Using probability we know that the expected value of the insurance company is $141.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.So, the expected value of the insurance company:
Probability = 0.9987So, 1.0000 - 0.9987 = 0.0013Now, get the expected value as follows:
E(x) = 0.9987 × 154 + 0.0013(-9987)E(x) = 153.7998 + (-12.9831)E(x) = 153.7998 - 12.9831E(x) = 140.8167Rounding off: $141
Therefore, using probability we know that the expected value of the insurance company is $141.
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The complete question is given below:
There is a .9987 probability that a randomly selected 27-year-old male lives through a year. a life insurance company charges $154 for ensuring that the male will live through the year. if the male does not survive the year, the policy pays out $100,000 as a death benefit.
What is the expected value for the insurance company?
Solve and graph 3x+1<10
The given inequality is
3x + 1 < 10
Subtracting 1 from both sides of the inequality, we have
3x + 1 - 1 < 10 - 1
3x < 9
Dividing both sides of the equation by 3, we have
3x/3 < 9/3
x < 3
The number line is shown below
The values to the left of 3 are all less than 3. The circle is not shaded because 3 is not included in the values of x.
Prove the segments joining the midpoint if consecutive sides of an isosceles trapezoid form a rhombus.
DEFG is a rhombus by definition of rhombus (option B)
Explanation:
To prove that DEFG is a rhombus, we will find the distance between all the 4 sides of the quadrilateral. A rhombus has all 4 sides equal.
Distance formula is given as:
[tex]$$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$$[/tex][tex]\begin{gathered} distance\text{ DE: D}(-a-b,\text{ c})\text{ and E}(0,\text{ 2c}) \\ x_1=-a-b,y_1=c,x_2=0,y_2\text{ = 2c} \\ distance\text{ DE = }\sqrt{(0\text{ - }(-a-b))^2\text{ + }(2c\text{ - c})^2} \\ distance\text{ DE = }\sqrt{(0\text{ +}a+b)^2\text{ + c}^2}\text{ } \\ distance\text{ DE = }\sqrt{(\text{a + b})^2+c^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ EF: E}(0,\text{ 2c})\text{ and F}(a\text{ + b, c}) \\ x_1=0,y_1=2c,x_2=a+b,y_2\text{ = c} \\ distance\text{ EF = }\sqrt{(c\text{ - 2c})^2+\text{ }(a\text{ + b - 0})^2} \\ distance\text{ EF = }\sqrt{(-c)^2+(a+b)^2}\text{ } \\ \text{distance EF = }\sqrt{c^2\text{ + }(a+b)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ GF: G}(0,\text{ 0})\text{ and F }(a+b,\text{ c}) \\ x_1=0,y_1=0,x_2=a+b,y_2\text{ = c} \\ distance\text{ GF = }\sqrt{(c\text{ - 0})^2+\left(a+b-0\right)^2} \\ distance\text{ GF = }\sqrt{c^2+(a+b)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ DG: D}(-a-b,\text{ c})\text{ and G }(0,\text{ 0}) \\ x_1=-a-b,y_1=c,x_2=0,y_2\text{ = 0} \\ distance\text{ GD = }\sqrt{(0-c)^2+(0-(-a-b))^2} \\ distance\text{ GD = }\sqrt{(-c)^2+\left(0+a+b\right)^2} \\ distance\text{ GD = }\sqrt{c^2\text{ + }(a+b)^2} \end{gathered}[/tex]From our calculation, Distance DE = Distance EF = Distance GF = Distance GD
All 4 sides are equal (congruent)
DEFG is a parallelogram with congruent sides. So DEFG is a rhombus by definition of rhombus (option B)
1. How does someone find the equation of a boundary line?2. How does someone determine if the points on the boundary line are solutions to the inequality?
Answer:
D: Find the boundary line equation by replacing the inequality sign with =
Explanation:
Part 1
Given any inequality, say:
[tex]yTo find the equation of the boundary line, replace the inequality sign with the equality(=) sign. This gives the equation of the boundary line to the inequality above as:[tex]y=x+5[/tex]The correct choice is D.
