Answer:
The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857
Step-by-step explanation:
It is said that Actuary Rahul examines a low risk policy
Probability of a low risk policy having a claim = 10% = 0.1
Actuary Toby examines high risk policy
Probability of a high risk policy having a claim = 20% = 0.2
Let the number of policies examined by actuary Rahul before he finds a claim and stop be n
Probability that actuary Rahul examines exactly n policies = [tex]0.9^{n-1} (0.1)[/tex]
Probability that Toby examines more than n policies = [tex]0.8^n[/tex]
Since the claim statuses of policies are mutually independent, the probability that both events happen simultaneously = [tex]0.9^{n-1} (0.1) (0.8)^n[/tex]
probability that both events happen simultaneously = [tex]\frac{0.1}{0.9} (0.72^{n})[/tex]
The probability that Actuary Rahul examines fewer policies that Actuary Toby = [tex]\sum\limits^ \infty_1 {\frac{0.1}{0.9} 0.72^{n} }[/tex] = [tex]\frac{1}{9}\sum\limits^ \infty_1 { 0.72^{n} } = \frac{1}{9} (\frac{0.72}{1-0.72} ) = \frac{1}{9} (\frac{0.72}{0.28} )[/tex]
The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857
3x - 2y = 12
Find the x and y intercepts
Answer:
x-intercept: 4 y-intercept: - 6
Step-by-step explanation:
To find the y-intercept, we must first solve for y.
Isolate variable y on the left side of the equation by subtracting 3x from both sides.
- 2y = - 3x + 12
Now divide both sides by - 2 to find y.
y = 3/2x - 6
The y-intercept is - 6. (remember formula y = mx + b, where b is the y-intercept)
To find the x-intercept, we must solve for x.
Isolate variable x on the left side of the equation by adding 2y to both sides.
3x = 2y + 12
Now divide both sides by 3 to find x.
x = 2/3y + 4
The x-intercept is 4. (remember formula x = my + b, where b is the x-intercept)
Answer:
4 and - 6
Step-by-step explanation:
3x-2y=12
x= 0 ⇒ -2y=12 ⇒ y= -6y=0 ⇒ 3x= 12 ⇒ x= 4You currently drive 300 miles per week in a car that gets 15 miles per gallon of gas. You are considering buying a new fuel-efficient car for $12,000 (after trade-in on your current car) that gets 50 miles per gallon. Insurance premiums for the new and old car are $800 and $600 per year, respectively. You anticipate spending $1200 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car?
Answer:
No, it is not less expensive to keep the old car as the price calculation is higher then the New Car
Purchasing new car is less expensive
Step-by-step explanation:
NEW CAR EXPENSES= $21,240
OLD CAR EXPENSES= $25,800
NB: Kindly check attached picture for calculations
Please help! I'm stuck on this one :(
Answer:
[900, 1300]
Step-by-step explanation:
According to the empirical rule, 95% is within ±2 standard deviations.
1100 − 2(100) = 900
1100 + 2(100) = 1300
round off the number 0.007326 correct to 3 significant figures 3 decimal places
Answer:0.007
Step-by-step explanation:
Calculate the product of 8/15, 6/5, and 1/3.
B. 16:15
D. 16/75
A. 48
0115
Answer:
16/75, D
Step-by-step explanation:
6/5*1/3. We can cross simplify to make it 2/5*1/1. That is 2/5. Then, 2/5*8/15 is 16/75 which is answer choice D.
1.x2+3x+3=0
2.x2-2x-3=0
3.x2-6x+9=0
4.-x2+3=0
Step-by-step explanation:
the two A's in the buttom is correct
How much of other chemicals must be evaporated from 400 grams of a hand sanitizer that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? Correct your answer to the nearest whole number
Answer:
Mass of other chemicals to be evaporated is 24 grams.
