A machinist produced 22 items during a shift. Three of the 22 items were defective and the rest were not defective. In how many different orders can the 22 items be arranged if all the defective items are considered identical and all the nondefective items are identical of a different class?

The correct answer would be B.

The lower e is used for continuous compounding and it is raised by the interest rate times the amount of time

Formula  that describes the value of an initial investment of [tex]\$300[/tex] growing at an interest rate of [tex]6\%[/tex] compounded continuously is equals to [tex]A(t) = 300e^{.06t}[/tex].

" Compounded continuously is defined as the interest calculation and reinvestment of the amount over infinite period."

Formula used

[tex]A(t) = P e^{rt}[/tex]

[tex]A(t) =[/tex] Final amount

[tex]P =[/tex] Principal amount

[tex]t =[/tex]  time period interest is applied

[tex]r=[/tex] rate of interest

According to the question,

Given,

Principal amount [tex]= \$300[/tex]

Rate of interest [tex]= 6\%[/tex]

As per the given condition interest compounded continuously,

Substitute the value in the formula of interest compounded continuously  we get,

[tex]A(t) = 300 e^{\frac{6}{100} t}\\\\\implies A(t) = 300 e^{.06 t}[/tex]

Hence, Option (B) is the correct answer.

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Step-by-step explanation:

(a) If g is the number of gallons left in the tank, and t is the time in hours since 8AM:

g = 8 gal − (1 gal / 24 mi) (60 mi / 1 hr) (t hr)

g = 8 − 2.5t

(b) If d is the distance traveled:

d = 60 mi/hr × t hr

d = 60t

(c) When George runs out of gas, g = 0.

0 = 8 − 2.5t

t = 3.2

The distance he travels is:

d = 60(3.2)

d = 192

George travels 192 miles.

3.2 hours after 8AM, the time is 11:12AM.

Answer:

Step-by-step explanation:

Part 1:

An equation of sine wave can be written as y = 5 Sin(2x + 3).

The amplitude of the above equation is 5.

The period of the function is [tex]\frac{2\pi }{2} = \pi[/tex].

The frequency of the function is [tex]\frac{1}{\pi }[/tex].

Part 2:

[tex]y = 2 Sin(3x + 5) + 9.......(1)\\y = 5 Sin(4x + 8) + 12.....(2)\\y = 3 Sin(x + 6) + 2......(3)[/tex]

The above given equations numbered 1, 2 and 3 represents three different sound waves.

For (1), the frequency is [tex]\frac{1}{\frac{2\pi }{3} } = \frac{3}{2\pi }[/tex].

For (2), the frequency is [tex]\frac{4}{2\pi } = \frac{2}{\pi }[/tex].

For (3), the frequency is [tex]\frac{1}{2\pi }[/tex].

Frequency of sounds refers the speed of vibration.

The taken three siounds has different frequencies.

Answer:

Step-by-step explanation:

p = 120 ± 4

Answer: she has 310 small marbles, 62 medium marbles and 188 large marbles.

Step-by-step explanation:

Let w represent the number of small marbles Amy has.

Let x represent the number of medium marbles Amy has.

Let y represent the number of large marbles Amy has.

a) She has five times as many small marbles as medium marbles. This means that

w = 5x

b) The number of large marbles is two more than three times the number of medium marbles. This means that

y = 3x + 2

c) If Amy has a total of 560 marbles, it means that

5x + x + 3x + 2 = 560

9x = 560 - 2

9x = 558

x = 558/9 = 62

w = 5x = 62 × 5

w = 310

y = 3x + 2 = 3 × 62 + 2

y = 188

Answer:

A. s = 5x

B. y = 3x + 2

C y=166

Step-by-step explanation:

Answer: The larger rug is 4 times larger

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

The small circular rug covers an area of approximately 67 square feet. This means that

67 = πr²

r² = 67/π = 67/3.14 = 21.34

r = √21.34 = 4.62

If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be

2 × 4.62 = 9.24

The area of the larger rug would be

3.14 × 9.24² = 268.06ft²

Therefore

268.06/67 = 4

The larger rug is 4 times larger

Answer: $4.50 per candle

Step-by-step explanation:

$32.55 - $17.50 - $1.55 = $13.50 for all the candles

To find the price of a single candle we divide our answer by 3

13.50/3 = $4.50

Answer:

A

Step-by-step explanation:

Answer:

$ 270

Step-by-step explanation:

Do 250 X 1.08 to get the answer

Using the percentage increase formula, John's bank account value of $250 will increase by 8% to $270 after one year.

