Consider a car owner who has an 80% chance of no accidents in a year, a 20% chance of being in a single accident in a year, and no chance of being in more than one accident in a year. For simplicity, assume that there is a 50% probability that after the accident the car will need repairs costing $500, a 40% probability that the repairs will cost $5,000, and a 10% probability that the car will need to be replaced, which will cost $15,000. What is the expected loss for the car owner per year

Answer:

62.5 percent

Step-by-step explanation:

There are a total of 8 choices, 5 of which are less than 6

5/8 is also 62.5percent

Answer:

62.5%

Step-by-step explanation:

There are 5 numbers out of 8 that are less than 6 so there is a 5/8 chance getting them or 62.5% chance.

Answer:

the plane travels 980 mph in still air and the  jet stream is traveling at 210mph

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

9+10y=21

Subtract 9 from both sides:

10y=21-9=12

Divide both sides by 10 to isolate y:

y=1.2

Hope this helps!

Answer:

y = 6/5 = 1 1/5 = 1.2

Step-by-step explanation:

9 + 10y = 21

Subtract 9 from each side

9-9 + 10y = 21-9

10 y = 12

Divide each side by 10

10y/10 = 12/10

y = 6/5

y = 1.2

Answer:

Step-by-step explanation:

The objective is to compute that more runs are scored in games for which DH is used

Let [tex]\mu_1[/tex] denote the population mean number of runs scored for DH group

Let [tex]\mu_2[/tex] denote the population mean number of runs scored for DH group

Let [tex]n_1[/tex]  and  [tex]n_2[/tex]  denote the sample sizes for DH and no DH

From the available information

[tex]n_1=n_2=20[/tex]

The population standard deviation of runs score is 2.54 for both the groups.

That is [tex]\sigma _1^2=\sigma_2^2=2.54[/tex]

The null hypothesis is [tex]H_0:\mu_1\leq \mu_2[/tex]

The alternative hypothesis is [tex]H_1:\mu_1>\mu_2[/tex]

Let the level of significance [tex]\alpha =0.10[/tex]

Since, the population standard deviation for both the group is known , even though the sample size is less than 30 , use z test

The test statistic is

[tex]z=\frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\mu_1^2}{n_1} +\frac{\mu_2^2}{n_2} } }[/tex]

The sample mean for the DH group is computed as

[tex]\bar x_1=\frac{1}{n_1} \sum_{i=1}^{n_1}\\\\=\frac{1}{20} (0+6+8+2+2+4+7+7+6+5+1+1+5+4+4+5+7+11+10+0)\\\\=\frac{92}{20}\\\\=4.6[/tex]

The sample mean of no DH is computed as

[tex]\bar x_2=\frac{1}{n_2} \sum_{i=1}^{n_1}\\\\=\frac{1}{20} (3+6+2+4+0+5+7+6+1+8+12+4+6+3+4+0+5+2+1+4)\\\\=\frac{83}{20}\\\\=4.15[/tex]

The test statistic is

[tex]z=\frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\mu_1^2}{n_1} +\frac{\mu_2^2}{n_2} } }[/tex]

[tex]=\frac{4.60-4.15}{\sqrt{\frac{2.54^2}{20} +\frac{2.54^2}{20} } } \\\\=\frac{0.45}{\sqrt{0.32258+0.32258} } \\\\=\frac{0.45}{0.803219}\\\\=0.5602[/tex]

P-Value

From the alternative hypothesis, it is clear that the test is one tailed test

P-value = P(Z > z)

[tex]1-P(Z\leq z)\\\\1-P(Z\leq 0.5602)[/tex]

1 - normsdist (0.5602)

(using excel function "normsdist(z)")

= 1 - 0.7123

= 0.2877

Therefore, the P-Value is 0.2877

Decision Rule

Reject the null hypothesis , if the p-value is less than the level of significance . that is p-value is < 0.10

Here, the p-value is 0.2877 which is greater than the level of significance 0.10

so , fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that more runs scored in games for which DH is used.