Step-by-step explanation:
The initial mass of the hand sanitizer = 400 grams, and has an alcohol content of 24%.
mass of its alcohol content = [tex]\frac{24}{100}[/tex] × 400
= 96 grams
mass of non-alcoholic content = 400 - 96
= 304 grams
If the percentage of alcohol is increased to 30%, then;
mass of its alcohol content = [tex]\frac{30}{100}[/tex] × 400
= 120 grams
The mass of other chemicals to be evaporated = 120 - 90
= 24 grams
The circle above has an area of 144 pi cm^2. What is the area of the blue sector? Use 3.14 for pi.
Answer:
150.72 cm^2
Step-by-step explanation:
The blue area has an angle of 120 degrees, and 120/360 = 1/3, which shows that the blue area is 1/3 of the circle. In that case, the blue area is just 144pi/3. That simplifies to 48 pi.
48*3.14 = 150.72
Which angle is in standard position?
On a coordinate plane, 2 rays form an angle and both rays are not on the y- or x-axis.
On a coordinate plane, 2 rays form an angle and both rays are not on the y- or x-axis.
On a coordinate plane, 2 rays form an angle. One ray sits on the x-axis.
On a coordinate plane, 2 rays form an angle and both rays are not on the y- or x-axis.
Mark this and return
Answer:
(C)On a coordinate plane, 2 rays form an angle. One ray sits on the x-axis.
Step-by-step explanation:
An angle is stated in the standard position with respect to the x-axis.
Therefore, for an angle to be in standard position, one of its rays must be on the x-axis.
From the given options, only Option C has a ray on the x-axis and therefore is the angle that is in standard position.
Answer:
The answer to this question is C) (the third graph)
Answers to the entire test are
1. A) Quadrant 1
2. B) –270° and 90°
3. D) 126° + (720n)°, for any integer n
4. A) –90° and 630°
5. A) (the first graph)
6. D) n = 6
7. C) x = y + 360 n, for any positive integer n
8. B) 10°
9. C) (the third graph)
10. C) 495°
Step-by-step explanation:
Just took it. Edg 2021. Hope this helps :) (smiley's name is George, George says hi)
the table shows miles driven by a car and the gallons of gas used to drive those miles. how many miles did the car travel on a gallon of gas?
Answer:
May we see the graph?
Step-by-step explanation:
Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine a differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)
Answer:
[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]
A(0) = 70 (i.e the pounds of salt dissolved into the tank)
Step-by-step explanation:
Given that:
a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved.
The rate at which pure water is pumped into the tank is 4 gal/min
After stirring; the pure water is then pumped out at the same rate.
The objective is to determine the differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)
Taking the differential of:
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex] ---- (1)
where ;
[tex]R_{in[/tex] = 0
[tex]R_{out} =\dfrac{A(t)}{400}*4[/tex]
[tex]R_{out} =\dfrac{A}{100}[/tex]
replacing them into (1) ; we have:
[tex]\dfrac{dA}{dt}=0 - \dfrac{A}{100}[/tex]
[tex]\dfrac{dA}{dt}=- \dfrac{A}{100}[/tex]
[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]
A(0) = 70 (i.e the pounds of salt dissolved into the tank)
The differential equation for the amount of salt A(t) in the tank at time t > 0 is [tex]\frac{dA}{dt} + \frac{A}{100} = 0[/tex]
A (0)= 70
Given that,
Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/minThe Calculation is as follows:[tex]dA\div dt=R_{in}-R_{out}[/tex]
Rin=0
[tex]R_{out}=A(t)\div 400 \times (4)\\\\ =A\div 100[/tex]
so,
[tex]dA\div dt=R_{in}-R_{out}\\\\dA\div dt=0- A\div 100[/tex]
So,
[tex]dA\div dt +A\div 100=0[/tex]
A(0)=70
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In a large class in statistics, the final examination grades have a mean of 67.4 and a standard deviation of 12. Assuming that the distribution of these grades is normal, the number of passes in a class of 180 is:_________ (if you get a number with decimals points, round up to the next whole number)
Answer:
The number of passes in a class of 180 is 75.
