What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di).

The sample size for the given problem is 1499.

What is sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Given:

An urban economist wishes to estimate the proportion of Americans who own their homes.

p cap = 0.669

1 - p cap = 0.331

margin of error = E = 0.02

 [tex]Z_a_l_p_h_a_/_2[/tex]= 1.645

Sample size = n

[tex]n = (Z_a_l_p_h_a_/_2/E)^2*Pcap*(1 - Pcap)\\= (\frac{1.645}{0.02})^2*0.669*0.331\\ = 1499[/tex]

Hence, the sample size for the given problem is 1499.

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The amount of time it would take for 20% of the water to leak from a full vase is equal to 24.128 minutes.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

From the diagram of the cone (see attachment), we have the following parameters:

Diameter of cone = 4.8 in.

Height of cone = 10 in.

Radius of cone = diameter/2 = 4.8/2 = 2.4 in.

Substituting the given parameters into the formula, we have;

Volume of cone, V = 1/3 × 3.142(2.4² × 10)

Volume of cone, V = 60.32 in³.

For the volume of water that has leaked, we have:

Volume of water leaked = 20/100 × 60.31

Volume of water leaked = 12.062 in³.

For the required amount of time, we have:

Time = Volume/Rate

Time = 12.064/0.5

Time = 24.128 minutes.

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Answer:

3 ,0

Step-by-step explanation:

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field \nabla f whose value at a point p is the "direction and rate of fastest increase". Wikipedia

Answer:

1/3

Step-by-step explanation:

We need two easy-to-read points on grid intersections.

Look at the point on the y-axis. It is (0, 3).

Now go up to the right until you find the next easy-to-read point.

It is (3, 4) which is on a grid intersection.

gradient = run/rise

rise = distance in y (vertical distance)

run = distance in x (horizontal distance)

We start at (0, 3) and go to (4, 4) by going only vertically and horizontally.

From (0, 3), go 1 unit up. That is a rise of 1.

Then go 3 units right. That is a run of 3.

gradient = rise/run = 1/3

Answer: 1/3

The probability that the islanders will win exactly two games is 0.359.

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Given that,

The probability of winning is 4/7.

Then the probability to lose is 1 - 4/7 = 3/7.

If islanders win exactly two games out of four, it implies that they will lose 2 as well.

Now, the probability of winning exactly two games can be found using binomial distribution as given below,

⁴C₂(4/7)²(3/7)²

= 6 × 16/49 × 9/49

= 864/2401

= 0.359

Hence, the probability of winning exactly two games is 0.359.

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Answer:

Step-by-step explanation:

a 23

b 43

c 56

a)The probability that a customer selected will have more than two credit cards is 0.11 ,b)expected value is 1.34 and c)standard deviation is 0.96.

Given, probability distribution table

X p(X)

0 0.18

1 0.44

2 0.27

3 0.08

4 0.03

where,X= number of credit cards people own

Thus, the probability that a customer selected will have more than two credit cards is 0.11 ,expected value is 1.34 and standard deviation is 0.96.

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Your question is incomplete, Here is the complete question.

A bank vice president feels that each savings account customer has, on average, three credit cards. He collected data over a period of time and found the probability distribution given in the following table. The random variable X, represents the number of credit cards people own.

X p(X)

0 0.18

1 0.44

2 0.27

3 0.08

4 0.03

If necessary, use a leading zero and round to 2 decimal places, e.g, 0.25.

(a) Find the probability that a savings account customer selected at random will have more than two credit cards ?

(b) Find the expected value of the number of credit cards a randomly selected customer owns ?

(c) Find the standard deviation of the number of credit cards a randomly selected customer owns ?

