Solve for b.
2²376.
b+5=20-b
b=

Answer:

\(x=10\,\,\,\text{and}\,\,\,x=-2\)

Step-by-step explanation:

\(|x-4|=6\\\\x-4=6\,\,\,\text{and}\,\,\,x-4=-6\\\\x=10\,\,\,\text{and}\,\,\,x=-2\)

Make sure to always create two equations when solving an absolute value equation!

(a) The marginal distributions of X and Y are:

P(X = 0) = 0.5, P(X = 1) = 0.4

P(Y = 0) = 0.4, P(Y = 1) = 0.3, P(Y = 2) = 0.15, P(Y = 3) = 0.15

(b) The expected values of X and Y are:

E[X] = 1, E[Y] = 0.9

(c) The variances of X and Y are:

Var(X) = 0.24, Var(Y) = 1.44

(d) The covariance of X and Y is:

Cov(X, Y) = 0.1

(e) The correlation between X and Y is:

Corr(X, Y) = 0.1701

For the joint probability density function f(x, y) = 1 / (10x) where 0 ≤ x ≤ 10 and 0 ≤ y ≤ x:

Cov(X, Y) = 5/2

Corr(X, Y) = (15√76) / 152

(a) To find the marginal distributions of X and Y, we sum the probabilities over the other variable.

Marginal distribution of X:

P(X = 0) = P(X = 0, Y = 0) + P(X = 0, Y = 1) + P(X = 0, Y = 2) + P(X = 0, Y = 3)

= 0.2 + 0.2 + 0.05 + 0.05 = 0.5

P(X = 1) = P(X = 1, Y = 0) + P(X = 1, Y = 1) + P(X = 1, Y = 2) + P(X = 1, Y = 3)

= 0.2 + 0.1 + 0.1= 0.4

Marginal distribution of Y:

P(Y = 0) = P(X = 0, Y = 0) + P(X = 1, Y = 0)

= 0.2 + 0.2 = 0.4

P(Y = 1) = P(X = 0, Y = 1) + P(X = 1, Y = 1)

= 0.2 + 0.1 = 0.3

P(Y = 2) = P(X = 1, Y = 2) + P(X = 0, Y = 2)

= 0.1 + 0.05 = 0.15

P(Y = 3) = P(X = 1, Y = 3) + P(X = 0, Y = 3)

= 0.1 + 0.05 = 0.15

(b) To find E[X] and E[Y], we multiply each value of X and Y by its respective probability and sum them.

E[X] = 0 × P(X = 0) + 1 × P(X = 1)

= 0 × 0.5 + 1 × 0.4 = 0.4

E[Y] = 0 × P(Y = 0) + 1 × P(Y = 1) + 2 × P(Y = 2) + 3 × P(Y = 3)

= 0.3 + 0.3 + 0.3

= 0.9

(c) To find Var(X) and Var(Y), we need to calculate the expected values of X² and Y².

E[X²] = (0² × P(X = 0)) + (1² × P(X = 1))

= 0 + 0.4

= 0.4

E[Y²] = (0²× P(Y = 0)) + (1² × P(Y = 1)) + (2² × P(Y = 2)) + (3² × P(Y = 3))

= 0 + 0.3 + 0.6 + 1.35

= 2.25

Var(X) = E[X²] - (E[X])²

= 0.4 - 0.16

= 0.24

Var(Y) = E[Y²] - (E[Y])²

= 1.44

(d) To find Cov(X, Y), we need to calculate the expected value of X × Y.

Cov(X, Y) = (0× 0 × P(X = 0, Y = 0)) + (0 × 1 × P(X = 0, Y = 1)) + (1×0 × P(X = 1, Y = 0)) + (1 × 1 × P(X = 1, Y = 1))

= 0 × 0× 0.2 + 0 × 1 × 0.2 + 1 × 0× 0.2 + 1 ×1 × 0.1

= 0.1

(e) The correlation between X and Y, denoted by ρ(X, Y), can be calculated using the formula:

ρ(X, Y) = Cov(X, Y) / √(Var(X) × Var(Y))

Substituting the values:

ρ(X, Y) = 0.1 / √(0.24×1.44)

= 0.1 / √(0.3456)

= 0.1 / 0.5879

= 0.1701

Therefore, the correlation between X and Y is approximately 0.1701.

