The mean number of claims per policy is 1.4 and the sample variance and standard deviation are 0.956 and 0.977 respectively is the answer.
a) To find the mean number of claims per policy, we need to calculate the weighted average of the number of claims.
Number of claims: 0, 1, 2, 3, 4, 5, 6
Number of policies: 21, 13, 5, 4, 2, 3, 2
First, we calculate the product of the number of claims and the corresponding number of policies for each category:
0 claims: 0 * 21 = 0
1 claim: 1 * 13 = 13
2 claims: 2 * 5 = 10
3 claims: 3 * 4 = 12
4 claims: 4 * 2 = 8
5 claims: 5 * 3 = 15
6 claims: 6 * 2 = 12
Next, we sum up these products: 0 + 13 + 10 + 12 + 8 + 15 + 12 = 70
Finally, we divide the sum by the total number of policies (50) to find the mean:
Mean number of claims per policy = 70 / 50 = 1.4
Therefore, the mean number of claims per policy is 1.4.
b. To find the sample variance and standard deviation, we need to calculate the deviations from the mean for each category, square the deviations, and then calculate the average.
Deviation from the mean:
0 - 1.4 = -1.4
1 - 1.4 = -0.4
2 - 1.4 = 0.6
3 - 1.4 = 1.6
4 - 1.4 = 2.6
5 - 1.4 = 3.6
6 - 1.4 = 4.6
Square the deviations:
(-1.4)^2 = 1.96
(-0.4)^2 = 0.16
(0.6)^2 = 0.36
(1.6)^2 = 2.56
(2.6)^2 = 6.76
(3.6)^2 = 12.96
(4.6)^2 = 21.16
Now, we sum up these squared deviations:
1.96 + 0.16 + 0.36 + 2.56 + 6.76 + 12.96 + 21.16 = 46.92
To find the sample variance, divide the sum of squared deviations by the number of data points minus 1 (n-1):
Sample variance = 46.92 / (50 - 1) = 46.92 / 49 ≈ 0.956
To find the sample standard deviation, take the square root of the sample variance:
Sample standard deviation = √(0.956) ≈ 0.977
Therefore, the sample variance is approximately 0.956 and the sample standard deviation is approximately 0.977.
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Given the figure below, find the values of x and z.
Answer:
x = 12
z = 101
Step-by-step explanation:
Hello There!
First lets find z
Well the angle that has a measure of 79 degrees and angle z are supplementary angles meaning that the sum of the two is 180
So we can find the missing angle by subtract the given angle (79 in this case) from 180
180 - 79 = 101 so z = 101
Now lets find x
The angle that has a measure of 79 degrees and the angle labeled (6x+7) are vertical angles
If you didn't know vertical angles are congruent
That being said lets create an equation to solve for x
79 = 6x + 7
now we solve for x
step 1 subtract 7 from each side by
7 - 7 cancels out
79 - 7 = 72
now we have 72 = 6x
step 2 divide each side by 6
72/6=12
6x/6=x
we're left with x = 12
A: x>106
B: x<106
C: x=106
Which one is it?
Answer:
x is equal to 106
Step-by-step explanation:
when x is on the opposite side of 2 intersecting lines, it will be the same angle as the angle opposite to it
A proton moves along the x-axis with u2 -1.0 x 10⁷ m/s.
As it passes the origin, what are the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position? Give your answer using unit vectors Express your answer in terms of the unit vectors i, j, and k. Use the 'unit vector button to denote unit vectors in your answer.
The magnetic field using the unit vector notation B = Bx i= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i.
To determine the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position caused by a moving proton, we can use the formula for the magnetic field produced by a moving charge:
B = (μ₀ / 4π) * (qv × r / r³)
where B is the magnetic field, μ₀ is the permeability of free space (constant), q is the charge of the proton, v is its velocity, × denotes the cross product, r is the position vector, and r³ represents the magnitude cubed of the position vector.