Answer:

a = 5q²

b = r²s

Step-by-step explanation:

The given identity is [tex]a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})[/tex]

we have to use this identity to factor of two cubes given as [tex]125q^{6}-r^{6}s^{3}=(5q^{2})^{3}-(r^{2}s)^{3}[/tex]

As this expression is in the form of a³- b³

Here a is 5q² and b is r²s.

Answer:

a=5q2  b=r2s the expression factored is also (5q2-r2s) (25q4+5q2r2s+1r4s2)

Step-by-step explanation:

Answer : The value of angle B and angle D is 25⁰ and 35⁰ respectively.

Step-by-step explanation :

As we know that the opposite angles are equal in parallelogram.

According to the given figure,

∠A = ∠C

and

∠B = ∠D

Given:

∠B = (3n - 5)⁰

∠D = (2n + 15)⁰

From this we conclude that:

∠B = ∠D

(3n - 5)⁰ = (2n + 15)⁰

3n - 5⁰ = 2n + 15⁰

3n - 2n = 15⁰ - 5⁰

1n = 10⁰

n = 10⁰

∠B = (3n - 5)⁰ = (3×10 - 5)⁰ = 25⁰

∠D = (2n + 15)⁰ = (2×10 + 15)⁰ = 35⁰

Therefore, the value of angle B and angle D is 25⁰ and 35⁰ respectively.

Answer:

Step-by-step explanation:

Area of rectangular menu

Length × breadth

3×2=6sq feet

Answer:

6 ft^2

Step-by-step explanation:

area of rectangle = length * width

area = 3 ft * 2 ft

area = 6 ft^2

Answer:

It will have a population of 61,779 in 2000.

Step-by-step explanation:

The population for the city, in t years after 1900, can be modeled by a exponential function with constant growth rate in the following format:

[tex]P(t) = P(0)(1+r)^{t}[/tex]

In which P(0) is the population in 1900 and r is the growth rate.

Population of 24,000 in 1900

This means that [tex]P(0) = 24000[/tex]

Population of 29,000 in 1920.

1920 is 1920 - 1900 = 20 years after 1900.

This means that P(20) = 29000. So

[tex]P(t) = P(0)(1+r)^{t}[/tex]

[tex]29000 = 24000(1+r)^{20}[/tex]

[tex](1+r)^{20} = \frac{29000}{24000}[/tex]

[tex]\sqrt[20]{(1+r)^{20}} = \sqrt[20]{\frac{29000}{24000}}[/tex]

[tex]1 + r = 1.0095[/tex]

So

[tex]P(t) = P(0)(1+r)^{t}[/tex]

[tex]P(t) = 24000(1.0095)^{t}[/tex]

What population will it have in 2000

2000 is 2000 - 1900 = 100 years after 1900. So this is P(100).

[tex]P(t) = 24000(1.0095)^{t}[/tex]

[tex]P(100) = 24000(1.0095)^{100} = 61779[/tex]

It will have a population of 61,779 in 2000.

Answer:

first you need to multiply -6 and 3

Answer:

-6 and 3

Step-by-step explanation:

sorry it was an late answer I'm just tryna gain points :D

Answer:

The answer is the last one because if the diagonals of a quadrilateral bisect each other then it's a parallelogram.

Answer:

Last answer choice

Step-by-step explanation:

One of the prerequisites for a quadrilateral to be a parallelogram is for the diagonals to bisect each other. Since K is the midpoint, this means that it is halfway between the ends of each of the diagonals, and that they therefore bisect each other. Hope this helps!