To find the future value of John's bank account, we will use the percentage increase formula. If his account increased by 8% this year to $250, we can calculate next year's balance by multiplying $250 by 1.08 (which represents a 100% principal plus an 8% increase).

Step-by-step calculation:

Therefore, the value of John's bank account if it increases by the same percentage over the next year will be $270.

Answer:

Aidan got 56% of votes.

Step-by-step explanation:

Given:

Aidan is running for student body president. In today's election, he received 462 votes out of a total of 825 votes cast.

Now, to find the percent of votes did Aidan get.

Total votes cast = 825 votes.

Votes he received = 462 votes.

Now, to get the percent of votes Aidan get:

[tex]\frac{Votes\ he\ received}{Total\ votes\ cast} \times 100[/tex]

[tex]=\frac{462}{825} \times 100[/tex]

[tex]=0.56\times 100[/tex]

[tex]=56\%.[/tex]

Therefore, Aidan got 56% of votes.

Answer:

56%

Step-by-step explanation:

Aidan got fifty-six percent of the votes.

To solve this problem, start by letting p represent the unknown percent and write the percent as the fraction p over one hundred.

Write a second ratio that expresses the part-whole relationship between the numbers four hundred sixty-two over eight hundred twenty-five.

Set up a proportion between the two ratios.

Write the cross product equation. Eight hundred twenty-five p equals one hundred times four hundred sixty-two, or eight hundred twenty-five p equals forty-six thousand two hundred.

Divide each side of the equation by eight hundred twenty-five to solve for p.

p equals fifty-six.

Aidan received fifty-six percent of the votes cast.

Answer: the value of y is 180

Step-by-step explanation:

If y varies directly as x, then as y increases,x increases and as y decreases, x decreases.

We would introduce a constant of proportionality, k. Therefore,

y = kx

When y = - 18, x = - 2

Therefore,

- 18 = - 2 × k

Dividing the left hand side and the right hand side of the equation by

- 2, it becomes

- 2k/ -2 = - 18/-2

k = 9

The expression becomes

y = 9x

Therefore, when x = 20,

y = 9 × 20 = 180

Yo sup??

since y varies directly with x we can say

y=kx

at y=-18, x=-2 then

-18=k*(-2)

k=9

therefore

y=9x

at x=20

y=9*20

=180

Hope this helps.

Answer:

C) ¼ ∫ u⁵ du, where u = sin(4x)

Step-by-step explanation:

∫ cos(4x) sin⁵(4x) dx

Using u substitution:

u = sin(4x)

du = 4 cos(4x) dx

¼ du = cos(4x) dx

¼ ∫ u⁵ du

Answer:

1998

y=6x+1944

Step-by-step explanation:

The percentage of Male workers who prefer a female boss over a male boss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss

it is explicit from the question that 9% of male workers prefer female boss in 1998. but we can predict a model for this by getting the slope of the graph

y=the year

x=the percentage of men who prefer a female boss

s=y2-y1/(x2-x1)

s=1998-1974/(9-5)

s=24/4

s=6

therefore we have

y=mx+c

y=6x+c........1

when y=1998,x=9

1998=6(9)+c

c=1944

from equation 1

y=6x+1944

Answer:

B, An  n-by-m array.

Step-by-step explanation:

when working with  2D arrays, rows come first and then columns. so all options here are correct except option B

Answer: 623 inches

Step-by-step explanation:

We can model this escalator as a right triangle, in which its length is the hypotenuse and its vertical rise ([tex]x[/tex]) is on of the sides of the triangle (as shown in the figure).

So, if we want to find [tex]x[/tex] we have to use the trigonometric function sine:

[tex]sin(15\°)=\frac{opposite-side}{hypotenuse}[/tex] (1)

Here, the opposite side is [tex]x[/tex] and the hypotenuse is [tex]200 ft 9 in[/tex].

