It’s multi-step linear equations I have to solve for the x but in this question is asking “expand, and then solve for x” what did it mean by expand 5a - (2a + 15) = 24

The expected return of the stock portfolio is 9.3%.

From the properties of stock portfolio we know that,

Expected return of a portfolio = RF + BP ( RM - RF )

E(RP) = RF + BP ( RM - RF )

RF= risk free rate =3%

RM = expected market return = 10%

BP = beta of portfolio

BP = ∑(Wi × Bi)

Wi is weight of stock i and Bi is the beta of stock i .

Wi= investment in stock / total investment

Beta of portfolio(BP)

=(0.5×1) + (0.35×0.2) + (0.33)

= 0.50 +0.07+0.33

=0.9

E(RP)

= RF + BP ( RM - RF )

= 0.03 + 0.9(0.30-0.03)

= 0.03 +0.063

= 0.093

Hence the expected rate = 0.093 × 100% = 9.3%

The stock market portfolio of an investor consists of stocks, funds, and possibly other market-traded securities. In general, cash and bond assets are often present in investment portfolios. Various assets with different sizes, industries, and other characteristics are included in a varied portfolio.

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Given that the baker has a total of 18 cups of flour, you know that the baker needs:

- This amount of flour for a batch of banana pancakes:

- This amount of flour for a batch of apple pancakes:

You know that the baker makes 8 batches of banana pancakes.

Let be "x" the greatest number of whole batches of apple pancakes that the baker can make.

You can set up this equation using the given data:

Now you need to solve for "x", in order to find its value:

Since the number of cups cannot be greater than 18 cups, you need to round down:

Hence, the answer is: Third option.

She could take

1.- {x|x Scoop}

2.- {x|x Light}

3.- {x|x Lanark}

4.- {x|x Scoop, Light}

5.- {x|x Scoop. Lanark}

6.- {x|x Light, Lanark}

Given

Find

Exact solution by quadratic formula

Explanation

Quadratic formula is given by

here a = 1 , b = -3 and c = 1

substitute the values in quadratic formula ,

Final Answer

Therefore , the correct option is 4.

Answer:

0, that is not possible

Step-by-step explanation:

Since she gets a discount she will always pay less

We would test if np and n(1 - p) is at least 10

p = sample proportion

p = x/n

where

x = number of success

n = sample size

From the information given,

p = 41% = 41/100 = 0.41

n = 118

np = 48.38

n(1 - p) = 118(1 - 0.41) = 69.62

Both values are greater than or equal to 10. Thus, the distribution is approximately normal.

The mean of the distribution = p = 0.41

Standard deviation = √(p(1 - p)/n

By substituting the values,

standard deviation = √(0.41(1 - 0.41)/118 = √0.00205 = 0.045

We want to find P(p ≥ 0.5)

We would standardize 0.5 into a z score by applying the formula,

z = (x - mean)/standard deviation

z = (0.5 - 0.41)/0.045 = 2

From the normal distribution table, the probability value corresponding to a z score of 2 is 0.9773

P(p ≥ 0.5) = 1 - 0.9773

P(p ≥ 0.5) = 0.023

the probability that the majority (more than 50%) watched the Super Bow is 0.023

The number that satisfies the equation is

Doing the square root on both sides

On complex number we use the definition:

Therefore, the number that satisfies the equation is

That means that a solution is a complex number.

Complex numbers have two parts, the complex part and the real part:

Look that a and b are real coefficients, but z is a complex number because we have b multiplying i, the complex unit.

But why complex numbers are so important?

• Complex numbers can be used to solve polynomial equations, that we couldn't solve before

• Complex numbers can connect exponential function with trigonometric functions

Complex numbers are a powerful set that we can use to solve many complex problems in physics and mathematical, it may seem hard but they actually make things easier, sometimes working with complex numbers is way easier than working with real numbers.

For the given function,

             Vertical Asymptote:-  x =-3

             Horizontal asymptote:- y =20

             Oblique asymptote :- No oblique asymptote

Asymptote:

                     A vertical asymptote is found by letting the denominator equal zero. A horizontal asymptote is found by comparing the leading term in the numerator to the leading term in the denominator. The degree of the numerator is greater than the degree of the denominator, so there is no horizontal asymptote.

                                                            Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator

given,

            R(x) = [tex]\frac{20x}{x+3}[/tex]

Vertical Asymptote:-

                                  Equate denominator to zero

                                    x +3 = 0

                                        x = -3

Horizontal asymptote:-

                                   Here degree on x in numerator and denominator is same,

              so horizontal asymptote will be,  

                                y= 20/1

                                y = 20

Oblique asymptote:-

                                 There won't be any slant asymptote, because degree in numerator is equal to the degree in denominator.