Step-by-step explanation:
The problem does not state, so I will suppose the passing grade is 70.
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 67.4, \sigma = 12[/tex]
Proportion of students who passed:
This is 1 subtracted by the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 67.4}{12}[/tex]
[tex]Z = 0.22[/tex]
[tex]Z = 0.22[/tex] has a pvalue of 0.5871.
1 - 0.5871 = 0.4129
Out of 180:
0.4129*180 = 74.32
Rounding up
The number of passes in a class of 180 is 75.
What is the value of x if f(x) = 76
Answer:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace f(x) with 0 and solve for x
No solution
Plz help fast!!! will give brainiest to first correct answer For which distributions is the median the best measure of center? Select each correct answer.
Answer:
The top left picture and top right picture
Step-by-step explanation:
(−98)+(−97)+(−96) + ⋯ +(−1)+0+1+2+ ⋯ +98+99+100
Answer:
199
Step-by-step explanation:
All of the terms of the sum cancel except the last two.
The total is 199.
Find the volume of a juice box that is 3 inches by 1/12 in by 4 inches
Answer:
The volume of the box is [tex]1 in^{3}[/tex]Step-by-step explanation:
This problem is on the mensuration of solid shapes, a box/cube.
Given data
[tex]Length l = 3in\\\\Width w= \frac{1}{12}in \\\\Height h = 4in[/tex]
we know that the expression for the volume of a cube is
[tex]volume= l*w*h\\\\substituting \\\\volume= 3* \frac{1}{12}* 4\\ volume= \frac{12}{12} = 1 in^{3}[/tex]
The decimal $0.76$ is equal to the fraction $\frac{4b+19}{6b+11}$, where $b$ is a positive integer. What is the value of $b$?
Answer:
The value of b is 19.
Step-by-step explanation:
With what the problem states, we have that:
[tex]\frac{4b + 19}{6b + 11} = 0.76[/tex]
Doing cross multiplication
[tex]4b + 19 = 0.76(6b + 11)[/tex]
[tex]4b + 19 = 4.56b + 8.36[/tex]
[tex]4.56b - 4n = 19 - 8.36[/tex]
[tex]0.56b = 10.64[/tex]
[tex]b = \frac{10.64}{0.56}[/tex]
[tex]b = 19[/tex]
The value of b is 19.
What must be a factor of the polynomial function f(x) graft on the coordinate plane below
X - 6
x - 3
x + 1
x +6
Answer:
Option D.
Step-by-step explanation:
The given graph represents the function f(x).
If graph of a function f(x) intersect x axis at x=c, then (x-c) is a factor of f(x).
From the given graph it is clear that the graph of f(x) intersect x axis at x=-6,-3,0. It means factors of given function are
[tex](x-(-6))=(x+6)[/tex]
[tex](x-(-3))=(x+3)[/tex]
[tex](x-0)=x[/tex]
It means (x+6), (x+3) and x are factors of given function.
Therefore, option D is correct.
Answer:
The answer is (x+6)
Step-by-step explanation:
Just took the test
Hope this helps
Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics: Try 1 Try 2 Gain n \overline x s \overline x s \overline x sCoached 427 500 92 529 97 29 59Uncoached 2733 506 101 527 101 21 52Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.toat 90% confidence.Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let \mu_1 be the score gain for all coached students. Let \mu_2 be the score gain for uncoached students.(a) Give the alternative hypothesis: \mu_1 - \mu_20.(b) Give the t test statistic:(c) Give the appropriate critical value for \alpha =5%: .
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:
Try 1 Try 2 Gain
n x s x s x s
Coached 427 500 92 529 97 29 59
Uncoached 2733 506 101 527 101 21 52
Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.
at 90% confidence.
Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1 be the score gain for all coached students. Let μ2 be the score gain for uncoached students.