Answer:

19467649.76 lb-ft^2/s^2

Step-by-step explanation:

diameter of the pool d = 20 ft

radius = d/2 = 20/2 = 10 ft

height of pool side h = 6 ft

depth of water d = 5 ft

the force on the bottom of the pool due to the water in the pool is

F = pgdA

where p = density of water = 62.4 lb/ft^3

g = acceleration due to gravity = 32.17 ft/s^2

Area A = [tex]\pi r^{2}[/tex] = [tex]3.142 * 10^{2}[/tex] = 314.2 ft^2

Force on pool bottom = 64.2 x 32.17 x 5 x 314.2 = 3244608.29 lb-ft/s^2

work done = force times the height the water will be pumped

work = F x h = 3244608.29 x 6 = 19467649.76 lb-ft^2/s^2

The work (in ft-lb) is required to pump all of the water out over the side is :

Formula:

F = pgdA

p = density of water = 62.4 lb/ft^3

g = acceleration due to gravity = 32.17 ft/s^2

Area A = [tex]\pi r2\\[/tex] = 314.2 ft^2

The work (in ft-lb) is required to pump all of the water out over the side is 19467649.76 lb-ft^2/s^2.

Learn more :

https://brainly.com/question/13102487referrer=searchResults

Answer:

[tex]\boxed{\sf \ \ age = 10\ \ }[/tex]

Step-by-step explanation:

Hello,

let's write the mean computation, we note x the age of the additional person

[tex]\dfrac{14+14+18+18+22+x}{6}=16[/tex]

[tex]<=> 14+14+18+18+22+x = 6*16=96\\\\<=> x = 96 - ( 14+14+18+18+22)= 10[/tex]

So the age of the person is 10

hope this helps

Answer:

10

Step-by-step explanation:

The mean is the sum of terms divided by number of terms.

Let x be the age of the person who entered the room.

(14+14+18+18+22+x)/6 = 16

(x + 86)/6 = 16

x + 86 = 96

x = 10

The age of the person who entered the room is 10.

Answer:  b) they ARE similar because BRAD:KELY is 1:2

Step-by-step explanation:

In order for the shapes to be similar they must have congruent angles and proportional sides.

With the options a through d given, we can assume that their sides are proportional.  Since BRAD is smaller than KELY, BRAD would have the smaller number in the ratio.

Answer:

They are similar because Brad and Kelly are 1:2

Step-by-step explanation:

Answer:

33 degrees

Step-by-step explanation:

114+2x =180 right?

so 2x = 180-114 = 66

then x = 33

Answer:

C

Step-by-step explanation:

Not A b/c the difference b/w 85 and 17 is not 76

Not D b/c the difference b/w 97 and 17 is not 76

Not B b/c 16 is not 20% of 92

By the process of elimination the answer is C

Answer:

It may look simple to the owner because he is not the one losing a job. For the three machinists it represents a major event with major consequences

Answer:

a) Critical value = -1.4052

Since we are checking if the mean time is less than 10 minutes, the rejection area would be

z < -1.4052

b) Option C is correct.

Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

That is, the mean time is significantly less than 10 minutes.

Step-by-Step Explanation:

a) Using z-distribution, the critical value is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction (checking if the claim is less than 10 minutes significantly)

P(z < Critical value) = 0.08

From the z-tables, critical value = -1.4052

Since we are checking if the mean time is less than 10 minutes, the rejection area would be

z < -1.4052

b) We first give the null and alternative hypothesis

The null hypothesis is that there isn't significant evidence to suggest that the mean time is less than 10 minutes.

And the alternative hypothesis is is that there is significant evidence to suggest that the mean time is less than 10 minutes.

To now perform this hypothesis test, we need to obtain the test statistic

Test statistic = (x - μ)/σₓ

x = sample mean = (Σx/N)

The data is

1.2, 2.8, 1.5, 19.3, 2.4, 0.7, 2.2, 0.7, 18.8, 6.1, 6, 1.7, 29.1, 2.6, 0.2, 10.2, 5.1, 0.9, 8.2

Σx = 119.7

N = Sample size = 19

x = sample mean = (119.7/19) = 6.3

μ = standard to be compared against = 10 minutes

σₓ = standard error = (σ/√N)

where N = Sample size = 19

σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean = 6.3

N = Sample size = 19

Σ(x - xbar)² = 1122.74

σ = (√1122.74/19) = 7.687

σₓ = (7.687/√19) = 1.7635

Test statistic = (x - μ)/σₓ

Test statistic = (6.3 - 10)/1.7635

= -2.098 = -2.10

z = -2.10 and is in the rejection region, (z < -1.4052), hence, we reject the null hypothesis and the claim and say that the mean time is significantly less than 10 minutes.

