A driver and a passenger are in a car accident. Each of them independently has probability 0.3 of being hospitalized. When a hospitalization occurs, the loss is uniformly distributed on [0, 1]. When two hospitalizations occur, the losses are independent. Calculate the expected number of people in the car who are hospitalized, given that the total loss due to hospitalizations from the accident is less than 1.

Answer:

C. 1/25

Step-by-step explanation:

5^-2=5^(2*-1)

5^2=25

25^-1=1/25

Answer:

It is C 1/25 because it won't be -25 because a negative times a negative is a positive

Step-by-step explanation:

Answer:

300/60=5 more words per minute

80+5 = 85 words per minute

or

80 x 60 = 4800 + 300 = 5100

5100 / 60 = 85 words per minute

Hope this helps

Step-by-step explanation:

Answer:

26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

Step-by-step explanation:

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, we have that:

[tex]\mu = 4.2, \sigma = 1.3[/tex]

Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

This is 1 subtracted by the pvalue of Z when X = 5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 4.2}{1.3}[/tex]

[tex]Z = 0.615[/tex]

[tex]Z = 0.615[/tex] has a pvalue of 0.7308.

1 - 0.7308 = 0.2694

26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

Answer:

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

P-value = 0.003.

Step-by-step explanation:

If we perform a regression analysis relating x and y, we get the best fitting line with equation:

[tex]y=15.82x+92.9[/tex]

and a correlation coefficient r:

[tex]r=0.693[/tex]

We have to test the hypothesis, where the alternative hypothesis claims that there is a relationship between these two variables, and the null hypothesis claiming there is no relationship (meaning that the correlation is not significantly different from 0).

This can be written as:

[tex]H_0: \rho=0\\\\H_a:\rho\neq0[/tex]

where ρ is the population correlation coefficient for x and y.

The significance level is assumed to be 0.05.

The sample size is n=16.

The degrees of freedom are df=14.

[tex]df=n-2=16-2=14[/tex]

The test statistic can be calculated as:

[tex]t=\dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\dfrac{0.693\sqrt{14}}{\sqrt{1-(0.693)^2}}=\dfrac{2.593}{0.721}=3.597[/tex]

For a test statistic t=2.05 and 14 degrees of freedom, the P-value is calculated as:

[tex]\text{P-value}=2\cdot P(t>3.597)=0.003[/tex]

The P-value (0.003) is smaller than the significance level (0.05), so the effect is significant enough.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

Answer:

A) -x + y = 2

B) x + 2y = 4

we add both equations

3 y = 6

y = 2

We put y = 2 into equation B)

x + 2 * 2 = 4

x = 0

***********************************************

A) -2x + y = 6

B) x + y = 0

We multiply B) by 2

B) 2 x + 2 y = 0 then we add A)

A) -2x + y = 6

3y = 6

y = 2

Therefore x = -2

Step-by-step explanation:

Answer:

[tex]70 \: cm^2[/tex]

Step-by-step explanation:

Area of parallelogram.

[tex]A=bh[/tex]

[tex]b \times h[/tex]

[tex]14 \times 5[/tex]

[tex]=70[/tex]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: μ = 904

For the alternative hypothesis,

Ha: μ < 904

This is a left tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 10,

Degrees of freedom, df = n - 1 = 10 - 1 = 9

t = (x - µ)/(s/√n)

Where

x = sample mean = 805

µ = population mean = 904

s = samples standard deviation = 158

t = (805 - 904)/(158/√10) = - 1.98

We would determine the p value using the t test calculator. It becomes

p = 0.039

Since alpha, 0.05 > than the p value, 0.03953, then we would reject the null hypothesis. Therefore, the correct option is:

2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.

Answer:

  it is the complement of 28°

Step-by-step explanation:

Angle DAB made by a tangent and a chord to the point of tangency is equivalent to every other inscribed angle that intercepts the same arc. Those angles have half the measure of the central angle ACB intercepting the same arc.

