a) The monthly payment increases by approximately $6.60 for a $1000 increase in the principal. b) The monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08. c) The monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
To solve these problems, we'll use the partial derivatives of the monthly payment function with respect to the principal P, interest rate r, and the length of the loan in months N.
Given values:
- Principal P = 450,000
- Interest rate r = 0.075
- Loan term N = 312 (26 years)
- Monthly payment [tex]\( f(450000, 0.075, 312) = 1962 \)[/tex]
Partial derivatives:
- [tex]\(\frac{\partial f}{\partial P} = 0.0066 \)[/tex]
- [tex]\(\frac{\partial f}{\partial r} = 7849 \)[/tex]
- [tex]\(\frac{\partial f}{\partial N} = -1.3672 \)[/tex]
a) The change in monthly payment per 1000 increase in loan principal
The partial derivative [tex]\(\frac{\partial f}{\partial P}\)[/tex] tells us the rate of change of the monthly payment with respect to the principal. To find the change in the monthly payment for a $1000 increase in the principal:
[tex]\[\Delta f \approx \frac{\partial f}{\partial P} \cdot \Delta P\][/tex]
Here, [tex]\(\Delta P = 1000\):[/tex]
[tex]\[\Delta f \approx 0.0066 \cdot 1000 = 6.6\][/tex]
So, the monthly payment increases by approximately $6.60 for a $1000 increase in the principal.
b) The change in monthly payment if the interest rate changes from [tex]\( r = 0.075 \) to \( r = 0.08 \)[/tex]
The partial derivative [tex]\(\frac{\partial f}{\partial r}\)[/tex] tells us the rate of change of the monthly payment with respect to the interest rate. To find the change in the monthly payment for a change in the interest rate from 0.075 to 0.08, we calculate the difference in the rates:
[tex]\[\Delta r = 0.08 - 0.075 = 0.005\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial r} \cdot \Delta r\][/tex]
[tex]\[\Delta f \approx 7849 \cdot 0.005 = 39.245\][/tex]
So, the monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08.
c) The change in monthly payment if the length of the loan changes from 26 to 24 years
The partial derivative [tex]\(\frac{\partial f}{\partial N}\)[/tex] tells us the rate of change of the monthly payment with respect to the length of the loan in months. To find the change in the monthly payment for a change in the loan term from 26 years (312 months) to 24 years (288 months), we calculate the difference in months:
[tex]\[\Delta N = 288 - 312 = -24\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial N} \cdot \Delta N\][/tex]
[tex]\[\Delta f \approx -1.3672 \cdot (-24) = 32.8128\][/tex]
So, the monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
The complete question is
The monthly payment for a home loan is given by a function f(P, r, N) where P is the principal (the initial size of the loan), r the interest rate, and N is the length of the loan in months. Interest rates are expressed as a decimal: A% interest rate is denoted by r = 0.075. If P = 450000, r = 0.075 and N = 312 (a 26-year loan), then the monthly payment is f(450000, 0.075, 312) = 1962. Furthermore, with these values we have
[tex]\frac{\partial f}{\partial P}=0.0066, \quad \frac{\partial f}{\partial r}=7849, \quad \frac{\partial f}{\partial N}=-1.3672[/tex]
Estimate
a) The change in monthly payment per 1000 increase in loan principal.
b) The change in monthly payment if the interest rate changes from r = 0.075 to r = 0.08
c) The change in monthly payment if the length of the loan changes from 26 to 24 years.
The prices of five used cars are given below. Which price is an outlier to the data set?
$16,250, $11,495, $10,022, $9,053, $12,244
$9,053
$11,495
$12,244
There are no outliers.
Answer:
There are no outliers
Step-by-step explanation:
An outlier is a number thats far different than the numbers selected. All of these numbers are close to each other.
Answer:
Option D. there are no outliers.
Step-by-step explanation:
The given prices of five used cars in the data set we have to find the outlier number.
Outlier number in a data set is very different from the data set values. It may be more greater or more lower numbers from the other numbers.
