Please Also Include explanation

The interest that the savings earned in a year in terms of hours of work is B. 20 hours.

Interest is the additional earning obtained from an investment.

It is computed as the principal multiplied by the annual percentage rate (APR) and the period.

Earnings per hour = $10

Investment = $4,000

APR = 5%

Period of investment = 1 year

Interest earned = $200 ($4,000 x 5% x 1)

Interest earned expressed as hours = 20 hours ($200/$10)

Thus, the investor, who earns $10 per hour, earns 20 hours in interest by investing $4,000 at 5% in a year.

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For part A, first of all, you need to multiply both sides by 2.

4x - 1 = 2x + 14

Then, you need to add 2 to both sides.

4x = 2x + 15

Now, you need to subtract 2x from both sides.

2x = 15

Finally, you need to divide both sides by 2.

x = 7.5

So the answer to part A is 7.5

Now for part B.

First of all, you need to multiply both sides by 3.

9x + 6 = 2x + 13

Next, you need to subtract 6 from both sides.

9x = 2x + 7

Now, you need to subtract 2x from both sides.

7x = 7

Finally, you need to divide both sides by 7.

x = 1

So the answer to part B is 1

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 90+90+x+(x-50)~~ = ~~360\implies 2x+130=360\implies 2x=230 \\\\\\ x=\cfrac{230}{2}\implies x=115\hspace{12em}\stackrel{x}{115^o}\qquad \stackrel{x-50}{65^o}[/tex]

Because a 270° rotation around the origin and a subsequent reflection over the x-axis translate ABC onto LMN, the figures are congruent.

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and form. Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another. In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

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Answer:

your teacher should help you

Step-by-step explanation:

becuase it sayi Mrs.lewis

Triangles with the provided side lengths of 3.5, 3.5, and 9 cannot be formed.

According to the Properties of triangle, the length of the third side of a triangle must be greater than the sum of any two of a triangle's sides.

Given the side lengths are 3.5, 3.5 and 9;

Sum of two sides = 3.5 + 3.5 = 7 cannot exceed 9

Thus, it is clear that a triangle cannot be formed using the specified side lengths of 3.5, 3.5, and 9.

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We conclude that the mean commute time in the U.S. is less than half an hour.

We are given that a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time.

In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.

Let  = mean commute time in the U.S..

So, Null Hypothesis, :  [tex]H_0:[/tex] μ ≥  30 minutes    {means that the mean commute time in the U.S. is more than or equal to half an hour}

Alternate Hypothesis,  :   [tex]H_A[/tex]: μ  < 30 minutes     {means that the mean commute time in the U.S. is less than half an hour}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

                          T.S. =  (X -μ)/[tex]{\frac{s}{\sqrt{n} } }[/tex]   ~ [tex]t_n_-_1[/tex]

where,  X = sample mean commute time = 27.6 minutes

           s = sample standard deviation = 19.6 minutes

           n = sample of people from the 2000 U.S. Census = 500

So, the test statistics  =   (27.6 - 30)/[tex]\frac{19.6}{\sqrt{500} }[/tex] ~ [tex]t_4_9_9[/tex]

                                      =  -2.738

The value of t test statistic is -2.738.

Also, P-value of test statistics is given by the following formula;

          P-value = P( [tex]t_4_9_9[/tex]   < -1.645)

Since, we know that at large sample size, the t distribution follows like normal distribution, that means;

             P( [tex]t_4_9_9[/tex]  < -1.645)  =  P(Z < -1.645) = 1 - P(Z ≤ 1.645)

                                        =  1 - 0.95002 = 0.04998

Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.

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Amar owes $2,000 on his credit card with a minimum percentage of 4% or $60, whichever is higher.

The Minimum Payment due is $ 80 as it is higher from the minimum payment of $60.

Given :

Credit Card amount = $2000

Minimum Percentage = 4%

By using the below formula we can find the minimum balance

Minimum Balance = Credit Card Amount * Minimum Percentage

Minimum Balance = $2000 * 4%

            = $80

So According to the question Amar owes $2000 on his credit card with a minimum percentage of 4% or a minimum payment of $60, whichever is higher.

So the minimum percentage of 4% or minimum balance is higher than $60.

So that’s why the minimum payment due is $80.