Part 2
When drawing the boundary line:
• Use a solid line for the inequalities: ≤ or ≥
,• Use a broken line for the inequalities: < or >
If the boundary line is solid, the points on the boundary line are solutions to the inequality, otherwise, they are not.
triangles FIM and LAK below are similar with m
8
Explanation
as the triangles are similar we can set a proportion
Step 1
Let
[tex]\text{ratio}=\frac{\text{longest side}}{\text{smallest side}}[/tex]so
a) for triangle FIM
[tex]\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{middle side}} \\ ratio_1=\frac{FM}{FI}=\frac{6}{4}=\frac{3}{2} \\ ratio_1=\frac{3}{2} \end{gathered}[/tex]b) for triangle LAK
[tex]\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{smallest side}} \\ ratio_2=\frac{LK}{LA}=\frac{12}{LA} \\ ratio_2=\frac{12}{LA} \end{gathered}[/tex]as the tringles are similar, the ratios are similar
hence
[tex]\begin{gathered} \text{ratio}_1=ratio_2 \\ \frac{3}{2}=\frac{12}{LA} \end{gathered}[/tex]Step 2
now, solve for LA
[tex]\begin{gathered} \frac{3}{2}=\frac{12}{LA} \\ \text{cross multiply } \\ 3\cdot LA=12\cdot2 \\ 3LA=24 \\ \text{divide both sides by 3} \\ \frac{3LA}{3}=\frac{24}{3} \\ LA=8 \end{gathered}[/tex]therefore, the answer i
8
I hope this helps you
Which inequality symbol should be placed in the blank to make the statement true? - 12_ -8
Answer:
<
Step-by-step explanation:
Negative 12 is less than negative 8.
Find the missing side of the triangle.A. √11 miB. 2√2 miC. 1 miD. √19 mi
Since we have a right-angled triangle, we can use the Pythagoras Theorem:
[tex]a^2+b^2=c^2[/tex]where a and b are the shorter sides of the triangle and c is the hypotenuse.
a = x; b = 3 mi; c = sqrt(10).
We substitute our values and then we solve for x:
[tex]\begin{gathered} x^2+3^2=(\sqrt[]{10})^2 \\ x^2=10-3^2 \\ x^2=1 \\ x=1 \end{gathered}[/tex]Therefore, the missing side of the triangle is 1 mi.
This is a one step inequality can you help my find the answer I don't know how to do this X + 7 < 19
Answer:
X<12
Step-by-step explanation:
A fitness club offers two water aerobics classes. There are currently 40 people in the moming class and
attendance is growing at a rate of 2 people per month. The afternoon class has 22 members and is growing at
a rate of 8 people per month. In how many months will there be the same number of people in each class and
how many people will be in each class?
please help
Answer:
3 months
Step-by-step explanation:
You would set the equations = to each other to identify when they will be the same number of __. The equations to begin with is 40 + 2x and 22 + 8x, you would do 40 + 2x = 22 + 8x and algebraically solve for X, which is the months. so 18 = 6x, x = 3
E3.This table shows the times, in minutes, It took 40 sixth grade students to run 1 mile.frequency15time (minutes)4 to less than 66 to less than 88 to less than 1010 to less than 1212 to less than 1414 to less than 16131272INTLDraw a histogram for the information in the table.321
The histogram is shown below:
What are the coordinates of the focus of the parabola?y=18x2+2x
The equation of the given parabola is
[tex]y=\frac{1}{8}x^2_{}+2x[/tex]Rewrite the equation in the vertex form
[tex]y=a(x-h)^2+k[/tex]The equation becomes
[tex]\begin{gathered} y=\frac{1}{8}x^2+2x \\ y=\frac{1}{8}(x^2+16x) \\ 8y=x^2+16x \\ 8y=x^2+6x+64-64 \\ 8y=(x+8)^2-64 \end{gathered}[/tex]Divide through the equation by 8
This gives
[tex]y=\frac{1}{8}(x+8)^2-8[/tex]Comparing the equation with the vertex form
It follows
[tex]a=\frac{1}{8},h=-8,k=-8[/tex]The focus of a parabola in vertex form is given as
[tex]F=(h,k+\frac{1}{4a})[/tex]Substitute h = -8, k = -8 and a = 1/8 into the formula for focus
This gives
[tex]F=(-8,-8+\frac{1}{4(\frac{1}{8})})[/tex]Simplify the expression
[tex]\begin{gathered} F=(-8,-8+\frac{1}{\frac{1}{2}}) \\ F=(-8,-8+2) \\ F=(-8,-6) \end{gathered}[/tex]Therefore, the focus of the parabola is at (-8, -6)
i need help with this!
