6. Add
2р + 6q
4р — 8q​

Answer:

Ok, the probability of winning is:

For the first draw, we have 13 diamonds in a 52 card deck, the probability of drawing a diamond is:

p1 = 13/52

for the second draw we have 12 diamonds and 51 cards in the deck, now the probability is:

p2 = 12/51

the total probability is equal to the product of the individual probabilities, this is:

P = p1*p2= (13/52)*(12/51) = 0.059

now, the expected value can be calculated as follows.

EV = (P1*X1 + P2*X2)

where P1 is the probabilty of event 1, and X1 is the event 1,

In this case X1 is the event of winning $29, then P1 = 0.059

X2 will be the event of loosing $4, so P2 = 1 - 0.059 = 0.941

Then the expected value for 1 round of the game is:

EV = (0.059*$29 - 0.941*$4) = -$2.05

So if you play 891 times, expected value of 891 times the expected value for 1 round, this is:

891*EV = 891*(-$2.05) = -$1826.55

So you loss around  $1826.55

There are 48 different possible outcomes.

The total number of possible outcomes in a scenario like this is determined by finding the product of the number of possible outcomes for each individual event.

Independent events are events that are not affected by each other and have no influence on each other's outcome. The probability of two independent events occurring together is the product of their individual probabilities.

When flipping a coin, there are 2 possible outcomes (heads or tails).

When rolling a fair die with 4 sides, there are 4 possible outcomes (1, 2, 3, or 4).

When rolling a fair die with 6 sides, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6).

To find the total number of possible outcomes, we multiply the number of outcomes for each event:

2 * 4 * 6 = 48

Therefore, there are 48 different possible outcomes.

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Answer:

3

Step-by-step explanation:

Answer:

15x-18

Step-by-step explanation:

Distribute-

24x-18-9x

Combine like terms

15x-18

Step-by-step explanation:

(x+7)²=8

(x)² +2(x)(7)+(7)²=8

x²+14x+49=8

x²+14x+49-8=0

x²+14x+41=0

The experimental probability that fewer than two of the next three spins land on reward A is 1/6

Here is the fundamental probability formula: The number of possible outcomes divided by the number of ways an event could occur is the probability of that item happening. Let's examine how to get the data you require and determine the probability of an event.

In theory, there is a 25% chance that the spinner will land on reward A.

\(P(A) =\frac{The Number Of Ways Event A Can Occur}{The total number Of Possible Outcomes}\)

\(P(A)=\frac{1}{6}\)

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

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Approximately 0.0668 or 6.68% of people have a score above 50 in the given normal distribution.

To compute the z-score, we can use the formula:

z = (X - μ) / σ

Where:

X = observed value

μ = mean of the distribution

σ = standard deviation of the distribution

Given:

X = 60

μ = 10

σ = 30

Substituting these values into the formula:

z = (60 - 10) / 30

z = 50 / 30

z = 1.667 (rounded to three decimal places)

Therefore, the z-score is approximately 1.667.

Moving on to the second question, we need to find the proportion of people with a score above 50 in a normal distribution with a mean of -30 and a standard deviation of 15.

To calculate this proportion, we can use a standard normal distribution table or a statistical calculator. From the standard normal distribution table, we can find the area to the left of 50, which is 0.9332 (rounded to four decimal places).

Since we want the proportion above 50, we subtract this value from 1:

Proportion = 1 - 0.9332 = 0.0668 (rounded to four decimal places)

Therefore, approximately 0.0668 or 6.68% of people have a score above 50 in the given normal distribution.

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Answer:

x= 8.2

Step-by-step explanation:

first we need to find the hypotenuse of the smaller triangle

3² + 4² = C

9 + 16 = 25

√25 = 5

now that we found the hypotenuse of the smaller triangle then we now find the hypotenuse of the larger one (x)

6.5² + 5² = C

42.25 + 25 = 67.25

√67.25 = 8.2

Answer: At the Month May Jordan as able to get enough money to buy the phone.