2. Let the joint probability density function of (X, Y) be given by:

f(x, y) = 1 / (10x)

0 ≤ x ≤ 10 and 0 ≤ y ≤ x

To find Cov(X, Y) and Corr(X, Y), we need to calculate the expected values of X, Y, X², Y², and XY.

E[X] = ∫(0 to 10) ∫(0 to x) x × (1 / (10x)) dy dx

= ∫(0 to 10) (1/10) dx

= 1

E[Y] = ∫(0 to 10) ∫(0 to x) y × (1 / (10x)) dy dx

= ∫(0 to 10) (y/10x) × [y] (0 to x) dx

= (1/20) × [(100)/2]

= 5/2

E[X²] = ∫(0 to 10) ∫(0 to x) (x²) × (1 / (10x)) dy dx

= ∫(0 to 10) (x/10) dx

= 5

E[Y²] = ∫(0 to 10) ∫(0 to x) (y²)×(1 / (10x)) dy dx

= ∫(0 to 10) (y²/10x) × [y] (0 to x) dx

= ∫(0 to 10) (1/10x) × [y³/3] (0 to x) dx

= 100/9

E[XY] = ∫(0 to 10) ∫(0 to x) (xy)×(1 / (10x)) dy dx

= ∫(0 to 10) (y/10) dx

= 5

Cov(X, Y) = E[XY] - E[X] × E[Y]

= 5 - 1 × (5/2)

= 5 - 5/2 = 5/2

Corr(X, Y) = Cov(X, Y) / √(Var(X) × Var(Y))

Var(X) = E[X²] - (E[X])^2

= 5 - 1²

= 4

Var(Y) = E[Y²] - (E[Y])²

= 100/9 - (5/2)²

= 19/9

Corr(X, Y) = (5/2) / √(4 × 19/9)

= (5/2) / √(76/9)

= (15√76) / 152

Therefore, Cov(X, Y) is 5/2 and Corr(X, Y) is (15√76) / 152.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ4

Answer:

x=5/3

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+4x=10

Step 1: Simplify both sides of the equation.

2x+4x=10

(2x+4x)=10(Combine Like Terms)

6x=10

6x=10

Step 2: Divide both sides by 6.

6x /6 = 10 /6

x= 5 /3

Answer:

5/3 or 1.6 repeated

Step-by-step explanation:

Hope this helps :-)

Multiply the roots of the first and third terms together. Compare to the middle terms with the result in step two. If the first and last terms are perfect squares, and the middle term's coefficient is twice the product of the square roots of the first and last terms, then the expression is a perfect square trinomial.

Answer:

The highest common factor of 10 and 18 is 2

Step-by-step explanation:

10:  1,10,2,5

18: 1,18,2,9,3,6,

Look which is common in both of these and both of them have 2 in common.

The HCF of 10 and 18 is 2.

To find the highest common factor (HCF) of 10 and 18, we can determine the largest number that divides evenly into both of them.

We can start by listing the factors of each number:

Factors of 10: 1, 2, 5, 10

Factors of 18: 1, 2, 3, 6, 9, 18

From the lists, we can see that the common factors of 10 and 18 are 1 and 2.

To find the HCF, we select the largest common factor, which is 2. Therefore, the HCF of 10 and 18 is 2.

The HCF represents the largest number that divides evenly into both given numbers, without leaving any remainder. In this case, 2 is the highest common factor, as it is the largest number that can divide both 10 and 18 without leaving any remainder.