Given information:
u = -1.0 x 10⁷ m/s (velocity of the proton)
Position vector r = 1 cm i
Let's calculate the magnetic field at the given position:
First, we convert the position vector from centimeters to meters:
r = (1 cm, 0 cm, 0 cm) = (0.01 m, 0 m, 0 m)
Next, we substitute the values into the formula and simplify:
B = (μ₀ / 4π) * (qv × r / r³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / (0.01 m)³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 0.000001 m³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 10^-18 m³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²) i
Now, we can express the magnetic field using the unit vector notation:
B = Bx i
= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i
where Bx represents the magnitude of the magnetic field in the x-direction.
Please note that the direction of the magnetic field will depend on the orientation of the velocity vector of the proton.
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A certain college graduate borrows $6600 to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate k that is required to pay off the loan in 5 years. (Round your answer to two decimal places.) k = $ per yr
The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.
To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:
A = P * [tex]e^{(rt)[/tex],
where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:
0 = 6600 * [tex]e^{(0.10 * 5)[/tex]- k * 5,
Simplifying the equation, we have:
[tex]e^{(0.5)[/tex] = k / 6600.
Now, we can solve for k by multiplying both sides of the equation by 6600:
k = 6600 * [tex]e^{(0.5)[/tex],
Using a calculator or software, we find that k is approximately $943.57 per year.
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Country Financial, a financial services company, uses surveys of adults age and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of adults showed indicating that their financial security was more than fair. In February of 2010, a sample of adults showed indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. - Select your answer - - Select your answer - b. What is the sample proportion indicating that their financial security was more than fair in 2012
Complete question :
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. H : Pi - P2 - Select your answer HA : P1 P2 - Select your answer - b. What is the sample proportion indicating that their financial security was more than fair in 2012? Round your answer to two decimal places. In 2010?
Answer:
H0 : p1 - p2 = 0
H1 : p1 - p2 ≠ 0
Phat 2010 = 0.35
Phat 2012 = 0.41
Step-by-step explanation:
The null and alternative hypothesis :
H0 : p1 - p2 = 0
H1 : p1 - p2 ≠ 0
The null means there is no difference in proportion for the two years while the alternative claims that there is difference in proportion for the two years.
Sample proportion for 2010:
Phat = x / n
x = 315 ; n = 900
Phat = 315 / 900
Phat = 0.35
Sample proportion for 2012 :
Phat = x / n
x = 410 ; n = 1000
Phat = 410 / 1000
Phat = 0.41
jet travelling at 500 km/h for 4 hours.
Answer: jet travels a total of 2000 km in total
Step-by-step explanation:
A rectangular prism with a length of 5 inches a width of 4 inches and a height of 3 inches is how many square inches
Answer:
20
Step-by-step explanation:
length x width = area
4 x 5 = 20
(not 100% sure, but I hope this helps)
This pattern follows the rule multiply by 2. What other feature do you observe? 4, 8, 16, 32, 64, 128
Answer:
Each number is 2 to the power some integers.
Step-by-step explanation:
The pattern is 4,8,16,32,64,128.
It follows the exponent of 2.
4=2*2 =[tex]2^{2}[/tex]
8=2*2*2=[tex]2^{3}[/tex]
16= [tex]2^{4}[/tex]
32 =[tex]2^{5}[/tex]
64=[tex]2^{6}[/tex]
128 =[tex]2^{7}[/tex]
so, it is 2 to the power integers.
Need help with this question thank you!
Answer:
You asked this question like 4 times
Step-by-step explanation:
The answer is
(5,-1)
(-4,0)
the Median.)
Find quartile 2 using the data below:
23, 45, 52, 28, 42, 87, 56, 32, 48, 55, 24, 63, 68, 76, 67
Answer:
52
Step-by-step explanation:
if you put the numbers in order from least to greatest you'll see that 52 is in the middle
PLSS HELP IMMEDIATELY!!! i’ll give brainiest if u don’t leave a link!
