2 ( 15 marks) An urn contains seven black balls and five white balls. Three balls are randomly awn from the urn without replacement and let X denote the number of black balls drawn. Then e three balls are put back to the urn. Next, four balls are randomly drawn from the urn without placement and let Y denote the number of black balls drawn. Let A=X+Y and B=X−Y . a. Find Cov(A,B) . b. Find Var(A+B) . c. Are A and B independent? Why?

Answer:

3/5 - 13/5 => -6.9 + 4.9

2x - 3 => x - 3 + x

5/3 - x + 1/3 => -3/2x + 2 + 1/2x

2x - 6 => -6 + 2x

3x + 0 => 3x

Step-by-step explanation:

Hope it helps :)

Answer: 4

Step-by-step explanation:

Answer: About 75 years

Step-by-step explanation:

2.5x30=75

The volume of the prism is  222. 4 m³

The formula for calculating the volume of a pentagonal prism is expressed as;

V = [1/2 x 5 x b x a] x h of the prism

Given that the parameters are;

Now, substitute the values, we get;

Volume , = ( 1/2 × 5 × 4.6 × 3.17) × 6.1

Multiply the values

Volume , V = (72.91/2) × 6.1

divide the values in the bracket

Volume = 36. 46 × 6.1

Multiply the values

Volume = 222. 4 m³

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(a) Prοbability οf at least 3 peοple believe that they have seen a UFO 0.857.

(b) Prοbability οf 3 οr 4 peοple believe that they have seen a UFO 0.181.

(c) Prοbability οf Exactly 4 peοple believe that they have seen a UFO 0.00049 (rοunded tο 3 decimal places).

Prοbability is a branch οf mathematics that deals with the study οf randοmness and uncertainty in events. It is the measure οf the likelihοοd οr chance that an event will οccur. Prοbability is expressed as a number between 0 and 1, where 0 indicates that the event will nοt οccur and 1 indicates that the event will οccur with certainty.

This is a binοmial prοbability prοblem, where the prοbability οf success (p) is 0.1 and the sample size (n) is 15.

(a) At least 3 peοple believe that they have seen a UFO:

Using the cοmplement rule, the prοbability οf having less than 3 peοple whο believe they have seen a UFO is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = (0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³

where X is the number οf peοple whο believe they have seen a UFO in the sample. Therefοre, the prοbability οf having at least 3 peοple whο believe they have seen a UFO is:

P(X ≥ 3) = 1 - P(X < 3) = 1 - [(0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³] = 0.170

Sο the prοbability οf at least 3 peοple believing they have seen a UFO is 0.170.

(b) 3 οr 4 peοple believe that they have seen a UFO:

Using the binοmial prοbability fοrmula, we can calculate the prοbabilities fοr 3 and 4 peοple believing they have seen a UFO and then add them tοgether:

P(X = 3) = (15 chοοse 3)(0.1)³(0.9)¹² = 0.185

P(X = 4) = (15 chοοse 4)(0.1)⁴f(0.9)¹¹ = 0.099

Therefοre, the prοbability οf having 3 οr 4 peοple whο believe they have seen a UFO is:

P(3 οr 4) = P(X = 3) + P(X = 4) = 0.185 + 0.099 = 0.284

Sο the prοbability οf 3 οr 4 peοple believing they have seen a UFO is 0.284.

(c) Exactly 4 peοple believe that they have seen a UFO:

Using the binοmial prοbability fοrmula, we can calculate the prοbability fοr 4 peοple believing they have seen a UFO:

P(X = 4) = (15 chοοse 4)(0.1)⁴ (0.9)¹¹ = 0.099

Sο the prοbability οf exactly 4 peοple believing they have seen a UFO is 0.099.

Hence,

(a) P(X ≥ 3) = 0.857

(b) P(3 ≤ X ≤ 4) = 0.181

(c) P(X = 4) = 0.00049 (rοunded tο 3 decimal places)

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a) The theoretical probability of a fair coin landing on heads is 1/2

b) The experimental probability of landing on heads is 40%. Note that the experimental probability is lower than the theoretical probability.

Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. Thus, it is possible for either of the teams to get the ball first.

Part B: The frequency of each outcome after flipping the coin 10 times may vary, but for example:

Heads: 4

Tails: 6

The experimental probability of landing on heads can be calculated by dividing the frequency of heads by the total number of flips: 4/10 = 0.4 or 40%.