In the given data set all the numbers are close to each other.
Therefore, Option D. there are no outliers.
Need help please asp thank you so much
Answer:
x = -1, 3
Step-by-step explanation:
so what you need to do is graph each one because that's what the questions ask. One way for you to check your answer is to set the two equations equal to each other.
-x + 5 = x^2 - 3x + 2
you want to end up with one equation and having the equation equal 0. So add x to both sides to cancel out the x on the left side and then subtract 5 from both sides to cancel out the 5 on the left side.
0 = x^2 - 2x - 3
now you factor
0 = (x - 3) (x + 1)
x = -1, 3
how does the area of triangle ABC Compare to the area of parallelogram ghjk
Answer:
Area of parallelogram divided by 2 is the triangles are.
Area of parallelogram = B x H and triangle area = 1/2 x B x H
Step-by-step explanation:
Answer:
A ) The area of Δ ABC is 2 units greater than area of parallelogram GHJK.
Step-by-step explanation:
The diameter of the planet mars is approximately 6.794 × 10^6 meters. Which is an equivalent way to express that measure?
a- 6.794 billion meters
b- 679.4 million meters
c- 67.94 million meters
d- 6.794 million meters
Answer:
It is D.
Step-by-step explanation:
10^ 6 = 1,000,000 = 1 million.
So it is 6.794 million meters.
Emma is building a wall around her burning it has taken 45 minutes and she is 75% done what is the time it will take to finish building her wall
➷ 45 minutes is 3/4 of the total time
A simple way to do this is to find 1/4 of the time
To do this, divide by 3:
45/3 = 15
15 minutes is 1/4 of the time
To find the whole time, multiply this value by 4:
15 x 4 = 60
Subtract the time already passed from this:
60 - 45 = 15
It will take her 15 more minutes to finish building her wall.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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The length of the small leg of a 30 -60 -90 degree triangle is 5. What is the perimeter of the triangle?
Answer:
option (B)
15 + 5√3
Step-by-step explanation:
In a 30-60-90 triangle, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle.
Given in the question,
length of small leg = 5
As we know that
The hypotenuse is equal to twice the length of the shorter leg
hypotenuse = 2(5) =10The longer leg is equal to multiplying the shorter leg by the square root of 3
other leg = 5√3Perimeter of a triangle = sum of the length of three sides
= 5√3 + 10 + 5
= 15 + 5√3
For the following question, find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. Please help!!
Answer:
option(D)
x= 30 , y = 10√3
Step-by-step explanation:
Given in the question, a right angle triangle whose
hypotenuse = 20√3
We will use pythagorus theorem and trigonometry identities to find the value of x and y
Formula to use
sinФ = base / hypotenusesin(30) = y / 20√3
y = sin(30) x 20√3
y = 10√3
hypotenuse² = base² + height²
(20√3)² = (10√3)² + x²
(20√3)² - (10√3)² = x²
x² = 900
x = √900
x = 30
so, the value of x = 30 and y = 10√3
Answer:
[tex]x=30,y=10\sqrt{3}[/tex]
Step-by-step explanation:
Recall the mnemonics SOH CAH TOA.
We use the cosine ratio to find the value of [tex]x[/tex].
[tex]\cos(30\degree)=\frac{Adjacent}{Hypotenuse}[/tex]
This implies that;
[tex]\cos(30\degree)=\frac{x}{20\sqrt{3}}[/tex]
[tex]\frac{\sqrt{3}}{2} =\frac{x}{20\sqrt{3}}[/tex]
Cross multiply to get;
[tex]2x=20\sqrt{3}\times \sqrt{3}[/tex]
[tex]2x=60[/tex]
[tex]x=30[/tex]
Using the sine ratio
[tex]\sin(30\degree)=\frac{y}{20\sqrt{3} }[/tex]
[tex]\frac{1}{2}=\frac{y}{20\sqrt{3} }[/tex]
Tis implies that;
[tex]y=\frac{1}{2} \times 20\sqrt{3}[/tex]
[tex]y=10\sqrt{3}[/tex]
The correct choice is D.
