a)
The cost per payment is 155.5.
b)
The value of 3 in the standard deviation principle is 1376.711.
We have,
a)
To calculate E(X^ 105), we first need to find the probability distribution of X after applying the deductible of 105.
Any loss below 105 will result in no payment, and any loss above or equal to 105 will result in payment equal to the loss minus the deductible.
Thus, the probability distribution of the payments.
Payment: 0 0 0 29 29 75 75 75 75 105 245 419 419
Probability: 0 0 0 1/12 1/12 1/6 1/6 1/6 1/6 1/12 1/12 1/12 1/12
Using this probability distribution, we can calculate E(X^ 105) as follows:
E(X^ 105) = 0^2 * 0 + 29^2 * (1/12 + 1/12 + 1/12 + 1/12) + 75^2 * (1/6 + 1/6 + 1/6 + 1/6) + 105^2 * (1/12) + 245^2 * (1/12) + 419^2 * (1/12)
= 34390.5833
The cost per payment ex(105) is simply the expected payment per policyholder, which can be calculated as follows:
ex(105) = 29 (1/3) + 75 * (2/3) + 105 * (1/6) + 245 * (1/6) + 419 * (1/6)
= 155.5
b)
The standard deviation principle states that the total cost of claims, including the deductible, should be equal to the product of the standard deviation and the value of the insurance against risk.
In this case, the insurance against risk is the maximum amount that the insurance company is willing to pay per policyholder, which is 105. Thus, we have:
105 + Bo = s(X) x VaR
where s(X) is the standard deviation of X and VaR is the value at risk, which is the amount that the company expects to pay out with a certain probability (usually 99% or 99.5%).
We can solve for Bo as follows:
Bo = s(X) * VaR - 105
Assuming a VaR of 99%, we need to find the 1% percentile of X, which is the value x such that P(X ≤ x) = 0.01.
From the empirical distribution, we can see that the 1% percentile is 94. Thus, we have:
VaR = 105 - 94 = 11
To calculate s(X), we first need to find the mean of X, which is:
mean(X) = (94 + 3104 + 2134 + 4*180 + 210 + 350 + 524)/13 = 224
Using the formula for the sample standard deviation, we get:
s(X) = √((1/12)((94-224)^2 + 3(104-224)^2 + 2*(134-224)^2 + 4*(180-224)^2 + (210-224)^2 + (350-224)^2 + (524-224)^2))
= 142.701
Now,
Bo = 142.701 x 11 - 105
= 1376.711
Thus,
The cost per payment is 155.5.
The value of 3 in the standard deviation principle is 1376.711.
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what is 104 subtracted by 18
Answer:
104-18=86 and also 18-104=-86
Step-by-step explanation:
Which exponents are equivalent to 2 exponent 6? Choose ALL that apply.
Answer:
the entire right column
Step-by-step explanation:
your solutions should simply to 64
Answer:2*2*2*2*2*2 and 4*16 and 8*8
Step-by-step explanation:
2*2*2*2*2*2=64
4*16=64
8*8=64
6*6*6*6*6*6=46656
2*6=12
12*12=144
NEED ANSWER ASAP : The formula gives the maximum height y of a projectile launched straight up, given acceleration a and initial velocity v.
y=v^2/2a
Solve for v.
Responses
v=2ay√/a
v equals fraction numerator square root of 2 a y end root over denominator a end fraction
v=4a^2y^2
v equals 4 a squared y squared
v=4y^2/a^2
v equals fraction numerator 4 y squared over denominator a squared end fraction
v=2ay−−−√
The required expression is v = √2ay.
Let acceleration is given by: a
and initial velocity is given by: v
So, The maximum height(y) is
y= v² sinθ / 2a
As, θ=90 then
y = v² /2a
v² = 2ay
v = √2ay
Thus, the required expression is v = √2ay.
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recall the equation for a circle with center (h,k)and radius r. at what point in the first quadrant does the line with equation y
The equation for a circle with centre (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. To find the point where the line with equation y = mx intersects the circle in the first quadrant, we can substitute y = mx into the equation for the circle.