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

sin²x = (sec x - cos x) / sec x is,

sin²x + cos²x = 1

(proved)

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

sin²x = (sec x - cos x) / sec x

We will prove that,

sin²x + cos²x = 1

sec x = 1/cos x

Now,

sec x - cos x

= 1/cos x - cos x

= (1 - cos²x) / cos x

Now,

sin²x = (1 - cos²x) / [(cos x) x 1/cos x]

sin²x = 1 - cos²x

sin²x + cos²x = 1

Proved

Thus,

sin²x = (sec x - cos x) / sec x is,

sin²x + cos²x = 1

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Scores on one variable plotted against scores on a second variable.

The correct answer is (b)

Now, According to the question:

Let's know:

A scatterplot shows:

A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.

Hence, The correct answer is (b) i.e.,

Scores on one variable plotted against scores on a second variable.

Given,

In the question:

A scatterplot shows:

a. the average value of groups of data.

b. scores on one variable plotted against scores on a second variable.

c. the frequency with which values appear in the data

d. the proportion of data falling into different categories.

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Answer:

49 bracelets

Step-by-step explanation:

Let the number of bracelets that can be made be x.

First, let us convert 3.5 hours into minutes.

3.5 * 60 = 210 minutes

Accordingly,

Time (min)            Number of bracelets

30                      ⇒            7

210                    ⇒           x

Now, we can make an expression like this using cross multiplication.

30x = 7 × 210

30x = 1470

Divide both sides by 30.

x = 49

T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).

To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.

For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).

As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).

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The sampling distribution is t= 88 degrees of freedom.

To find the sampling distribution of the sample mean difference we need to do a two-sample t-test: equal variances.

When we do a two-sample t-test, we have to take into account the following assumptions:

1) the sample variances are normal.

2) the sample variances of both populations are equal.

Now, let the sample size be [tex]n_x[/tex] and [tex]n_y[/tex] respectively and the means be [tex]x^-[/tex] and [tex]y^-[/tex] respectively.

Now, we are assuming that the distribution of x and y are

[tex]x\sim N([/tex]mewx, [tex]\sigma x = \sigma[/tex])

[tex]y\sim N[/tex] (mewy, [tex]\sigma y = \sigma[/tex])

Accordingly, the system of hypothesis is defined by:

Null hypothesis: mewx=mewy

alternatively, it can also be mewx≠ mewy

Then, the random  sample t is distributed as [tex]t\sim t_n_x+ny-2[/tex] with the degrees of freedom given as df= [tex]n_x+n_y-2[/tex] =40+50-2= 88

So, in this case answer will be 88 degrees of freedom.

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Plants C and D have the same ratios of green bottles to total bottles recycled.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The table is given in the question,

As per the given question, the required solution would be as:

For plant A,

The ratio of green bottles to total bottles

⇒ 16/172 = 4/43

For plant B,

The ratio of green bottles to total bottles

⇒ 12/135 = 4/45

For plant C,

The ratio of green bottles to total bottles

⇒ 14/154 = 1/11

For plant D,

The ratio of green bottles to total bottles

⇒ 18/198 = 1/11

Thus, plants C and D have the same ratios of green bottles to total bottles recycled.

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Answer:

µT = 2 (The mean of T is 2)

σT = 1 (The standard deviation of T is 1)

Step-by-step explanation:

This involves the transformation and combination of random variables. We know that the coin flips are independent as the knowledge of one coin flip will not affect the next or another coin flip.

The question has a transformation of H by essentially multiplying it by 4 that, then turns it into T. Knowing that we can multiply the mean of 0.5 by 4 with rules of a linear transformation when multiplying each observation by a positive constant. With that, we get the mean of T to equal 2.

Since we know it is independent, we can solve for standard deviation. To do so, we have to add 0.5 squared 4 times and square root it. That will look like this: Squareroot(0.5^2+0.5^2+0.5^2+0.5^2). That will give you 1 as the standard deviation for T.

I may utilize the Cp Criterion, AICp, and SBCp to aid in choosing the optimal model. All of them impose sanctions for introducing predictions.

What is subset regression model?

Best subsets regression is a model-building regression analysis that is exploratory. It compares every model that might be built using a specified set of predictors.