The test statistic is less than the critical point, hence, we reject the null hypothesis and the claim and conclude that the mean time is less than 10 minutes.

Hope this Helps!!!

The critical value for the test based on the sampling distribution is -1.4052 and one needs to reject the claim.

From the complete information given, the descriptive statistics from the sample information has been given. The sample mean and variance are given. Therefore, the value of the test statistics from the information is -1.4052.

Also, the conclusion is to reject the claim since the test statistic is smaller than the critical point.

Therefore, the correct option is to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

Learn more about sampling on:

https://brainly.com/question/17831271

Answer:

The 98% CI for the mean travel time to the major city is [20.70; 26.14]minutes

Step-by-step explanation:

Hello!

The variable of interest is

X: commute time to a major city.

This variable has a normal distribution

X~N(μ;σ²)

The standard deviation is known to be:

σ= 4.2 minutes

A random sample of n= 13 commute times was taken:

11.5, 13.2, 14.7, 17.1, 18.7, 21.8, 22.4, 25, 26.9, 27.6, 31.1, 35.9, 38.6

You need to estimate the population mean travel time by calculating a 98% CI.

Since the variable has a normal distribution and the population standard deviation is known ,the statistic to use for this interval is the standard normal, then the formula for the interval is:

[X[bar] ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{Sigma}{\sqrt{n} }[/tex]]

The value of the statistic for the 1 - α: 0.98 interval is:

[tex]Z_{1-\alpha /2}= Z_{0.99}= 2.334[/tex]

Next is to calculate the sample mean:

X[bar]= ∑X/n= 304.5/13= 23.42 minutes

[23.42 ± 2.334 * ([tex]\frac{4.2}{\sqrt{13} }[/tex])]

[20.70; 26.14]minutes

With a 98% confidence level you'd expect that the interval [20.70; 26.14]minutes will contain the true mean travel time to the major city.

I hope this helps!

Answer:

a) Null hypothesis (H0): the mean guest bill for a weekend is $600.

Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.

b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600.

c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.  

Step-by-step explanation:

a) The accountant, as he wants to see if there is evidence to support the claim that the mean guest bill has increased significanty, should write the hypothesis like that:

Null hypothesis (H0): the mean guest bill for a weekend is $600.

Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.

A sample of bills of the period in study needs to be taken in order to have a representation of the actual population of bills and then perform a t-test, as the sample mean and standard deviation will be used to perform the test.

b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600. If the P-value was low but not enough, they may take another sample to perform the test again or leave it like that.

c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.  

Answer:

As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that listening to music while solving math problems will make a particular brain area more active.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=35\\\\H_a:\mu> 35[/tex]

The significance level is 0.01.

The sample has a size n=1.

The sample mean is M=58.

The standard deviation of the population is known and has a value of σ=10.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{1}}=10[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{58-35}{10}=\dfrac{23}{10}=2.3[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.3)=0.0107[/tex]

As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.

Answer:

y = 2x+4

Step-by-step explanation:

First we need to find the slope using two points

(-2,0) and (0,4)

m = (y2-y1)/(x2-x1)

m = (4-0)/(0--2)

   = 4/+2

   = 2

we have the y intercept  which is 4

Using the slope intercept form of the line

y = mx+b where m is the slope and b is the y intercept

y = 2x+4

Answer:

His overall final​ score is 80.1.

His letter grade is a B.

Step-by-step explanation:

To find his grade, we multiply each grade by it's weight.

Grades and weights:

His midterm score is 64​. The midterm counts 20% = 0.2.

His project score is 80​. The project score counts 20% = 0.2.

His homework score is 94. The homework score counts 30%.

His final exam score is 77. It counts 30%.

What is his overall final​ score?

64*0.2 + 80*0.2 + 94*0.3 + 77*0.3 = 80.1

His overall final​ score is 80.1.

What letter grade did he earn​ (A, B,​ C, D, or​ F)?