Comparing the experimental probability of 0.4 to the theoretical probability of 0.5, we can see that the experimental probability is lower than the theoretical probability.

This difference may be due to random chance or factors such as the way the coin is flipped, the surface it lands on, or the wind. As more flips are made, the experimental probability should approach the theoretical probability.

Note that Theoretical probability is the likelihood of an event occurring based on reasoning or calculation, without actually performing the event.

Experimental probability is the probability of an event occurring based on actual repeated trials or experiments. It is determined by dividing the frequency of the event by the total number of trials.

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The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.

The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x

R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.

r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill.

we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease.

The slope of the regression line gives us the rate of change of the dependent variable y (i.e. the monthly utility bill) with respect to a unit change in the independent variable x (i.e. the size of the house).The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.

The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x

The coefficient of determination (R²) is a measure of the proportion of variation in the dependent variable that is explained by the independent variable. It is calculated as the` of the explained variation to the total variation.R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.

The coefficient of correlation (r) is a measure of the strength and direction of the linear relationship between the two variables. It can take values between -1 and +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill. This indicates that as the size of the house increases, the monthly utility bill decreases.

Based on the information provided, we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease. However, we should keep in mind that correlation does not imply causation, and there may be other factors that affect the monthly utility bill besides the size of the house.

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The probability that Harry, Jason, and Sarah will all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)

The solution to the question is given below; The mean score of the GMAT exam is μ = 550 and the standard deviation is σ = 115.There are three friends - Harry, Jason, and Sarah - who want to be admitted to business schools. Harry requires a score of 650 or above, while Jason requires a score of 630 or higher and Sarah requires a score of 670 or above. Because the admission procedure is independent for each of the friends, the joint probability can be calculated using the multiplication rule.

The probabilities that Harry, Jason, and Sarah will achieve the desired scores are calculated separately using the z-score equation, which is as follows;For Harry:Z = (650 - 550) / 115 = 0.87 Probability of Harry getting admitted = P(z > 0.87) = 0.1949 (using z-table)For Jason:Z = (630 - 550) / 115 = 0.7 Probability of Jason getting admitted = P(z > 0.7) = 0.2413 (using z-table)For Sarah:Z = (670 - 550) / 115 = 1.04 Probability of Sarah getting admitted = P(z > 1.04) = 0.1492 (using z-table)The probability that Harry, Jason, and Sarah will all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)

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In response to the question, we may say that  As a result, the angle of trigonometry inclination of the ramp is 4 degrees, to the closest degree.

The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. Consequently, studying geometry entails learning about the characteristics of all geometric forms.

The ratio of an angle's opposing side (such as the rise of a ramp) to its adjacent side is known as the tangent (the length of the ramp).

Angle's tangent is equal to its opposite and adjacent sides.

In this instance, the ramp's opposite side represents its 3/4-foot rise, and the ramp's adjacent side is its 12-foot length.

Angle's tangent is equal to 3/4 / 12 (or 0.0625).

We may take the inverse tangent (or arctangent) of this number to determine the angle itself.

Amount = arctan (0.0625)

Calculating the answer, we obtain:

Angle is 3.58 9 degrees.

When we convert this to degrees, we get:

a 4 degree angle

As a result, the angle of inclination of the ramp is 4 degrees, to the closest degree.

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The difference quotient for f(x)=x is (x+h-x)/h, which simplifies to 1/h. The average rate of change of f(x)=x on the interval (1,3) is 1/2, since h=2.

The difference quotient for f(x)=x can be found by taking the difference between f(x+h) and f(x) and then dividing by h. In this case, f(x+h) = x + h and f(x) = x, so the difference quotient is (x+h-x)/h, which simplifies to 1/h. To calculate the average rate of change of f(x)=x on the interval (1,3), we need to plug in the values of h and x. Here, x is the first endpoint of the interval, which is 1, and h is the length of the interval, which is 2. Thus, the average rate of change is 1/2.