Answer:
19. 7
20. 11
21. -12
22. 15
23. 77
24. −6
Step-by-step explanation:
Simply plug the values of a, b and c into each equation and evaluate using a calculator or manually
The common ratio for the home prices in an Austin neighborhood is 1.08 every year for the past 5 years increasing or decreasing? and is it linear or exponential? therefore interpret the change?
Lindsey, this is the solution:
Ratio for the home prices in an Austin neighborhood = 1.08 every year
1. It is an increasing ratio because it is higher than 1.
2. It is linear because the rate of change is constant (1.08)
3. Interpretation : The common ratio means that every year for the past 5 years the home prices in the Austin neighborhood grew 8%.
The United States is the worlds leading exporter of wheat with approximately 27.8 billion metric tons per year . Suppose turkey exports 10% of the U.S total . About how many metric tons are exported by turkey ?
Answer: 3 billion
Step-by-step explanation:
27.8 x 10% = 2.78 billion which rounds to 3
Select the graph of the piecewise function given by: ƒ(x) = 0 for 0 ≤ x < 4ƒ(x) = 3 for 4 ≤ x < 8ƒ(x) = 6 for 8 ≤ x < 12
Given,
ƒ(x) = 0 for 0 ≤ x < 4
ƒ(x) = 3 for 4 ≤ x < 8
ƒ(x) = 6 for 8 ≤ x < 12
To select the graph of the given piecewise function.
The solid circle represents the inclusion of the point. Similarly, the hollow circle represents the exclusion of the point.
Option A:
It can be observed in option A that the circles are represented properly and the function is properly shown in the respective interval.
As a result, option A is correct.
Option B:
It can be observed that option B does not follow the proper circle for denoting the endpoints of the interval.
As a result, option B is incorrect.
Option C:
Bob is spending money at a constant rate. Suppose he initially has $1000, and after 8 months, he has $200.
Which of these expresses the rate at which Bob's amount of money is changing?
The required rate at which Bob's amount of money is changing is $100 per month.
Given that,
Bob is spending money at a constant rate. Suppose he initially has $1000, and after 8 months, he has $200. The expression of the rate at which Bob's amount of money is changing is to be determined.
Here,
Initial money = $1000
Rest money = $200
Time = 8 months,
Rate = [1000 - 200] / 8
Rate = [800] / 8
Rate = $100
Thus, the required rate at which Bob's amount of money is changing is $100 per month.
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this is a practice assessment! Therefore it isn’t for a grade . I just need help solving this
We are given a quadrilateral inscribed in a circle, therefore, the sum of opposite angles is equal to 180 degrees, therefore:
[tex]\angle O+\angle M=180[/tex]Replacing the values we get:
[tex]100+x=180[/tex]Solving for "x":
[tex]\begin{gathered} x=180-100 \\ x=80 \end{gathered}[/tex]Therefore, the value of "x" is 80 degrees.
Fractions and Mixed Numbershogy Commercing eng yourStephan owns a landscaping compary. Today, he is mowing three lawns: one is 1/4 of an acre, one is of 1/2 an acre, and one is 1 1/3 acres. How many acres of lawn is Stephan going to nowtoday. Simplify your answer and write it as a mixed fraction if necessary25 acresSvendoseSotPassHold
We would add each of the given fraction. Thus, the number of acres that he is going to mow
A company makes pens. They sell each pen for $ 6
Answer:
a. -3,000
b. 1,750
Explanation:
We were given the following information:
A company makes pens:
Each pen is sold at $6 per unit
Revenue = 6 * x
Manufacture Cost = 2 * x
Start-up Cost = $7,000
Cost = Manufacture Cost + Start-up Cost = 2 * x + 7,000
Profit = Revenue - Cost
a) The profit is calculated for 1,000 pens as shown below:
