Which of the following statemants are tue? For any discrete random variable X and oonetants a and b : A. E(aX+b)=(a+b)E(X). B. E(ax+b)=aE(X)+b. c. V(aX+b)=(a+b) 2
V(X). D. V(aX−b)=a 2
V(x)+b. 13. Consider the following information: where A={ Visa Card },B={ MasterCard },P(A)=5 , ​
P(B)=.4, and P(A∩B)=25. Calculate each of the following probabilities. a. P(B,A) b. P(B∣A) c. P(A∣B) d. P(A ′
∣B) e. Given that an imdividual is selected at random and that he or she has at least one card, what is the probability that he or she has a Visa card

Therefore, the differential of y = x² sin 2x is dy/dx = 2x³ cos 2x + 2x sin 2x. Therefore, the differential of y = √(4+ 5x) is dy/dx = 5/(2√(4+ 5x)).

(a) To find the differential of y = x² sin 2x, we will use the product rule of differentiation, which states that if y = f(x)g(x), then the differential dy/dx is given by:

dy/dx = f(x)g'(x) + g(x)f'(x)

where f'(x) and g'(x) represent the derivatives of f(x) and g(x) with respect to x, respectively. Applying this rule to the given function, we get:

y = x² sin 2x

f(x) = x², g(x) = sin 2x

f'(x) = 2x, g'(x) = 2 cos 2x

dy/dx = f(x)g'(x) + g(x)f'(x)

dy/dx = x²(2 cos 2x) + sin 2x(2x)

dy/dx = 2x³ cos 2x + 2x sin 2x

(b) To find the differential of y = √(4+ 5x), we will use the chain rule of differentiation, which states that if y = f(g(x)), then the differential dy/dx is given by:

dy/dx = f'(g(x))g'(x)

where f'(x) and g'(x) represent the derivatives of f(x) and g(x) with respect to x, respectively. Applying this rule to the given function, we get:

y = √(4+ 5x)

f(x) = √x, g(x) = 4+ 5x

f'(x) = 1/(2√x), g'(x) = 5

dy/dx = f'(g(x))g'(x)

dy/dx = (1/(2√(4+ 5x)))(5)

dy/dx = 5/(2√(4+ 5x))

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Yes, one pair of sides is both parallel and congruent

I think that's it

As the y-intercept increases, the graph of the line shifts up;

As the y-intercept decreases, the graph of the line shifts down

There are two perspectives on this issue. The graphical technique would be the first method.

If we merely alter the y-intercept, the slope remains unchanged;

The vertical axis is the y-axis;

A higher or lower y-intercept can be obtained by shifting the line's point of intersection with the y-axis, respectively.

Now, using algebraic reasoning, a line has the general form of the following equation:

When x = 0, the y-intercept is essentially computed as follows:

y = b:

The graph shifts up or down depending on how much we change the b value, which also affects how much the y value changes.

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Answer:

Slope= y=1/2x+6

Step-by-step explanation:

Hope it helps.

Answer:

x=145

Step-by-step explanation:

x+10+x=720-460

Answer:

125°

Step-by-step explanation:

Accumulate every detail given:

720 = 120+100+120+120+ (x+10) + x

720 = 120+100+120+120+2x+10

720=470+2x

Flip the equation to avoid negative equation

470+2x=720

2x=720

x=250/2

x=125

125 Is the final answer

Answer:

108

Step-by-step explanation:

"five times a number x, decreased by 2" can be expressed as: 5x - 2

Now,

5x - 2 = 5*22 - 2 = 110 - 2 = 108

The minimized SOP expression for F(A,B,C,D,E) using a five-variable Karnaugh map is D'E' + BCE'. A five-variable Karnaugh map is a graphical tool used to simplify Boolean expressions.

The map consists of a grid with input variables A, B, C, D, and E as the column and row headings. The cell entries in the map correspond to the output values of the logic function for the respective input combinations.

To find the minimized SOP expression, we start by marking the cells in the Karnaugh map corresponding to the minterms given in the function: 2m(4,5,6,7,9,11,13,15,16,18,27,28,31). These cells are identified by their binary representations.

Next, we look for adjacent marked cells in groups of 1s, 2s, 4s, and 8s. These groups represent terms that can be combined to form a simplified expression. In this case, we find a group of 1s in the map that corresponds to the term D'E' and a group of 2s that corresponds to the term BCE'. Combining these groups, we obtain the expression D'E' + BCE'.

The final step is to check for any remaining cells that are not covered by the combined terms. In this case, there are no remaining cells. Therefore, the minimized SOP expression for the given logic function F(A,B,C,D,E) is D'E' + BCE'.

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Answer:

Please check the attached figure!

Step-by-step explanation:

Part a)

Point A is located at the x-coordinate x=-4 and y-coordinate y=1.

Hence, the coordinates of point A = (-4, 1)

Part b)

Point B(3, -2) has been plotted and is shown in the attached figure.