There are Cp Criterion, AICp and SBCp that I can use to help select the best model. They all place penalties for adding predictors.

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The equation for given Parallel & Perpendicular Lines points and slope and given below.

what is parallel and perpendicular lines?

In a plane, parallel lines are those whose distances between them are constant. Parallel lines do not cross. Lines that cross at a right angle of 90 degrees are said to be perpendicular.  

The equation of a line in slope-intercept form y = mx + c

1. substitute x = 0, y = 3 and m = -2 in equation

3 = -2*0 + c

c = 3, substitute in equation

Then y = -2x + 3

2. substitute x = -3 , y = - 5 and m = -( 3/5 ) in equation

-5 =  -( 3/5 )*(-3 ) + c

c = - 34/5 , substitute in equation

Then  5y = -3x - 34

3. substitute x = -8 , y = 6 and m = -(1/4) in equation

6 =  -(1/4)*(-8 )+ c

c = 8, substitute in equation

Then y = -2x + 8

The equation of line passing through two points is m = ( y2 - y1) / ( x2 - x1)

4. The given points is ( 1, 3) and  ( -3, -5) and substitute in above equation.

Then m = 2

substitute m = 2 and ( 1, 3) in equation y = mx + c

Then  c = 1

substitute m = 2 and c = 1 in equation of y = mx + c

Then the equation is y = 2x + 1

5. The given points is ( 1, 4) and  ( 6, -1 ) and substitute in above equation.

Then m = - (5/4)

substitute m = - (5/4) and ( 1, 4) in equation y = mx + c

Then  c = 21/4

substitute  m = - (5/4) and c = 21/4 in equation of y = mx + c

Then the equation is  4y = -5x + 21

6. The given points is ( -12,14)  and  ( 6, -1 ) and substitute in above equation.

Then m = - (5/6)

substitute m = - (5/6) and( -12,14) in equation y = mx + c

Then  c = 4

substitute  m = - (5/6) and  c = 4 in equation of y = mx + c

Then the equation is y = - ( 5/6 ) + 4

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The probability that mean blood pressure less than 118 is 0.9938.

We have given that,

blood pressure are normally distributed mean of 116

i.e. μ = 116

standard deviation σ = 4.8

n = 36

and we have to find probability that their mean blood pressure will be less than 118.

The formula to find the above probability is,

P(Z=X) = (x - μ) / (σ/[tex]\sqrt{n}[/tex] )

⇒ P(Z < 118) = (118 - 116) / 4.8/[tex]\sqrt{36}[/tex]

                   = 2 / (4.8/6)

                   = 2/0.8

  P(Z < 118) = 2.5

From the z-table the value of z at 2.5 is 0.9938,

⇒ P(Z < 118) = 0.9938.

Therefore the probability that their mean blood pressure will be less than 118 is 0.09938.

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the value for dferror for this analysis is 8.

What is error?

Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.

df-error = (df-within treatment) - (df-subjects)

df-subjects = n - 1 = 5 - 1 = 4 {n is the no of subjects}

df-within treatment = 12

df-error = 12 - 4 = 8

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The mean mark of the group would be 8.

Used the concept of mean that states,

Mathematicians find the mean by adding up all the numbers in a data collection, then dividing that total by the number of numbers.

Given that,

There is a group of students who were given a spelling test.

The table shows their marks.

By dividing the total number of students by the sum of each mark's frequency and each mark, you can determine the group's mean grade:

[tex]\text { Mean Mark } = [ (6 \times 5) + (7 \times 4) + (8 \times 7) + (9 \times 10) + (10 \times 4) ] \div30[/tex]

                    [tex]= [ 30 + 28 + 56 + 90 + 40 ] \div 30[/tex]

                    [tex]= 244 \div 30[/tex]

                    [tex]= 8.1333333333...[/tex]

                    [tex]= 8 (\text{ nearest whole number}})[/tex]

Therefore, the value of the mean is 8.