[tex]\begin{gathered} Profit=Revenue-Cost \\ \text{For the making of 1,000 pens, it means: }x=1,000 \\ Revenue=6\cdot x=6\times1,000 \\ Revenue=\text{\$}6,000 \\ Cost=2\cdot x+7,000 \\ Cost=2\times1,000+7,000 \\ Cost=2,000+7,000 \\ Cost=\text{\$}9,000 \\ \\ Profit=6,000-9,000 \\ Profit=-\text{\$}3,000 \\ \\ \therefore Profit=-\text{\$}3,000 \end{gathered}[/tex]Hence, the profit is -3,000
b) We will calculate for the number of pens needed to be sold for the company to break even as shown below. We have:
[tex]\begin{gathered} \text{At breakeven: }Revenue=Cost \\ \Rightarrow6x=2x+7,000 \\ \text{We will calculate for the value of the variable ''x'':} \\ 6x=2x+7,000 \\ \text{Subtract ''2x'' from both sides, we have:} \\ 6x-2x=7,000 \\ 4x=7,000 \\ \text{Divide both sides by ''4'', we have:} \\ x=\frac{7,000}{4} \\ x=1,750 \\ \\ \therefore x=1,750 \end{gathered}[/tex]Hence, the breakeven occurs when the company has made 1,750 pens
If R(-2,-1) is the midpoint of ST and S(-14,3),find the coordinates of t
Answer
Explanation
Mathematically, if a point R(x, y) divides the coordinates S (x₁, y₁) and T (x₂, y₂) internally in the ratio m:n then point R(x, y) is given as
x = [(mx₂ + nx₁)/(m + n)]
y = [(my₂ + ny₁)/(m + n)]
For this question, we are given that
R (x, y) = R(-2, -1)
S (x₁, y₁) = S (-14, 3)
T (x₂, y₂) = ?
Since it is divided equally into two parts (As per the midpoint), m : n = 1 : 1
x = -2
y = -1
x₁ = -14
y₁ = 3
x₂ = ?
y₂ = ?
m = 1
n = 1
x = [(mx₂ + nx₁)/(m + n)]
-2 = [(1 × x₂) + (1 × -14)]/(1 + 1)
-2 = [x₂ - 14]/2
[tex]\begin{gathered} -2=\frac{x_{2}-14}{2} \\ \text{Cross multiply} \\ x_{2}-14=2\times-2 \\ x_{2}-14=-4 \\ x_{2}=-4+14 \\ x_{2}=10 \end{gathered}[/tex]y = [(my₂ + ny₁)/(m + n)]
-1 = {
given the following list of axioms drawing model on a separate sheet of paper to properly represent the information describing drawing in your own words there exists by points each line contains only these Five Points there exist two lines each line contains at least two points
Five random points, 3 of them collinear:
To go through all the points with only two lines, one of the five points has to be colinear with other 2 points.
If the fifth point wasn't colinear, we would need another line to draw.
If four of the five points were colinear between them, we could have had a line that goes through this 4 points, and the other line going through the remaining point.
If the five points were colinear, we would have need only one line to go through them.
Which value of y makes the equation true?
-2y-9=-11
Answer:
Y=1
Step-by-step explanation:
To solve this we can start by isolating the y value.
To get rid of the -9 we add nine to both sides leaving us with
-2y=-2
Then we want to only have y = ?
So we divide -2 by -2 and get one
y=1
Simplify the complex rational expression by the method of your choice. 1——x-6———-1 - 1 —- x-6
To find:
The simplified form of the rational expression.
Solution:
The given rational expression can be simplified as follows:
[tex]\begin{gathered} \frac{\frac{1}{x-6}}{1-\frac{1}{x-6}}=\frac{\frac{1}{x-6}}{\frac{x-6-1}{x-6}} \\ =\frac{1(x-6)}{(x-6)(x-7)} \\ =\frac{1}{x-7} \end{gathered}[/tex]Thus, the answer is:
[tex]\frac{1}{x-7}[/tex]Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter greater than 15 inches.
Given:
[tex]\begin{gathered} \mu=10\text{ }inches \\ \sigma=2.2\text{ inches} \end{gathered}[/tex]To find- P(X>15)
Explanation-
We know that a z-score is given by-
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the raw score, mu is the mean and sigma is the standard deviation.
Hence, the proportion of trees having a diameter greater than 15 inches will be-
[tex]\begin{gathered} P(x>15)=P(\frac{x-\mu}{\sigma}>\frac{15-\mu}{\sigma}) \\ P(x>15)=P(Z>\frac{15-10}{2.2}) \end{gathered}[/tex]On further solving, we get
[tex]\begin{gathered} P(x\gt15)=P(Z\gt\frac{5}{2.2}) \\ P(x\gt15)=P(Z\gt2.2727) \end{gathered}[/tex]With the help of an online tool, the probability will be
[tex]P(x>15)=0.0115[/tex]Since the significance level is not mentioned, we assumed it is 0.05.