It is clear from the attached diagram that point B is located at the x-coordinate x=3 and y-coordinate y=-2. Hence, the coordinates of point B = (3, -2)

Part C)

Point C has the same x-coordinate as point A i.e. x=-4 and the same y-coordinate as point B i.e. y=-2.

Hence, the coordinates of point C = (-4, -2). Point C is also plotted as shown in the diagram.

Answer: 21

Step-by-step explanation:

The measure of the tangent to the circle CD = 21

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the 2 tangents to the circle be AE and BD respectively

The measure of the line segment BD = 56

Now , the ratio of the line AE is

AC : AE = 5 : 3

The measure of AE = measure of CD

Let the value of AC = 5x

Let the value of AE = 3x

Now , the measure of AE = measure of BD

Substituting the values in the equation , we get

5x + 3x = 56   be equation (1)

On simplifying the equation , we get

8x = 56

Divide by 8 on both sides of the equation , we get

x = 7

Now , the measure of CD = 3x

Substituting the value of x in the equation , we get

CD = 3 ( 7 ) = 21

Therefore , the measure of CD = 21

Hence , the measure of CD = 21

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The null hypothesis (H0) says about the treatment is that it does not affect the scores.

Hypothesis testing is the statistical method that uses the data from a sample to conclude a population parameter or a population distribution.

There are two types of hypothesis testing. They are the null hypothesis and the alternative hypothesis.

It is given that,

A researcher selects a sample and administers a treatment to the individuals in the sample.

A hypothesis test is conducted on the sample.

So, the null hypothesis (H0) says about the treatment is that it does not affect the score obtained.

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Answer:

54

Step-by-step explanation:

Given f(x) = 6(1 - x), what is the value of f(-8)?

F(-8)=6(1--8)        -- plug -8 into f(x) and x spots.

F(-)8=6(9)      ---then solve

F(-8)=54     --- so the function to f(-8) is 54

Answer:

plot the points on the grid

Step-by-step explanation:

(-1, 1)

(0,-2)

(1,3)

(2,4)

Answer:

the output is 52 and the equation is y=5x+27

Answer:

0.487 kg

b.) the newborn weighs 0.487kg more than the weight predicted by the regression equation

Step-by-step explanation:

Given the Regression equation:

Weight = - 5.58 + 0.1686 length

Length of newborn = 48 cm

Actual Weight of newborn = 3kg

Predicted weight from regression model:

Weight = - 5.58 + 0.1686(48)

Predicted Weight = 2.513kg

Hence, residual = (Actual - predicted)

Residual = (3kg - 2.513kg) = 0.487kg

Since the actual weight is more or greater than the predicted weight:

b.) the newborn weighs 0.487kg more than the weight predicted by the regression equation

Answer:

Step-by-step explanation:

To solve, we first need to know how to find the average of a group of numbers. To find the average of a group of numbers, you add all the numbers together and divide that answer by the number of numbers you have. For instance, to find the average of 1, 2, 3, 4 and 5, we would add all the numbers together, which would equal 15. We would then divide that number by 5, because there are 5 numbers total: 15/5 = 3. So the average is 3.

Now, to find the average in your problem, we need to look at what we know:

He received an 85 and 60 on two of the test scores

He needs an overall average of 70

Let's set this up in equation form:

%2885+%2B+60+%2B+x%29%2F3+%3E=+70

Now, let's get rid of our fraction on the left. We can do this by multiplying the entire equation by 3, giving us:

85 + 60 + x >= 210

Next, combine the numbers on the left, which will give us:

145 + x >= 210

Finally, subtract 145 from both sides, which will give us our answer:

145 + x - 145 >= 210 - 145 =

x >= 65

So, in order to average at least 70, he must score a 65 or higher on his third test.

Answer:

Step-by-step explanation:

using proportion

12 : 3 = x : 4

x = 12 * 4 : 3

x = 48 : 3

x = 16

using Pythagorean theorem

√(20²-12²) =

√(400 - 144) =

√256 =

16

A simple linear regression model is appropriate when the response variable is influenced by only one explanatory variable.

A simple linear regression model assumes a linear relationship between the response variable (y) and a single explanatory variable (x).

It is suitable when we want to understand how changes in the explanatory variable affect the response variable.

In the given options, the situation where the response variable y is influenced by one explanatory variable aligns with the requirements of a simple linear regression model.

This means that the relationship between y and x can be adequately described by a straight line.

The model aims to estimate the slope and intercept of this line, allowing us to make predictions and draw conclusions about the impact of the explanatory variable on the response variable.

If the response variable y is influenced by two or more explanatory variables, a multiple linear regression model would be more appropriate.

Multiple linear regression allows for the analysis of the combined effects of multiple predictors on the response variable, accounting for their individual contributions.

Similarly, if the explanatory variable x is influenced by two or more response variables, a different modeling technique, such as multivariate regression, would be more suitable.

Therefore, the situation where the response variable y is influenced by one explanatory variable is the scenario where a simple linear regression model is appropriate.

