Question 2: Let X and Y be continuous RVs with normal distributions, X-N(3,4), Y~N(-4,9) and Z = 4 - 3X - 2Y a) Find P(Z > 2) b) Find P(3 > Z > 1) his c) Find P(Z > 31Y 5)

Answer:

- 6 vertical, -3 horizontal

Answer:

t = ±2.179

Step-by-step explanation:

Given:

Regression equation = Y = 30 + 2.56X

Sample size, n = 14

Standard error, e = 0.97

Significance level, \( \alpha \) = 0.05

Required:

Find the critical value

At level of significance = 0.05

Degrees of freedom, df = n - 2 = 14 - 2= 12

Find critical value:

Using t table, two tailed, df = 12, we have:

\( t_\alpha_/_2_, _d_f = t_0_._0_2_5_,_1_3 = 2.179 \)

Therefore, the critical value,

t-critical = ±2.179

In this exercise we will use the knowledge of degrees of freedom and the data reported in the exercise to calculate the critical temperature of the system, so:

\(t-critical = +/- 2.179\)

Given in the exercise we have to:

in this exercise we want to find the critical value in this way, we will have that it will be:

Using t table, two tailed, df = 12, we have:

\(T_{\alpha /2} , df = t_{0.025,13)= 2.179\)

Therefore, the critical value corresponde to;

\(t-critical = +/- 2.179\)

See more about critical temperature at brainly.com/question/14562729

Answer:

the correct answer is 257

A. Substract the price of 3lb to the price of 5lb

B. Same procedure, this time substract the price of 5lb to the price of 7lb

C. To find the rate of change divide the difference between the price of 5lb and 7lb by 2lb.

The unit rate is $3.99 per pound of candy.

D. According to the picture, Oscar was correct.

Answer:

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

This seating creates a triangle, in which means we should use pythagoras theorem to solve it. Because 15 and 8 are both legs we need to square 15 and 8 and add them. After that we need to take the square root of it.

Steps:

15^2 + 8^2 = 289

sqrt289 = 17

Answer:

for -9x+2>18 its x<-16/9 and for 13x+15≤-4 its x<-19/13

Step-by-step explanation:

The final conclusion is limit of the sequence as n approaches infinity is 2.

In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity.

To determine the limit of the sequence defined by an = 2 − (0.2)n as n approaches infinity, we can substitute infinity for n in the expression. Doing so gives us:

lim n→[infinity] an = lim n→[infinity] (2 − (0.2)n) = 2 − lim n→[infinity] (0.2)n

Since 0.2 is between -1 and 1, we know that as n approaches infinity, (0.2)n approaches 0. Therefore, we have:

lim n→[infinity] an = 2 − lim n→[infinity] (0.2)n = 2 - 0 = 2

So the limit of the sequence as n approaches infinity is 2.

To learn more about limits, visit https://brainly.in/question/54160812

#SPJ11

Answer:

There are two correct answers for this question depending on how you think of it.

3x or -3

Step-by-step explanation:

3x could be right because the rest of them are negative. But also on the other case -3 because the rest have x's and this one doesn't

Hope this helps :)

If im too late im so sorry...

Have a nice day!

Answer:

3(5+x)

Step-by-step explanation:

15+3x

5*3 + 3*x

Factor out 3

3(5+x)

The surface area of a square pyramid is 2619 m².

The surface area of a square pyramid given by the formula:

A = a² + 2al

where,

a = base length of square pyramid

l = slant height or height of each side face

We have:

a = 27 m

l = 35 m

A = a² + 2al

A =  27² + (2*27*35)

A = 729 + 1890

A = 2619 m²

Learn more about square pyramid on:

https://brainly.com/question/22744289

#SPJ1

Answer:

C = 4d+5c+6a

Step-by-step explanation:

This is quite simple, for you have 3 different items. To find the cost of it, you simply give each type of mix a variable and put their costs as the value before the variable. This equation would come out to be:

C = 4d+5c+6a

The value of the triple integral is -16.

Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.

The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:

∭E f(x, y, z) dV

We can set up the triple integral as follows:

∫∫∫ 16y dV

Where the limits of integration are:

0 ≤ x ≤ 2

0 ≤ y ≤ (2- \(x^2\)z)/(2y)

0 ≤ z ≤ 2/\(x^{2y\)

Note that the upper bound of integration for y is not a constant, but depends on both x and z.

Integrating with respect to y first, we get:

∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)

= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)

= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz

= ∫\(0^2 (32/x^2 - 16z)\) dz

= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz

= 16 - 16(2)

= -16

Therefore, the value of the triple integral is -16.

To learn more about triple integral  visit:https://brainly.com/question/30404807

#SPJ11

Answer:

81.25

Step-by-step explanation:

Because you want to know the total distance, calculate how many digits -49.75 is away from 0. It is 49.75 digits away from 0.