(x-h)^2 + (mx-k)^2 = r^2
Expanding and simplifying:
x^2 - 2hx + h^2 + m^2x^2 - 2kmx + k^2 = r^2
Grouping the x terms:
(1 + m^2)x^2 - 2(h+km)x + h^2 + k^2 - r^2 = 0
This is a quadratic equation in x, which we can solve using the quadratic formula:
x = [2(h+km) ± sqrt(4(h+km)^2 - 4(1+m^2)(h^2+k^2-r^2))] / 2(1+m^2)
Simplifying:
x = (h+km) ± sqrt[(h+km)^2 - (h^2+k^2-r^2)m^2] / (1+m^2)
Since we're looking for a point in the first quadrant, we want the positive solution for x. Once we find x, we can plug it back into y = mx to get the y-coordinate of the point.
Note that there may be 0, 1, or 2 solutions depending on the specific values of h, k, r, and m. If there are 2 solutions, one will be in the first quadrant and the other in the fourth quadrant. If there is 1 solution, it will be on the border between the first and fourth quadrants. If there are 0 solutions, the line does not intersect the circle in the first quadrant.
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What is 1/4 of 1 & 1/4
a. 1/4
b. 1/5
c. 5/16
d. 1/2
1/5
you take 1/4÷ 1 1/4 and you get 1/5
Bruce Lovegren was born on September 27, 1950. On April 14, 1977, he purchased a $15,000 10-year term life insurance policy. What was the annual premium he paid?
Bruce Lovegren paid a monthly annual premium of $125 for his $15,000 10-year term life insurance policy.
The monthly premium can be calculated by dividing the total cost of the policy by the number of months in the policy term:
monthly premium = total cost of policy / number of months in policy term
The total cost of the policy can be calculated by multiplying the annual premium by the number of years in the policy term:
total cost of policy = annual premium * number of years in policy term
The number of months in a year is 12.
Bruce Lovegren purchased the policy on April 14, 1977, so the policy was in effect for 10 years and 8 months, or 128 months.
The annual premium as follows:
total cost of policy = $15,000
number of years in policy term = 10
annual premium = total cost of policy / number of years in policy term
annual premium = $15,000 / 10
annual premium = $1,500
monthly premium = annual premium / 12
monthly premium = $1,500 / 12
monthly premium = $125
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Aaden wants to get a subscription to a library. There are two subscription options one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows.
what does point Q represent in this context?
a. A number of books and their cost where the subscription with the annual fee costs less
b. A number of books and their cost where the subscription the charges per book costs less
c. A number of books and their cost where both subscriptions cost the same
d. A number of books and their cost that is not possible with either subscription
Point R in this context represents the number of books borrowed and their cost where both subscription options cost the same.
The correct option is A.
Let's analyze the two subscription options:
Subscription with a fixed annual fee: This option charges a fixed $96 annual fee, regardless of the number of books borrowed.
The cost function for this subscription is a horizontal line at y = $96.
Subscription that charges per book borrowed: This option charges $3 per book borrowed. The cost function for this subscription is a linear function with a slope of $3.
When we plot the cost functions on a graph with the number of books borrowed on the x-axis and the cost on the y-axis, we will see that the two lines intersect at a point. This point of intersection is point R.
At point R, the cost of both subscriptions is the same. Therefore, the correct answer is c.
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The complete question:
Aaden wants to get a subscription to a library. There are two subscription options one of which charges a fixed 96-dollar annual fee and the other which charges 3 dollars per book he borrows.
What does point R represent in this context?
a. A number of books and their cost where the subscription with the annual fee costs less
b. A number of books and their cost where the subscription the charges per book costs less
c. A number of books and their cost where both subscriptions cost the same
d. A number of books and their cost that is not possible with either subscription
The complete question is given in the attached image.
a box has a volume of 140 cm Square if its breadth is 5 cm and it's length is 7 cm find it's height
Answer:
To find the height of the box, we need to use the formula for volume of a box: Volume = length x breadth x height
Given the values for length and breadth, we can substitute them into the formula and solve for height: 140 = 7 x 5 x height
Simplifying the equation, we get: 140 = 35 x height
Dividing both sides by 35, we get: height = 4
Therefore, the height of the box is 4 cm
Karl has taken a three-year personal loan of $5000 at 7.25% per year, compounded monthly. The loan requires monthly payments. What is the total amount Karl will pay to the bank?