In isosceles triangle ABC the base angles (shown as 28°) are the complement of half the measure of the central angle. Hence angle DAB will be the complement of the angle marked 28°.

  angle DAB = 90° -28° = 62°

Answer:

j=13, g=20.8, h=24

Step-by-step explanation:

The overall shape given and the shape within, are both right triangles. With right triangles, you are allowed to use the pythagorean theorem formula ([tex]a^{2} + b^{2} = c^{2}[/tex]) in order to solve for some sides. In this case, that would be j and h. The five in the smaller triangle is represented by b and the 12 is the hypotenuse so it is represented by c. When you plug in those numbers in the pythagorean theorem formula, you will find the value of j to be 13. When looking at this, we see that 12 is the second greatest value in the right triangle values that we just found, so we know the the opposing angle for that one will be 60 degrees. The 5's opposing side is therefore 30 degrees. When subtracting 90 and 30, we get 60, so therefore you can use the 30 60 90 formula to find the sides of the bigger triangle. The 60 degrees represents g. This formula will be [tex]a\sqrt{3}[/tex]. The a is 12 since it is the smallest value. So therefore, g is [tex]12\sqrt{3}[/tex], which is 20.8. Now that we have this side, we can just use the pythagorean theorem formula to find the remaining side. Therefore, h is going to be 24

Answer:

h = 16.23 m

The cannonball will hit the wall at 16.23m from the ground.

Step-by-step explanation:

Given;

Initial speed v = 62m/s

Angle ∅ = 25°

Horizontal distance d = 260 m

Height of wall y = 20

Resolving the initial speed to vertical and horizontal components;

Horizontal vx = vcos∅ = 62cos25°

Vertical vy = vsin∅ = 62cos25°

The time taken for the cannon ball to reach the wall is;

Time t = horizontal distance/horizontal speed

t = d/vx (since horizontal speed is constant)

t = 260/(62cos25°)

t = 4.627 seconds.

Applying the equation of motion;

The height of the cannonball at time t is;

h = (vy)t - 0.5gt^2

Acceleration due to gravity g = 9.81 m/s

Substituting the given values;

h = 62sin25×4.627 - 0.5×9.81×4.627^2

h = 16.2264134736

h = 16.23 m

The cannonball will hit the wall at 16.23m from the ground.

Answer:

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622

The margin of error is:

M = T*s = 2.2622*0.3 = 0.68

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF

The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

Answer:

The required probability is 0.4828.

Step-by-step explanation:

We are given that a company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B.

Five percent of all type A goggles are returned within 10 days after the sale, whereas only two percent of type B are returned.

Let the probability that production is of Type A = P(A) = 30%

Probability that production is of Type B = P(B) = 1 - P(A) = 1 - 0.30 = 70%

Also, let R = event that pair of goggles are returned

So, the probability that type A goggles are returned within 10 days after the sale = P(R/A) = 5%

Probability that type B goggles are returned within 10 days after the sale = P(R/B) = 2%  

Now, given a pair of goggles is returned within the first 10 days after the sale, the probability that the goggles returned are of type B is given by = P(B/R)

We will use the concept of Bayes' Theorem to calculate the above probability.

So,  P(B/R)  =  [tex]\frac{P(B) \times P(R/B)}{P(A) \times P(R/A)+P(B) \times P(R/B)}[/tex]

                   =  [tex]\frac{0.70 \times 0.02}{0.30 \times 0.05+0.70 \times 0.02}[/tex]

                   =  [tex]\frac{0.014}{0.029}[/tex]  =  0.4828

The PIN is 4829

Step-by-step explanation:

let s take 4 numbers a b c and d

the PIN is abcd

we know that

(1) a = b/2

(2) b+c=10

(3) d=b+1

(4) a+b+c+d=23

from (2) c = 10 - b

from (3) d = b + 1

so (4) gives

b/2 + b + 10 - b + b +1 = 23

so

3/2 b = 23 -11 = 12

b = 12*2/3 = 8

so d = 9

c = 10-8=2

and a = 4

so the PIN is 4829

thank you

Answer:

-14a^2b-42ab^2+56abc

Step-by-step explanation:

You can use the FOIL method

multiply the first numbers

then inner

then outer

then last

Answer: this is a guess but 7.69 percent chance that you will pick a blue candy

Step-by-step explanation:

Answer:

Choosing 1 blue and 1 green candy

Step-by-step explanation:

There are no red candies and there is only 1 blue candy.

