pol: Practice & Problem Solving 2.PS-22 Question Help Three sisters are saving for a special trip. The ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4. Together all 3 sisters have saved $60. How much has each girl saved? Answer questions 3–4. IS 4 squares long. Then, use the diagrams to show $60. (Type whole numbers.) 4. Complete the table. Helga's savings Maurice's savings Nora's savings $8 $ $24 $32 $ $6 $ $ 12 $4 $ $ $16 + Vi 1 1,0 More Enter your answer in the edit fields and then click Check Answer. 1 pant Clear All Check Answer remaining

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,

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 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.

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.

From the question we are to determine Britta most likely task in preparing a budget.

First let's know what a budget is.

A budget is an estimation of revenue and expenses over a specified future period of time and is utilized by governments, businesses, and individuals. A budget is basically a financial plan for a defined period, normally a year that is known to greatly enhance the success of any financial undertaking.

So with the above explanation of what a budget is, Britta most likely task is to allot a set amount of money for her expenses.

Therefore the correct option is C, which is She is allotting a set amount of money for her expenses.

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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The answer is option B

Given:

/16x^2 + x^2/3 + 3/8x^5

You need to simplfiy the expression given which will give you

6 3/x^5 or the second option

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

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

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.

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)

_____________________

Can you see the updates?

__________________

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

_________________

Can you see the updates?

Do you have any questions regarding the solution?

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

a.

Therefore, your score would be 70% then you will get a C

b.

Your score would be 82.5%, then you will get a B

c.

Your score would be 86.4%, then you will get a B

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.

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

We can find the horizontal asymptote of this kind of functions using the limit:

Therefore the equation of the horizontal asymptote is:

Answer:

0, that is not possible

Step-by-step explanation:

Since she gets a discount she will always pay less

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.

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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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

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

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

Given: The coordinates of a trapezoid as below

To Determine: The final step on the trapezoid after it is reflected over the x-axis and then reflected over the axis

Solution

Please note that a reflection over the x-axis and reflection over the y-axis is different from the last step, which is a reflection over the y-axis

The reflection over the y-axis could either be a rotation of 90^0 clockwise or anticlockwise.

So get the trapezid onto itself after a reflection over the y-axis from a reflection over teh x-axis requires two steps

We have step 1: Reflection over the x-axis, then

Step 2: Reflection over the y-axis

Hence, the final step is reflection over the y-axis

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.

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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The equation of the vertical parabola in vertex form is written as

Where (h, k) are the coordinates of the vertex and p is the focal distance.

The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.

Using this value for p and (3, 1) as the vertex, we have our equation

Answer:

4490.5

Step-by-step explanation:

5(898)+0.5

=4490.5

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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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