By accident, 8 burned out bulbs have additionally been mixed in with 30 good ones. Ken is replacing old bulbs in his house. If he selects two bulbs at random from the box of 38, what is the probability they both work?
P(Both Work) =
435 / 703
P(Both Work) =
28 / 703
P(Both Work) =
16 / 361
P(Both Work) =
169 / 256
Answer:
The correct answer option is P(Both Work) = 435 / 703
Step-by-step explanation:
We are given that in a box of total 38 bulbs, 8 are the defective ones while the rest are good.
If Ken selects two bulbs at random from the box, we are to find the probability that they both work.
1st bulb: P (bulb works) = [tex]\frac{30}{38} [/tex]
2nd bulb: P (bulb works) = [tex]\frac{29}{37} [/tex]
P (Both Work) = [tex]\frac{30}{38} \times \frac{29}{37}[/tex] = 435 / 703
Answer:
The correct answer is first option. P(Both Work) = 435/703
Step-by-step explanation:
It is given that,
There are 8 burned bulbs and 30 good bulbs.
Therefore total number of bulbs = 8 + 30 = 38
To find the probability
We have to take two working bulbs from total bulbs.
Total bulbs = 38
The probability of taking two working bulbs = P(Both Work)
P(Both Work) = 30C₂/38C₂
= (30 * 29)/(38 * 37) = 435/703
Therefore the correct answer is first option
Which fraction converts to a repeating decimal number? A. 1/12 B. 7/8 C. 14/25 D. 17/20 E. 6/10
Answer:
Step-by-step explanation:
You’re answer is 1/12
Answer:
1/12
Step-by-step explanation:
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that a red card appears?
1/4
1/2
1/13
0.26
Answer:
P (red) = 1/2
Step-by-step explanation:
It is given that a card is drawn from a well-shuffled deck of 52 cards and we are to find the probability of getting a red card.
We know that there are total 26 red cards in a deck (13 hearts and 13 diamonds).
Therefore, the probability of getting a red card P (red) = [tex] \frac { 2 6 } { 5 2 } [/tex] = 1/2
The probability of drawing a red card from a well-shuffled 52-card deck is 1/2 since half of the cards in the deck are red (26 out of 52)
Explanation:This question pertains to the topic of probability in Mathematics. There are 52 cards in a standard deck, half of which are red (26 red cards: 13 hearts and 13 diamonds). Hence, the probability of drawing a red card is the number of red cards over the total number of cards in the deck.
So, the probability of drawing a red card from a well-shuffled 52-card deck is 26/52, simplified to 1/2. Hence the correct answer from the given choices is 1/2.
Learn more about Probability here:
https://brainly.com/question/32117953
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i have a super hard question and i need help
what is [tex]5^{2}[/tex] equal to?
Answer:
[tex]5^{2}[/tex] = 25 :) hope this helps
Step-by-step explanation:
Slaura walks 3/5 mile to school each day. Isaiah walk to school is 3 times as long as Slaura's. How far does Isaiah walk to school each day.
Answer:
1.8 miles
Step-by-step explanation:
3/5 * 3 for the extra mile that he walks
Answer:
1 4/5 miles to school. 3 3/5 miles if you wanted to know to school AND back.
Step-by-step explanation: You would take the 3/5 of a mile that Slaura walks every day and multiply it by 3. Your equation would be 3/5 x 3/1. Your answer for how many miles Isaiah walk to school everyday is 9/5 or 1 4/5 miles. If you wanted to know how many miles Isaiah walked to school AND back, then you would double 1 4/5 miles.
If you have 4 dollars and your mom stole 2 dollars what do you have?
Answer:
2
Step-by-step explanation:
20 points!!! Please Help
Does the equation x2 - 4x + y2 = -3 intersect the x-axis?
Answer:
Yes, twice
Step-by-step explanation:
The equation will intersect the x-axis when y = 0, so we have
x² - 4x = -3 now solve this quadratic for x...
x² - 4x + 3 = 0
factor...