To learn more about the greatest common factor;

https://brainly.com/question/11221202

#SPJ6

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

You can learn more about optimal mix at: brainly.com/question/30629565

#SPJ11

Answer:

the inclination of the line will decrease

Step-by-step explanation:

If Cassandra changes the amount she deposits from 18 to 14, the slope changes to 14. So the new equation is M=14n + 224. The 224 is still the same, because that is the initial amount, and the new situation hasn't said anything about changing that, so it will not have any vertical translations. With that being said, as a result the slope will be less, so you can see it as "less vertical", so the inclination of the line will decrease

The variance of the sample means that is found in the sample distribution that we have here is 0.3333

This is the measure of dispersion that is used to show the spread of the data that is contained in a data set

The formula that we are to use here is given as

b² - a² / b - a

we have to put the values in this question

(14 - 2)² / 14 - 2

= 144 / 12

= 12

From here we would have to solve for the variance.

The variance = 12 / 35

= 0.3333

Hence the variance that we have in the question is equal to 0.3333

Read more on variance here: https://brainly.com/question/25639778

#SPJ1

Answer:

Cost of jellybeans = x = $3.5

Cost of trail mix = y = $2

Step-by-step explanation:

Let

Cost of jellybeans = x

Cost of trail mix = y

8x + 3y = 34 (1)

2x + 5y = 17 (2)

Multiply (1) by 5 and (2) by 3

40x + 15y = 170 (3)

6x + 15y = 51 (4)

Subtract (4) from (3)

40x - 6x = 170 - 51

34x = 119

x = 119/34

x = 3.5

Substitute x = 3.5 into (1)

8x + 3y = 34

8(3.5) + 3y = 34

28 + 3y = 34

3y = 34 - 28

3y = 6

y = 6/3

y = 2

Cost of jellybeans = x = $3.5

Cost of trail mix = y = $2

Answer: false

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

\(17 + x =21\)

Subtract 17 on both sides

\(x = 4\)

Using statistical concepts, it is found that as the degrees of freedom increase, the t distribution approaches the z-distribution.

For large sample sizes, that is, a large number of degrees of freedom in the t-distribution, the t distribution approaches the z-distribution.

More can be learned about the t-distribution at https://brainly.com/question/16162795

#SPJ1

Answer:

70%

Step-by-step explanation:

28/40 = 14/20 = 7/10 = 0.7 = 70%

Answer:

70%

Step-by-step explanation:

100% A+  

Ri   |Wr

ght|ong

39 1 97.5% A+

38 2 95% A

37 3 92.5% A-

36 4 90% A-

35 5 87.5% B+

34 6 85% B

33 7 82.5% B-

32 8 80% B-

31 9 77.5% C+

30 10 75% C

29 11 72.5% C-

28 12 70% C-

27 13 67.5% D+

26 14 65% D

25 15 62.5% D-

24 16 60% D-

23 17 57.5% F

22 18 55% F

21 19 52.5% F

20 20 50% F

19 21 47.5% F

18 22 45% F

17 23 42.5% F

16 24 40% F

15 25 37.5% F

14 26 35% F

13 27 32.5% F

12 28 30% F

11 29 27.5% F

10 30 25% F

9 31 22.5% F

8 32 20% F

7 33 17.5% F

6 34 15% F

5 35 12.5% F

4 36 10% F

3 37 7.5% F

2 38 5% F

1 39 2.5% F

0 40 0% F

the answer is v= -5x + 1136

Answer:

$2.040

Step-by-step explanation:

Para calcular la cantidad que fue abonada en realidad, debes encontrar el valor del descuento calculando el 15% del valor total de la compra y este resultado se debe restar del total:

$2.400*15%= $360

$2.400-$360= $2.040

De acuerdo a esto, la cantidad abonada en realidad es: $2.040.