(a) Give the alternative hypothesis:
μ1 - μ2.
(b) Give the t test statistic:
(c) Give the appropriate critical value for \alpha =5%:
Solution:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean score gain for all coached students
x2 = sample mean score gain for all uncoached students
s1 = sample standard deviation score gain of coached students
s2 = sample standard deviation score gain of uncoached students
For a 90% confidence interval, the z score is 1.645
From the information given,
x1 = 29
s1 = 59
n1 = 427
x2 = 21
s2 = 52
n2 = 2733
x1 - x2 = 29 - 21 = 8
z√(s1²/n1 + s2²/n2) = 1.645√(59²/427 + 52²/2733) = 4.97
90% Confidence interval = 8 ± 4.97
a) The population standard deviations are not known. it is a two-tailed test. The random variable is μ1 - μ2 = difference in the score gain for coached and uncoached students.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 0
This is a right tailed test.
b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (29 - 21)/√(59²/427 + 52²/2733)
t = 2.65
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [59²/427 + 52²/2733]²/[(1/427 - 1)(59²/427)² + (1/2733 - 1)(52²/2733)²] = 9.14/0.1564
df = 58
c) from the t distribution table, the critical value is 1.67
In order to reject the null hypothesis, the test statistic must be smaller than - 1.67 or greater than 1.67
Since - 2.65 < - 1.67 and 2.65 < 1.67, we would reject the null hypothesis.
Therefore, at 5% significance level, we can conclude that the score gain for coached students is greater than the score gain for uncoached students.
What is the total surface area of the square pyramid below?
14 cm
10 cm
10 cm
Answers:
100 cm
200 cm
250 cm
Answer: A = 93.8 cm so if you round up it's about 100 cm
Step-by-step explanation:
Area means you have to multiply all measurements by each other in any order of course because it doesn't matter in this case.
14 * 10 * 10 = 1400
Now you can/should divide the answer which is (1400) by how many measurements you have times the sides it has, sides - which is 5 , measurements - which is 3, so it would look like this:
1400 / 15 = 93.8
A cereal box has a volume of 450 cubic cm. The length and width are 43 cm and 12 cm. HOW can you find the height? PLEASE HELP ME!!
WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
Volume of a rectangular prism=length x width x height
450=43*12*x
x=0.87209cm
Which of the following is a property of translations that is not also a property of other types of rigid motions? (1) they map line segments to other line segments of equal length (2) they map angles to other angles of the same size (3) they map lines to parallel lines (4) they map lines to perpendicular lines
Answer:
3 I think it's 3. sorry if I'm wrong
The correct answer is (3) they map lines to parallel lines
Transformation is the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
Translation is the movement of a point up, down, left or right in the coordinate plane.
Translation is a rigid transformation, that is, it preserves the size and shape of the figure. Reflection and rotation are also rigid transformation.
Translation maps lines to parallel lines whereas rotation does not since it changes the direction of the line.
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Which of the following graphs Represents the equation above -3x+ 2 y=
If x^6=20 and w^10=20, what is x^12 w^-10?
Answer:
[tex]x^{12} =400[/tex]
[tex]w^{-10} =\frac{1}{20}[/tex]
Step-by-step explanation:
[tex]x^{6} =20[/tex]
[tex]x^{12} =(x^{6} )^{2} =20^{2} =400[/tex]
[tex]w^{10} =20[/tex]
[tex]w^{-10} =\frac{1}{w^{10} } =\frac{1}{20}[/tex]
[tex]x^{12} *w^{-10} =400*\frac{1}{20} =20[/tex]
Triangle ABC was dilated and translated to form similar triangle A'B'C'.
On a coordinate plane, 2 triangles are shown. Triangle A B C has points (0, 2), (2, 2), and (2, 0). Triangle A prime B prime C prime has points (negative 4, negative 1), (1, negative 1), and (1, negative 6).
What is the scale factor of the dilation?