Now we have to transform  [tex]200 ft 9 in[/tex] to inches, in this case we only have to convert [tex]200 ft[/tex] to inches, knowing that [tex]1 ft=12 in[/tex]:

[tex]200 ft \frac{12 in}{1 ft}=2400 in[/tex]

[tex]200 ft + 9 in=2400 in+ 9 in=2409 in[/tex]

Substituting this value in (1):

[tex]sin(15\°)=\frac{x}{2409 in}[/tex] (2)

Isolating [tex]x[/tex]:

[tex]x=frac{sin(15\°)}{2409 in}[/tex]

Finally:

[tex]x=623.49 in \approx 623 in[/tex]

Answer: 233,168

Step-by-step explanation:

Formula: 1 + 2 + 3 + ... + n = n(n+1)/2

Sum of all the numbers below 1000 that is divisible by 3:

3 + 6 + 9 + ... + 999 = 3 (1 + 2 + 3 + ... + 333) = 3 x 333 x 334 / 2 = 166,833

Sum of all the numbers below 1000 that is divisible by 5:

5 + 10 + 15 + ... + 995 = 5 (1 + 2 + 3 + ... + 199) = 5 x 199 x 200 / 2 = 99,500

As we add up 166,833 and 99,500, the numbers that are divisible by 3*5 = 15 would be counted double. Therefore, subtract the result for numbers divisible by 15 just once:

Sum of all numbers below 1000 that is divisible by 15:

15 + 30 + 45 + ... + 990 = 15 (1 + 2 + 3 + ... + 66) = 15 x 66 x 67 / 2 = 33165

Therefore, [ 166,833 + 99,500 ] - 33,165 = 233,168

To find the sum of all the multiples of 3 or 5 below 1000, you need to find the sum of the multiples of 3 and 5 separately and then subtract the sum of the multiples of 15. The sum is 233,003.

To find the sum of all the multiples of 3 or 5 below 1000, we can use the concept of arithmetic series. First, we need to find the sum of the multiples of 3 and the sum of the multiples of 5 below 1000. Then, we need to subtract the sum of the multiples of 15 (since numbers that are multiples of both 3 and 5 have been counted twice).

Using the formula for the sum of an arithmetic series, the sum of the multiples of 3 below 1000 is given by:

3 + 6 + 9 + ... + 999 = (1/2)(3 + 999)(333) = 166,833

Similarly, the sum of the multiples of 5 below 1000 is:

5 + 10 + 15 + ... + 995 = (1/2)(5 +995)(199) = 99,500

Finally, the sum of the multiples of 15 below 1000 is:

15 + 30 + 45 + ... + 990 = (1/2)(15 + 990)(66) = 33,330

Now, we can calculate the sum of all the multiples of 3 or 5 by adding the sum of the multiples of 3 to the sum of the multiples of 5 and then subtracting the sum of the multiples of 15:

166,833 + 99,500 - 33,330 = 233,003

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Answer:

Step-by-step explanation:

Ben's car gets between 18 and 21 miles per gallon of gas. If his car's tank holds 15 gallons, it means that the least distance that Ben can drive on one tank of gas would be

18 × 15 = 270 miles.

Also, the most distance that Ben can drive on one tank of gas would be

21 × 15 = 315 miles.

Therefore the the range of distance that Ben can drive on one tank of gas is between 270 miles and 315 miles. If d represents the distance, then the range is

270 ≤ d ≤ 315)

Answer:

4%

Step-by-step explanation:

Let the stock be $10

A 20% decline = 80/100 * 10

= 8

A 30% increase = 30/100 * 8

= 2.4 + 8 = 10.4.

Overall increase = 10.4 - 10 = 0.4

Percentage overall increase = 0.4/10 * 100

= 4%

well, we know the sine, and we also know that we're on the II Quadrant, let's recall that on the II Quadrant sine is positive whilst cosine is negative.

