The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

Final answer:

The question asks to demonstrate that for a nonnegative integer-valued random variable X, the expected value E(X) equals the summation over all k of the probability P(X ≥ k). This is shown by expressing P(X ≥ k) as an infinite sum, switching the order of summation, and counting each probability P(X = i) exactly i times.

Explanation:

The student's question pertains to the calculation of the expected value (E(X)) of a nonnegative integer-valued random variable. Specifically, the question asks to show that for such a random variable X, the expected value can be expressed as E(X) = ∑₋∞ k=1 P(X ≥ k). To demonstrate this, we begin with the definition of expected value:

E(X) = μ = ∑ xP(x).

Next, we unpack P(X ≥ k) by writing it as an infinite sum of probabilities for all integers i starting from k:

P(X ≥ k) = ∑₋∞ i=k P(X = i).

To find the expected value, we consider the sum of all such probabilities over all k:

∑₋∞ k=1 P(X ≥ k) = ∑₋∞ k=1 ∑₋∞ i=k P(X = i).

We then switch the order of summation, so that we first sum over all possible values of i and then for each i, we sum over the corresponding k that contributes to P(X = i):

E(X) = ∑₋∞ i=1 P(X = i) ∑₉ i k=1.

By doing this, we count each P(X = i) exactly i times, which leads us to the initial definition of expected value, thus proving the given formula.

Answer:3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

khan acadamy hope this helps

Answer:

(D) 0.006

Step-by-step explanation:

Total number of cards :52

Please note that, all cards have a the possibility of appearing 4 times.

Hence total possible number of a '2' is 4 cards and so it is also for a '10'

Having this Understanding, let's solve the question properly.

The probability that the FIRST CARD is 2 = 4/52

Probability that the second card without replacement is a 10 = 4 / 51

P( 1st two and 2nd four)

4/52 * 4/51 = 4/663

= 0.0060332

Rounding to 3 decimal places = 0.006

Answer:

  9. (x, y) = (6√3, 3)

  10. (x, y) = (14, 14√2)

  11. (x, y) = (2√6, 3√2)

  12. (x, y) = (6, 2)

Step-by-step explanation:

Because you have memorized a short table of trig functions, you know that the ratio of side lengths of a 30°-60°-90° triangle is 1 : √3 : 2, and the ratio of side lengths of a 45°-45°-90° triangle is 1 : 1 : √2.

In each case, we compare the given side ratios to the known ratios for the kind of triangle we have. Then we multiply the triangle ratios by a scale factor that makes the given number match the corresponding ratio value. Matching the other ratio values, we can determine the values of the variables.

__

9. Using the side ratios for the 30-60-90 triangle, you have

  6 : x : y+9 = 1 : √3 : 2

Multiplied by 6, the ratios on the right are ...

  6 : x : y+9 = 6 : 6√3 : 12

  x = 6√3

  y +9 = 12

  y = 3

__

10. Using the side ratios for the 45-45-90 triangle:

  14 : x : y = 1 : 1 : √2

Multiplying the ratios on the right by 14, we have ...

  14 : x : y = 14 : 14 : 14√2

  x = 14

  y = 14√2

__

11. Again using the 30-60-90 ratios:

  √6 : y : x = 1 : √3 : 2

Multiplying the ratios on the right by √6, we have ...

  √6 : y : x = √6 : 3√2 : 2√6

  y = 3√2

  x = 2√6

__

12. Again, using the 45-45-90 ratios:

  x : 3y : 6√2 = 1 : 1 : √2

Multiplying the ratios on the right by 6, we have ...

  x : 3y : 6√2 = 6 : 6 : 6√2

  x = 6

  3y = 6

  y = 2

Answer: she used 6.525 pints of white paint.

Step-by-step explanation:

Kelly uses 8.7 paints of blue paint and white paint to paint her bedroom walls. If 1/4 of this amount is blue paint, it means that the amount of blue paint that she used in painting her bedroom walls is

1/4 × 8.7 = 2.175 pints of blue paint.

Since the rest of the paint is white, it means that the pints of white paint that she used to paint her bedroom walls is

8.7 - 2.175 = 6.525 pints of white paint

Answer:

she uses 6.525 pints of paint

Step-by-step explanation:

Answer:

164 pounds

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

y=\frac{1}{8}x+4

Step-by-step explanation:

first, we can quickly get rid of options 1 and 2, since the y-intercept is not -4, but +4.

this leaves us with options 3 and 4.

we can rule out option3, since the slope is not 4, but 1/8.

hope this helps :)

This is a very simple and easy problem. I'm not sure why you need someone else to solve it, but I hope this helps

a. Linear equation:

Let x be amount of movies rented

$8 + ($2.50 * x)

b.