One-fifth
Two-fifths
Five-halves
5
Answer:
Dilation is done by the scale factor of Five-halves.
Step-by-step explanation:
Please refer to the image attached,
The graph clearly shows the triangles [tex]\triangle[/tex]ABC and [tex]\triangle[/tex]A'B'C'.
Let us calculate the sides of triangles first then we will be able to find scale factor of dilation.
Using the distance formula:
Distance between 2 points [tex]P (x_1,y_1) \text{ and } Q (x_2,y_2)[/tex] is given by formula:
PQ = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Side AB is along x-axis, side AB =
[tex]\sqrt{(2-0)^2+(2-2)^2}\\\Rightarrow \sqrt{4}\\\Rightarrow 2\ units[/tex]
Similarly side, BC = 2 units
Now, in [tex]\triangle[/tex]A'B'C', A'B' can be calculated by distance formula:
[tex]\sqrt{(1+4)^2+(-1- (-1))^2}\\\Rightarrow \sqrt{25}\\\Rightarrow 5\ units[/tex]
B'C' = 5 units
The ratio of sides:
AB : A'B' = 2:5
[tex]\Rightarrow \dfrac{AB}{A'B'} = \dfrac{2}{5}\\\Rightarrow A'B' = \dfrac{5}{2} AB[/tex]
So, scaling factor is [tex]\dfrac{5}{2}[/tex] or 2.5.
OR
Scaling factor is Five-halves.
Answer:
The answer is C on Edge.
Step-by-step explanation:
Need helppppp asapppp
The answer is C. 65........
Answer:
25
Step-by-step explanation:
The angle of an arc is the same as the central angle. MarcCD is the same as the central angle COD which is given as 130o.
That means there are 50 degrees left for COA and DOA and because the chord and the diameter are equal, COA = DOA
That means that COA is 1/2 what is left over from 180 when 130 is subtracted from it.
1/2 * 50 = 25
The answer is A 25.
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 940(1.89)
Answer: The change represents growth with 89% of growth rate.
Step-by-step explanation:
The exponential function is given by :-
[tex]f(x)= Ab^x[/tex]... (i)
Where , A = initial value , b= multiplicative factor and x= time period
We call 'b' growth factor when b>1, we can write b= 1+r , where r is the rate of growth.We call 'b' decay factor when b<1 , we can write b= 1-r , where r is the rate of decay.The given function : [tex]y = 940(1.89)^x[/tex].
By comparing this to (i) , we get
b= 1.89 > 1 , thus it represent the growth.
Also,
[tex]b= 1+r\Rightarrow\ 1.89 = 1+r\\\\\Rightarrow\ r=1.89-1=0.89[/tex]
i.e. Percentage rate of growth = 0.89 x 100 = 89%.
Please help
Blake is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Blake need to invest, to the nearest dollar, for the value of the account to reach $910 in 10 years?
Answer:
A, of money in the account after 3 years subject to interest ... If you deposit P dollars at rate r, in decimal form, subject to compound interest paid
Step-by-step explanation:
Please answer this multiple choice question !! Will give brainliest !!
Answer: they deleted my answer but here is how to do it If that helps some
Step-by-step explanation:
way to solve a linear system algebraically is to use the substitution method. The substitution method functions by substituting the one y-value with the other. We're going to explain this by using an example.
y=2x+4
3x+y=9
We can substitute y in the second equation with the first equation since y = y.
3x+y=9
3x+(2x+4)=9
5x+4=9
5x=5
x=1
This value of x can then be used to find y by substituting 1 with x e.g. in the first equation
y=2x+4
y=2⋅1+4
y=6
The solution of the linear system is (1, 6).
You can use the substitution method even if both equations of the linear system are in standard form. Just begin by solving one of the equations for one of its variables.
LA=
Round your answer to the nearest hundredth.
A
2
5
B
Answer:
I'm not so clear with the question but I hope this helps