Answer:
C
Step-by-step explanation:
Use the SOR method with w = 1.2 to solve the following linear system with a tolerance TOL = 10-3 in the lo norm. - 4x1 + x2 – x3 + x4 = -2, X1 + 4x2 – X3 – X4 = -1, -X] – x2 + 5x3 + x4 = 0, X1 – x2 + x3 + 3x4 = 1.
Using the Successive Over-Relaxation (SOR) method with a relaxation factor of w = 1.2 and a tolerance of TOL = 10^-3 in the l2 norm, the linear system of equations can be solved iteratively. The solution will converge to the desired tolerance level.
The SOR method is an iterative technique used to solve linear systems of equations. It requires an initial guess for the solution and iteratively updates the values until the desired tolerance is reached.
To apply the SOR method, the given linear system can be rewritten as a matrix equation: AX = B, where A is the coefficient matrix, X is the solution vector, and B is the constant vector. The system can be solved by iterating through the equations and updating the values of X until convergence is achieved.
In this case, the SOR method is performed with a relaxation factor of w = 1.2, which helps to accelerate convergence. The tolerance is set to TOL = 10^-3, indicating the desired level of accuracy.
The SOR algorithm is then applied iteratively until the solution converges within the specified tolerance. The updated values of X are calculated using the SOR formula, and the process is repeated until the difference between consecutive iterations falls below the tolerance level.
By following this iterative process with the given parameters, the SOR method will yield the solution to the linear system of equations.
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In ΔEFG, the measure of ∠G=90°, GF = 48, EG = 55, and FE = 73. What ratio represents the cosecant of ∠F?
Answer:
Cosec <F = 73/55
Step-by-step explanation:
In ΔEFG, the measure of ∠G=90°, GF = 48, EG = 55, and FE = 73. What ratio represents the cosecant of ∠F?
First you must know that;
Cosecant <F = 1/sin<F
Given
∠G=90°, GF = 48, EG = 55, and FE = 73.
ED ,= hyp = 73
EG = opp = 55*side facing <F
Using DOH CAH TOA
Sin theta = opp/hyp
Sin <F= 55/73
Reciprocate both sides
1/sinF = 73/55
Cosec <F = 73/55
Given the following utility function:
X: -100 -90 -80 -65 -50 -35 -20 0 20 45 70 110 150
U (X): 0 3 4.5 6 7 8 9 10 11 12 13 14 15
(a) Calculate the probabilities p1 and p2 such that 45 is indifferent to the lotteries: (20, p1; 150, 1 −p1) and (−20, p2; 110, 1 −p2)
(b) Calculate the selling price and risk premiums of the lotteries: (−90, 0.5; −20, 0.5) and (−100, 0.2; −50, 0.3; −20, 0.4; 70, 0.1).
(c) Calculate the buying price for the following lottery (150, 0.4; 45, 0.6).
If utility function is given then we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.
(a) To find the probabilities p1 and p2, we set up the equation U(45) = p1 * U(20) + (1 - p1) * U(150) and solve for p1. Similarly, we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.
(b) The selling price of a lottery is the amount at which an individual is willing to sell the lottery. We compare the expected utility of the lottery to the utility of the certain amount. The risk premium is the difference between the selling price and the expected value of the lottery.
(c) The buying price is the amount an individual is willing to pay for a lottery. We set up the equation U(45) = p * U(150) + (1 - p) * U(45) and solve for p to find the buying price.
Note: The specific calculations for parts (a), (b), and (c) require the values of U(X) for each corresponding X value in the utility function.
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John is 30 years old. He will receive two payments of $2500 each. The first payment will be an unknown number of years in the future. The second payment will be five years after the first payment. At an annual effective interest rate of I=5%, the present value of the two payments is $2606. Determine at what age John will receive the second payment.