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To construct a 4x2 matrix D such that AD=I2, we can use the following matrix: D = [0 0 1 0; 0 0 0 1]. It is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C.

Constructing a matrix D such that AD=I2

Let A = -1 be a 1x1 matrix. We want to construct a 4x2 matrix D such that their product AD is equal to the 2x2 identity matrix I2. We can use the following matrix for D:

D = [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

To verify that AD=I2, we can compute the matrix product:

AD = [-1 0 0 0; 0 -1 0 0] [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

= [0 0 -1 0; 0 0 0 -1]

= -I2

Note that D only uses 1 and 0 as entries.

Now, it is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C. To see why, we can use the definition of matrix multiplication. Let C be a general 4x2 matrix:

C = [c11 c12; c21 c22; c31 c32; c41 c42]

Then, we can compute CA as:

CA = [-1 0; 0 -1] [c11 c12; c21 c22; c31 c32; c41 c42]

= [-c11 -c12; -c21 -c22; -c31 -c32; -c41 -c42]

Since CA is a 4x2 matrix and 4 is a scalar, it is not possible for CA to be equal to 4. Similarly, since the entries of C are only 0 or 1, it is not possible for CA to be equal to 14.

Therefore, there is no matrix C that satisfies the equations CA=4 or CA=14.

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Answer:

3200/4500=71.1%

so a 29.9% drop

Hope This Helps!!!

Answer:

b^12

Step-by-step explanation:

Multiply b^10 by b^2 by adding the exponents.

b^12

Answer:

Sides: a = 9.165   b = 4   c = 10

Step-by-step explanation:

Is that check mark supposed to be square root?

Answer:

\((4^{2} +(\sqrt{84} ^{2} )\\=100\)

Step-by-step explanation:

When the length of AB = (x+15)cm and MU=(4x-45)cm are equal ,it should be noted that the value of x is 20.

It should be noted that from the information, it was stated that the the length of AB = (x+15)cm and MU=(4x-45)cm are equal.

Therefore, it should be noted that we need to equate the equations that are given. This will be:

x + 15 = 4x - 45

Collect like terms

4x - x = 15 + 45

3x = 60

Divide through by 3

x = 60 / 3

x = 30

Therefore, when the length of AB = (x+15)cm and MU=(4x-45)cm are equal ,it should be noted that the value of x is 20.

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Given that the length of AB = (x+15)cm and MU=(4x-45)cm are equal. Find the value of x.

Answer:

x=2√10,−2√10

Step-by-step explanation:

Answer:

c or a

Step-by-step explanation:

Answer:

A(-3,-1)-----A'(-1,2)

B(2,1)------B'(4,4)

here

x is increased by -1--3=2

and

y is increased by2--1= 3

so

A.(x',y')=(x+2,y+3)

The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

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Box 1 uses less wrapping paper than box 2 by 2 sq. inches

A three-dimensional shape with six rectangular faces, eight vertices, and twelve edges is known as a cuboid.

Given that

Box 1 dimensions  = 11 x 5 x 8

Here l= 11 w = 5 h = 8

Box 2 dimensions = 16x4x6

Here l= 16 w =4 h = 6

We have to find which box uses less wrapping paper

We know that Total surface area of a Cuboid  = 2lw + 2lh + 2hw

= 2(lw+ lh + hw)

Box 1:

= 2(11x5 + 5x8+8x11)

= 2(55+40+88)

= 2(183) = 366 square inches

Box 2

= 2(16x4 + 4x 6+6x16)

= 2(64+24+96)

= 2(184) = 368 square inches

Therefore Box 1 uses less wrapping paper than box 1 by 2 sq. inches

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Answer:

a. 5x^2-7x+1

b. 2x^2-6x-6

Step-by-step explanation:

Answer:

By splitting the line segments into equal parts, we find that the length of the line segment formed by joining the mid-points is 5.5 units.

Step-by-step explanation:

Given lengths show that the length of JK is 5 units, KL is 4 units and LM is 6 units. Let the midpoint of JK be A. This means JK is splited into two equal parts JA and AK. Since the lengths of both the segments are same, it will be 5/2 = 2.5 units.

Now, let the midpoint of LM be B. So, we have two equal line segments LB and BM of length 6/2 = 3 units.

So, the length of the line segment formed by joining A and B will be 2.5 + 3 = 5.5 units

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Answer:

x=  

4

−5+  

33

​    

4

−5−  

33

​  

​  

Step-by-step explanation:

Answer:

A. (9 - 2.25)s ≥ 5,400

B. They will have to sell more than 800 sandwiches per month. I first started by solving the parentheses which is 6.75. Then I divided 5,400 by 6.75 to get 800.

C. It will now end up looking like this: (8 - 2.25)s ≥ 5,400. Then it will be 5.75. Then divide 5,400 by 5.75. Then you end up with 939.13. You have to round up when you are talking about inequalities with money so it will be 940. So they will have to sell 140 more sandwiches during that month.

Step-by-step explanation: