The expected value of an insurance policy for the company is calculated by subtracting the expected costs (probability of accident * average payout) from the premium paid by the customer. In this case, the insurance company can expect to retain $185.20 from the annual premium after estimated payouts.
Explanation:The subject of this question falls under the category of Mathematics, specifically in the field of probability and expected value. The expected value of an insurance policy is calculated as the product of the probability of an event (an accident in this case) and the corresponding payout, subtracted from the cost or premium of the policy. Here the insurance company estimates a 2.4% likelihood of an accident, which is a probability of 0.024, and the average payout being $2700.
First, determine the expected payout by the insurance company, which is computed by multiplying the probability of the event by the payout: 0.024 * $2700 = $64.80.
Then subtract this from the premium to calculate the company's expected value: $250 - $64.80 = $185.20.
This means, on average, the insurance company can expect to retain $185.20 from the annual premium after accounting for the estimated payouts from accidents.
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The expected value of this insurance policy for the company is approximately -$185.20.
Given information:
Likelihood of having an accident: 2.4% (expressed as a decimal, so (p = 0.024))
Average insurance payout: $2700
Annual premium charged: $250
The expected value ((E)) can be calculated as follows:
[tex][ E = (p \cdot \text{{Payout}}) - \text{{Premium}} ][/tex]
Substitute the given values: [ E = (0.024 x 2700) - 250 ]
Calculating: [ E = 64.8 - 250 = -185.2 ]
The expected value of this insurance policy for the company is approximately -$185.20.
Interpretation:
A negative expected value means that, on average, the insurance company is expected to lose money per policy sold.
In this case, the company charges a premium of $250 but expects to pay out an average of $2700 per accident. Therefore, the expected loss is $185.20 per policy.
i really need help with this angle of elevation and depression
Answer:
Step-by-step explanation
But the question does not say exactly what should be solve for.
trapizoid figure STUV is scaled version of figure WXYZ. The scale factor of figure STUV to figure WXYZ is 3:1. If ST= 117 mm and SV= 153 mm, what is the length of side WZ?
Answer:
39mm
Step-by-step explanation:
Final answer:
Using the scale factor of 3:1, the length of side WZ from trapezoid WXYZ can be calculated by dividing the known length of side SV from trapezoid STUV by the scale factor. The length of WZ is found to be 51 mm.
Explanation:
If trapezoid STUV is a scaled version of trapezoid WXYZ with a scale factor of 3:1, we can use this scale factor to determine the length of side WZ given the lengths of ST and SV. To find the length of WZ, we divide the length of SV by the scale factor. Since SV = 153 mm and the scale factor is 3, we perform the division 153 mm / 3 to get 51 mm as the length of WZ.
A proportion is a mathematical statement that two ratios or fractions are equal. It is used to express the equality of two fractions that compare two numbers or quantities to each other. For example, if we have two fractions a/b and c/d, a proportion states that these two fractions are equivalent: a/b = c/d. Proportions are fundamental in various branches of mathematics and applications, including solving problems involving scales, maps, and ratios in real-life scenarios.
How does this polynomial identity work on numerical relationships?
(y + x) (ax + b)
Let us take 'a' in the place of 'y' so the equation becomes
(y+x) (ax+b)
Step-by-step explanation:
Step 1:
(a + x) (ax + b)
Step 2: Proof
Checking polynomial identity.
(ax+b )(x+a) = FOIL
(ax+b)(x+a)
ax^2+a^2x is the First Term in the FOIL
ax^2 + a^2x + bx + ab
(ax+b)(x+a)+bx+ab is the Second Term in the FOIL
Add both expressions together from First and Second Term
= ax^2 + a^2x + bx + ab
Step 3: Proof
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
Identity is Found .
Trying with numbers now
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)
((10)+8)(7) =(2*25)+(4*5)+(40)+(16)
(18)(7) =(50)+(20)+(56)
126 =126
Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.
The ratio of
is equal to tan B.
The ratio of the vertical rise to the horizontal distance on the ramp is equal to tan B.
Explanation:The given figure represents a ramp with a length of 17 feet, rising 8 feet above the floor, and covering a horizontal distance of 15 feet. To find the ratio of the vertical rise to the horizontal distance (tan B), we can use the trigonometric function tangent (tan).
Tan B = vertical rise / horizontal distance = 8 feet / 15 feet = 0.5333
Lin is saving $300 per year in an account that pays 4.5% interest per year, compounded annually. How do I find the value after 20 years?
