A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year

Answers

Answer 1

Answer:

[tex]P(x \le 3) = 0.9920[/tex]

Step-by-step explanation:

Given

[tex]p = 6\%[/tex] --- proportion of drivers that had accident

[tex]n = 14[/tex] -- selected drivers

Required

[tex]P(x \le 3)[/tex]

The question is an illustration of binomial probability, and it is calculated using:

[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]

So, we have:

[tex]P(x \le 3) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3)[/tex]

[tex]P(x=0 ) = ^{14}C_0 * (6\%)^0 * (1 - 6\%)^{14-0} = 0.42052319017[/tex]

[tex]P(x=1 ) = ^{14}C_1 * (6\%)^1 * (1 - 6\%)^{14-1} = 0.37578668057[/tex]

[tex]P(x=2 ) = ^{14}C_2 * (6\%)^2 * (1 - 6\%)^{14-2} = 0.15591149513[/tex]

[tex]P(x=3 ) = ^{14}C_3 * (6\%)^3 * (1 - 6\%)^{14-3} = 0.03980719024[/tex]

So, we have:

[tex]P(x \le 3) = 0.42052319017+0.37578668057+0.15591149513+0.03980719024[/tex]

[tex]P(x \le 3) = 0.99202855611[/tex]

[tex]P(x \le 3) = 0.9920[/tex] -- approximated


Related Questions

Bạn được một cá nhân thuê làm tư vấn tài chính, anh ta nhận được 2 đề nghị hợp ký đồng làm
việc với thời hạn 5 năm theo 2 sự lựa chọn sau:
- Lựa chọn 1: Lương 3 triệu/năm
- Lựa chọn 2: Lương 1.5 triệu/năm và được thưởng 9 triệu khi kết thúc hợp đồng làm việc.
a. Nếu lãi suất 8% bạn sẽ khuyên anh ta nhận lựa chọn nào?
b. Nếu lãi suất tăng 10% theo bạn có cần phải đổi lựa chọn không?

Answers

I don’t know the language

A =
1
9


4 1 −8
7 4 4
4 −8 1

Answers

I don't know sorry I am weak in math

plz help and explain this :)

Answers

Answer:

y=3x+6

Step-by-step explanation:

in a line graph, y=mx+c

m refers to gradient, c refers to y-intercept.

since lines are parallel, both lines have the same gradient.

the line intersects (1,9)

x=1,y=9

9=3(1)+c

c=6

so y=3x+6

Answer:

y = 3x+6

Step-by-step explanation:

Parallel lines have the same slope

y = 3x+2 is in slope intercept form (y=mx+b where m is the slope and b is the y intercept)

So the slope is 3

Y = 3x+2

Using the point given substitute into the equation and solve for b

9 = 3(1)+b

9 =3+b

9-3 =b

6=b

y = 3x+6

Please help explanation if possible

Answers

Answer:

10% gain

Step-by-step explanation:

[P2-P1]/P1

(33-30)/30=3/30=.1 or 10% gain.

Answer:

10%

Step-by-step explanation:

→ Minus the new share from the old one

33 - 30 = 3

→ Divide the answer by the original price

3 ÷ 30 = 0.1

→ Multiply the answer by 100

0.1 × 100 = 10%

Which of the following pairs of functions are inverses of each other?
A. f(x) = 5 + x and g(x) = 5 - x
B. f(x) = 2x -9 and g(x)=x+9/2
C. f(x) = 3-6 and g(x)=x+6/2
D. f(x)= x/3+4 and g(x) = 3x - 4​

Answers

The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.

To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's analyze the given options:

A. f(x) = 5 + x and g(x) = 5 - x

To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.

B. f(x) = 2x - 9 and g(x) = x + 9/2

By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.

C. f(x) = 3 - 6 and g(x) = x + 6/2

Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.

D. f(x) = x/3 + 4 and g(x) = 3x - 4

After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.

In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.

Learn more about function here:

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Homework:Assignment 3 Question 20 Score: 0 of 1 point A vending machine dispenses coffee into ​-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of ounce. You can allow the cup to overfill ​% of the time. What amount should you set as the mean amount of coffee to be​ dispensed?