Answer:

A) The estimated solution of differential equation at t=2 using Euler's method with h=0.2 is y(2) ≈ 3.4085

B) t2 = 0.2, y2 = y1 + h * f(t1, y1) = 1 + 0.1 * (0.2 * 1) = 1.02

Step-by-step explanation:

A) Using Euler's method with h=0.2, we have:

t0 = 0, y0 = 1

t1 = 0.2, y1 = y0 + h * f(t0, y0) = 1 + 0.2 * (0 * 1) = 1

t2 = 0.4, y2 = y1 + h * f(t1, y1) = 1 + 0.2 * (0.2 * 1) = 1.04

t3 = 0.6, y3 = y2 + h * f(t2, y2) = 1.04 + 0.2 * (0.6 * 1.04) = 1.1264

t4 = 0.8, y4 = y3 + h * f(t3, y3) = 1.1264 + 0.2 * (0.8 * 1.1264) = 1.2541

t5 = 1.0, y5 = y4 + h * f(t4, y4) = 1.2541 + 0.2 * (1.0 * 1.2541) = 1.4293

t6 = 1.2, y6 = y5 + h * f(t5, y5) = 1.4293 + 0.2 * (1.2 * 1.4293) = 1.6597

t7 = 1.4, y7 = y6 + h * f(t6, y6) = 1.6597 + 0.2 * (1.4 * 1.6597) = 1.9569

t8 = 1.6, y8 = y7 + h * f(t7, y7) = 1.9569 + 0.2 * (1.6 * 1.9569) = 2.3351

t9 = 1.8, y9 = y8 + h * f(t8, y8) = 2.3351 + 0.2 * (1.8 * 2.3351) = 2.8112

t10 = 2.0, y10 = y9 + h * f(t9, y9) = 2.8112 + 0.2 * (2.0 * 2.8112) = 3.4085

Therefore, the estimated solution at t=2 using Euler's method with h=0.2 is y(2) ≈ 3.4085.

B) Using Euler's method with h=0.1, we have:

t0 = 0, y0 = 1

t1 = 0.1, y1 = y0 + h * f(t0, y0) = 1 + 0.1 * (0 * 1) = 1

t2 = 0.2, y2 = y1 + h * f(t1, y1) = 1 + 0.1 * (0.2 * 1) = 1.02

t3 = 0.3, y3 = y2 + h * f(t2, y2) = 1.02 + 0.1 * (0.3 * 1.02) = 1.0506

t4 = 0.4, y4 = y3 + h * f(t3, y3) = 1.0506 +

To know more about differential equation refer here

https://brainly.com/question/31583235#

#SPJ11

If A is true, B is false, C is true and D is false, then the truth value of the compound statement (A V B) → [(C ∨ B) ↔~D] is True.

To determine the truth value of the compound statement, follow these steps:

So, the truth value of the compound statement (A V B) → [(C ∨ B) ↔ ~D] when A is true, B is false, C is true, and D is false is True.

Learn more about compound statement:

brainly.com/question/28556870

#SPJ11

Statistical procedures that summarize and describe a series of observations are called descriptive statistics.

Descriptive statistics involve various techniques and measures that aim to summarize and describe the key features of a dataset. These procedures include measures of central tendency, such as the mean, median, and mode, which provide information about the typical or average value of the data. Measures of dispersion, such as the range, variance, and standard deviation, quantify the spread or variability of the data points.
In addition to these measures, descriptive statistics also involve graphical representations, such as histograms, box plots, and scatter plots, which provide visual summaries of the data distribution and relationships between variables. These graphical tools help in identifying patterns, outliers, and the overall shape of the data.
Descriptive statistics play a crucial role in providing a concise summary of the data, enabling researchers and analysts to gain insights, make comparisons, and draw conclusions. They form the foundation for further statistical analysis and inferential techniques, which involve making inferences about a population based on a sample.

Learn more about central tendency here:

https://brainly.com/question/12701821

#SPJ11

Answer:

36 times larger.

Step-by-step explanation:

V= \(\pi *r^{2}*\frac{h}{3}\) is the original volume of a cone formula.

If the radius is multiplied by 6 the new formula is:

V= \(\pi *(6x)^{2} * \frac{4}{3}\)

Which is simplified to:

V= \(\pi *36r^2*\frac{h}{3}\)

The only difference between the simplified formula and the original is the *36 so the new volume is 36 times larger when the radius is multiplied by 6.

say we're going to add "x" gallons of water, now how many gallons of alcohol is in pure water? well 0%, and 0% of "x" is (0/100) * x = 0.

the 3 gallons we know are 100% alcohol, how many gallons of alcohol is in it?  well (100/100) * 3 = 3.

the resulting mix will have x + 3 gallons total and it's going to be 15% alcohol, how many gallons of alcohol is that? (15/100) * (x+3).

now, the amount of alcohol never increased, so the original 3 gallons of only alcohol will remain even after the water has been added, so.