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You have to find the equation of the linear function h(x), given that you know two points of the said function.

h(3)=-2 → this notation indicates the ordered pair (3,-2)

h(-3)=16 → this notation indicates the ordered pair (-3,16)

The first step to determine the equation of any line or linear function is to calculate its slope. To do so you have to use the following formula:

Where

(x₁,y₁) are the coordinates of one point of the line

(x,₂,y₂) are the coordinates of a second point of the line

Using the ordered pairs:

(3,-2) as (x₁,y₁)

(-3,16) as (x,₂,y₂)

Calculate the slope as follows:

So the slope of the linear function is m=-3

To determine the equation you can use the point-slope form:

Where

m represents the slope

(x₁,y₁) are the coordinates of one point of the line

I will use the point (3,-2) and the slope m=-3 to determine the equation but you can use either ordered pair to do so.

Now, what's left is to write the equation in slope-intercept form:

-Distribute the multiplication on the parentheses term:

-Pass "+2" to the right side of the equal sign by applying the opposite operation to both sides of the equal sign "-2"

The equation of the linear function is:

To find the value of h(5), you have to replace the equation of the function with x=5 and calculate the corresponding h(x) value

So:

1) Firstly, let's express each plan by using linear equations.

Plan A:

5x+320

Note that the $320 payment is done once, then 5 per session.

Plan B

15x

2) To get to know when opting for plan A or Plan B is not relevant, we need to equate both equations and solve it for x (x stands for the number of sessions)

So if you attend 32 sessions then, doesn't really matter which plan is it.

3) Now, let's figure out which plan is more interesting to take:

So the plan B is cheaper to attend 1 session

1. The 90% confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019 is given as follows:

(11.59, 14.21)

2. The conditions for the confidence interval are of:

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 50 - 1 = 49 df, is t = 1.6766.

The remaining parameters are given as follows:

[tex]\overline{x} = 12.9, s = 5.52, n = 50[/tex]

Then the lower bound of the interval is of:

12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.

The upper bound of the interval is of:

12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.

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First, we need to identify the y-intercept that is the value of the coordinate y when the coordinate is 0 in this case our y-intercept is in 40

The y-intercept provide the start amount of water therefore the correct choice is D. the water level started at 40 mL

We are given the endpoints of a line PQ

We are asked to find the midpoint of line PQ.

Let us first find the distance of line PQ

Recall that the midpoint is at the halfway of the line PQ so divide the distance by 2

Answer:

4490.5

Step-by-step explanation:

5(898)+0.5

=4490.5

In this expression, we can solve it by applying the distributive property

3(2y-7)

6y-21

So, factor 3 multiplies each term inside the parentheses.

2)-(x+4)

The minus outside the bracket works like a -1 multiplying it

-(x+4)

-x-4

3) For this one, remember the rule for multiplying fractions and then simplifying:

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

6x+6 -5x-10

6x-5x+6-10

x-4

STEP - BY - STEP EXPLANATION

What to find?

The power function that the given graph resembles.

Given:

f(x)=(x − 3)³

First, we need to note that;

If f(x) is shifted left q - units, then the new formula of the function becomes f(x+q).

Let q=3

ANSWER

y=x³

Given data:

The given triangles.

The given triangles are congruent by side-angle-side (ASA) rule.

Thus, the given triangles are congruent by ASA.

The function is given as,

For x = -1 , the value of y is calculated as,

For x = 0 , the value of y is calculated as,

For x = 1 , the value of y is calculated as,

For x = 2, the value of y is calculated as,

SOLUTION

From this question, it means that

To be sure the required translation, let us see a quick look at the graph of the function and it's image

And

Now, we can see that the image is an enlarged form of the original function

Therefore this is a dilation. And since the increase in size is vertical, that is across the y-axis, It is a Vertical dilation.

Hence the correct answer is Vertical dilation.

In this case the answer is very simple. .

We must use the graph to find the answers.

Step 01:

Data

For x = 2 ===> y = 1

Step 02:

Direct variation equation

y = k * x

Constant of proportionality

x = 2 , y = 1

The solution is:

Constant of proportionality = k

k = 1/2

Direct variation equation

y = k * x

y = (1/2) * x

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Jeff = 2 tens 42 ones

Victor = 3 tens 51 ones

what number is = ?

