volume_A = pi * 6^2 * 15 / 4 = 424.115 ft3
If cylinder B has a diameter of 8 feet and height of 10 feet, we have:
Volume_A = pi * 8^2 * 10 / 4 = 502.6548 ft3
After pumping the water from A to B, the volume of the empty portion of B will be the difference of their volumes:
Volume_B - Volume_A = 502.6548 - 424.115 = 78.5398 ft3
Rounding to the nearest 10th of a cubic foot, we have a difference of 78.5 ft3
Hi, i know how to solve this question, but i was wondering if it was possible to solve #1 using the effective yearly rate. IE. (1+r/n)^n
Mike just bought a house for $1.3m. He paid $300k as a down-payment and the rest of the cost has been obtained from a mortgage. The mortgage has a nominal interest rate of 1.8% compounded monthly with a 30-year amortization period. The term (maturity) of the mortgage is 5 years.
1) What are Mike's monthly payments?
2) What does Mike owe at the end of the 5-year term (what is the balance at time 60, B60)?
Answers
Mike's monthly payments are approximately $19,407.43. At the end of the 5-year term (time 60), Mike owes approximately $1,048,446.96.
To solve the given problem, we can use the formula for calculating the monthly mortgage payments:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
r = Monthly interest rate
A = Loan amount
n = Total number of payments
First, let's calculate the monthly interest rate. The nominal interest rate is given as 1.8%, which means the monthly interest rate is 1.8% divided by 12 (number of months in a year):
r = 1.8% / 12 = 0.015
Next, let's calculate the total number of payments. The mortgage has a 30-year amortization period, which means there will be 30 years * 12 months = 360 monthly payments.
n = 360
Now, let's calculate Mike's monthly payments using the formula:
P = (0.015 * (1.3m - 300k)) / (1 - (1 + 0.015)^(-360))
Substituting the values:
P = (0.015 * (1,300,000 - 300,000)) / (1 - (1 + 0.015)^(-360))
Simplifying the expression:
P = (0.015 * 1,000,000) / (1 - (1 + 0.015)^(-360))
P = 15,000 / (1 - (1 + 0.015)^(-360))
Calculating further:
P = 15,000 / (1 - (1.015)^(-360))
P ≈ 15,000 / (1 - 0.22744)
P ≈ 15,000 / 0.77256
P ≈ 19,407.43
Therefore, Mike's monthly payments are approximately $19,407.43.
To calculate the balance at time 60, we can use the formula for calculating the remaining loan balance after t payments:
Bt = P * ((1 - (1 + r)^(-(n-t)))) / r
Where:
Bt = Balance at time t
P = Monthly payment
r = Monthly interest rate
n = Total number of payments
t = Number of payments made
Substituting the values:
B60 = 19,407.43 * ((1 - (1 + 0.015)^(-(360-60)))) / 0.015
B60 = 19,407.43 * ((1 - (1.015)^(-300))) / 0.015
B60 ≈ 19,407.43 * ((1 - 0.19025)) / 0.015
B60 ≈ 19,407.43 * 0.80975 / 0.015
B60 ≈ 19,407.43 * 53.9833
B60 ≈ 1,048,446.96
Therefore, at the end of the 5-year term (time 60), Mike owes approximately $1,048,446.96.
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Expand and simplify if possible (√2+5)(1+√2)
Answers
Answer:
7 + 6\(\sqrt{2}\)
Step-by-step explanation:
note that \(\sqrt{a}\) × \(\sqrt{a}\) = a
(\(\sqrt{2}\) + 5)(1 + \(\sqrt{2}\))
each term in the second factor is multiplied by each term in the first factor, that is
\(\sqrt{2}\)(1 + \(\sqrt{2}\)) + 5(1 +\(\sqrt{2}\)) ← distribute parenthesis
= \(\sqrt{2}\) + 2 + 5 + 5\(\sqrt{2}\) ← collect like terms
= 7 + 6\(\sqrt{2}\)
Leo designs a stand for the new statue on display at the local library. The stand is in the shape of a right trapezoidal prism. The base of the prism has an area of 3 ft2, and the prism stands 3.2 feet high. As Leo paints the stand, he calculates the surface area of the stand to be 35 ft2.
Leo is asked to purchase roping that will be used to close off the area around the statue. He purchases a length that is five times the perimeter of the stand in roping.
How much roping does he purchase?
Leo plans to add gold leaf to the sides of the stand but not to the two bases.
What percent of the area of the stand will have gold leaf? Round your answer to the nearest whole number.