\(\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{pure water}&x&0.00&0\\ \textit{pure alcohol}&3&1.00&3\\ \cline{2-4}&\\ mixture&x+3&0.15&0.15(x+3) \end{array} \begin{array}{llll} \\[3em] \leftarrow \textit{this amount}\\\\ \leftarrow \textit{must be equal to this one} \end{array} \\\\\\ 3 = 0.15(x+3)\implies 3=0.15x+0.45\implies 2.55=0.15x \\\\\\ \cfrac{2.55}{0.15}=x\implies 17=x\)

Answer: 641.56

Step-by-step explanation:

14.92x 38

566.96

14.92x 5

74.6

566.96+74.6= 641.56

Answer: the height of the tree is 27 feet

Step-by-step explanation: We can set up a proportion comparing the height of each object to the length of the shadow.

h s

h 15 = 18

       10

Cross multiply

10 ⋅ h = 18 ⋅ 15

10 h = 270

Use the multiplicative Inverse

10

h

10

=

270

10

h = 27

The probability that the player has all 8 of the number selected by the lottery commission is approximately 1.3 × 10^-9.

There are a total of 40 numbers that can be chosen for the lottery. Out of those 40 numbers, a player must select 8 numbers. The lottery commission will also randomly select 8 numbers from those 40. If a player has all 8 of the numbers selected by the lottery commission, then they will win. The number of ways to choose 8 correct numbers is simply 1, since there is only one set of 8 numbers that the player can choose that matches the 8 numbers selected by the lottery commission.

The number of ways to choose any 8 numbers from 40 is given by the combination formula:

P = (40! / (8! (40 - 8)!) = 769,046,685

Therefore, the probability that the player has all 8 numbers selected by the lottery commission is:

P(all 8 numbers are correct) = 1 / 769,046,685 = 1.3 × 10^-9 (approximately).

To learn more about probability visit : https://brainly.com/question/13604758

#SPJ11

Answer:

Bro just complete your project. That's just plagiarism.

Step-by-step explanation:

Sorry but the teacher WILL notice.

Answer:

C (50, - 40 )

Step-by-step explanation:

C is the midpoint of AB

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

here (x₁, y₁ ) = A (0, - 80 ) and (x₂, y₂ ) = B (100, 0 ) , then

C = ( \(\frac{0+100}{2}\) , \(\frac{-80+0}{2}\) ) = ( \(\frac{100}{2}\) , \(\frac{-80}{2}\) ) = (50, - 40 )

Answer:

Step-by-step explanation:

2+4

X +4

B.

2 4

3 х

WIN WIN

C.

3.2

3x

D.

2 6

3 x

Answer:

First, I would find the unit rate for   people 240 5

people who bike 48 1 . Next, I would

find the number of people who like to bicycle in a group of 360 people and

assume that only people that like to bicycle would own a mountain bike:

5 360 = = 72

1

x

x , . Finally, I would write the ratio 7 mountain bikes = 18 bicyclists= bicyclists 72

x

and

solve for x to see that there should be 28 mountain bikes.

Step-by-step explanation:

Answer:

20% of 25 is greater

Step-by-step explanation:

25% of 16 = 4

20% of 25 = 5

Answer:

20% of 25

Step-by-step explanation:

To find 25% of 16, we have to consider how much 25% is out of 100%

25/100 can be simplified to 1/4

So 1/4 of 16 (or 16/4) = 4

To find 20% of 25, we have to consider how much 20% is out of 100%

20/100 can be simplified to 1/5

So 1/5 of 25 (or 25/5) = 5

4 < 5

Therefore, 20% of 25 is greater than 25% of 16

a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1