At least 80 but less than 90 is a​ B. He scored 80.1, so his letter grade is a B.

Answer:

cos θ = -2/√29

Step-by-step explanation:

tan θ = -5/2, π/2 < θ < π

One method is to draw a triangle with the hypotenuse in quadrant II.  The height of the triangle is 5, and the base is -2.  The hypotenuse can be found using Pythagorean theorem:

c² = a² + b²

c² = (-2)² + (5)²

c = √29

Therefore, cos θ = -2/√29.

Another method is to use one of the Pythagorean identities.

tan²θ + 1 = sec²θ

(-5/2)² + 1 = sec²θ

25/4 + 1 = sec²θ

29/4 = sec²θ

cos²θ = 4/29

cos θ = -2/√29

*see attachment showing the 2 boxes

Answer:

3 ft²

Step-by-step explanation:

==>Given:

Box J with the following dimensions:

L = 4.5ft

W = 3ft

H = 2ft

Box F:

L = 3ft

W = 3ft

H = 3ft

==>Required:

Difference between the surface area of box J and box F

==>Solution:

Surface area = 2(WL + HL + HW)

=>S.A of box J = 2(3*4.5 + 2*4.5 + 2*3)

= 2(13.5 + 9 + 6)

= 2(28.5)

S.A of box J = 57 ft²

=>S.A of box F = 2(3*3 + 3*3 + 3*3)

= 2(9 + 9 + 9)

= 2(27)

S.A of box F = 54 ft²

Difference between box J and box F = 57 - 54 = 3 ft²

Answer:

a. x = 4

b. x = 17.5

Step-by-step explanation:

a. 5x/2 + 1 = 11

5x/2 = 10

5x = 20

x = 4

b. 2x/7 - 3 = 2

2x/7 = 5

2x = 35

x = 35/2

Answer:

a) x = 4

b) x = 17.5

Step-by-step explanation:

a)

(5x)/2 + 1 = 11

(5x)/2 = 10

5x = 20

x = 4

b)

(2x)/7 - 3 = 2

(2x)/7 = 5

2x = 35

x = 17.5

Answer:

y=2/3x

Step-by-step explanation:

the ratio is 2:3, so this would graph according to the information given

Answer:

y=2/3x

Step-by-step explanation:

Answer:

Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds.

Step-by-step explanation:

Dilation is a transformation process in which the dimensions of a given figure are resized to produce an image with the same shape. This is done with respect to a scale factor and center of dilation.

In the given question, the center of dilation is at the middle of side DC of rectangle ABCD (i.e on side DC).

Given that the scale factor is  [tex]\frac{4}{3}[/tex],

EF = HG =  [tex]\frac{4}{3}[/tex]  × AB = [tex]\frac{4}{3}[/tex] × 6 = 8 units

FG = EH =  [tex]\frac{4}{3}[/tex]  × BC =  [tex]\frac{4}{3}[/tex]  × 3 = 4 units

Therefore, rectangle EFGH is the result of dilation of ABCD.

Answer:

A. Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds

Step-by-step explanation:

Answer:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Step-by-step explanation:

For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:

[tex]X \sim exp (\lambda =\frac{1}{8.9}) [/tex]

And we want to find the following probability:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Answer: 1. point A

2. 90 degrees

3. 90 degrees clockwise

Step-by-step explanation:

BRAINLIEST??!?!

Options

Answer:

(C) (15,25)

Step-by-step explanation:

The profit p in dollars of selling x widgets and y gadgets is given by the function p(x,y)=7x+6y.

Option A

When x=0 and y=35

p(x,y)=7(0)+6(35)

p(x,y)=210

Option B

When x=10 and y=30

p(x,y)=7(10)+6(30)

p(x,y)=250

Option C

When x=15 and y=25

p(x,y)=7(15)+6(25)

p(x,y)=$255

Option D

When x=20 and y=15

p(x,y)=7(20)+6(15)

p(x,y)=$230

We observe that the point (15, 25) in Option C yields the highest profit ($255). Therefore, it is the point that maximizes profit.