To find the value after 20 years, use the future value of a series formula with the given parameters, resulting in an approximate amount of $9,321.
Explanation:To find the value of $300 saved annually at 4.5% interest compounded annually after 20 years, we use the future value of a series formula:
FV = [tex]P * ((1 + r)^n - 1) / r[/tex]
Where:
FV = Future value of the seriesP = Yearly deposit ($300)r = Annual interest rate (4.5% or 0.045)n = Number of years (20)Substituting the given values:
FV = $300 * ((1 + 0.045)^20 - 1) / 0.045
= $300 * ((1.045)^20 - 1) / 0.045
= $300 * (2.398 - 1) / 0.045
= $300 * 1.398 / 0.045
= $300 * 31.07
= $9,321
Therefore, after 20 years, the value will be approximately $9,321.
On a map, the distance from Los Angeles to San Diego is 6.35 cm. the scale is 1cm = 20 miles. What is the actual distance?
Answer:
The actual distance is 127 miles.
Step-by-step explanation:
Given:
On a map, the distance from Los Angeles to San Diego is 6.35 cm.
The scale is 1 cm = 20 miles.
Now, to find the actual distance.
Let the actual distance be [tex]x\ miles.[/tex]
And the distance on map is 6.35 cm.
So, 6.35 cm is equivalent to [tex]x\ miles.[/tex]
And as given on the scale 1 cm is equivalent to 20 miles.
Now, to get the actual distance by using cross multiplication method:
[tex]\frac{6.35}{x} =\frac{1}{20}[/tex]
By using cross multiplication we get:
⇒ [tex]127=x[/tex]
⇒ [tex]x=127\ miles.[/tex]
Therefore, the actual distance is 127 miles.
the area of a rectangular dog pen is 8 1/2 square feet. if the width is 3 2/5, what is the length, in feet?
Answer:
2 1/2 or 2.5
Step-by-step explanation:
The area is the length times the width. To solve for the length, you have this equation using the data you already have. 8 1/2 = 3 2/5 x length. 8 1/2 / 3 2/5 = length. 8.5/3.4 = length. length = 2.5 OR to do this fraction wise, you can make them fractions and divide, making 8/1 -> 16/2 + 1/2 = 17/2 and 3/1 - 15/5 + 2/5 = 17/5 and divide those, which ends up at 2 1/2 but fraction wise makes it more complicated
On a bike trip, you traveled 21 miles on
the second day. On the 3rd day, you traveled 3
second day.
e trip, you traveled 21 miles on the first day, and n miles on
y. On the 3rd day, you traveled 5 miles less than on the rest
a. Write an expression for the number of miles traveled in three day
b. Simplify the expression. Explain each step.
c. Find the number of miles traveled in three days when you traveled
19 miles on the second.
Answer:
She traveled 13 23/56 miles on the third day.
Step-by-step explanation:
HOPE THIS HELPED ;3
Are the fractions 3/9, 3/10, 3/11, and 3/12 in order from least to greatest
Answer:
The fractions [tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex] are not in order from least to greatest.
Step-by-step explanation:
Given order of fractions from least to greatest:
[tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex]
To check if the fractions are in correct order.
Solution:
The fractions given have same numerators but different denominators.
For fractions the higher the denominator the lower is the value of that fraction.
Thus, in the given list the least value fraction will be the fraction with the greatest denominator which is [tex]\frac{3}{12}[/tex] and the greatest value fraction will be the fraction with the least denominator which is [tex]\frac{3}{9}[/tex]
So, the order of the fractions from least to greatest is not correct. Instead the order is from greatest to least.
The correct order from least to greatest should be:
[tex]\frac{3}{12},\frac{3}{11},\frac{3}{10},\frac{3}{9}[/tex].
1/2(6 2/3+1/4)-5/24=
For this case we must simplify the following expression:
[tex]\frac {1} {2} (6 \frac {2} {3} + \frac {1} {4}) - \frac {5} {24} =[/tex]
We convert the mixed number to an improper fraction:
[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]
So, by rewriting we have:
[tex]\frac {1} {2} (\frac {20} {3} + \frac {1} {4}) - \frac {5} {24} =\\\frac {1} {2} (\frac {4 * 20 + 3 * 1} {4 * 3}) - \frac {5} {24} =\\\frac {1} {2} (\frac {80 + 3} {12}) - \frac {5} {24} =\\\frac {1} {2} (\frac {83} {12}) - \frac {5} {24} =[/tex]
[tex]\frac {83} {24} - \frac {5} {24} =\\\frac {83-5} {24} =\\\frac {78} {24} =\\\frac {39} {12} =\\\frac {13} {4} =\\3 \frac {1} {4}[/tex]
Answer:
[tex]3 \frac {1} {4}[/tex]
In the equation 3/4y+1/2=3 1/4, the fractional coefficient is what
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]
In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.
coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.
Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].
Find the indicated probability. Round to three decimal places. The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 11 participants there have been only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer women when 11 people are picked? 0.006 0.033 0.027 0.032
Answer:
0.033
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
Here, p = 0.5, q = 0.5, and n = 11.
We need to find P when r is 0, 1, and 2, then add up the results to get the total probability.
r = 0:
P = ₁₁C₀ (0.5)⁰ (0.5)¹¹⁻⁰
P ≈ 0.0005
r = 1:
P = ₁₁C₁ (0.5)¹ (0.5)¹¹⁻¹
P ≈ 0.0054
r = 2:
P = ₁₁C₂ (0.5)² (0.5)¹¹⁻²
P ≈ 0.0269
Therefore, the total probability is:
P = 0.0005 + 0.0054 + 0.0269
P = 0.0328
Round to the thousandths place, the probability is 0.033.
Alan is conducting a survey to find out the type of art preferred by students in the town’s high school. Identify the population of his survey and describe a possible sample of the population.
The other answer is wrong the following is the sample response.
Answer:
Sample Response: The population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors.
Step-by-step explanation:
just finished the assignment and this was the sample response.
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Have a great day!
Alan's survey population encompasses all students at the high school with art preferences. A sample could be randomly chosen from students from each grade or art class, reflecting the school's diversity and maintained by a random sampling method for fairness and representation.
Explanation:The population of Alan's survey is all the students at the town’s high school who have preferences for types of art. To conduct his survey, Alan needs to choose a sample, which is a smaller group from the population that can provide reliable information about the entire population's art preferences. An example of a possible sample would be selecting a certain number of students from each grade level or art class to ensure a variety of perspectives. It could also involve stratification by demographic characteristics such as age, gender, socioeconomic status, or ethnicity if these factors are believed to influence art preferences.
An efficient method to create a representative sample could be to use a random sampling technique where each student has an equal chance of being selected. For instance, Alan could use a random number generator to pick students from a list, or he might use a stratified random sampling by first dividing the student body into subgroups (such as by grade or art class) and then randomly selecting students from each subgroup.
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Adam burns 225 calories per 30 minutes of bicycling how many calories in 10 mins.
Answer:
7.2
Step-by-step explanation:
You divide 225 by 30 and get 7.2
Answer:
c
Step-by-step explanation:
Complete the equation of the line through (-8, -2) and (-4, 6)
Answer:
Equation of line is given by:
[tex]y=2x+14[/tex]
Step-by-step explanation:
Given points:
[tex](-8,-2)\ and\ (-4,6)[/tex]
Slope of line [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is a point on the line
[tex]m=\frac{6-(-2)}{-4-(-8)}[/tex]
[tex]m=\frac{6+2}{-4+8}[/tex]
[tex]m=\frac{8}{4}[/tex]
∴ [tex]m=2[/tex]
Point-slope equation of line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is slope of line.
Using point [tex](-8,-2)[/tex] and slope [tex]m=2[/tex] point-slope equation of line is given by:
[tex]y-(-2)=2(x-(-8))[/tex]
Simplifying.
[tex]y+2=2(x+8)[/tex]
Using distribution.
[tex]y+2=2x+16[/tex]
Subtracting 2 to both sides.
[tex]y+2-2=2x+16-2[/tex]
[tex]y=2x+14[/tex]
Thus, equation of line is [tex]y=2x+14[/tex]
The mass of two sacks of potatoes is 168 grams. One-eight of the mass of Sack A and three-quarter of the mass of Sack B is 76 grams. Write an equation to find the mass of Sack A.
Answer:
1/8(A)+(3/4)(168-A)=76 is an equation to find the mass of A, the mass of A is 80 grams.
Step-by-step explanation:
What do we know?
Both sacks together are 168 grams. Therefore;
A+B=168
One eighth of sack A and three quarters of sack B is equal to 76 grams. Therefore;
1/8(A)+(3/4)B=76
Let's solve using the substitution method to find A. First, we need to isolate and then substitute B for an expression containing A.
A+B=168
B=168-A
Now that we have isolated B, we can substitute '160-A' for B in the other equation.