Answer:
16 years
Step-by-step explanation:
Let us assume that he would received the first payment after t years
So
The following formula should be used
PV = P ÷ (1 + r)^t + P ÷ (1 + r)^t+5
$2,606 = $2,500 ÷ (1 + 0.05)^t + $2,500 ÷ (1 + 0.05)^t + 5
$2,606 = $2,500 ÷ 1.05^t (1 + 1 ÷ (1.05)^5)
1.05^t = $2,500 ÷ $2,606 (1.7835) = 1.71098
t = ln(1.71098) ÷ ln(1.05)
= 11
Therefore he would be received the second payment after
= 11 + 5
= 16 years
Write an equation of the line perpendicular to the given line that contains P.
SOMEONE HELP ME ILL GIVE YOU 50 POINTS I AM DESPERATE I AM IN A MATHS TEST!
Answer:
12:2
4:24
6:1
Step-by-step explanation:
those 3 are the correct ones
Find the surface area of a cubical planter
measuring 30 inches on a side.
30 x 30 = 900
This is the surface area of one side
900 x 6
Multiply by 6 to get the surface area of all 6 sides of the cube
900 x 6 = 5400
Choose the correct answer.
Between the years 1970 and 1976, what percentage change in the rate of exchange occurred in the German mark relative to the United States dollar (to the nearest percent)?
%
answer:
Between the years 1970 and 1976, what percentage change in the rate of exchange occurred in the German mark relative to the United States dollar (to the nearest percent)?
45 %
The percentage change in the rate of exchange occurred in the German mark relative to the United States dollar is 45%
How to determine the change in the rates?From the chart (table), we have the following rates in Germany:
Rate in 1970 = 27.42Rate in 1976 = 39.74The percentage change is then calculated using:
Percentage change= (Final - Initial)/Initial * 100%
This gives
Percentage change= (39.74 - 27.42)/27.42* 100%
Evaluate the quotient
Percentage change= 0.45* 100%
Evaluate the product
Percentage change= 45%
Hence, the percentage change in the rate of exchange occurred in the German mark relative to the United States dollar is 45%
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Jo records the number of text messages she receives each day she uses this information to draw this bar chart write 3 mistakes she has made
Answer:
X axis labels aren't evenly spaces
Y axis has no origin
Missing label
Step-by-step explanation:
Scale of a graph is important when displaying numerical data on a plot.
Based on the bar chart given, it could be seen that the x axis which is labeled days of the week is not adequately spaced. Data on both axis should he a recognizable.
2.)
Taking a look at the graph, it has no origin, the numbering of the vertical axis, number of text messages should start from 0
3.) Also, the x and y axis aren't labeled Hence charts should be well labeled to include x - axis and y-axis.
Answer:
X axis labels aren't evenly spaces
Missing label
there us no scale written starting at 0
Step-by-step explanation:
this will give u 3/3
What is equivalent to 8?
A:2^3
B:3^-2
C:2^-3
D:3^2
Answer: A:2^3
Step-by-step explanation:
8=2*2*2=(2)^3
Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!
Answer: n=4
Step-by-step explanation:
Given
3n-(2+n)=6
Expand Parenthesis (REMEMBER TO CHANGE SIGNS)
3n-2-n=6
Combine like terms
2n-2=6
Add 2 on both sides
2n-2+2=6+2
2n=8
Divide both sides by 2
2n/2=8/2
n=4
Hope this helps!! :)
Please let me know if you have any questions
Answer:
4
Step-by-step explanation:
4 Is the Answer because you have to multiply 4 to all the N's. Which means you have to multiply 4 by 3 which equals 12. Then 2+4=6. Then you would do 12-6=6. There's your answer. Here is the equation if it were like the problem: 12 - (2+4). I'm sure you can figure out the rest. Thanks. If you find any fault in my answer let me know! Have a good day!
I need help fast and for real no bots
Answer: d. 201.06
Step-by-step explanation:
To find area of a circle we use the equation 2pi(r) or in this case 2*pi(16)= 804.25in^2 but since we are looking for the shaded region which is 1/4 or one-fourth of the circle so divide 804.25/4 to get 201 or specifically 201.06
There is a sale on jeans where you will get 20% off the original price. If the jeans cost $65, how much will you SPEND on the jeans?
plzzzz answer
find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. a(3, 4, 1), b(0, 6, 2), c(3, 5, 6)
The lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.