Step 02:

Jeff = 2 tens 42 ones

2 * 10 = 20

42 * 1 = 42

----------

Victor = 3 tens 51 ones

Answer:

Jeff: 62

Victor: 81

Step-by-step explanation:

Jeff has a number with 2 tens, and 42 ones. We can write out our 2 tens like this: 10 + 10 = 20

Next, he has 42 ones. This is just another way of saying '42'

So, jeff picked a number that is 20 + 42 = 62

Now, Victor. Victor has a number with 3 tens. This is saying: 10 + 10 + 10 which is 30. He has 51 ones, which is just the number 51.

So, Victor's number is 30 + 51 = 81

The given information is:

- Sample mean = 25.42

- Standard deviation = 14.25724

Part 1.

We have a confidence interval (C.I.) of 80%.

We need to find the z-score for this C.I., so, let's see a diagram:

We have a two-sided confidence interval. So, we need to find the z-score for a cumulative probability of 80+10=90%=0.9.

By using a standard normal table, we can see that z-score for 0.9 is:

By using an online calculator, we find the exact z-score is 1.282.

The confidence interval is given by the formula:

Where x is the mean of the sample, Zc is the z-score for the given confidence level, s is the standard deviation and n is the number of elements in the sample n=50.

By replacing the known values, we obtain:

So, the lower and upper limits are:

The margin of error is equal to half the width of the entire confidence interval, and it is also the value we add and subtract to the mean to find the confidence interval, so the margin of error is 2.585.

EXPLANATION

2) 812: The place of the underlined digits corresponds to UNITS.

VALUE --> 812: eight hundred twelve

The area of the figure is 24 cm²

The figure is divided into two blocks, one is rectangle having the dimensions, length as 5cm and width as 4 cm, another is a square having side of 2 cm.

The area of the figure is the summation of the area of the rectangle and the  area of the square.

area of the rectangle = length x width = 4 x 5 = 20cm²

area of the square = side² = 2² = 4cm²

area of the figure = area of rectangle + area of the square

= 20 + 4

area of the figure is 24 cm²

Therefore, the area of the figure is 24 cm²

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We need to choose 5 members from the general only

The number of general members = 31

As the arrangement is not required

So, the number of committees will be:

so, the answer will be 169,911 committees

Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?​

_______________________

The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.

x + (x + 9) + (x + 4) = 2x + (4x - 2)

_____________________

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__________________

x + (x + 9) + (x + 4) = 2x + (4x - 2)

3x + 13 = 6x -2

6x - 3x = 13 + 2

3 x = 15

x = 15/3 miles

x = 5 miles

___________________________

5 + ( 5 + 9) + ( 5 + 4) = 2x + (4x - 2)

28 = 28

________________________

on Wednesday

x=5

x+ 4 = 9

_________________

Answer

On Wednesday he ran 9 miles

_________________

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Do you have any questions regarding the solution?

The parent function is:

y = x²

This is a quadratic function

The child functions are:

y = x - 4² whcih can be written as

y = x - 16

The second child function is

y = x + 3

The two child functions are linear functions while the parent function is a quadratic function.

The parent and child functions also differ in their ranges and domains

Domain = ( -∞ , ∞ )

Range = [0 , ∞ )

Domain = ( -∞ , ∞ )

Range = (-∞ , ∞ )

The difference between y = x - 4² and y = x + 3 is their intercepts on the y axis .

For y = x - 4², the y - intercept is -16

For y = x + 3, the y - intercept 3

This change is due to transformation (basically translation) on the x and y axes

The correct option is D

gaining 10 points cannot be represented by the number -10

-10 can represent all the given situations except gaining 10 points.

Because that will be an increase (+10), and not a decrease (-10)

Answer is: A withdrawal of $10.

Lixin has x number of classmates and plan to buy her a birthday gift worth $36.

So basically, they need to contribute 36/x dollars each in order to buy the gift.

But 5 of them will not contribute and it cost them to add $0.24 each

So from 36/x dollars, it become (36/x + 0.24) dollars each

Multiply this individual contribution by the number of her classmates which was reduced by 5. (x - 5)

The equation will be :

Simplify the equation :

Multiply both sides by x to remove the denominator.

Rearrange and combine like terms :

Divide both sides by 0.24 to make the coefficient of x^2 become 1 :

Solve by factoring completely :

Equate both factors to 0, then solve for x :

x - 30 = 0

x = 30

x + 25 = 0

x = -25

Neglect negative value since there is no negative value for the number of persons.

The answer is x = 30

To summarize :

i Expression in terms of x :

ii Equation in x that reduces to x^2 - 5x - 750 = 0

iii Number of classmates Lixin has.

x = 30

Answer:

this is 50. i = 50

Step-by-step explanation:

hope it helps you