≈≈≈Answer:
Step-by-step explanation:
To calculate the total amount Karl will pay to the bank, we need to find the monthly payment and then multiply it by the total number of payments over three years.
First, we need to calculate the monthly interest rate. Since the loan is compounded monthly, we divide the annual interest rate by 12:
Monthly interest rate = 7.25% / 12 = 0.006041667
Next, we need to calculate the total number of payments Karl will make over the course of the loan. Since he will be making monthly payments for three years, there will be a total of:
Total number of payments = 3 years x 12 months/year = 36 payments
To calculate the monthly payment, we can use the formula for the present value of an annuity:
Monthly payment = P * (r / (1 - (1 + r)^(-n)))
where P is the principal amount (in this case, $5000), r is the monthly interest rate, and n is the total number of payments.
Plugging in the values, we get:
Monthly payment = [tex]5000 * \frac{0.006041667}{(1-(1+0.006041667^{-36} )} = $154.96[/tex]
Finally, we can calculate the total amount Karl will pay to the bank by multiplying the monthly payment by the total number of payments:
Total amount paid = Monthly payment x Total number of payments = $154.96 x 36 = $5,578.56
Therefore, the total amount Karl will pay to the bank is $5,578.56
A cubical container is 4/5 filled with water. It contains 2.7l of water. Find the base area of the container
Answer:
225 cm²
Step-by-step explanation:
The container has 2.7L of water in it but it is only 4/5 full
Therefore if the container were to be filled entirely with water it would contain
2.7 x 5/4 = 3.375 Liters
This, therefore is the volume of the container is 3.375 L
3.375 L = 3.375 x 1000 cm³
= 3, 375 cm³
The volume of a cube of side a is given by
V = a³
The base area of a cube of side a is given by
A = a²
We have calculated the volume of the cube as 3.375 cm³
Therefore each side of the cubical container
[tex]a = \sqrt[3]{3375} = 15[/tex] cm
The base area is
a² = 15²
= 225 cm²
In this task, you need to evaluate the following four expressions and demonstrate at least 5 steps of evaluating them. Choose values with appropriate types for each expression.a. -(a%b-c/d+e*f)b. ! ((a>b) && (c
(a) The value of the expression -(a%b-c/d+e*f) is -27.5 when a = 10, b = 3, c = 5, d = 2, e = 4, and f = 6
(b) For the second expression the final result is : FALSE
a. -(a%b-c/d+e*f)
Step 1: Let's assume that a = 10, b = 3, c = 5, d = 2, e = 4, and f = 6.
Step 2: Evaluate the expression inside the parentheses: c/d = 5/2 = 2.5
Step 3: Evaluate the expression inside the parentheses: e*f = 4*6 = 24
Step 4: Evaluate the expression inside the parentheses: a%b = 10%3 = 1
Step 5: Add the results of steps 2, 3, and 4: 2.5 + 24 + 1 = 27.5
Step 6: Negate the result of step 5: -27.5
Therefore, the value of -(a%b-c/d+e*f) is -27.5 when a = 10, b = 3, c = 5, d = 2, e = 4, and f = 6.
b. ! ((a>b) && (cb) = false, (cb) && (c b) && (c > d))
Step 1: a > b = 6 > 4 = true
Step 2: c > d = 8 > 2 = true
Step 3: true && true = true
Step 4: !(true) = false
Final result: false
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Addisonisasalesperson.Shesoldacoatfor$75andearned10%commission.HowmuchcommissiondidAddisonearn?
5) A warehouse outside of a factory currently has an inventory of 1245 boxes. After an 8-
hour work day, the warehouse has 2000 boxes. Assume the warehouse was being filled at a
constant (linear) rate.
a) How many boxes per hour is the factory able to provide to the warehouse?
b) What would be the inventory at the end of a 40-hour work week?
c) How long will it take to fill the warehouse to its 50,000 box capacity?
6) In the year 2007, a FOREVER stamp cost cost $0.41. In 2023, the cost of a FOREVER
stamp was $0.63. Assume that the cost of stamps increased at a constant (linear) rate.
a) If price increases continue at the current rate, how much will a FOREVER stamp
cost in 2035?
b) In what year would you expect a FOREVER stamp to cost one dollar?