Work:

December:$5

January:$10

February:$20

March:$40

April:$80

May:$160 <--Answer

____________________________________________________________In the problem Jordan saves $5 at December, then at January Jordan saved $10 which is twice as December's saved money amount. February, Jordan saved $20, which is twice as January's saved money amount. March is $40, which is twice as February's saved money amount. For April it is $80, which is twice as March's money amount, May is $160 which is twice as April's money amount. Or another way to say this is by starting at $5. Then, keep multiplying by 2 for each month until you get $150 or more. When you do, stop at the month that gets you $150 or more. When i did this exact method, I got $160 on the Month of May. $160 is more than enough for Jordan to buy his phone. So the month May is the correct answer where Jordan can get enough money for his phone.

Answer: The fifth month; By April Jordan would have saved more than enough to buy a new phone.

Step-by-step explanation:

Dec $5

Jan $10

Feb $20

Mar $40

Apr $80

Dec + Jan = $15($5+$10)

Dec+ Jan + feb = $35($5+$10+$20=$35)

Dec+ Jan + feb + mar = $75 ($5+$10+$20+$40=$75)

Dec+ Jan + feb + mar + apr = $155

($5+$10+$20+$40+$80=$155)

Answer:

1024

Step-by-step explanation:

Answer:

1024

Step-by-step explanation:

9514 1404 393

Answer:

  C.

Step-by-step explanation:

The transformation ...

  g(x) = f(ax)

represents a horizontal compression of the graph by a factor of 'a'. Here, the original function graph is compressed by a factor of 3 horizontally, so the curve will look a lot narrower.

The appropriate choice is C.

The numbers that are in the range of the function are 130, 140, 160 and 180.

Since the function is C(x)  = 100 + 5x and the domain or input are 6, 8, 12 and 16, the numbers that are in the range of the functions are numbers we get when the input the individual values of x into the function.

So, when x = 6, C(6) = 100 + 5(6) = 100 + 30 = 130

when x = 8, C(6) = 100 + 5(8) = 100 + 40 = 140

when x = 12, C(6) = 100 + 5(12) = 100 + 60 = 160

when x = 16, C(16) = 100 + 5(16) = 100 + 80 = 180

So, the numbers that are in the range of the function are 130, 140, 160 and 180.

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Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?

Step-by-step explanation:

Answer:

Distributive Property

Step-by-step explanation:

This person, in the previous step distributed the 2 to 3x and -4 to get 6x-8.

Answer: the answer is 21

Step-by-step explanation:

If one angle measures 170°, and another angle measures (6k + 44)° and both are vertical angles that means the second angle should be the same as the first angle.

Vertical angles are congruent meaning they have an equal measure.

Now we have to find k

(6k + 44) = 170

subtract 44 - 44 and 170 - 44

(6k) = 126

divide 6 by 6, that leaves with just k on the left.

126 divided by 6  equals to 21

k = 21

Hope this helps!

According to the given question we have functions g(f(0)) = 11.Thus, g(f(0)) = g(1) = 1² + 4(1) + 6 = 11.

The given functions f(x) = √3x +1 and g(x) = x² + 4x + 6 are two different functions.

The problem requires us to find g(f(0)), which means finding g of the value of f of 0.

So, let's start with the calculation of f(0)

then we will move forward with the calculation of g(f(0)).For f(x) = √3x +1,

we are asked to find f(0) which is as follows: f(0) = √3(0) + 1 = 1

Thus, we have obtained f(0) = 1.

Now,

we need to find g(f(0)) by plugging f(0) = 1 into g(x) = x² + 4x + 6.g(f(0)) =

g(1) = 1² + 4(1) + 6g(f(0)) = g(1) = 1 + 4 + 6g(f(0)) = g(1) = 11

Therefore, g(f(0)) = 11.Thus, g(f(0)) = g(1) = 1² + 4(1) + 6 = 11.

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1.The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

We are given that the base diameter is 20cm, so the radius is half of that, which is 10cm.

Therefore, the volume of the cylinder is:

V = πr^2h

V = π(10cm)^2(5cm)

V = π(100cm^2)(5cm)

V = 500π cm^3

Hence, the volume of the cylinder is 500π cubic centimeters.

2.We are given that the height of the cylinder is 22 1/4 and the diameter is 2 2/5 times its height. First, we need to find the radius of the base.