(x - 3)(x - 1) = 0,
so at x = 1 and x = 3, the function crosses the x-axis
See the graph below
Yes, because the center is on the x-axis, the circle will intersect 2 times, at x=1 and at x=3
How many 1020 flats can fit on a 10’*6’table
42 flats per table is your answer
84%, percent of Astrid's books are fiction. What fraction of Astrid's books are fiction?
Stear Corp. bought a machine on January 1, 2012 for $37,500. The company follows a policy of calculating depreciation using the Written-Down-Value method at 8% per annum. The accounting period of Stear Corp. is from January to December. What will be the amount of depreciation added to the Accumulated Depreciation Account for the year 2013?
A. $5,520
B. $2,760
C. $6,000
D. $5,760
Answer:
2,760
Step-by-step explanation:
PLATO.
Consider the inequality -5(x+7) is less than -10. Write an inequality representing the solution for x.
Answer:
x > -8
Step-by-step explanation:
First you distribute the -5 and get
-5x-35 < 10
Then you add 35 to both sides and get
-5x<45
Then dived by NEGATIVE 5 (since it is negative you flip the less than signs to greater than) and get
x> -8
Simplify the expression csc0/cot0 (picture provided)
Answer: option b.
Step-by-step explanation:
You must keep on mind the following identities:
[tex]csc\theta=\frac{1}{sin\theta}\\\\cot\theta=\frac{1}{tan\theta}[/tex]
[tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]
Therefore, you can simplify the expression given in the problem as you can see below:
- Substitute identities:
[tex]\frac{csc\theta}{cot\theta}=\frac{\frac{1}{sin\theta}}{\frac{1}{tan\theta}}\\\\=\frac{tan\theta}{sin\theta}\\\\=\frac{\frac{sin\theta}{cos\theta}}{sin\theta}\\\\=\frac{sin\theta}{(cos\theta)(sin\theta)}\\\\=\frac{1}{cos\theta}[/tex]
By definition:
[tex]\frac{1}{cos\theta}=sec\theta[/tex]
The correct answer is B, or sec theta.
Just got it right on edge 2020, hope this helps!! :)
What is the area of a circular wrestling region with a 42 ft diameter
Answer:
The area of a circular wrestling region with a 42 fr diameter is
A≈1385.44ft²
Tyrone wrote an equivalent expression for 28 + x - 2n + 7 - n - 5x + 4. His equivalent expression was -3n - 5x + 39 + x. What error did Tyrone make?
A. Tyrone neglected to combine the x terms.
B. Tyrone added the constants instead of subtracting them.
C. Tyrone neglected to add the coefficients of the n terms.
D. Tyrone made an error when he added the constants.
Answer with Step-by-step explanation:
We are given an expression:
28 + x - 2n + 7 - n - 5x + 4
We have to find its equivalent expression
On combining the like terms of the above expression
28+4+7+x-5x-2n-n
= 39-4x-3n
= -3n-4x+39
According to Tyrone the equivalent expression was:
-3n - 5x + 39 + x
The error Tyrone made was:
A. Tyrone neglected to combine the x terms
Answer:
The answer is A
Step-by-step explanation:
Which translation results in a circle whose center is at the origin? Question 5 options: Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down. Circle open parentheses x minus 1 close parentheses squared plus open parentheses y plus 2 close parentheses squared equals 4 translated 1 unit left and 2 units down. Circle open parentheses x minus 2 close parentheses squared plus open parentheses y plus 3 close parentheses squared equals 4 translated 2 units right and 3 units up. Circle open parentheses x minus 3 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 4 translated 3 units left and 5 units up.