7) In January of 2021, there were 980,000 games available on the Apple App Store. By July
of 2021, there were 984,200 games available. If we assume that the number of available
games is steadily increasing at a constant (linear) rate,
a) How many games does this pattern predict will be available in January 2022?
b) At this rate, when will there be 1,000,000 games available for purchase in the Apple
App Store?
Thee factory is able to provide 94.38 boxes per hour to the warehouse.
How to calculate the valueRate = (2000 - 1245) / 8 = 94.38 boxes per hour
Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.
Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2
Therefore, the inventory at the end of a 40-hour work week would be:
1245 + 3775.2 = 5020.2 boxes
rate = (50000 - 1245) / time
Simplifying this equation, we get:
time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).
Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,
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"price by mathematical induction
Prove that n! > 2^n for all n ∈ Z≥4"
By the principle of mathematical induction, we can conclude that n! > 2ⁿ for all n ∈ Z≥4.
What is mathematical induction?The art of demonstrating a claim, theorem, or formula that is regarded as true for each and every natural number n is known as proof.
We can prove by mathematical induction that n! > 2ⁿ for all n ∈ Z≥4.
First, we will prove the base case n = 4:
4! = 4 x 3 x 2 x 1 = 24
2⁴ = 16
Since 24 > 16, the base case is true.
Next, we assume that the inequality is true for some arbitrary k ≥ 4:
k! > [tex]2^k[/tex]
To complete the induction step, we must prove that the inequality is also true for k + 1:
(k+1)! = (k+1) x k!
(k+1)! > (k+1) x [tex]2^k[/tex] (by the induction hypothesis)
(k+1)! > 2 x [tex]2^k[/tex]
(k+1)! > [tex]2^{(k+1)[/tex]
Since the inequality is true for k+1, this completes the induction step.
Therefore, by the principle of mathematical induction, we can conclude that n! > 2ⁿ for all n ∈ Z≥4.
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What is the product of
8.2
×
1
0
2
8.2×10
2
and
3.4
×
1
0
5
3.4×10
5
expressed in scientific notation?
The product of the numbers is 2.788 x 10^8.
What is a scientific notation?Scientific notation is a method of expressing very large numbers so that they can be easily understood. The process involves expressing the number in terms of the power of ten. For example; 1230000000000 = 1.23 x 10^12.
In the given question, the product of 8.2 x 10^2 and 3.4 x 10^5 is required.
Thus;
8.2 x 10^2 * 3.4 x 10^5 = 8.2 * 3.4 x 10^5 * x 10^2
= 8.2 * 3.4 x 10^(2+5)
= 27.88 x 10^7
= 2.788 x 10^8
Therefore, the product of the numbers expressed in scientific notation is 2.788 x 10^8.
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Write an equation for the relationship
Shown in the table. Then find the
Unknown value (?) in the table.
X- 4, 10, 12, 18, 23
Y- -1, 0.5, 1, ?, 3.75
The equation for the relationship would be y = 0.25x - 2 and the unknown value would be 2. 5.
How to find the equation ?To find the equation, you first need to find the slope of the line by picking two points and applying the slope formula. The two points are (4, -1) and (12, 1).
The slope is:
= (y2 - y1) / (x2 - x1)
= ( 1 - ( - 1 ) ) / ( 12 - 4)
= 2 / 8
= 0. 25
We can then find the full equation :
y - ( - 1 ) = 0.25 (x - 4)
y = 0.25x - 2
The unknown y value when x is 18 is:
y = 0.25 ( 18 ) - 2
y = 2. 5
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A trampoline park has a trampoline that is 8 yards wide and 12 yards long. Approximate the distance (in yards) between opposite corners of the trampoline to the
nearest tenth
Answer:
~14.4
Step-by-step explanation:
You can use the Pythagorean Theorem to find the hypotenuse (corner to corner) of the line between the corners of the rectangle.
A^2 + b^2 = c^2
8^2 + 12^2 = 208
√208 = 14.42
When would you need to transfer measurements from the metricsystem to the US system and from the US system to the metricsystem.
You might need to transfer measurements from the metric system to the US system and vice versa in various situations.