$8 + ($2.50 * 10)

= $8 + $25.0

= $33

The solution to the equation x + 3 = -(x + 1) is x = -2, which is not listed among the provided options. There may be an error in the question or provided options.

To find the value of x that satisfies the equation x + 3 = -(x + 1), we need to solve for x.

First, expand the right side of the equation: x + 3 = -x - 1. Then, add x to both sides of the equation to get 2x + 3 = -1. Finally, subtract 3 from both sides to obtain 2x = -4. Dividing both sides by 2 yields x = -2.

Upon examining the options provided, none of them match our solution. Therefore, there must be a mistake in the provided options or in the question as posed, because our correct solution is x = -2. This means the correct answer is not listed among the options a. x = 8, b. x = 8/3, c. x = -8/3, or d. x = -8.

Answer:

[tex]vXw =-36i+33j+26k[/tex]

Step-by-step explanation:

v = 3i + 8j – 6k

w = –4i – 2j – 3k

The cross product

[tex]v X w=\left|\begin{array}{ccc}i&j&k\\3&8&-6\\-4&-2&-3\end{array}\right|[/tex]

[tex]=i\left|\begin{array}{cc}8&-6\\-2&-3\end{array}\right|-j\left|\begin{array}{cc}3&-6\\-4&-3\end{array}\right|+k\left|\begin{array}{cc}3&8\\-4&-2\end{array}\right|\\[/tex]

[tex]=i(-24-12)-j(-9-24)+k(-6+32)\\vXw =-36i+33j+26k[/tex]

Answer:

B

Step-by-step explanation:

I think this is your full question and hope it is correct.

Which system of equations could be graphed to solve the equation below?

log(2x+1)=3x-2

A. y1=3x, y2=2x

B. y1=log(2x+1), y2=3x-2

C. y1=log2x+1, y2=3x-2

D. y1=log(2x+1+2), y2=3x

My answer:

We know that: log(2x+1)=3x-2  and they are a equation of log and linear so we need to make system of equation.

The left side is: [tex]y_{1}[/tex] => [tex]y_{1} = log( 2x+1)[/tex]

The right side is : [tex]y_{2} = 3x -2[/tex]

The system of equations are:

[tex]\left \{ {{y_{1} =log(3x+1)} \atop {y_{2} =3x -2}} \right.[/tex]

Now we have two new function with x and y.

Answer:

The range of values for the sample mean is between a lower limit of 19 and an upper limit of 21.

Step-by-step explanation:

sample mean = 20

sd = 10

n = 25

standard error = 1

Lower limit of sample mean = sample mean - standard error = 20 - 1 = 19

Upper limit of sample mean = sample mean + standard error = 20 + 1 = 21

The range of values for the sample mean is between 19 and 21.

Answer:

a) P ( E | F ) = 0.54545

b) P ( E | F' ) = 0

Step-by-step explanation:

Given:

- 4 Coins are tossed

- Event E exactly 2 coins shows tail

- Event F at-least two coins show tail

Find:

- Find P ( E |  F )

- Find P ( E | F prime )

Solution:

- The probability of head H and tail T = 0.5, and all events are independent

So,

                    P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT)  = 6*(1/2)^4 = 0.375

                    P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)

      = 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875

- The probabilities for each events are:

                    P ( E ) = 0.375

                    P ( F ) = 0.6875

- The Probability to get exactly two tails given that at-least 2 tails were achieved:

                    P ( E | F ) = P ( E & F ) / P ( F )

                    P ( E | F ) = 0.375 / 0.6875

                    P ( E | F ) = 0.54545

- The Probability to get exactly two tails given that less than 2 tails were achieved:

                    P ( E | F' ) = P ( E & F' ) / P ( F )

                    P ( E | F' ) = 0 / 0.6875

                    P ( E | F' ) = 0                

The probability of drawing two chips of different colors from the bag is 35/33.

The probability of drawing the chips:

Calculate the total number of ways to draw 2 chips: 12 chips total, so 12C2 = 66 ways.

Calculate the number of ways to draw 2 chips of different colors: (5 blue chips × 7 non-blue chips) + (7 non-blue chips × 5 blue chips) = 70 ways.

Probability = Number of favorable outcomes / Total outcomes = 70/66 = 35/33.

the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]

To find the probability that the two selected chips are of different colors, we can use the concept of complementary probability.

The complementary event of selecting two chips of different colors is selecting two chips of the same color.

Let's calculate the probability of selecting two chips of the same color and then subtract that from 1 to find the probability of selecting two chips of different colors.