The diameter of the base is 2 2/5 times the height, so we can write:

d = (12/5)h

Substituting in the given value of h, we get:

d = (12/5)(22 1/4) = 54.4 cm

Therefore, the radius of the base is:

r = d/2 = 27.2 cm

Now, we can use the formula for the volume of a cylinder:

V = πr^2h

Substituting in the values of r and h, we get:

V = π(27.2cm)^2(22 1/4 cm)

V ≈ 50,873.36 cm^3

Rounding to the nearest hundredth, we get:

V ≈ 50,873.36 cm^3 ≈ 50,873.35 cm^3

Hence, the volume of the cylinder is approximately 50,873.35 cubic centimeters.

Answer:

When it is perpendicular to the ground.

Step-by-step explanation:

Answer:

\(\frac{a}{25}\) That is the answer if you're finding the exact form...

Step-by-step explanation:

Simplify the expression

Answer:

the ratio would be 2:10 or 1:5 (simplified)

Answer:

36

Step-by-step explanation:

16 + 9 = 25

so you multiply both by 4 you have a total of 100

so 9 × 4 = 36%

a) The Probability density function of given uniform distribution example is

F(x) = 1/3.5 for 8.5 < x< 12

Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where

x ---> minimum value and y---> maximum value

Probability density function is a probability function which defines the density of continuous random variable lying between specified range

values. It is denoted by f( a<X<b)

Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.

We have following informations,

weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.

Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.

this implies a = 8.5 , b = 12

F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12

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#Complete Qestion :

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?

We have shown that f(x) = sin x is (a) strictly increasing in (0, 2π ​) (b) strictly decreasing in (2π, π) (c) neither increasing nor decreasing in (0,π).

The function f(x) = sin x is given, and we need to show that it is (a) strictly increasing in (0, 2 π ​) (b) strictly decreasing in ( 2 π ​ ,π) (c) neither increasing nor decreasing in (0,π).

Now let's find the derivative of f(x) = sin x, which is: f′(x) = cos x

Now, we know that f(x) = sin x is increasing if its derivative is positive.

Similarly, f(x) = sin x is decreasing if its derivative is negative and constant if its derivative is zero.

Let's use this to solve the given problem.

(a) To show that f(x) = sin x is strictly increasing in (0, 2π ​ ), we need to show that f′(x) > 0 for x ∈ (0, 2π ​ ).

We know that the cosine function is positive in (0, π/2) and negative in (π/2, π) and so on.

Therefore, cos x > 0 in (0, π/2) and (3π/2, 2π)

Hence, f′(x) > 0 in (0, π/2) and (3π/2, 2π).

(b) To show that f(x) = sin x is strictly decreasing in (2π, π), we need to show that f′(x) < 0 for x ∈ (π, 2π).

We know that the cosine function is negative in (π, 3π/2) and positive in (3π/2, 2π).

Therefore, cos x < 0 in (π, 3π/2) and (2π, 5π/2).

Hence, f′(x) < 0 in (π, 3π/2) and (2π, 5π/2).

(c) Finally, we need to show that f(x) = sin x is neither increasing nor decreasing in (0,π).

This is because f′(x) = cos x changes sign at x = π/2.

Hence, f(x) = sin x is neither increasing nor decreasing in (0,π).

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Answer:

18x + 15

Step-by-step explanation:

First, deal with the first part of the question:

5(4x+3)

We multiply the outside of the brackets with the inside. So, we do

5 x 4x = 20x

and 5 x 3 = 15

then put them together:

20x+15

Now, the second part:

- 2x

We cannot simplify this further so we put the two parts together:

20x + 15 - 2x

Collect like terms (20x - 2x) =

18x + 15

I hope this helped. If you have any further questions, do ask.

- profparis

Answer: 26, 21, 16, 11, 6, 1 (You're going up by 5 each time)

Step-by-step explanation: Good luck! :D

The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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An inverse relationship can not direct.

We know that an inverse proportion represents inverse or indirect relation between two quantities.

In inverse relationship, one value increases while the other value decreases, and vice versa.

But in case of direct relationship, if one quantity increases , the other quantity also increases, and  if one quantity decreases , the other quantity also decreases.

When two quantities 'm' and 'n' are inversely proportional to each other, it means when the value of m increases while the value of quantity  'n' decreases, and vice versa.

Also, an inverse relationship always has a negative slope.

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