Now calculate how many digits 31.5 is away from 0. It is 31.5 digits away from 0.

Finally, add those two distances together so that you know the total distance:

49.75+31.5 = 81.25

Answer:

in the picture

HOPE ITS HELP

The beam is made of four planks with widths of d = 125 mm and h = 270 mm. The load on the beam is w = 6 kN/m and P = 12 kN, with a = 5 m and b = 3 m.The distance x from the left end of the beam to the point of maximum bending can be determined using the formula below.

Let the bending moment at the point of maximum bending be Mmax.

Mmax = P(a-b) + w((a^2)/2 - ab).

First, calculate the maximum bending moment:

Mmax = 12(5-3) + 6((5^2)/2 - 5*3) = 3 kN.m.

Now we can calculate the distance x from the left end of the beam to the point of maximum bending.

x = (Mmax * (h/2)) / (w * d^2) = (3 * 0.135) / (6 * (0.125^2)) = 3.24 m

In this case, the beam is made of four planks with widths of d = 125 mm and h = 270 mm. The load on the beam is w = 6 kN/m and P = 12 kN, with a = 5 m and b = 3 m. The maximum bending moment can be found using the formula

Mmax = P(a-b) + w((a^2)/2 - ab).

When we plug in the values for P, w, a, and b,

we get

Mmax = 12(5-3) + 6((5^2)/2 - 5*3) = 3 kN.m.

The distance x from the left end of the beam to the point of maximum bending can be determined using the formula

x = (Mmax * (h/2)) / (w * d^2).

Plugging in the values for Mmax, h, w, and d, we get x = (3 * 0.135) / (6 * (0.125^2)) = 3.24 m.

Therefore, the distance from the left end of the beam to the point of maximum bending is 3.24 m.

To know more about maximum bending :

brainly.com/question/30902819

#SPJ11

If the probability of obtaining a score less than x = 70 is p = 0.0013, the score that corresponds to a probability of 0.0013 is x = 38.2.

We are referring to a normal distribution with a mean (µ) of 100 and a standard deviation (σ) of 20. You want to find the probability of obtaining a score less than x = 70, and you provided that the probability (p) is 0.0013. In a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score less than x = 70 is p = 0.0013. Based on the information given, we know that the probability of obtaining a score less than x = 70 is p = 0.0013. This means that the z-score for x = 70 is -3.09 (found using a standard normal distribution table or calculator).

To find the z-score, we use the formula:

z = (x - µ) / σ

Plugging in the values we know:

-3.09 = (70 - 100) / 20

Solving for x:

-3.09 = (x - 100) / 20

-3.09 * 20 = x - 100

-61.8 + 100 = x

x = 38.2

Therefore, the score that corresponds to a probability of 0.0013 is x = 38.2.

More on probability: https://brainly.com/question/30255967

#SPJ11

The  |120-x| simplifies to 120-x when x is less than 120.

S If x is less than 120, then the expression |120-x| simplifies to 120-x. This is because the absolute value bars mean that the result must be positive,

so if x is already less than 120, then subtracting x from 120 will give a positive result.

For example, if x is 115, then |120-x| would equal |120-115|, which simplifies to |5|, which equals 5.  

To learn more about : simplifies

https://brainly.com/question/723406

#SPJ11

Answer:

this involves dividing numbers by making use of their place values or value

Step-by-step explanation:

hope this is helpful

Given an arithmetic sequence like the one in the question with "a" being the 1st term and "d" being the common difference, the equation to find the nth term of the sequence can be written thus;

In the question, we've also been asked to find the 24th term of the sequence.

To do that, we need to substitute the values of the variables a, n and d into the above equation.

From the sequence -4, -9, -14, -19, the 1st term(a) is -4, the common difference is -5 and n = 24.

Let's substitute and find the 24th term of the sequence;

Therefore, the 24th term of the sequence is -119.

The direct materials quantity variance is \(\$89,600\) unfavorable.

To calculate the direct materials quantity variance, we need to compare the actual quantity of materials used to the standard quantity allowed for the production of \(5,500\)  units.

The standard quantity of materials for \(5,500\) units can be calculated as:

Standard quantity = \(7\) pounds/unit × \(5,500\) units = \(38,500\) pounds

The actual quantity of materials used was 37,100 pounds.

The direct materials quantity variance can be calculated as:

Quantity variance = (Standard quantity - Actual quantity) × Standard price per pound

\(Quantity variance = (38,500 pounds - 37,100 pounds) * $64/pound\)

\(Quantity variance = 1,400 pounds * \$64/pound\)

\(Quantity variance = \$89,600 unfavorable\)

Therefore, the direct materials quantity variance is \(\$89,600\) unfavorable.

Learn more about variance

https://brainly.com/question/14116780

#SPJ11

If national savings is less than domestic investment, it means that the country is spending more than it is saving. This can result in a deficit in the current account balance.