Answer:

Step-by-step explanation:

[tex]\int\limits^{\infty}_0 {A^2_1} (e^{-r/a})r^2dr= {A^2_1}\int\limits^{\infty}_0r^2(e^{-r/a})^2\, dr)[/tex]

[tex]=A_1^2\int\limits^{\infty}_0 r^2e^{-2r/a}\ dr[/tex]

[tex]=A_1^2[\frac{r^2e^{2r/a}}{-2/a} |_0^{\infty}-\int\limits^{\infty}_0 2r\frac{e^{-2r/a}}{-2/a} \ dr][/tex]

[tex]=A^2_1[0+\int\limits^{\infty}_0 a\ r\ e^{-2r/a}\ dr][/tex]

[tex]=A^2_1[\frac{a \ r \ e^{-2r/a}}{-2/a} |^{\infty}_0-\int\limits^{\infty}_0 \frac{a \ e^{-2r/a}}{-2/a} \ dr][/tex]

[tex]=A_0^2[0-0+\int\limits^{\infty}_0 \frac{a^2}{2} e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} \int\limits^{\infty}_0 e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} [\frac{e^{-2r/a}}{-2/a} ]^{\infty}_0[/tex]

[tex]=\frac{A_1^2a^2}{2} -\frac{a}{2} [ \lim_{r \to \infty} [e^{-2r/a} -e^0]\\\\=\frac{A_1^2a^2}{2} -(\frac{a}{2}) (0-1)[/tex]

[tex]=\frac{A_1^2a^3}{4}[/tex]

[tex]\therefore A_1^2\int\limits^{\infty}_0 r^2(e^{-r/a}) \ dr =\frac{A_1^2a^3}{4}[/tex]

Find the unique positive value of A1

[tex]=4\pi (\frac{A_1^2a^3}{4} )\\\\=A_1^2a^3\pi\\\\A_1^2=\frac{1}{a^3\pi} \\\\A_1=\sqrt{\frac{1}{a^3\pi} }[/tex]

Answer:

B. The radius

Step-by-step explanation:

The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle so we need to know the radius for it

Answer:

The expected value of the random variable with the given probability distribution = 12 .52

Step-by-step explanation:

Given data

 x    :   0         1            5       10     1000

p(x)  :  0.33  0.32   0.24     0.10    0.01

The expected value of the given random variable of given probability distribution

E(X)  =  ∑ x p ( X = x)

E(X)  =  0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01

E (X)  =  12.52

Answer:

There are 60 marbles in the bag

Step-by-step explanation:

The total number of marbles  times the probability of red marbles = number of red marbles

total * 7/10 = 42

Multiply each side by 10/7

total * 7/10 * 10/7 = 42*10/7

total

60

There are 60 marbles in the bag

Answer:

200 feet

Step-by-step explanation:

Area of the warehouse [tex]=60,000$ ft^2[/tex]

Let the length of the warehouse=l

The warehouse's width is exactly  [tex]\dfrac23[/tex] of its length

Therefore: Width of the warehouse[tex]=\dfrac23l[/tex]

Area =Length X Width

Therefore:

[tex]\dfrac23l*l=60000\\$Cross multiply\\2l^2=60000*3\\2l^2=180000\\$Divide both sides by 2\\2l^2 \div 2=180000 \div 2\\l^2=90000\\l^2=300^2\\$Length, l=300 feet\\Recall: Width =\dfrac23l\\$Therefore, Width of the warehouse=\dfrac23*300=200$ feet[/tex]

Answer:

No, the events are not mutually exclusive because they share the common outcomes of the student working and playing volleyball on certain days.