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Answer:

- X - 2x = 2x

- X 5y = -5y

(5x - 8y) (2x - 5y)

5x X 2x = 10x^2

5x X -5y = -25xy

-8y X 2x = -16xy

-8y X -5y = 40y^2

therefore

= 10x^2 + 40y^2 -25xy -16xy

Answer:3 and multiplication

Step-by-step explanation: 3 times 9 equals 27.

The account balance after 18 years is $8951.6.

Given the principle is (P) = $4000

The rate of interest (r) = 4.5%

Time (t) = 18 years

It is given that, the compound interest compounded quarterly.

So the amount after 18 years is given by,

[tex]A=P\left(1+\frac{r}{400}\right)^{4t}=4000\left(1+\frac{4.5}{400}\right)^{4\times18}\approx8951.6[/tex]

So the amount after 18 years is $8951.6 approximately.

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To hypothesize that autism is a quantitative trait normally distributed in the population.

Hypothesis that autism is a quantitative trait normally distributed in the population is actually showing the assumption that we can calculate the level of autism in the population in numbers as well as it is present in everyone at some level just like weight.

There are two types of data:

• Quantitative: Any information that can be counted is referred to as quantitative data and is given a numerical value. You can find out “how many,” “how much,” or “how often” using quantitative variables.

• Qualitative: Qualitative information is descriptive in character and communicated verbally as opposed to numerically.

Hence, here they are assuming that we can measure the level of autism in the population.

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An identification and interpretation of the slope in this scenario is: The slope is −0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c          .......equation 1.

Where:

From the information provided, we have the following equation:

y = 3.9 - 0.1x

Rewriting the equation in slope-intercept form, we have:

y = -0.1x + 3.9         .......equation 2.

Comparing equation 1 and equation 2, we have:

Slope, m = -0.1

y-intercept, c = 3.9, which also represents the initial value.

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Answer:

14, or f(-3)= 14

Step-by-step explanation:

Input the -3, so you will get f(-3)= -1/3(-3) + 13.
Do -1/3 x -3, which will get you 1.
Do 1 + 13, which will get you 14.
So, the answer will be 14, or f(-3)= 14.

Answer:

0.0401907 = 0.040 (to 3dp)

The age of Flo based on the ratio is 21 years.

From the information illustrated, the ages of Michael, Flo, Ella and Arlo add up to 60 years and the ratio of Michael's age to Flo's age to 3:7:6:4.

In this case, Flo is represented as 7 and the total ratio is (3+7+6+4) = 20

Therefore the age will be:

= 7/20 × Total age

= 7/20 × 60.

= 21

Flo is 21 years

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Answer:

Geometric and the ratio is 1/3

It is geometric because you are multiplying to get to the next number in the sequence. in order to get to the next number you have to multiply by 1/3. 36*1/3=12. 12*1/3=4.

Nicoletta can withdraw $55 from her savings account for 24 weeks until the balance reaches $0 .

Nicoletta sells jewelry during summer vacation .

From the table we can gather the following information:

Expenses = $ 26

Revenue = $132

Profit = $(132-26) = $ 106

Now she sells for 10 weeks.

profit each week  = $ 106

Total profit over 10 weeks = $ 106 × 10 = $ 1060

Money deposited in the account after 10 weeks = $ 1060

Money originally in the account = $260

Total amount of money in savings account

= $ 1060 + $260

= $ 1320

She withdraws 55 each week.

Number of weeks it will sustain at that rate = 1320 / 55 =24

Hence the savings account will have 0 after 24 weeks.

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Answer 13:1 The ratio stays the same in this problem is says so it will always be that. 169/13=13 13/13=1 That means there's 13 wins for every 1 loss.

Step-by-step explanation:

Answer:  for the first question it is 4

Step-by-step explanation:

5x -3x= 15-7

2x=8

2x/2x      8/2

x=4

Answer:

[tex]10x + 17 - 5x = 27 \\ 10x - 5x = 27 - 17 \\ 5x = 10 \\ x = \frac{10}{5} \\ x = 2 [/tex]

A symmetrical likeness between two halves of an item, when one half is the mirror image of the other, is characterized as being proportional and balanced. As an illustration, many forms such as square, rectangle, and circle are symmetric along their respective lines of symmetry.