Some examples include:
1. International trade: If you are exporting or importing goods, it's essential to convert measurements to the recipient's preferred system, ensuring proper understanding of product specifications.
2. Travel: When traveling to a different country, you may need to convert distances, speed limits, or temperatures to better understand local road signs or weather conditions.
3. Cooking and recipes: When following a recipe from a different country, converting ingredient measurements can be crucial for accurate results.
4. Construction and engineering: Working on projects with international collaboration may require converting measurements to ensure all parties understand the specifications.
5. Science and education: As the metric system is the standard for scientific research, it may be necessary to convert US measurements to metric for consistency in data reporting and understanding.
Remember to use appropriate conversion factors when transferring measurements between the metric system and the US system to ensure accurate results.
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CRITICAL THINKING
Solve the problem. Show your work.
Find the total area of the flower and vegetable garden.
Use the formula for the area of a rectangle.
6 ft
4 ft
flowers
vegetables
8 ft
Garden
Answer:
Step-by-step explanation:
Formula of rectangle: base x height (b*h)
base: 8ft
height: 6+4= 10
8 x 10 = 80
Area of rectangle: 80ft
The diameter of a circle is 7 cm. Find its area to the nearest whole number.
Answer:
Step-by-step explanation:
Answer: A=38.48
Step-by-step explanation:
A=πr^2
7/2=3.5
3.5x3.5=12.25
12.25π
38.48
Hope this helps! :)
Which of the following is a formula for the surface area, S, of a cube with edges of length 2x?
a. S=24x
b. S=24x^2
c. S=12x
S=12x^2
Answer:
The formula for the surface area, S, of a cube with edges of length 2x is:
S = 6(2x)^2
Simplifying the expression inside the parentheses gives:
S = 6(4x^2)
Multiplying 6 by 4x^2 gives:
S = 24x^2
Therefore, the formula for the surface area of a cube with edges of length 2x is S = 24x^2, which is option (B).
Step-by-step explanation:
Pls helps me out with this! ASAP
The tables are completed as follows:
Table 1: f(x) = 30.Table 2: f(x) = 1.301.How to complete the table?For Table 1, we have an exponential function defined as follows:
f(x) = b^x.
We have that when x = 0.699, f(x) = 5, hence the base b is obtained as follows:
b^0.699 = 5
b = 5^(1/0.699)
b = 10.
Hence, when x = 1.477, the value of f(x) is given as follows:
f(x) = 10^1.477
f(x) = 30.
Table 2 is the inverse of table 1. For Table I, we have that when x = 1.301, f(x) = 20, hence for table 2, we have that f(x) = 1.301 when x = 20.
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Find a value of the standard normal random variable z, call it zo such that the following probabilities are satisfied. a. P(z ≤ zo) = 0.0151 b. P(-z0 ≤ z ≤ z0)=0.99 c. P(- zo ≤ z ≤ z0)=0.90 d. P(-z0 ≤ z ≤ zo) = 0.8154
e. P(-z0 ≤ z ≤ 0)= 0-2755 f. P(-2 < z < z)=0.9746 g. P(z >z0)=0.5 h. P (z ≤ zo)= 0.0043
The values of the standard normal random variable z, such that the probability of the following are satisfied: a. zo = -2.17; b. zo = 2.58; c. zo = 1.645; d. zo = 1.44.; e. zo = 0.37; f. zo = 1.96; g. zo = 0; h. zo = 0.
a. P(z ≤ zo) = 0.0151:
zo = -2.17.
b. P(-z0 ≤ z ≤ z0)=0.99
Since the standard normal distribution is symmetric, therefore, finding the z-score corresponding to probability: (1+0.99)/2 = 0.995.
zo = 2.58.
c. P(-zo ≤ z ≤ zo)=0.90:
Using the same reasoning as above, z-score for probability: (1+0.90)/2 = 0.95.
zo = 1.645.
d. P(-z0 ≤ z ≤ zo) = 0.8154:
probability of being outside and inside the range (-zo, zo) respectively:
P(z ≤ -zo) = P(z ≥ zo) = (1 - 0.8154)/2 = 0.0923
P(-zo ≤ z ≤ zo) = 1 - P(z ≤ -zo) - P(z ≥ zo) = 1 - 2(0.0923) = 0.8154
z-score for probability: (1+0.8154)/2 = 0.9077.