1. Probability of selecting two blue chips:

[tex]\[ P(\text{blue, blue}) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144} \][/tex]

2. Probability of selecting two red chips:

[tex]\[ P(\text{red, red}) = \frac{4}{12} \times \frac{4}{12} = \frac{16}{144} \][/tex]

3. Probability of selecting two yellow chips:

[tex]\[ P(\text{yellow, yellow}) = \frac{3}{12} \times \frac{3}{12} = \frac{9}{144} \][/tex]

Now, let's add these probabilities together because any of these scenarios results in two chips of the same color:

[tex]\[ P(\text{same color}) = P(\text{blue, blue}) + P(\text{red, red}) + P(\text{yellow, yellow}) \]\[ P(\text{same color}) = \frac{25}{144} + \frac{16}{144} + \frac{9}{144} = \frac{50}{144} \][/tex]

Finally, we subtract this probability from 1 to find the probability of selecting two chips of different colors:

[tex]\[ P(\text{different colors}) = 1 - P(\text{same color}) \]\[ P(\text{different colors}) = 1 - \frac{50}{144} = \frac{144}{144} - \frac{50}{144} = \frac{94}{144} \][/tex]

So, the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]

Answer:

All numbers greater than or equal to -3.

Step-by-step explanation:

Just took the edge test.

Answer:

yeah. its d

Step-by-step explanation:

edge test 2020

The inequality is:

[tex]n > \frac{m}{4}[/tex]

Membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount

Solution:

Given that,

A pool charges $4 each visit or you can buy a membership

Let "n" be the number of times you visit the pool

Let the membership amount of the pool be "m"

A pool charges $4 each visit

Therefore, cost for "n" visit is: $ 4n

The inequality showing that a membership is less expensive than paying each visit to the pool is:

4n > m

Divide both sides by "4"

[tex]n > \frac{m}{4}[/tex]

Therefore, membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount

Answer:

[tex]TA=(144+36\sqrt{3})\ units^2[/tex]

Step-by-step explanation:

we know that

The total area or surface area of the regular pyramid is equal to the area of the triangular base plus the area of its three lateral triangular faces

so

step 1

Find the area of the triangular base B

Is an equilateral triangle

Applying the law of sines

[tex]B=\frac{1}{2}(12^2)sin(60^o)[/tex]

[tex]B=\frac{1}{2}(144)\frac{\sqrt{3}}{2}[/tex]

[tex]B=36\sqrt{3}\ units^2[/tex]

step 2

Find the area of the lateral triangular faces

[tex]A=3[\frac{1}{2}(12)h][/tex]

Find the height

Applying the Pythagorean Theorem

[tex]10^2=6^2+h^2[/tex]

[tex]h^2=100-36\\h^2=64\\h=8\ units[/tex]

Find the area of the lateral triangular faces

[tex]A=3[\frac{1}{2}(12)8]=144\ units^2[/tex]

therefore

The total area is

[tex]TA=(144+36\sqrt{3})\ units^2[/tex]

Assuming it is .005y^2 + 10y not .005*y*2 + 10y

Profit = Revenue - Cost

Profit = (.005y^2 + 10y) - (20y + 1,000,000)

Profit at 30,000 cars so y = 30000

Profit = (.005(30000)^2 + 10(30000)) - (20(30000) + 1,000,000)

Profit = $3,200,000

Answer: The account balance will be $6596 after 7 years.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $4500

r = 5.5% = 5.5/100 = 0.055

n = 4 because it was compounded 4 times in a year.

t = 7 years

Therefore,.

A = 4500(1 + 0.055/4)^4 × 7

A = 4500(1 + 0.01375)^28

A = 4500(1.01375)^28

A = $6596

The horizontal distance the plane has covered is 3940 feet

Explanation:

The plane makes an angle 10° with the ground when it took off from the field.

We need to find the horizontal distance the plane when it has flown 4000 feet.

The length of the hypotenuse is 4000 feet.

Let the horizontal distance be x.

We shall find the value of x using the cosine formula.

The formula is given by

[tex]cos \theta=\frac{adj}{hyp}[/tex]

Substituting the values, we have,

[tex]cos \ 10^{\circ}=\frac{x}{4000}[/tex]

Substituting the value for cos 10°, we get,

[tex]0.985=\frac{x}{4000}[/tex]

Multiplying both sides of the equation by 4000, we get,

[tex]0.985\times 4000=x[/tex]

Simplifying, we get,

[tex]3940=x[/tex]

Thus, the horizontal distance the plane has covered is 3940 feet

Answer:

Step-by-step explanation:

The coefficient of determination = [tex]r^{2}[/tex] = [tex]0.885^{2}[/tex] = 0.7832

It means about 78% variation in waist size of males can be explained by their weight and about 23% can not be explained.

Answer:

It is  [tex]11\frac{9}{10}[/tex]  miles far from Chester to Durbin.