Answer:
case 1) Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down
Step-by-step explanation:
Verify the 4 Options
case 1) Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down
The equation of the circle is
[tex](x+2)^{2}+(y-6)^{2}=4[/tex]
The center of the circle is the point [tex](-2,6)[/tex]
The rule of the translation is
[tex](x,y)-------> (x+2,y-6)[/tex]
Applying the rule to the center
[tex](-2,6)-------> (-2+2,6-6)[/tex]
[tex](-2,6)-------> (0,0)[/tex]
Therefore
The translation results in a circle whose center is at the origin
case 2) Circle open parentheses x minus 1 close parentheses squared plus open parentheses y plus 2 close parentheses squared equals 4 translated 1 unit left and 2 units down
The equation of the circle is
[tex](x-1)^{2}+(y+2)^{2}=4[/tex]
The center of the circle is the point [tex](1,-2)[/tex]
The rule of the translation is
[tex](x,y)-------> (x-1,y-2)[/tex]
Applying the rule to the center
[tex](1,-2)-------> (1-1,-2-2)[/tex]
[tex](1,-2)-------> (0,-4)[/tex]
Therefore
The translation results in a circle whose center is not at the origin
case 3) Circle open parentheses x minus 2 close parentheses squared plus open parentheses y plus 3 close parentheses squared equals 4 translated 2 units right and 3 units up
The equation of the circle is
[tex](x-2)^{2}+(y+3)^{2}=4[/tex]
The center of the circle is the point [tex](2,-3)[/tex]
The rule of the translation is
[tex](x,y)-------> (x+2,y+3)[/tex]
Applying the rule to the center
[tex](2,-3)-------> (2+2,-3+3)[/tex]
[tex](2,-3)-------> (4,0)[/tex]
Therefore
The translation results in a circle whose center is not at the origin
case 4) Circle open parentheses x minus 3 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 4 translated 3 units left and 5 units up
The equation of the circle is
[tex](x-3)^{2}+(y-5)^{2}=4[/tex]
The center of the circle is the point [tex](3,5)[/tex]
The rule of the translation is
[tex](x,y)-------> (x-3,y+5)[/tex]
Applying the rule to the center
[tex](3,5)-------> (3-3,5+5)[/tex]
[tex](3,5)-------> (0,10)[/tex]
Therefore
The translation results in a circle whose center is not at the origin
in a church, the ratio of adults to children is 6 to 11. if there are 306 people in the church, how many children are there?
Answer:
198
Step-by-step explanation:
If the ratio of adults to children is 6:11, then 6/17 of the people are adults and 11/17 of the people are children.
11/17 × 306 = 198
There are 198 children.
Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy adults are Normally distributed with mean =3.2 micrograms per deciliter (ug/dl) and standard deviation sigma = 1.5. What is the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults?
Answer:
0.7325 to 5.6675 ug/dl
Step-by-step explanation:
The middle 90% will be 45% above the mean and 45% below the mean. This means
0.5-0.45 = 0.05 and
0.5+0.45 = 0.95
We use a z table. Look in the cells; find the values as close to 0.05 and 0.95 as we can get.
For 0.05, we have 0.0505 and 0.0495; since these are equidistant from 0.05, we use the value between them. 0.0505 is z=-1.64 and 0.0495 is z=1.65; this gives us z=-1.645.
For 0.95, we have 0.9495 and 0.9505; since these are equidistant from 0.95, we use the value between them. 0.9495 is z = 1.64 and 0.9505 is z=1.65; this gives us z = 1.645.
Now we use our z score formula,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our two z scores are 1.645 and -1.645; our mean, μ, is 3.2; and our standard deviation, σ, is 1.5:
[tex]1.645=\frac{X-3.2}{1.5}[/tex]
Multiply both sides by 1.5:
[tex]1.5(1.645)=\frac{X-3.2}{1.5}\times 1.5\\\\2.4675 = X-3.2[/tex]
Add 3.2 to each side:
2.4675+3.2 = X-3.2+3.2
5.6675 = X
[tex]-1.645=\frac{X-3.2}{1.5}[/tex]
Multiply both sides by 1.5:
[tex]1.5(-1.645)=\frac{X-3.2}{1.5}\times 1.5\\\\-2.4675=X-3.2[/tex]
Add 3.2 to each side:
-2.4675+3.2 = X-3.2+3.2
0.7325 = X
Our range is from 0.7325 to 5.6675.