zo = 1.44.
e. P(-zo ≤ z ≤ 0) = 0.2755:
Using symmetry of standard normal distribution:
P(-zo ≤ z ≤ 0) = P(0 ≤ z ≤ zo) = (1 - 0.2755)/2 = 0.36225
zo = 0.37.
f. P(-2 < z < zo) = 0.9746:
zo = 1.96.
g. P(z > zo) = 0.5:
Since the standard normal distribution is symmetric:
P(z > zo) = P(z < -zo) = 0.5
zo = 0.
h. P(z ≤ zo) = 0.0043:
zo = 0.
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Water is steadily dripping from a faucet into a bowl. You want to write an equation that represents the number of milliliters y of water in the bowl after x seconds. What is the constant of proportionality for the relationship between the number of milliliters y of water in the bowl and the time in seconds x? What is the equation?
Water from Dripping Faucet
Time in
Seconds (x)
Milliliters
in Bowl (y)
20
320
35
560
45
720
60
960
The constant of proportionality is nothing
The equation that represents the number of milliliters y of water in the bowl after x seconds is: y = 16x
The constant of proportionality for this relationship is the slope of the linear function that passes through any two points on the line. We can use the points (20, 320) and (60, 960) from the table to find the slope:
slope = (960 - 320) / (60 - 20) = 640 / 40 = 16
Therefore, the equation that represents the number of milliliters y of water in the bowl after x seconds is: y = 16x
What is the Constant of Proportionality?The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant variation, or even the rate of change.
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In these activities, we use the following applet to select a random sample of 8 students from the small college in the previous example. At the college, 60% of the students are eligible for financial aid. For each sample, the applet calculates the proportion in the sample who are eligible for financial aid. Repeat the sampling process many times to observe how the sample proportions vary, then answer the questions.
Use the applet to select a random sample of 8 students. Repeat to generate many samples. The applet gives the sample proportion for each sample. Examine the variability in the sample proportions you generated with the applet. Which of the following sequences of sample proportions is most likely to occur for 5 random samples of 8 students from this population?
Group of answer choices
a) 0.250, 0.125, 0.500, 0.500, 0.875
b) 0.600, 0.600, 0.600, 0.600, 0.600
c) 0.375, 0.625, 0.500, 0.500, 0.875
Option c) has moderate variability and is closer to the true proportion and thus is the most likely sequence of sample proportions to occur for 5 random samples of 8 students from this population.
To determine which sequence of sample proportions is most likely to occur for 5 random samples of 8 students from a population where 60% are eligible for financial aid, we'll examine the variability in the sample proportions generated with the applet.
Given the options:
a) 0.250, 0.125, 0.500, 0.500, 0.875
b) 0.600, 0.600, 0.600, 0.600, 0.600
c) 0.375, 0.625, 0.500, 0.500, 0.875
Option b) has no variability, which is unlikely in random sampling.
Option a) has very high variability, which is also unlikely.
Option c) has moderate variability and is closer to the true proportion of 0.60, making it the most likely sequence of sample proportions to occur for 5 random samples of 8 students from this population.
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Help me pls. paying a lot of points
Answer:
33.3333%
Step-by-step explanation:
Answer:3/6 or 1/2
Step-by-step explanation:
Based on the Normal model N( 100, 15) describing IQ scores, what percent of people's IQs would you expect to be a) over 80? b) under 90? c) between 112 and 132?
The percentage of people's IQ over 80 is 9.18%, the percentage of people's IQ under 90 is 25.14% and the percentage of people's IQ between 112 and 132 is 8.23%
Then,
a) Over 80:
The z-score for 80 is (80-100)/15 = -1.33
Using a standard normal distribution table , we can evaluate that the area under the normal curve to the right of -1.33 is approximately 0.9082.
Therefore, the percentage of people's IQs that will be over 80 is approximately
(1-0.9082) x 100%
= 9.18%.
b) Under 90:
The z-score for 90 is (90-100)/15 = -0.67
Using a standard normal distribution table, we can evaluate that the area under the normal curve to the left of -0.67 is approximately 0.2514.