1. National savings refers to the total amount of money that a country saves, which includes savings by households, businesses, and the government.
2. Domestic investment refers to the total amount of money that is being invested within the country, such as in infrastructure, businesses, and capital goods.
3. If national savings is less than domestic investment, it means that the country is not saving enough to cover its investment needs.
4. This situation can lead to a deficit in the current account balance, which is the difference between a country's exports and imports of goods and services, as well as other income and transfers.
5. When national savings is less than domestic investment, the country may have to rely on foreign sources of funds to finance its investment needs, which can result in a current account deficit.

6. A current account deficit means that the country is importing more than it is exporting and is relying on external financing to cover the gap.
7. A current account deficit can have both positive and negative implications. On the positive side, it can attract foreign investment and help finance economic growth. However, it can also make the country vulnerable to external shocks and lead to an increase in external debt.
8. To address a situation where national savings is less than domestic investment, the country can take measures to encourage saving, such as through tax incentives or promoting a culture of saving. Additionally, policies can be implemented to attract domestic and foreign investment to bridge the investment gap.

To know more about economic growth refer to:

https://brainly.com/question/30849181

#SPJ11

After graphing the equations, we found that the solution of the given pair of equations is (2,5).

What is meant by an equation?

A formula called an equation uses the equals symbol (=) to denote the equality of two expressions. An equal sign ("=") links two expressions together to form an equation. The two expressions on either side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero. As we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

The complete question is given below.

The equations are:

y = 7x - 9

y = 3x - 1

A) y = 7x - 9

 Slope = 7

 y - intercept = (0,-9)

  y = 3x - 1

slope = 3

y - intercept = (0,-1)

Now we can graph these equations.

B) The solution of this pair of equations is the point where both the lines intersect. This can be seen in the graph below.

The intersecting point is (2,5).

Therefore after graphing the equations, we found that the solution of the given pair of equations is (2,5).

To learn more about the equation, follow the link.

brainly.com/question/22688504

#SPJ1

the equations that can be used to find the lengths of the sides of the triangle are:

0.5(x)(x + 2) = 24

x(x + 2) = 24

x2 + 2x – 24 = 0

The area of a right triangle is the amount of space contained within the triangle's boundaries. It is equal to one-half of the product of the lengths of the triangle's two legs.

More specifically, if a right triangle has legs of lengths a and b, and a hypotenuse of length c, then its area A is given by:

A = (1/2) × a × b

Substituting the given values, we get:

1/2 (a)(b) = 24

Simplifying, we get:

a×b = 48

Now, we can use the given answer options to see which ones can be used to find the lengths of the legs of the triangle:

0.5(x)(x + 2) = 24: This equation can be used to find the lengths of the legs by solving for x and x + 2, and then plugging these values into the expression for the legs.

x(x + 2) = 24: This equation is equivalent to the first equation, so it can also be used to find the lengths of the legs.

x² + 2x – 24 = 0: This equation can be used to find the values of x and x + 2, which can then be used to find the lengths of the legs using the expression for the legs.

x² + (x + 2)² = 100: This equation does not directly relate to the area of the triangle or the lengths of its legs, so it cannot be used to find the lengths of the legs.

Therefore, the equations that can be used to find the lengths of the legs of the triangle are:

0.5(x)(x + 2) = 24

x(x + 2) = 24

x²+ 2x – 24 = 0

To know more about area, visit:

https://brainly.com/question/27683633

#SPJ1

Answer:

supplement angle : 107

complement angle : 17

Step-by-step explanation:

supplement :

180 - 73 = 107

complement :

90 - 73 = 17

A system of linear equations are 0.08x - 0.01y = 9, 0.005x + 0.01y = -3.

To determine the values of x and y at which the profit function r(x, y) is maximized, we can take the derivative of the profit function with respect to x and y, set them equal to zero, and solve the resulting system of equations. This will give us the critical points where the profit is maximized.

The profit function is given as r(x, y) = 9x + 6y - 0.04x² + 0.01xy - 0.01y² - 500.

Taking the partial derivative with respect to x:

∂r/∂x = 9 - 0.08x + 0.01y

Setting this derivative equal to zero:

9 - 0.08x + 0.01y = 0

Simplifying the equation:

0.08x - 0.01y = 9

Taking the partial derivative with respect to y:

∂r/∂y = 6 + 0.01x - 0.02y

Setting this derivative equal to zero:

6 + 0.01x - 0.02y = 0

Simplifying the equation:

0.02y = 0.01x + 6

0.01y = 0.005x + 3

Combining the two equations, we have a system of linear equations:

0.08x - 0.01y = 9

0.005x + 0.01y = -3

Solving this system of equations, we find the values of x and y that maximize the profit function r(x, y).

Learn more about linear equations here

https://brainly.com/question/14323743

#SPJ11