[tex]\bf sin^2(\theta)+cos^2(\theta)=1~\hspace{10em} tan(\theta )=\cfrac{sin(\theta )}{cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ sin^2(a)+cos^2(a)=1\implies cos^2(a) = 1-sin^2(a) \\\\\\ cos^2(a) = 1-[sin(a)]^2\implies cos^2(a) = 1-\left( \cfrac{3}{4} \right)^2\implies cos^2(a) = 1-\cfrac{3^2}{4^2} \\\\\\ cos^2(a) = 1-\cfrac{9}{16}\implies cos^2(a) = \cfrac{7}{16}\implies cos(a)=\pm\sqrt{\cfrac{7}{16}}[/tex]

[tex]\bf cos(a)=\pm\cfrac{\sqrt{7}}{\sqrt{16}}\implies cos(a)=\pm\cfrac{\sqrt{7}}{4}\implies \stackrel{\textit{on the II Quadrant}}{cos(a)=-\cfrac{\sqrt{7}}{4}}\\\\[-0.35em]~\dotfill\\\\tan(a)=\cfrac{sin(a)}{cos(a)}\implies tan(a)=\cfrac{~~\frac{3}{4}~~}{-\frac{\sqrt{7}}{4}}\implies tan(a)=\cfrac{3}{4}\cdot \cfrac{4}{-\sqrt{7}}\\\\\\tan(a)=-\cfrac{3}{\sqrt{7}}\implies \stackrel{\textit{rounded up}}{tan(a) = -1.13}[/tex]

Answer:

(1) ADB = CDB = 90°

(2) c sinA

(3) (sinA)/a = (sinB)/b

Step-by-step explanation:

1. ADB = CDB = 90°

2. c sinA

since,

sin A = x/c , sin C = x/a

so x = c sinA and a sinC

3. from reflective property of x,

since x = c sinA

and x = a sinC

we substitute each equivalently

that is,

c sinA = a sinC

dividing each sides of the equation by ac we have ,

(c sinA)/ac = ( a sinC)/ac

simplifying we have,

(sinA)/a = (sinB)/b

Therefore the above equation is referred to as the SINE RULE.

Answer:

The question continues ; Which of the following is true ;

Jaylan basis in the partnership is $12,00 and Caspers is 10,000

Jaylan and Casper each have a basis in the partnership of 12,000

Jaylan will have a larger share of the profits than Casper

The first and third answers are both correct

Answer ; Jaylan and Casper each have a basis in the partnership of 12,000

Step-by-step explanation:

Both Jaylan and casper will have a partnership basis of $12,000 , it was mentioned initially in the question that (Jaylan and casper are equal partners in J&C racoon hats), equal partners implies both Jaylan and casper with have equal profit and equal losses as the case maybe Irrespective of the amount each contributed. Hence Jaylan and Casper each have a basis in the partnership of 12,000.

Answer: The  length of the shorter side of a golden rectangle is about 24.7 inches.

Step-by-step explanation:

Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.

Since 1.62 > 1 , so

[tex]\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}[/tex]

If the length of the longer side is 40 inches , then we have

[tex]\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}[/tex]

Hence, the  length of the shorter side of a golden rectangle is about 24.7 inches.

To find the length of the shorter side of a golden rectangle with a longer side of 40 inches, divide 40 by the golden ratio (1.62), yielding approximately 24.7 inches as the length of the shorter side, rounded to the nearest tenth.

To calculate the length of the shorter side of a golden rectangle with a longer side length of 40 inches, we use the ratio of the sides of a golden rectangle. Given that this ratio is about 1 to 1.62, we divide the length of the longer side by the golden ratio (approximately 1.62) to find the length of the shorter side.

Using this method:

Let's do the calculation:

Length of shorter side ≈ 24.7 inches (rounded to the nearest tenth)

Answer:

3 employees

Step-by-step explanation:

The complete question is

The manager of a fast food restaurant collected data to study the relationship between the number of employees working registers and the amount of time customers waited in line to order. He made a scatter plot of the data and created a trend line with the equation y = -70x + 300, where y is the total amount of time waited in seconds and x is the number of employees working registers. Maria went to the restaurant and waited 90 seconds to place her order. Use the trendline equation to predict how many employees were working. Round to the nearest whole number if necessary.