Step-by-step explanation:

Given:

Its 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via barton and Chester, is 35 miles.

Now, to find the distance from Chester to durbin.

Distance from Alston to Barton = [tex]10\frac{3}{5} =\frac{53}{5} \ miles.[/tex]

Distance from Barton to Chester = [tex]12\frac{1}{2}\ miles =\frac{25}{2} \ miles.[/tex]

As, given the distance from Alston to Durbin, via barton and Chester, is 35 miles.

Thus, the total distance = 35 miles.

So, we add the distance of Alston to Barton and Barton to Chester and get the distance from Alston to Chester:

[tex]\frac{53}{5} +\frac{25}{2}[/tex]

[tex]=\frac{106+125}{10}[/tex]

[tex]=\frac{231}{10} \ miles.[/tex]

Distance from Alston to Chester  [tex]=\frac{231}{10} \ miles.[/tex]

Now, to get the distance from Chester to durbin we subtract distance from Alston to Chester from the total distance:

[tex]35-\frac{231}{10} \\\\=\frac{350-231}{10} \\\\=\frac{119}{10} \\\\=11\frac{9}{10}\ miles.[/tex]

Therefore, it is  [tex]11\frac{9}{10}[/tex]  miles far from Chester to Durbin.

Answer: 2.1 feet

Step-by-step explanation:

The ladder forms a right angle triangle with the wall and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the wall represents the opposite side of the right angle triangle.

The distance, d from the bottom of the ladder to the base of the wall represents the adjacent side of the right angle triangle.

To determine the distance, d from the bottom of the ladder to the base of the wall, we would apply we would apply the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 65 = d/5

d = 5Cos 65 = 5 × 0.4226

d = 2.1 feet

Answer:

The answer to your question is 2² 3² or (4)(9)

Step-by-step explanation:

Data

factor 36

Process

1.- Divide 36 by prime numbers starting from 2, then 3, 5, 7, etc.

                          36  2

                           18  2

                            9   3

                            3   3

                             1

2.- Write 36 as a composition of prime numbers

                         36 = 2²3²

3.- The prime factors of 36 are 2² x 3²

Answer:

[tex]\text{Area of margin}=145\text{ cm}^2[/tex]

Step-by-step explanation:

We have been given that a painting is drawn on a cardboard 22 cm long and 12 cm wide such that there is a margin of 2.5 meter cm along each side. We are asked to find the area of the margin.

The total area of the margin would be equal to area of whole cardboard minus area of painting.

[tex]\text{Area of whole cardboard}=22\text{ cm}\times 12\text{ cm}[/tex]

[tex]\text{Area of whole cardboard}=264\text{ cm}^2[/tex]

Since there is a margin of 2.5 meter cm along each side, so sides of painting would be 2,5 cm smaller on four sides. The sides painting would be [tex]22-5=17[/tex] and [tex]12-5=7[/tex].

[tex]\text{Area of painting}=17\text{ cm}\times 7\text{ cm}[/tex]

[tex]\text{Area of painting}=119\text{ cm}^2[/tex]

[tex]\text{Area of margin}=264\text{ cm}^2-119\text{ cm}^2[/tex]

[tex]\text{Area of margin}=145\text{ cm}^2[/tex]

Therefore, the total area of the margin is 145 squared cm.

We are given a velocity equation, and from that, we want to find the initial velocity such that we know the velocity for a given time.

We will see that the initial velocity is 124 ft/s

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

Let's see how to solve this:

We have that the velocity equation:

v(t) = v₀ - (32 ft/s^2)*t

Where I added the units of the gravitational acceleration, which are in ft over seconds squared.

We want to get the value of the initial velocity, v₀, given that after 3 seconds the velocity is 28ft/s.

This means that:

v(3s) = 28 ft/s = v₀ - (32 ft/s^2)*3s

We can solve this for v₀:

28 ft/s = v₀ - (32 ft/s^2)*3s

28 ft/s + (32 ft/s^2)*3s = v₀

124 ft/s = v₀

So we can see that the initial velocity is 124 ft/s

If you want to learn more, you can read:

https://brainly.com/question/9163788

Answer:

56

Step-by-step explanation:

8C3 = 56

Answer:

15 feet

Step-by-step explanation:

525 = ½(30+40)h

525 = 35h

h = 525/35

h = 15 feet

Answer:

  -5

Step-by-step explanation:

The power rule can be used.

  f(x) = 5x^-1

  f'(x) = 5(-1)x^(-1-1)

  f'(x) = -5x^-2

Then ...

  f'(-1) = -5(-1)^-2

  f'(-1) = -5

_____

The attached graph shows the value of the derivative at x=-1, along with a tangent line having that slope at the point (-1, f(-1)).