Therefore, the percentage of people's IQs that will be under 90 is approximately
0.2514 x 100%
= 25.14%.
c) Between 112 and 132:
The z-score for 112 is (112-100)/15 = 0.8
The z-score for 132 is (132-100)/15 = 2.13
Using a standard normal distribution table, we can calculate that the area under the normal curve between these two z-scores is approximately 0.0823.
Therefore, the percentage of people's IQs that will be between 112 and 132 is approximately
0.0823 x 100%
= 8.23%.
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+ BrushPro is an one-man paint business owned by Banele. If x offices are painted per month, BrushPro's monthly profit, P, is given by the function P(x) = -x} + 27x2 + 132x + 2970, where 0 < x < 34. U
The maximum profit occurs when 34 offices are painted per month, and the maximum profit is R13500.
Based on the given information, Brush Pro is an one-man paint business owned by Banele and their monthly profit, P, depends on the number of offices painted per month, x. The profit function is given as P(x) = -x + 27x^2 + 132x + 2970, where 0 < x < 34.
To find the maximum profit, we need to find the vertex of the parabolic function. The vertex is located at x = -b/2a, where a = 27, b = 132.
x = -132/(2*27) = -2.44
Since x must be between 0 and 34, the maximum profit will occur at x = 0 or x = 34. We need to evaluate P(0) and P(34) to determine which one is the maximum.
P(0) = -0 + 27(0)^2 + 132(0) + 2970 = 2970
P(34) = -34 + 27(34)^2 + 132(34) + 2970 = 13500
Therefore, the maximum profit occurs when 34 offices are painted per month, and the maximum profit is R13500.
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Using the partial fractions technique, the function f(x) = 68x+168/ x^2+2x-24 can be written as a sum of partial fractions
We can express f(x) as a sum of partial fractions as: f(x) = (-10 / (x + 6)) + (78 / (x - 4))
To write the function f(x) = [tex](68x + 168) / (x^2 + 2x - 24)[/tex] as a sum of partial fractions, we first need to factor the denominator:
[tex]x^2 + 2x - 24 = (x + 6)(x - 4)[/tex]
So we can write:
f(x) = (68x + 168) / ((x + 6)(x - 4))
Now we can use the method of partial fractions to express f(x) as a sum of simpler fractions:
f(x) = A / (x + 6) + B / (x - 4)
where A and B are constants that we need to find. To do this, we can multiply both sides of the equation by the common denominator (x + 6)(x - 4):
(68x + 168) = A(x - 4) + B(x + 6)
Expanding and collecting like terms, we get:
68x + 168 = (A + B) x + (6B - 4A)
Since this equation holds for all values of x, we can equate the coefficients of x and the constant terms separately:
68 = A + B
168 = 6B - 4A
Solving these two equations simultaneously, we get:
A = -10
B = 78
Therefore, we can express f(x) as a sum of partial fractions as:
f(x) = (-10 / (x + 6)) + (78 / (x - 4))
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Which of the following would have resulted in a violation of the conditions for inference? (a) If the entire sample was selected from one classroom (b) If the sample size was 15 instead of 25 (c) If the scatterplot of x = foot length and y = height did not show a perfect linear relationship (d) If the histogram of heights had an outlier (e) If the standard deviation of foot length was different from the standard deviation of height
A perfect linear relationship is essential for making accurate inferences in regression analysis. If the relationship between the variables is not linear, the results from the analysis may not be valid or reliable.
Option (a) would have resulted in a violation of the conditions for inference, as it would not be a representative sample of the population. Inference relies on the sample being representative of the population, and selecting the entire sample from one classroom would not be a random selection from the population.
Options (b), (c), (d), and (e) do not necessarily violate the conditions for inference. The sample size of 15 may affect the precision of the estimate, but it does not necessarily violate the conditions for inference.
A perfect linear relationship is essential for making accurate inferences in regression analysis. The scatterplot not showing a perfect linear relationship is expected in most cases, as perfect linear relationships are rare in real-world data. The histogram having an outlier may affect the distribution, but it does not necessarily violate the conditions for inference. And the standard deviation of foot length is different from the standard deviation of height is expected, as they are measuring different variables.
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