Final answer:
The range of arsenic blood concentrations corresponding to the middle 90% of healthy adults is approximately 0.765 ug/dl to 4.035 ug/dl.
Explanation:
The middle 90% of a Normally distributed data set falls within approximately two standard deviations of the mean. In this case, the mean is 3.2 ug/dl and the standard deviation is 1.5. To find the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults, we can calculate the upper and lower boundaries.
First, we need to find the Z-scores that correspond to the 5th and 95th percentiles. The Z-score formula is:
Z = (x - mu) / sigma
Applying the formula, we get:
Z_lower = (x_lower - 3.2) / 1.5 = -1.53
Z_upper = (x_upper - 3.2) / 1.5 = 1.53
Next, we need to find the corresponding x values. Rearranging the Z-score formula, we can solve for x:
x = Z * sigma + mu
Plugging in the Z scores, we have:
x_lower = -1.53 * 1.5 + 3.2 = 0.765
x_upper = 1.53 * 1.5 + 3.2 = 4.035
Therefore, the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults is approximately 0.765 ug/dl to 4.035 ug/dl.
Predict how many times you will roll a number less than 5 if you roll a standard number cube 250 times
Final answer:
The probability of rolling a number less than 5 on a six-sided die is 2/3. When rolling the die 250 times, this probability suggests that a number less than 5 would be rolled approximately 167 times.
Explanation:
To predict the number of times you will roll a number less than 5 when rolling a standard six-sided die (with faces numbered 1 through 6), it's important to first understand the probability of rolling a number less than 5 for any single roll. Our numbers of interest here are 1, 2, 3, and 4.
The probability P of rolling any one of these four numbers on a six-sided die is 4 out of 6 (since there are 4 favorable outcomes and 6 possible outcomes in total), which simplifies to 2/3. This means that on any given roll, you have a 2/3 chance of rolling a number less than 5.
When rolling the die 250 times, we would expect this 2/3 probability to hold true on average. Therefore, we calculate the expected number of times a number less than 5 appears as follows:
Expected number of rolls less than 5 = Total number of rolls × Probability of rolling a number less than 5
Expected number of rolls less than 5 = 250 × 2/3
Expected number of rolls less than 5 = approximately 166.67
Since we cannot roll a die a fraction of a time, we would predict that you would roll a number less than 5 approximately 167 times out of 250 rolls.
Hotels’ use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelers’ familiarity with ecolabels used by hotels, Exercise 2.64 (p. 80). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, “Suppose the response is measured on a continuous scale from 10 (not familiar at all) to 50 (very familiar).” The mean and standard deviation for the Energy Star ecolabel are 44 and 1.5, respectively. Assume the distribution of the responses is approximately normally distributed a. Find the probability that a response to Energy Star ex- ceeds 43 between 42 and 45 think it is likely that t b. Find the probability that a respo nse to Energy Star falls c. If you observe a response of 35 to an ecolabel, do vou he ecolabel was Energy Star? Explain.
Answer:
a) 0.7486; b) 0.6518; c) No
Step-by-step explanation:
We use z scores to answer these questions. The formula for a z score is
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our mean, μ, is 44; our standard deviation, σ, is 1.5.
For part a,
We want P(X > 43):
z = (43-44)/1.5 = -1/1.5 = -0.67
Using a z table, we see that the area under the curve to the left of this is 0.2514. However, we want the area to the right; this means we subtract from 1:
1 - 0.2514 = 0.7486
For part b,
We want P(42 ≤ X ≤ 45):
z = (42-44)/1.5 = -2/1.5 = -1.3
z = (45-44)/1.5 = 1/1.5 = 0.67
Using a z table, the area under the curve to the left of z = -1.3 is 0.0968. The area under the curve to the left of z = 0.67 is 0.7486.
The area between them is 0.7486 - 0.0968 = 0.6518.