Step-by-step explanation:

A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.

In this case, A and B have outcomes in common since the student both works and plays volleyball on Tuesdays and Thursdays. Thus, the events are not mutually exclusive.  

Answer:

7x -14 = jl

Step-by-step explanation:

Assuming a straight line

jm+ ml = jl

5x-8 + 2x-6 = jl

Combine like terms

7x -14 = jl

Answer:

D is 10

b/12

Step-by-step explanation:

Answer:

4 pounds of lime and 5 pounds of pears

Step-by-step explanation:

I + P = 9

0.5l + 1.5P = 9.5

I = 9 - P

0.5(9 - P) + 1.5P = 9.5

4.5-0.5P + 1.5P = 9.5

4.5 + P (1P) = 9.5

P = 9.5-4.5 = 5

I = 9 - 5 = 4

Answer: 4 pounds of lime and 5 pounds of pears

Answer:

[tex]x+6y[/tex] where x is the cost of one adult ticket and y is the cost of one child ticket.

Step-by-step explanation:

This is an incomplete question since we would need to know the cost of the adult ticket and the cost of the children ticket.

However, let's say that the price is x dollars per adult and y dollars per child.

Now, we need to find out how much one adult and 6 children paid.

Thus, we would have to multiply the cost per adult by the number of adults and the cost per child per number of children and then sum up these two results.

Writing this in an algebraic way we would have:

[tex]1(x)+6y\\x+6y[/tex]

Thus, 1 adult and 6 children would have paid x + 6y dollars where x is the cost of the adult ticket and y is the cost of the children ticket.

(For example, if an adult ticket is 6 dollars and a child ticket is 4 dollars we would have that they paid 6 + 6(4) = 6 + 24 = 30 dollars)

Answer:

1x1x6x5x4x3x2x1 = 720 also they can sit in:

6x1x1x5x4x3x2x1 = 720

6x5x1x1x4x3x2x1 = 720

6x5x4x1x1x3x2x1 = 720

6x5x4x3x1x1x2x1 = 720

6x5x4x3x2x1x1x1 = 720

6x5x4x3x2x1x1x1 = 720 or you could have gone 720 x 7

Answer:an=20(-1/2)^n-1

Step-by-step explanation:

Answer:

D. It would be less steep

Step-by-step explanation:

The first graph moves at a rate of 5/1 which is a greater fraction than 3/4

Answer:

2.5 sec

Step-by-step explanation:

Height of wall = 2.5 m

initial speed of ball = 14 m/s

height from which ball is kicked = 0.4 m

we calculate the speed of the ball at the height that matches the wall first

height that matches wall = 2.5 - 0.4 = 2.1 m

using  =  + 2as

where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)

=  + 2(-9.81 x 2.1)

= 196 - 41.202

= 154.8

v =  = 12.44 m/s

this is the velocity of the ball at exactly the point where the wall ends.

At the maximum height, the speed of the ball becomes zero

therefore,

u = 12.44 m/s

v = 0 m/s

a = -9.81 m/s^2

t = ?

using V = U + at

0 = 12.44 - 9.81t

-12.44 = -9.81

t = -12.44/-9.81

t = 1.27 s

the maximum height the ball reaches will be gotten with

=  + 2as

a = -9.81 m/s^2

0 =  + 2(-9.81s)

0 = 196 - 19.62s

s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.

height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m

we calculate for the time taken for the ball to travel down this height

a = 9.81 m/s^2 (positive in downwards movement)

u = 0

s = 7.49 m

using s = ut + a

7.49 = (0 x t) +  (9.81 x  )

7.49 = 0 + 4.9

 = 7.49/4.9 = 1.53

t =  = 1.23 sec

Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec

Answer:

[tex]\frac{8}{49}[/tex]

Step-by-step explanation:

Orange: [tex]\frac{4}{7}[/tex]

Red: [tex]\frac{2}{7}[/tex]

[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]