1/8(A)+(3/4)(168-A)=76
1/8(A)-3/4(A)+126=76
1/8(A)-3/4(A)+126=-50
-5/8(A)=-50
A=80
Ms. Fuller has 2 2/6 pies left over from her party. Write the number of pies left over as a fraction greater than 1.
Answer:
[tex]\frac{14}{6}[/tex]
Step-by-step explanation:
A mixed fraction of the form [tex]a\frac{b}{c}[/tex] can be converted into an improper fraction by writing it in the form [tex]\frac{(ac)+b}{c}[/tex] . By applying this formula , we can see that [tex]2\frac{2}{6} = \frac{12 +2}{6} =\frac{14}{6}[/tex] . As numerator is greater than the denominator , we can see that the answer is greater than one and thus it is an improper fraction.
10 POINTS!!! will give Brainliest
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
The volume of the prism will be given by 204.7 cubic cm.
Step-by-step explanation:
The area of a triangle whose three side lengths are given is equal to
Δ = [tex]\sqrt{s(s - a)(s - b)(s - c))}[/tex] .......... (1)
Where, a, b, and c are the three side lengths and s is the half perimeter i.e.
[tex]s = \frac{a + b + c}{2}[/tex] ......... (2)
Now, in our case, [tex]s = \frac{6 + 7 + 6}{2} = 9.5[/tex] {From equation (2)}
So, Δ = [tex]\sqrt{9.5(9.5 - 6)(9.5 - 7)(9.5 - 6)} = 17.05[/tex] sq. cm.
{From equation (1)}
Hence, the volume of the prism will be given by (17.05 × 12) = 204.7 cubic cm. (Answer)
if sec thita . sin thita =0,then find the value of thita
Answer:
[tex]\large\boxed{\theta=k\pi,\ k\in\mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]\sec\thets\cdot\sin\theta=0\iff \sec\theta=0\ \vee\ \sin\theta=0\\\\\sec\theta\neq0\ \text{for any value of}\ \theta\\\\\sin\theta=0\Rightarrow\theta=k\pi\ \text{where}\ k\in\mathbb{Z}[/tex]
plz hurry!!!! thank you!!!!
Answer:
[tex]m\angle KLM=53.13^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle KOM
In the triangle KOM
we have
[tex]KO=MO=r=5\ units[/tex]
[tex]KM=8\ units[/tex]
Applying the law of cosines
[tex]8^2=5^2+5^2-2(5)(5)cos(KOM)[/tex]
[tex]64=50-50cos(KOM)[/tex]
[tex]50cos(KOM)=50-64[/tex]
[tex]50cos(KOM)=-14[/tex]
[tex]cos(KOM)=-14/50[/tex]
[tex]m\angle KOM=cos^{-1}(-14/50)[/tex]
[tex]m\angle KOM=106.26^o[/tex]
step 2
Find the measure of the arc KM
we know that
[tex]arc\ KM=m\angle KOM[/tex] ----> by central angle
we have
[tex]m\angle KOM=106.26^o[/tex]
so
[tex]arc\ KM=106.26^o[/tex]
step 3
Find the measure of angle KLM
we know that
The inscribed angle is half that of the arc comprising
[tex]m\angle KLM=\frac{1}{2}[arc\ KM][/tex]
we have
[tex]arc\ KM=106.26^o[/tex]
substitute
[tex]m\angle KLM=\frac{1}{2}[106.26^o][/tex]
[tex]m\angle KLM=53.13^o[/tex]
Solve for m.
3.6m=14.4
Answer:
4
Step-by-step explanation:
3.6m = 14.4
m = 14.4 ÷ 3.6
m = 4
What percent of 500 is 150
Answer:
30%
Step-by-step explanation:
We can translate the question into an equation.
500x=150
x=150/500
x=3/10=30%
answer: 30%
in trapezium abcd, as shown in the figure, ab is parallel to dc, ad=dc=bc=20cm and ‹a=60°. find: (i) length of ab (ii) distance between ab and dc
Answer:
AB = 40 cm
Distance = [tex]10\sqrt{3}[/tex] cm
Step-by-step explanation:
Draw two heights DE and CF. These heights together with bases of trapezoid form rectangle DEFC. In this rectangle, DC=EF=20 cm.
Consider right triangle ADE. In this triangle, angle ADE has the measure of 30° (the sum of the measures of all interior angles is always 180°, so m∠ADE=180°-60°-90°=30°)
Leg opposite to 30° angle is equal to half of the hypotenuse, so
[tex]AE=\dfrac{1}{2}AD=\dfrac{1}{2}\cdot 20=10\ cm[/tex]
Similarly, in triangle CBF, BF=10 cm.
Hence,
[tex]AB=AE+EF+FB=10+20+10=40\ cm[/tex]
The height of the trapezoid (the second leg of triangle ADE) is the distance between DC and AB. By the Pythagorean theorem,
[tex]AD^2=AE^2+DE^2\\ \\DE^2=20^2-10^2=400-100=300\\ \\DE=\sqrt{300}=10\sqrt{3}\ cm[/tex]
Mary says 1/8 is
greater than 1/4 because 8 is greater than 4.
Is Mary's reasoning correct? Explain.
Answer:
No, Mary is incorrect. If you turn the fractions into decimals, 1/4 would be 0.25 and 1/8 would be 0.12½. Since 0.25 is greater than 0.12½, Mary is incorrect.
Mary's reasoning is incorrect because in fractions, the larger the denominator, the smaller the fraction's value, making 1/4 greater than 1/8.
Mary's reasoning that 1/8 is greater than 1/4 because 8 is greater than 4 is not correct. In the context of fractions, the larger the denominator (the bottom number), the smaller each part of the whole it represents. Thus, 1/4 is actually greater than 1/8 because dividing something into 4 parts results in larger parts than dividing it into 8 parts. This can be further understood by transforming both fractions into equivalent fractions with a common denominator or by converting them into decimal form (0.25 for 1/4 and 0.125 for 1/8) to directly compare their sizes.
Find the sum of the first 56 terms of the following sequence {-8, -1, 6, ...}
A. 10,332
B. 1,344
C. 10,584
Answer:
A
Step-by-step explanation:
Given sequence [tex]-8,\ -1,\ 6,\ ...[/tex]
In this sequence,
[tex]a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...[/tex]
Hence,
[tex]d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7[/tex]
Find 56th term:
[tex]a_{n}=a_1+(n-1)\cdot d\\ \\a_{56}=-8+(56-1)\cdot 7\\ \\a_{56}=-8+385\\ \\a_{56}=377[/tex]
The sum of 56 terms is
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_{56}=\dfrac{-8+377}{2}\cdot 56=\dfrac{369}{2}\cdot 56=369\cdot 28=10,332[/tex]
what is the differance look at the link
Answer:
The difference is [tex]\frac{3}{4}[/tex] inches.
Step-by-step explanation:
See the attached number line where the worm lengths in inches are plotted.
From the number line plotted in the attached photo, it is clear that the shortest worm has the length of [tex]\frac{3}{4}[/tex] inches and the longest worm has the length of [tex]1\frac{1}{2}[/tex] inches i.e. [tex]\frac{3}{2}[/tex] inches.
Therefore, the difference in length between the shortest and longest worm is [tex](\frac{3}{2} - \frac{3}{4}) = \frac{3}{4}[/tex] inches. (Answer)
evaluate √7x(√x-7√7
pls & thanks!
Answer:
[tex]x\sqrt{7} - 49\sqrt{x}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}\sqrt{7x}(\sqrt{x} - 7\sqrt{7}) & = & \sqrt{7x}\times\sqrt{x}- 7\sqrt{7}\times\sqrt{7x} \\ & = & \sqrt{7}\times\sqrt{x}\times\sqrt{x} - 7\sqrt{7}\times\sqrt{7}\times\sqrt{x}\\& = & \sqrt{7}\times x - 7\times 7\times\sqrt{x}\\& = &\mathbf{ x\sqrt{7} - 49\sqrt{x}}\\\end{array}[/tex]
Assume that the quadrilateral shown is a parallelogram. Which expression represents the area of the parallelogram?
Answer:
B. x² + 16x + 15
Step-by-step explanation:
Area of parallelogram = base x height
A = (x + 15) (x + 1) = x² + 16x + 15
What is the y-intercept of f(x)=8x^5-3x^3+12
The y intercept is (0, 12)
Solution:
Given function is:
[tex]f(x) = 8x^5 - 3x^3 + 12[/tex]
To find: y intercept
y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.
To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y
Substitute x = 0 in given function
[tex]f(0) = 8(0) -3(0) + 12[/tex]
y = 0 - 0 + 12
y = 12
Thus y - intercept is (0, 12)
Jenni wrote a rational number that is positive. Which of the following is not a possible number that she wrote?
51/4
0
7/8
1
Answer:
There is no answer.
0 is rational since it can be written as a fraction (0/5, 0/69)
1 is obviously rational. 7/8 is .875 and 5 1/4 is 5.25