Thus, the proportion of trees having a diameter greater than 15 inches is 0.0115.
The answer is 0.0115.
m³ +9n when m = 4
and n = 5
Answer:
109
Step-by-step explanation:
you first cube 4 which means 4x4x4
64
then multiply 9x5 and get 45
then add 45+64 and you get your answer
Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is rent
Ethan's income:4500
$975 was spent in rent
percentage of Ethan's expenses on rent:
[tex]\begin{gathered} =\frac{975}{4500}\times100 \\ =21.7 \end{gathered}[/tex]percentage of Ethan's income on rent=21.7%
A store is selling scooter for $40. You have coupon and purchase it for $15. What percentage was the coupon?
We can solve this problem by applying the rule of three:
[tex]\begin{gathered} 40\text{ dollars ------100\%} \\ 15\text{ dollars ------ x} \end{gathered}[/tex]hence,
[tex]x=\frac{(15)(100)}{40}[/tex]and it yields
[tex]x=\frac{1500}{40}[/tex]which result in x= 37.5. It means that 15 dollars corresponds to 37.5%
A school is planning a 4th grade field trip. There are 157 students and 9 teachers in the 4th gradeIf each bus holds 45 people, how many buses does the school need to make the field trip?Which of the following equations can be used to solve this problem?
Given:
A school is planning a 4th grade field trip. There are 157 students and 9 teachers in the 4th grade. Each bus holds 45 people.
Required:
To find the number of buses does the school need to make the field trip.
Final Answer:
There area total
[tex]\begin{gathered} =157+9 \\ =166 \end{gathered}[/tex]166 people.
Let the number of bus be x.
Each bus holds 45 people, therefore
[tex]\begin{gathered} 45x=166 \\ x=\frac{166}{45} \\ x=3.68 \\ x\approx4 \end{gathered}[/tex]Final Answer:
4 buses need to make the field trip.
Find the slope of the line that goes through the points (2,-6) and (11,15).Slope,m=___Enter your answer as an integer or a reduced fraction in the form A/B
Answer:
m = 7/3
Explanation:
The slope of a line that passes through two points (x1, y1) and (x2, y2) can be calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (x1, y1) = (2, -6) and (x2, y2) = (11, 15), we get:
[tex]m=\frac{15-(-6)}{11-2}=\frac{15+6}{9}=\frac{21}{9}=\frac{7}{3}[/tex]Therefore, the slope is 7/3
Your Aunt is having a baby. You have created a party game for a baby shower. It is called pick the gender. You put pink and blue tiles into a bag. You ask two guests to pick one tile each out of the bag without looking. You tell your guests that if they are the same color, player A wins and if they are two different colors, then player B wins.How many tiles of which colors did you put into the bag to make sure that both players have an equal chance of winning?
There have to be an equal number of pink and blue tiles in the bag make sure that both players A and B have an equal chance of winning as they events of probability.
What is probability of an event?If an event say A can occur in a-ways and fail to occur in b-ways and as well (a + b)-ways are equally likely, then the probability of A is given as P(A) = a/(a + b).
Let the probability of having a winner at the party be P(W) = 1, which is a certain event.
then addition of the probability of player A = P(A) winning and the probability of player B = P(B) winning must be equal to 1.
Hence,
P(A) + P(B) = (1/2) + (1/2)
P(A) + P(B) = 1
This implies there must be equal number of the pink and blue tiles.
Thus, there have to be equal number of pink and blue tiles so that any of the event occurring must result in the two players having equal chance of winning.
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h(n) = -2n + 3g(n) = 4nFind (h•g)(-2)
Given:
h(n)=-2n+3
g(n)=4n
The objective is to find
[tex](h\cdot g)(-2)[/tex]Let's rewrite the required function as
[tex]\begin{gathered} (h\cdot g)=h\lbrack g(n)\rbrack \\ h\lbrack g(n)\rbrack=-2(4n)+3 \\ h\lbrack g(n)\rbrack=-8n+3 \\ (h\cdot g)(-2)=-8(-2)+3 \\ (h\cdot g)(-2)=16+3 \\ (h\cdot g)(-2)=19 \end{gathered}[/tex]Hence the value of (hog)(-2)=19