A symmetrical likeness between two halves of an item, when one half is the mirror image of the other, is characterized as being proportional and balanced. As an illustration, many forms such as square, rectangle, and circle are symmetric along their respective lines of symmetry. Translational, rotational, and reflectional symmetry are the three different forms of symmetry. Symmetrical pictures may be seen in a variety of objects, including leaves, fruits, animals, insects, spiderwebs, flowers, and a great deal more. As an illustration, many forms such as square, rectangle, and circle are symmetric along their respective lines of symmetry.

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For the function F(x, y) = x³ + y³ - 3x² - 6y² - 9x ,  the local maximum value is 5 and the local minimum value is -3. The graph is discontinuous, so we cannot locate the saddle points.

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function.

We have the following function -

F(x, y) = x³ + y³ - 3x² - 6y² - 9x

We will plot the 3 dimensional graph of this function. From the model it can be seen that, the local maximum value is 5 and the local minimum value is -3. Since the graph is discontinuous, we cannot locate the saddle points.

Therefore, for the function F(x, y) = x³ + y³ - 3x² - 6y² - 9x ,  the local maximum value is 5 and the local minimum value is -3. The graph is discontinuous, so we cannot locate the saddle points.

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Answer: y^2 - z^2 + 2xy - 2xz

Step-by-step explanation:

(x+y)^2 - (x+z)^2

(x^2 + 2xy + y^2) - (x^2 + 2xz + z^2)

x^2 + 2xy + y^2 - x^2 - 2xz - z^2

x^2 - x^2 + 2xy - 2xz + y^2 - z^2

y^2 - z^2 + 2xy - 2xz

Answer:

The domain is the time, in minutes from 0 to however long it takes to drain the cooler.

The range is from 12 quarts water to empty.

Step-by-step explanation:

I don't see a graph, but will use the given information to identify a domain and range for the information provided.

The domain is the range of values that are possible for the x axis.  In this case, the x axis it time, in minutes.  If we set x as the time, in minutes, that the water has been draining, time = 0, is the start of the process.  

The y axis, the range, starts at 12 quarts at time = 0.  It then decreases with time until the cooler is empty.  The range of the function is thus 12 quarts to 0 quarts:  Full to empty.

If we knew the actual rate that the cooler drains (e.g., quarts/minute), we could estabish an upper limit to the domain.  If a graph were shown of the data, this rate could be calculated and an upper end to the domain could be set.  If the rate were 2 quarts/minute, the upper end of the domain would be (12 quarts/2 quarts/minute) = 6 minutes.  The domain would be 0 - 6 minutes.

The table that accurately identifies the three points of the graph is table 1.

A proportional relationships are relationships between two variables where their ratios are equivalent.

The variables are time in hours and earnings.

Therefore,

y = kx

where

A student earns $8.50 per hour working in a library.

Hence,

y = 8.50x

when x = 2

y = 8.50(2) = 17 dollar

when x = 4

y = 8.50(4) = 34 dollar

when x = 8

y = 8.50(8) =  68 dollar

Therefore, the table that reflects the graph is table 1.

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The radius of the roundabout whose circumference is given is: 55 feet.

What is circumference?

The perimeter of a circle or ellipse is known as its circumference in geometry (from the Latin circumferens, meaning "carrying around"). That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

As given in the question ,  

The circumference of the roundabout is 345.4 feet.

and we need to find the radius,

We know that, the circumference is calculated by:

Circumference = 2 π r

So, putting value of circumference,

345.4 = 2 (3.14) r

r = 345.4/6.28

r = 55 feet

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(1, 0) is the solution of the line y = 3x - 3

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

The given line is

y = 3x - 3

To test whether (1, 0) is a solution of the line y = 3x - 3

Putting x = 1

y = 3[tex]\times[/tex] 1 - 3 =

y = 3 - 3

y = 0

(1, 0) is the solution of the line y = 3x - 3

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Lines 5(x+3) and y=5x+1 both are parallel.

What are parallel lines?

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

Here, we have

Given equations = 5(x+3) and y=5x+1

Now we write both equations in standard form and we get

y = 5x + 3,

y = 5x + 1

Then, we compare the slopes of both equations and we get

Slope = 5

Hence, the slope of both equations is the same. so, the given lines are parallel.

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