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Answer:

11250

Step-by-step explanation:

The coordinates of point B is (-6, 6) if the point A(6,-6) is rejected over the origin and it’s image is point B

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

Point A(6,-6) is reflected over the origin and it’s image is point B

The rule for transformation:

(x, y) --> (-x, -y)

(6, -6)  --> (-6, 6)

Thus, the coordinates of point B is (-6, 6) if the point A(6,-6) is rejected over the origin and it’s image is point B

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A comparison of hot coffee and cold lake is, the heat from the coffee will be absorbed by the cold lake through convection method of heat transfer.

Heat is transferred through the convection, which is basically large-scale movement of molecules inside gases and the liquids. Conduction is basically used to move heat from one of the object to the fluid initially, but fluid motion is all responsible for the bulk of the heat transfer.

Conservation of energy

The principle of conservation of the energy states that the total energy of an isolated system is always in conserved state.

Heat lost by all the hot coffee = Heat absorbed by all the cold lake

Heat transfer process

Heat from the coffee will all be absorbed by the cold lake through convection method of the heat transfer.

Thus, the comparison of hot coffee and the cold lake is, the heat from the coffee will all be absorbed by the cold lake through convection method of the heat transfer.

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Answer:

yes I will get suspicious and then

Step-by-step explanation:

he was in a meeting

Answer: x = 126

Step-by-step explanation:

We know that 50% of 120 is 60. So, to increase 120 by 50%, we add 60. This gets us 180. Next, we find 30% of 180. This is 54. So, we subtract 54 from 180. So, x = 126

The date that Chris will have both training sessions again is May 9.

In mathematics, a multiple simply means the product of any quantity. It should be noted that a multiple illustrate to the product of a number given.

In this situation, since Christ has bowling training every 8 days and hockey training every 2 days. The lowest common multiple for 2 and 8 is 8.

Therefore, the next date will be the addition of the day of the training and the number of days that are needed when the lowest common multiple was calculated. This will be illustrated thus:

= May 1 + 8 days

= May 9

The next training is May 9.

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Answer:  18 cookies

Step-by-step explanation:

27 divided by 1.50 = 18

Answer:

Step-by-step explanation:

6 cookies

The simplified version of the expression (x¹/² y¹/⁹)³ is (x³/² y¹/³)

From the question, we have the following parameters that can be used in our computation:

(x^1/2 y^1/9 )^3

Rewrite the expression properly

So, we have

(x¹/² y¹/⁹)³

Open the brackets

This gives

(x¹/² y¹/⁹)³ = (x¹/²)³ * (y¹/⁹)³

Evaluate the expression in brackets

(x¹/² y¹/⁹)³ =(x³/² y¹/³)

Hence, the solution is (x³/² y¹/³)

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The exponential equation of the logarithmic equation ㏑ (x² - 5 · x + 17) = 3 · x + 2 is x² - 5 · x + 17 = e³ˣ ⁺ ².

In this question we find that a logarithmic equation, in which we must eliminate the log operator must be eliminated by relationship between logarithmic and exponential equations, whose relationship is shown below:

Logarithm of an exponential equation

㏒ aˣ = x

Exponential up to an logarithmic equation

[tex]a^{\log x}[/tex] = x

Now, we proceed to eliminate the log operator by algebra properties and relationship between logarithmic and exponential equations:

㏑ (x² - 5 · x + 17) = 3 · x + 2

By using an "exp" operators, we get the following expression:

x² - 5 · x + 17 = e³ˣ ⁺ ²

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The statement opportunity cost for Germany to produce 1 beer is 1/2 motorcycles is true.

The German economy would be better off if it produced beer and traded motorcycles with the US.

Germans would benefit from specializing in producing beer and engaging in trade with the United States since their opportunity cost is lower (1/2 is less than 3).

A country is said to be having a comparative advantage in producing a good if it can produce it at a lower opportunity cost. Germany has a lower opportunity cost in producing beer so it has a comparative advantage in making beer.

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