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Answer:

I believe the answer is D

Step-by-step explanation:

if you want an explanation let me know and have a great day and I'm 100% sure that D is the right answer

Answer:

1. rhombus and square

2. rhombus, rectangle, square

3. rectangle and square

4. rectangle, squares, rhombus

5. same as 3

6. rhombus, rectangle, square

7. rhomus, rectangle, square

8. rectangle, square

Step-by-step explanation:

Answer:

1

explanation in head

42

Step-by-step explanation:

42-7=69z3

Answer: To find out how long after the rocket is launched will it be 10 feet from the ground, we need to solve for t in the equation:

h = -16t^2 + 150t + 40

We know that when the rocket is 10 feet from the ground, h = 10:

10 = -16t^2 + 150t + 40

Subtracting 10 from both sides:

0 = -16t^2 + 150t + 30

Dividing both sides by -2:

0 = 8t^2 - 75t - 15

Using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 8, b = -75, and c = -15.

Plugging in these values:

t = (-(-75) ± sqrt((-75)^2 - 4(8)(-15))) / 2(8)

Simplifying:

t = (75 ± sqrt(5715)) / 16

Therefore, the rocket will be 10 feet from the ground approximately 0.26 seconds and 8.05 seconds after it is launched.

Your welcome (:

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

In this you have to use means and extremes method, when you multiply 72 and 16 you’ll get 1152. Then divide it with 64, you’ll get 18.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{Original equation/problem }\\\\\large\boxed{\mathsf{72:64}}\\\\\large\textsf{Both numbers (72 \& 64) are factors of 4, so we will DIVIDE them by 4}\\\\\large\boxed{\mathsf{\rightarrow 72\div4: 64\div4}}\\\\\large\textsf{Which results in}\downarrow\\\\\large\boxed{\mathsf{\rightarrow 18:16}}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{\bold{18}:16}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

We can conclude that 5/8 is between the benchmark fractions 1/2 and 3/4.

A fraction represents a part of a whole or a ratio between two quantities. It consists of a numerator (the top number) and a denominator (the bottom number), separated by a horizontal line. The numerator represents the part or quantity being considered, while the denominator represents the whole or total quantity.

To determine between which two benchmark fractions 5/8 lies, we can compare it to the nearest benchmark fractions, which are 1/2 and 3/4.

To summarize, 1/2 < 5/8 < 3/4.

For example, the fraction 3/4 represents three parts out of a total of four parts, or a ratio of three to four. This can also be expressed as a decimal (0.75) or a percentage (75%).

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The 25 percent of 401.16m is equal to 100.29m, rounded to 2 decimal places as 100.30m.

To calculate 25% of 401.16m, we can use the formula:

percentage × value = result

where the percentage is 25%, the value is 401.16m, and the result is what we want to find.

So, we can write:

25% × 401.16m = (25/100) × 401.16m = 0.25 × 401.16m = 100.29m

Therefore, 25% of 401.16m is equal to 100.29m.

To round this to 2 decimal places, we need to look at the third decimal place, which is 9. Since 9 is greater than or equal to 5, we round up the second decimal place, which is 0. Therefore, the final answer rounded to 2 decimal places is:

100.29m rounded to 2 decimal places is 100.30m.

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After answering the given query, we can state that The light's limits are equation therefore represented by the equations y = (3/4)x and y = -(3/4)x.

A mathematical statement known as an equation demonstrates the equality of two expressions when they are joined by the equals symbol ('='). As an illustration, 2x - 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' joins the two phrases together. An equation is a mathematical formula with two algebraic expressions on either side of the equal symbol (=). It shows how the left and right formulas have an equivalent connection. In any formula, L.H.S. equals R.H.S. (left side = right side).

We must rewrite the provided equation in terms of y in order to ascertain the equation denoting the boundaries of the light.

Starting with the expression provided:

[tex]9x^2 - 16y^2 + 576 = 0\\-16y^2 + 576 = -9x^2\\y^2 - 36 = (9/16)x^2[/tex]

When both edges are squared:

y = ±(3/4)x

The light's limits are therefore represented by the equations y = (3/4)x and y = -(3/4)x.

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Answer:

Step-by-step explanation:

Let's break down the information provided in the problem:

The man spends 2/3 of his high salary on rent and food.

This means that he has 1/3 of his salary remaining.

He then spends 1/4 of this remaining amount on transportation.

He has 6000 rupees left.

