Multiply (5 + 4i)(3+ 2i)

Answer:

68

Step-by-step explanation:

Hope this helped! :)

Answer:

First, it’s a loyalty program.  They are rewarding their loyal customers with a lower price.  This is good for building long term clients and maximizing lifetime revenue of a customer.  However, as a loyalty program it has a pretty big flaw.  After the customer gets his free coffee, he is back to ground zero and has no built up financial incentive to return.  Of course he does still know he gets a lower price if he buys 10 more.

Step-by-step explanation:

step 1. f(4) = 3(4) + K = 7 (plug in values)

step 2. K = -5 (subtract 12 from each side)

step 3. therefore f(x) = 3x - 5

step 4. f(2) = 3(2) - 5 = 1 (plug in x= 2)

1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

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Answer:

you solve for the variables. there is three ways to do so.

1. graphing.

2. substitution method.

3. elimination method.

Answer:

Area = 100 ft^2

Step-by-step explanation:

To calculate the area of this composite shape, you need to find the area of all shapes and add them together.

1. Break the composite shape into different shapes.

Shapes: one rectangle, one square,  and one triangle.

2. Find the area of each of them.

Rectangle

L= 8ft    

W= 10ft

A= L x W

A= 8ft x 10ft

A= 80ft^2

Square

L= 4ft

W=10ft - 6ft = 4ft

A= L x W

A= 4ft x 4ft

A= 16ft^2

Triangle

A= 1/2 x base x height

b= 14ft -8ft-4ft = 2ft

h= 10ft - 6ft =4ft

A= 1/2 (2ft x 4ft)

A= 1/2 (8 ft^2)

A= 4ft^2

3. Add all the areas.

Area = Rectangle Area+ Square Area+ Triangle Area

A = 80ft^2 + 16ft^2 + 4ft^2

A= 100ft^2

Hope this helps!

Answer:

The way to represent this it is

\( 12.33 - \frac{0.27}{\sqrt{n} } < \mu < 12.33 + \frac{0.27}{\sqrt{n} } \)

Step-by-step explanation:

From the question we are told that

The sample mean is

The standard deviation is

Given that the confidence level is 95% then the level of significance is mathematically represented as

\(\alpha = (100-95)\)

\(\alpha = 0.05\)

The critical value for \(\frac{\alpha }{2}\) is obtained from the normal distribution table that value is

\(Z_{\frac{\alpha }{2} } = 1.96\)

Now the margin of error is mathematically represented as

\(E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }\)

\(E = \frac{0.27}{\sqrt{n} }\)

Now the error range to show a 95% confidence is mathematically represented as

\(\= x - E < \mu < \= x + E\)

           \( 12.33  -   \frac{0.27}{\sqrt{n} } <  \mu < 12.33  +   \frac{0.27}{\sqrt{n} } \)

Here notice that the significant figure is keep to three to match the significant figure of the given values

Thus, 715,000 =  7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.

The number of times that decimal point must be moved to obtain a number between 1 and 10 is the exponent in scientific notation. The decimal point is shifted to the left in order to represent this number in scientific notation.

The main goal of scientific notation is to simplify computations using numbers that are abnormally large or small. With scientific notation, every digit counts because zeros are just no longer used to denote the decimal point.

Given expression:

715,000 __ 7.15 x 10⁵

LHS = 715,000

Take the RHS value :

= 7.15 x 10⁵

This, can be simplifies as:

= 7.15 x 100,000

Now multiply the two values,

= 715,000 (RHS values)

as, LHS  = RHS

LHS = 715,000

715,000 (RHS values)

Thus, 715,000 =  7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.

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The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

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The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545

\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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Hey there!

5x = 120 {Obtain a formula for x }

=> \(\fbox{5x = 120}\) { Divide both side by 5}

=> \(\fbox{5x/5 = 120/5}\) { divide 5x by 5}

=> \(\fbox{x = 120/5}\) { Divide 120 by 5}

=> \(\fbox{x = 24}\)

Therefore, x = 24°

Answer:

Step-by-step explanation:

A type I error occurs when the null hypothesis is rejected in favor of the alternative hypothesis when the null hypothesis is actually true.

A type II error occurs when the researcher fails to reject the null hypothesis when the null is false.

H0: woman has cancer in the other breast

Ha: woman does not have cancer In the other breast

A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?

This error is a type I error as the patient does have cancer which should warrant failing to reject the null but the null was rejected in favour of the alternative.

A Type II error would be coming to the conclusion that the woman does have cancer in the other breast when in fact she does not have cancer in the other breast.

This is a second type of error that can occur and it is a type II error: failing to reject the null when not true.

Answer:

yes

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

the frist one is 2 the second on is 3.5 and the third one is 3 and the last on is 2.9

Answer:

55/72 feet squared

Step-by-step explanation:

The area of a rectangle is Length x Height, or Width x Height.

Here, we have a width of 5/6 feet and a height of 11/12 feet.

We multiple 5/6 and 11/12 to get 55/72 feet squared.

Given

The length (l) is 5in longer than it's width

Volume of the box = 300 in

The diagram below illustrates the problem:

The volume (V) of a cuboid which is the volume of the box can be found using the formula:

Substituting the given sides and volume:

Hence, the width of the rectangular piece is 18 in

The length(l) of the rectangular piece:

Hence, the dimensions of the piece of metal is 23 in by 18 in

Answer Summary

The original width is 18 in

Answer: It is C

Step-by-step explanation:

The slop for Kitten A is 1/4 or 4

Kitten B has a slop of 2/6 or 3 so the answer is,

Answer:

Step-by-step explanation:

If Robert is 7 1/2 months old you need to multiply 7 1/2 by 12 because there are 12 months in a year.  

7x12=84  

1/2x12=6

6+84=90

Step-by-step explanation:

4/4 of the pie = 8 slices

1/4 of the pie = 8 slices / 4 = 2 slices

Hence Julie ate 2 slices of the pie.

Answer:

2 slices of pie she ate

Step-by-step explanation:

She ate 2/8th of the slice.

Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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The sum of the scores is equal to 160.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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Note that the roots of the equation Unequal and rational (Option D)

The roots of the equation   (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.

x - 3 = ±√4

⇒ x - 3 = ±2

Solve for x

For the positive square root.

x - 3 = 2

x = 2 + 3

x = 5

For the negative square root.

x - 3 = -2

x = -2 + 3

x = 1

Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The roots of the equation (x - 3)² = 4 are

A.Unequal and irrational.

B.Equal and rational.

C.  Equal and irrational.

D.  Unequal and rational.