Answers

Answer:

19.92

Step-by-step explanation:

To overfill 5% of the time ;

The Zscore (value) to the left of (1 - 0.05) = 0.95 is 1.645

Using this Zscore value with the Zscore formula :

Zscore = (x - μ) / σ

σ = 0.05 ; x = 20 ounce

Substituting into the Zscore formula :

1.645 = (20 - μ) / 0.05

1.645*0.05 = 20 - μ

0.08225 = 20 - μ

μ = 20 - 0.08225

μ = 19.91775

μ = 19.92

Solve x∕3 < 5 Question 5 options: A) x ≥ 15 B) x > 15 C) x < 15 D) x ≤ 15

Answers

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )

x < 15 → C

Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?
HELP PLS

Answers

Answer:

(x-4)^2=-8(y-3)

This is a parabola.

Step-by-step explanation:

Since the directrix is horizontal, the parabola faces up or down. Since the focus is below the directix it faces down. This means p will be negative in the equation (x-h)^2=4p(y-k).

p also tells us the half the distance between the focus and the directrix. The distance between 1 and 5 is 4, so p=-2.

The vertex is half way point between focus (4,1) and directrix y=5.

So the vertex is (4, [1+5]/2 )= (4 ,6/2)=(4,3). This is (h,k) in our equation.

(x-h)^2=4p(y-k)

(x-4)^2=4×-2(y-3)

(x-4)^2=-8(y-3)

There are 8 midsize cars and 15 compact cars and 6 will be selected. What is the probability of selecting all midsize cars?

Answers

Answer:

Assuming order does not matter, the probability of selecting all midsize cars is 0.000277373, or [tex]\frac{4}{14421}[/tex].

Step-by-step explanation:

First, we must find the n(Total arrangements of selections)=(8+15)C6

n(Total arrangements of selections)=23C6

n(Total arrangements of selections)=100,947

Second, we must find the n(Arrangements where all are midsize cars)=8C6

n(Arrangements where all are midsize cars)=28

To find the probability of selecting all midsize cars, we divide the n(Arrangements where all are midsize cars) by the n(Total arrangements of selections):

P(All midsize cars)= [tex]\frac{28}{100,947}[/tex]

P(All midsize cars)= [tex]\frac{4}{14421}[/tex]=0.000277373.

A party rental company has chairs and tables for rent. The total cost to rent 6 chairs and 5 tables is $63. The total cost to rent 2 chairs and 3 tables is $35. What is the cost to rent each chair and each table?

Answers

Answer:

1.75dollars - the value of each chair,  10.5 dollars - the value of each table

Step-by-step explanation:

The value of chair is x, the value of table is y. Then 6chairs cost 6x, 5 tables cost 5y. 6x+5y= 63

Then the value of 2 chairs is  2x,  for 3 tables  it is equal to 3y. 2x+3y=35

We have the system of equations6x+5y= 63 and 2x+3y=35

Multiply the second one by -3

-3(2x+3y)= -3*35

-6x-9y= -105.

Plus the first equation and the second one multiplied by -3 (the right side to the right side and the left side to the left side with sign= between them)

6x+5y-6x-9y= 63-105

-4y= -42

y=10.5 dollars - the value of a table

6x+5*10.5=63

6x= 63-52.5

6x=10.5

x=1.75dollars - the value of a chair

A supervisor records the repair cost for 22 randomly selected VCRs. A sample mean of $75.50 and standard deviation of $18.07 are subsequently computed. Determine the 99% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

The t value for 99% CI for 21 df is 2.831.

The critical value that should be used in constructing the confidence interval is (64.593, 86.407).

Step-by-step explanation:

Now the sample size is less than 30 and also population standard deviation is not known.

Then we will use t distribution to find CI

t value for 99% CI for 21 df is TINV(0.01,21)=2.831

The margin of error is [tex]E=t\times\frac{s}{\sqrt{n}}\\\\=2.831\times\frac{18.07}{\sqrt{22}}\\\\=10.907[/tex]

Hence CI is[tex]CI=\overline{x} \pm E\\\\ =75.50 \pm 10.907\\\\=(64.593,86.407 )[/tex]

What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)

Answers

Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Help with this Area question

Answers

Step 1: Find the area of the rectangle

A = base x height

A = 39 x 20

A = 780

Step 2: Find the area of the semi-circles

---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.

A = pi x r^2

A = pi x 10^2

A = 100pi = 314

Step 3: Find the area of the figure

Area = area of the rectangle - area of the semi-circles

A = 780 - 314

A = 466 cm^2

Hope this helps!

Answer:

466 cm^2

Step-by-step explanation:

This one is done basically the same as the other.

Rectangle = 20 x 39

Circle = (3.14) x 10^2

Rectangle = 780

Circle = 314

rectangle - circle

780 - 314 = 466

Assume 2 in every 3000 students at the local community college have to quit due to serious health issues. An insurance company offers them ​$12000 policy for ​$40a year. What is the amount the insurance company should expect to make on average on every student that​ pays?
The amount the insurance company should expect to make on average on every student that pays is ​$

Answers

Answer:

$32

Step-by-step explanation:

Multiply $40*3000 students. Subtract 2 students that might receive a $12000 policy each. Divide by 3000 students to find average payout.

ZDAC = ZBAD.
What is the length of BD?
Round to one decimal place.

Answers

Answer:

BD = 4.1

Step-by-step explanation:

DA is an angle bisector which also divides the opposite side of the angle it bisects in a way that it is proportional to tye other two sides.

By implication, we would have the following:

AB/BD = AC/DC

AB = 5.3

AC = 5.5

DC = 4.3

BD = ?

Plug in the values

5.3/BD = 5.5/4.3

Cross multiply

BD*5.5 = 4.3*5.3

BD*5.5 = 22.79

Divide both sides by 5.5

BD = 22.79/5.5

BD = 4.1 (to 1 decimal place)

A restaurant interest survey of 230 citizens in a town showed that 80 want a new Chili's, 120 want a new Red Lobster, and 20 want both. Determine the probability that:
...​

Answers

Answer:

2/23

6/23

5/23

Step-by-step explanation:

60 only want chilis

20 wants both

100 only want red lobster

50 want neither

The right solution to the given question is "[tex]\frac{2}{23}[/tex]", "[tex]\frac{6}{23}[/tex]" and "[tex]\frac{5}{23}[/tex]".

According to the question,

[tex]a+b+c+d = 230[/tex][tex]b = 20[/tex][tex]a+b = 80[/tex]

By putting the value of "b", we get

[tex]a+20=80[/tex]

                [tex]a = 80-20[/tex]

                [tex]a = 60[/tex]

[tex]b + c=120[/tex]

By putting the value of "b", we get

      [tex]20+c=120[/tex]

              [tex]c = 120-20[/tex]

              [tex]c = 100[/tex]

[tex]d = 230-60-100-20[/tex]

By putting the values of "a", "b", "c" and "d", we get    

       [tex]d = 50[/tex]

(a)

P(both Chili's and Red lobster),

= [tex]\frac{b}{a+b+c+d}[/tex]

= [tex]\frac{2}{23}[/tex]

(b)

P(only chili's),

= [tex]\frac{a}{a+b+c+d}[/tex]

= [tex]\frac{6}{23}[/tex]

(c)

P(neither),

= [tex]\frac{d}{a+b+c+d}[/tex]

= [tex]\frac{5}{23}[/tex]

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Find the missing side length in the image below

Answers

Answer:

87.5

Step-by-step explanation:

Let the missing side be x.

28 / 35 = x / 50

4 / 7 = x / 50

4 ( x ) = 7 ( 50 )

4x = 350

x = 350 / 4

x = 87.5

Choose the expression that represents “divide 0.04 by n.”

Answers

Answer:

.04/n=4/100n or 4÷100n

The best basketball player

Answers

Answer:

c

Step-by-step explanation:

hope it helps!!!!!!!!!!!!!!

Which polynomial function is best represented by the graph?

ƒ(x) = –x(x – 1)4
ƒ(x) = x2(x + 1)3
ƒ(x) = x2(x – 1)3
ƒ(x) = x(x – 1)4

Answers

Answer: ƒ(x) = x2(x – 1)3

For the function in the graph, find the values of f(-4), f(-1), and f(1).​

Answers

Answer:

f(-4) = -1

f(-1) = -4

f(1) = 4

Step-by-step explanation:

We need to find the y value for the x values

f(-4) means find the y value for x= -4

f(-4) = -1

f(-1) = -4

f(1) = 4

Math geometry worth 30 points

What is the value of x?

Answers

Answer:

x = 3

Step-by-step explanation:

First, use trigonometric function to find RT.

θ = 60°

Opposite = 2√3

Hypotenuse = RT

Apply SOH:

Sin θ = Opp/Hyp

Plug in the values

Sin 60° = 2√3/RT

RT*Sin 60° = 2√3

Divide both sides by Sin 60°

RT = 2√3/sin 60°

RT = 2√3 × √3/2 (sin 60° = √3/2)

RT = (2√3 × √3)/2

RT = (2 × 3)/2

RT = 3

✔️Find x

θ = 45°

Opposite = x

Adjacent = 3

Apply TOA:

Tan θ = Opp/Adj

Substitute

Tan 45° = x/3

3 × Tan 45° = x

3 × 1 = x (tan 45° = 1)

3 = x

x = 3

write fifty and two hundreds eight thousandths as a mixed decimal

Answers

Answer:

Pretty sure it's 0.528

Place the labels in the chart
If you can draw this out for me or describe were they are that will be very helpful:)

Answers

Answer:

Check the image

The measure of AD is v10. Find the AREA of the parallelogram below.
Leave answers in exact form (no decimals). Simplify all radicals and
rationalize the denominator. (You may write roots in the following ways:
2root5 or 2r5)

WILL GIVE BRAINLIEST

Answers

Please look at the Picture for the answer with the steps on how to get it. Thank you. Would really appreciate it if given branliest

Help ! Please and thanks

Answers

The correct answer is that 1 & 8 are alternate exterior angles
they are alterate exterior angles

which fraction has a greater value than 0.4

Answers

Answer:

0.4 as a fraction is 2/5, so as long as the fraction is greater than 2/5 then you are good

5/9 || 0.55

Step-by-step explanation:

PLS HELP I DONT KNOW THIS ONE

Answers

Answer:

x+3

---------------

(x-3)(x-2)(x-4)

Step-by-step explanation:

x+4             x^2 -16

---------------÷ -------------

x^2 - 5x+6     x+3

Copy dot flip

x+4                x+3

--------------- * -------------

x^2 - 5x+6     x^2 -16

Factor

x+4                x+3

--------------- * -------------

(x-3)(x-2)     (x-4)(x+4)

Cancel like terms

1                   x+3

--------------- * -------------

(x-3)(x-2)     (x-4)1

x+3

---------------   x cannot equal 3,2,4 -4

(x-3)(x-2)(x-4)

if 2 shirts cost 18.80, how much would 9 shirt cost.

Answers

Answer:

84.60

Step-by-step explanation:

We can write a ratio to solve

18.80             x

---------   = --------------

2 shirts    9 shirts

Using cross products

18.80 *9 = 2x

169.2 =2x

Divide each side by 2

169.2/2 =2x/2

84.60 =x

Aliana is supposed to get back to a customer with an answer about a refund by the end of the day, but she won't have all the approvals she needs to process the refund by that time. What should she do? O a) Call the customer only when she has processed the refund Ob Tell the customer that she should have called about the problem earlier Oc) Explain to the customer that her bosses are the ones that are taking forever O di Apologize to the customer and say that she will call her tomorrow with an update

Answers

Answer:

"ob" is the answer of this long question

Answer:

D

Step-by-step explanation:

reason:

not A cuz the customer has to wait for a long time, and she feel waste of time

not B cus it's the store's responsiblity, not customer. if she said that, the customer would feel be disrespected. and i swear she never comes back that store.

C if she said that, customer also feel waste of time when she has to talk with Aliana who cant solve her problem

and the boss will think Ali couldnt have no problem-solving skills

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