To solve for the amount he pays on transportation, we can use the following steps:

Calculate the amount of money he has left after spending 2/3 of his salary on rent and food:

Remaining amount = (1/3) * high salary

Calculate the amount he spends on transportation using the information that he spends 1/4 of the remaining amount:

Transportation cost = (1/4) * remaining amount

Substitute the value of remaining amount from step 1 into step 2:

Transportation cost = (1/4) * [(1/3) * high salary]

We are given that the man has 6000 rupees left, so we can set the equation above equal to 6000 and solve for high salary:

(1/4) * [(1/3) * high salary] = 6000

Simplifying the equation above:

(1/12) * high salary = 6000

Solving for high salary:

high salary = 6000 * 12 = 72000

Finally, substituting high salary from step 6 into step 3 to find transportation cost:

Transportation cost = (1/4) * [(1/3) * 72000] = 6000

Therefore, the man pays 6000 rupees on transportation.

The measurements for LM is 30 units and MN is 15 units.

We know that the scale factor for the dilation is 3, which means that each side of triangle RST was multiplied by 3 to create triangle LMN.

Therefore:

LM = 3(RS)

MN = 3(ST)

To find RS and ST, we can use the fact that TAN R = 5/2.5.

Recall that tangent is the ratio of the opposite side to the adjacent side of a right triangle, so we can set up the following equation:

TAN R = RS/ST = 5/2.5

Cross-multiplying, we get:

RS = 5ST/2.5

Simplifying:

RS = 2ST

Now we can substitute this expression for RS into the equations for LM and MN:

LM = 3(RS) = 3(2ST) = 6ST

MN = 3(ST)

So the measurements for LM and MN are:

LM = 6ST

MN = 3(ST)

From triangle RST,

ST = 5

LM = 6 x 5 = 30 units

MN = 3 x 5 = 15 units

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Answer: (a) The possible outcomes and their probabilities are:

Value of x Probability

0 0.6561 (0 F's and 4 S's)

1 0.2916 (1 F and 3 S's, or 2 F's and 2 S's, or 3 F's and 1 S)

2 0.0486 (2 F's and 2 S's)

3 0.0036 (1 S and 3 F's)

4 0.0001 (4 F's and 0 S's)

(b) The most likely value of x is the one with the highest probability, which is x = 0.

(c) The probability that at least two of the four selected homeowners have earthquake insurance is equal to 1 minus the probability that 0 or 1 of them have earthquake insurance:

P(at least 2 of the 4 have earthquake insurance) = 1 - P(x = 0) - P(x = 1)

= 1 - 0.6561 - 0.2916

= 0.0523

Therefore, the probability that at least two of the four selected homeowners have earthquake insurance is 0.0523.

Enjoy!!!!!

Probability distribution of x is calculated by finding probabilities of each possible outcome, the most likely value of x is 0 with a probability of 0.6561, probability of at least two homeowners having earthquake insurance is 0.0523.

(a) The probability distribution of x can be found by calculating the probabilities of each possible outcome (0, 1, 2, 3, 4 homeowners with insurance) and associating them with their respective x values.

Value of x | Probability
--- | ---
0 | (.9)(.9)(.9)(.9) = 0.6561
1 | (.1)(.9)(.9)(.9) + (.9)(.1)(.9)(.9) + (.9)(.9)(.1)(.9) + (.9)(.9)(.9)(.1) = 0.2916
2 | (.1)(.1)(.9)(.9) + (.1)(.9)(.1)(.9) + (.1)(.9)(.9)(.1) + (.9)(.1)(.1)(.9) + (.9)(.1)(.9)(.1) + (.9)(.9)(.1)(.1) = 0.0486
3 | (.1)(.1)(.1)(.9) + (.1)(.1)(.9)(.1) + (.1)(.9)(.1)(.1) + (.9)(.1)(.1)(.1) = 0.0036
4 | (.1)(.1)(.1)(.1) = 0.0001

(b) The most likely value of x is 0, as it has the highest probability (0.6561).

(c) The probability that at least two of the four selected homeowners have earthquake insurance can be found by adding the probabilities of the outcomes with 2, 3, and 4 homeowners with insurance:

P (at least 2 of the 4 have earthquake insurance) = 0.0486 + 0.0036 + 0.0001 = 0.0523

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The correct graph of f(x) include the following: D. Graph D.