Answers
Answer:
A: 45 5/16
B: The present of the area as 83%
Step-by-step explanation:
(a)
35= 3+3+3.2x+3.2x+3.2x+3.2x
35= 6 + 12.8
29/12.8 +12.8x/12.8
X=2.265625 = 2/12/64
1x = 2 17/64 * 4 + 9 1/16
P = 45 5/16
(b)
The present of the area as 83%
35 – the bases or 6 = 29
29/35 + 0.82857142857
0.82857142857 * 100 = 82.8571428571
Rounded to the nearest whole number is 83%
A researcher is interested if the number of pets people own (the x-variable) is related to their stress on a scale of 0-80 (the y-variable). Given these sample data points: A data table for X and V Calculate and show all your work: a. cov xy
(the covariance of x and y ) b. s x
(the standard deviation of x ) c. s y
(the standard deviation of y ) d. r xy
(the correlation of x and y )
Answers
To calculate the statistical measures for the given data points, we need the actual values of the X and Y variables.
Without the specific data values, we cannot perform the calculations. However, I can explain the formulas and concepts behind each measure.
a. Covariance (cov xy): Covariance measures the relationship between two variables and indicates the extent to which they vary together. It is calculated by taking the sum of the products of the differences between each corresponding X and Y value and the means of X and Y, respectively, and dividing by the number of data points minus one.
b. Standard deviation of X (s x): The standard deviation measures the dispersion or spread of a dataset. It is calculated by taking the square root of the variance of X. Variance is the average of the squared differences between each X value and the mean of X.
c. Standard deviation of Y (s y): Similar to the standard deviation of X, the standard deviation of Y measures the spread of the Y variable. It is calculated by taking the square root of the variance of Y, which is the average of the squared differences between each Y value and the mean of Y.
d. Correlation of X and Y (r xy): Correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A positive value indicates a positive linear relationship, while a negative value indicates a negative linear relationship. Correlation is calculated by dividing the covariance of X and Y by the product of their standard deviations.
To accurately calculate the covariance, standard deviations, and correlation, the actual data points for X and Y are required. With the specific data, these calculations can be performed to determine the relationship between the number of pets people own (X) and their stress levels (Y) on a scale of 0-80.
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PLEASE HELP 80 POINTS!!!!!
Answers
Answer: reflection across x axis and y axis?
Step-by-step explanation: repost question with the possible answers!
D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find (a) the eqquilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point.
D(x)=3000−10x, S(x) = 900+25x
(a) What are the coordinates of the equilibrium point?
______(Type an ordered pair.)
(b) What is the consumer surplus at the equilibrium point?
$____ (Round to the nearest cent as needed.)
(c) What is the producer surplus at the equilibrium point?
$____ (Round to the nearest cent as needed.)
Answers
The equilibrium point is (60, 2400), the consumer surplus at the equilibrium point is $48,000, and the producer surplus at the equilibrium point is $36,000.
(a) The equilibrium point occurs when the quantity demanded by consumers equals the quantity supplied by producers. To find this point, we need to set the demand function equal to the supply function and solve for x.
Demand function: D(x) = 3000 - 10x
Supply function: S(x) = 900 + 25x
Setting D(x) equal to S(x):
3000 - 10x = 900 + 25x
Simplifying the equation:
35x = 2100
x = 60
Therefore, the equilibrium point occurs at x = 60.
(b) Consumer surplus at the equilibrium point can be found by calculating the area between the demand curve and the equilibrium price. Consumer surplus represents the difference between the price consumers are willing to pay and the actual market price.
At the equilibrium point, x = 60. Plugging this value into the demand function:
D(60) = 3000 - 10(60)
D(60) = 3000 - 600
D(60) = 2400
The equilibrium price is $2400 per unit. To find the consumer surplus, we need to calculate the area of the triangle formed between the demand curve and the equilibrium price.
Consumer surplus = (1/2) * (2400 - 900) * 60
Consumer surplus = $48,000
(c) Producer surplus at the equilibrium point represents the difference between the actual market price and the minimum price at which producers are willing to sell their goods.
To find the producer surplus, we need to calculate the area between the supply curve and the equilibrium price.
At the equilibrium point, x = 60. Plugging this value into the supply function:
S(60) = 900 + 25(60)
S(60) = 900 + 1500
S(60) = 2400
The equilibrium price is $2400 per unit. To find the producer surplus, we need to calculate the area of the triangle formed between the supply curve and the equilibrium price.
Producer surplus = (1/2) * (2400 - 900) * 60
Producer surplus = $36,000
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multi-step equation
solve:
2p-3p-p=9-15-6
Answers
Answer:
p=-6
Step-by-step explanation:
2p-3p-p=9-15-6
or, -2p= -12
or, p= -12/-2
or, p= -6