For part c,
A response of 35 has a z score of
z = (35-44)/1.5 = -9/1.5 = -6
This is 6 standard deviations below the mean. This is more than the amount required to make this an outlier, or an unlikely response.
Find the area and the perimeter, i just need the Perimeter thanks
Answer:
[tex]\large\boxed{P=(3\pi+4)\ ft}[/tex]
Step-by-step explanation:
We have 3/4 of a circle and the square.
The perimeter is equal to the sum of a 3/4 of a circumference of a circle and two sides of a square.
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
r - radius
We have r = 2 ft. Substitute:
[tex]C=2\pi(2)=4\pi\ ft[/tex]
3/4 of a circumference:
[tex]\dfrac{3}{4}\cdot4\pi=3\pi\ ft[/tex]
The length of a side of a square is a = 2ft.
Calculate the perimeter:
[tex]P=3\pi+(2)(2)=(3\pi+4)\ ft[/tex]
A company surveyed 1000 people on their age and the number of jeans purchased annually. The results of the poll are shown in the table. Jeans Purchased Annually 0 1 2 3 or More Total Under 12 0 69 78 73 220 12-18 10 75 70 65 220 19-25 40 77 97 76 290 over 25 36 86 128 20 270 Total 86 307 373 234 1000 A person is selected at random. Compute the probability of the following. (a) The person is over 25 and purchases 3 or more pairs of jeans annually. 0.2 Incorrect: Your answer is incorrect. (b) The person is older than 18 or purchases 1 pair of jeans annually. 0.163 Incorrect: Your answer is incorrect. (c) The person is in the age group 12-18 and purchases at most 2 pairs of jeans annually. 0.07 Incorrect: Your answer is incorrect.
The probabilities are;
a) 0.03
b) 0.691
c) 0.2.
How to calculate probability.
Given information
A company surveyed 1000 people on their age and the number of jeans purchased annually. The results of the poll are shown in the above table.
a) The person is over 25 and purchases 3
or more pairs of jeans annually
P(25 and 3 or Jeans)
[tex] = \frac{30}{1000} [/tex]
= 0.03
b) The person is older than 18 or purchases
1 pair of jeans annually.
[tex] = \frac{560 + 274 - 143}{100} [/tex]
[tex] = \frac{691}{1000} [/tex]
= 0.691
c) The person is 12 - 18 in the age group
and purchases at most 2 pairs of jeans annually
[tex] = \frac{17 + 61 + 122}{1000} [/tex]
[tex] = \frac{200}{1000} [/tex]
= 0.2
Complete question
A company surveyed 1000 people on their age and the number of jeans purchased annually. The results of the poll are shown in the table. A person is selected at random. Compute the probability of the following. The person is over 25 and purchases 3 or more pairs of jeans annually. The person is older than 18 or purchases 1 pair of jeans annually. The person is in the age group 12-18 and purchases at most 2 pairs of jeans annually.
jeffrey is flying a kite but it got caught at the top of a 15 foot tree tha is 60 feet away from where he is standing. if the strong is tight, how long is the string that he has let out?
Found this on a website! Hope this is helpful!
Max is 33 and smokes. How much would he save next year on a $75,000 policy if he quit smoking compared to if he continued smoking? Show your work or explain how you got your answer.
Answer:
Max would save $126 if he quit smoking.
Step-by-step explanation:
It is given that the age of max is 33.
From the given table it is clear that the monthly premium for every $25000 of coverage for age group 31-40 non smoker male is 5.50 and smoker male is $9.00.
Total yearly premium for $75000 for non smoker male of 33 age is
[tex]P_1=5.50\times 3\times 12=198[/tex]
Total yearly premium for $75000 for smoker male of 33 age is
[tex]P_2=9.00\times 3\times 12=324[/tex]
If he quit smoking then he save
[tex]Saving=P_2-P_1[/tex]
[tex]Saving=324-198[/tex]
[tex]Saving=126[/tex]
Therefore max would save $126 if he quit smoking.