Domain format: (-∞, -2) U (2, ∞).

Range format: (1, ∞).

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. On the other hand (conversely), the range of any piecewise-defined function simply refers to the union of all of the ranges of each sub-function over its entire sub-domain.

By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce that the range and domain are as follows;

Range = (1, ∞).

Domain = (-∞, -2) U (2, ∞).

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Answer:

252 square

Step-by-step explanation:

The florist can make 23 bunches of flowers with the lilies, carnations, and roses they have for the wedding.

What is the ratio?

A ratio is a comparison of two or more quantities that indicates their relative sizes or amounts. It expresses the relationship between two or more numbers or values by dividing one by the other.

Let's start by finding out how many flowers in each bunch are lilies.

Since 60 percent of the flowers are lilies, we can calculate that 0.6 x 40 = 24 of the flowers in each bunch are lilies.

That means the remaining 16 flowers in each bunch are split between carnations and roses.

Let's use the ratio of 3:5 to split these flowers between carnations and roses.

First, we need to find the total number of parts in the ratio:

3 + 5 = 8

That means for every 8 flowers in the bunch, 3 are carnations and 5 are roses.

Now we can set up an equation to find out how many bunches of flowers the florist can make:

140 (number of carnations) ÷ 3 (number of carnations in each 8-flower group) = 46.67

So the florist can make 46 bunches of flowers with the carnations they have.

But we need to make sure that there are enough roses to go with these carnations.

If 3 of every 8 flowers in each bunch are carnations, that means 5 of every 8 flowers are roses.

So for each bunch, there are 5/8 x 16 = 10 roses.

To make 46 bunches of flowers, the florist will need 46 x 16 = 736 flowers in total.

If 24 of every 40 flowers in each bunch are lilies, that means 16 of every 40 flowers are carnations and roses combined.

So for 736 flowers, there will be 368 carnations and roses.

Since each bunch contains 16 flowers, the florist can make 368 ÷ 16 = 23 bunches of flowers with the carnations and roses they have.

Therefore, the florist can make 23 bunches of flowers for the wedding.

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The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.

There are three options available with E-Education to fulfill the company's need for additional space.

The decision tree for the available options is made below;

                                                         Option1         Option2          Option3

$ $ $

Cost of Moving to New Building                         1000000        2000000

Leasing cost                                    1000000      1300000 1500000

Total Cost of the Option             2000000 1500000          1500000

Conclusion: The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.

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Answer:

3 people are getting candy

Step-by-step explanation:

9x3

The standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.

1. 80th percentile of the amount absorbed
Given that the amount (in ng/cm²) of active ingredient in the skin two hours after application is lognormally distributed with μ = 2.6 and σ = 2.1. The 80th percentile of the amount absorbed is to be found. Let X be the random variable representing the amount of active ingredient absorbed. We know that X follows a log-normal distribution with parameters μ = 2.6 and σ = 2.1. We are to find the value x such that P(X ≤ x) = 0.8We know that for a log-normal distribution X ~ log N (μ, σ). Then we can obtain the corresponding normal distribution with mean and variance of ln(X) as follows:µ1 = ln(X) = µ, σ1^2 = ln(1 + (σ^2/µ^2)) = σ^2From the normal distribution, we can use the standard normal tables to determine the required probability. Thus Z = (ln(x) - µ)/σ and P(X ≤ x) = P(Z ≤ (ln(x) - µ)/σ) = 0.8We can use the standard normal tables to determine the z-score for P(Z ≤ z) = 0.8, which is 0.84. Then we can find ln(x) using:0.84 = (ln(x) - 2.6)/2.1 or ln(x) = 2.6 + (0.84)(2.1) = 4.374x = e^4.374 = 79.1 ng/cm²Therefore, the 80th percentile of the amount absorbed is 79.1 ng/cm² rounded to one decimal place.2. Standard deviation of the amount absorbedThe standard deviation of a lognormal distribution is given by σx = [(e^(σ^2) - 1)(e^(2μ + σ^2))]^(1/2)From the given data, we have μ = 2.6 and σ = 2.1. Therefore,σx = [(e^(2.1^2) - 1)(e^(2(2.6) + 2.1^2))]^(1/2) = 1819.9 ng/cm² rounded to one decimal place. Therefore, the standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.

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