To find the lengths of the sides of the triangle with vertices A(3, 4, 1), B(0, 6, 2), and C(3, 5, 6), we can use the distance formula.
The distance formula between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in three-dimensional space is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
Let's calculate the lengths of the sides of the triangle:
Side AB:
d₁ = √((0 - 3)² + (6 - 4)² + (2 - 1)²)
= √((-3)² + 2² + 1²)
= √(9 + 4 + 1)
= √14
Side BC:
d₂ = √((3 - 0)² + (5 - 6)² + (6 - 2)²)
= √(3² + (-1)² + 4²)
= √(9 + 1 + 16)
= √26
Side AC:
d₃ = √((3 - 3)² + (5 - 4)² + (6 - 1)²)
= √(0² + 1² + 5²)
= √(0 + 1 + 25)
= √26
Now, let's analyze the triangle based on the lengths of its sides:
Since all three sides have different lengths (√14, √26, and √26), the triangle is neither an isosceles triangle (which has at least two sides of equal length) nor a right triangle (which satisfies the Pythagorean theorem).
In summary, the lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.
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Cari’s Bakery, Inc., began operations in October. The owner contributed cash of $14,400 and a delivery truck with fair value of $19,200 to the company.
Which of the following describes how these transactions would affect the company’s equity accounts?
A) Increase contributed capital by $33,600
B) Increase earned capital by $33,600
C) Increase contributed capital by $14,400 and earned capital by $19,200
D) Increase earned capital by $14,400 and contributed capital by $19,200
E) None of these are correct.
The transaction would affect the company's equity accounts by increasing contributed capital by $14,400 and earned capital by $19,200. The correct answer is option C.
Equity accounts are a component of the balance sheet that represents the net worth of a business. The equity accounts include contributed capital and earned capital. Contributed capital, also referred to as paid-in capital, is the value of cash or other assets contributed to a company by investors in exchange for shares of ownership in the company. Contributed capital represents the long-term financial interests of owners in the business.
Earned capital is the amount of money that a business earns through its operations. It is also referred to as retained earnings. The difference between a business's assets and liabilities is its equity. It represents the total value of the assets that a company owns after all liabilities have been settled. According to the question, the owner contributed cash of $14,400 and a delivery truck with a fair value of $19,200 to the company. This transaction will increase contributed capital by $14,400 (the cash contribution) and increase earned capital by $19,200 (the delivery truck contribution).Therefore, option C: Increase contributed capital by $14,400 and earned capital by $19,200 is the correct answer.
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What does 5/9 + 1/3 equal to?
Answer:
= 5/9 + 1/3
=5/9 + 3/9
= 5+3/9
=8/9
can somebody help me first answer gets brainiest pls help
11. Find the following GCD and LCM. (a) GCD (360, 4000) (c) GCD (627, 205143) (b) LCM (360, 4000) (d) LCM (627, 205143)
The required answers are:
(a) GCD = 40 (b) LCM = 36000 (c) GCD = 33 (d) LCM = 1032933
GCD and LCM of the given numbers are:
(a) Prime factors of 360: 2 x 2 x 2 x 3 x 3 x 5.Prime factors of 4000: 2 x 2 x 2 x 2 x 5 x 5 x 5.GCD = 2 x 2 x 2 x 5 = 40.
(b) LCM = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 = 36000.
(c) Prime factors of 627: 3 x 11 x 19.Prime factors of 205143: 3 x 3 x 7 x 7 x 11.GCD = 3 x 11 = 33.
(d) LCM = 3 x 3 x 7 x 7 x 11 x 19 = 1032933.
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Drag and drop all methods of showing Triangle Similarity or Triangle Congruence into the appropriate box. SAS, SSS, ASA, AAS, CPOCTAC, HL, AA
Similar Triangle Justifications Congruent Triangle Justifications
Answer:
hi
Step-by-step explanation:
by