Let

x ---> is the number of employees working registers

y ---> is the total amount of time waited in seconds

we have

[tex]y=-70x+300[/tex]

This is the equation of a line in slope intercept form

where

The slope is equal to

[tex]m=-70\ \frac{seconds}{employee}[/tex] ---> is negative because is a decreasing function

The y-intercept is equal to

[tex]b=300\ sec[/tex]

For y=90 seconds

substitute in the linear equation and solve for x

[tex]90=-70x+300[/tex]

[tex]70x=300-90\\70x=210\\x=3\ employees[/tex]

To predict the number of employees based on a 90-second wait time, substitute 90 into the given trend line equation and solve for y. For example, using y = -0.1x + 10, we get approximately 1 employee. Ensure you use the specific trend line equation provided for accurate results.

To predict how many employees were working based on Maria's wait time of 90 seconds, we need the trend line equation that describes the relationship between waiting time and the number of employees.

Assuming we have a trend line equation of the form y = mx + b,

you can substitute 90 for x and solve for y.

For example, if the trend line equation is y = -0.1x + 10, substituting 90 for x:

y = -0.1(90) + 10

y = -9 + 10

y = 1

Therefore, according to this trend line, approximately 1 employee would be working. Always remember to check your specific trend line equation and solve accordingly.

Answer:

Step-by-step explanation:

Let h represent the number of hours that Jamarcus can rent the truck.

To rent a truck, the charge is $16 per hour and also a fueling fee of $25

The total cost of renting the truck for x hours would be

16h + 25

Since Jamarcus wants to rent the truck and can spend no more than $125, the inequality representing the situation would be

16h + 25 ≤ 125

16h ≤ 125 - 25

16h ≤ 100

h ≤ 6.25

2) 3x - 5 ≥ - 11

3x ≥ - 11 + 5

3x ≥ - 6

x ≥ - 6/3

x ≥ - 2

The correct graph is option A

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)

To find, the area of the shape (quadrilateral) = ?

We know that,

The area of quadrilateral = [tex]\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]

= [tex]\dfrac{1}{2} [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)][/tex]

= [tex]\dfrac{1}{2} [1(4)+5( 0)+7( -4)+1}( 0)][/tex]

= [tex]\dfrac{1}{2} [4+0-28+0][/tex]

= [tex]\dfrac{1}{2} [32][/tex]

= 16 square units.

Thus, the area of the shape (quadrilateral) is 16 square units.

Answer:

g6h12

Step-by-step explanation:

Answer:  mmmmm.

Step-by-step explanation:

Answer: the cost of Parker's tuition is $17955

Step-by-step explanation:

Let x represent the cost of Parker's tuition.

Parker was able to pay 44% of his college tuition with his scholarship. This means that the amount that he was able to pay with his scholarship would be

44/100 × x = 0.44 × x = 0.44x

The amount that is remaining for him to pay would be

x - 0.44x = 0.56x

If he paid the remaining $10,054.52 with a student loan, it means that

0.56x = 10054.52

x = 10054.52/0.56

x = 17954.5

Rounding up to the nearest whole number, it becomes

x = $17955

Answer:

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle

DF represents the hypotenuse of the right angle triangle.

With m∠D as the reference angle,

DE represents the adjacent side of the right angle triangle.

EF represents the opposite side of the right angle triangle.

To determine EF, we would apply the Sine trigonometric ratio

Sin θ = opposite side/hypotenuse. Therefore,

Sin 26 = EF/4.5

0.44 = EF/4.5

EF = 4.5 × 0.44 = 1.98 yo 2 decimal places

Answer:

a) 21.2%

b)  $176.05 or more

c) 15.87%    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $155

Standard Deviation, σ = $25

We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) P(spends more than $175 per week on groceries)

P(x > 175)

[tex]P( x > 175) = P( z > \displaystyle\frac{175 - 155}{25}) = P(z > 0.8)[/tex]

[tex]= 1 - P(z \leq 0.8)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%[/tex]

b) P(X > x) = 0.2

We have to find the value of x such that the probability is 0.2

P(X > x)  

[tex]P( X > x) = P( z > \displaystyle\frac{x - 155}{25})=0.2[/tex]  

[tex]= 1 -P( z \leq \displaystyle\frac{x - 155}{25})=0.2 [/tex]  

[tex]=P( z \leq \displaystyle\frac{x - 155}{25})=0.8 [/tex]  

Calculation the value from standard normal z table, we have,  

[tex]P(z < 0.842) = 0.8[/tex]

[tex]\displaystyle\frac{x - 155}{25} = 0.842\\\\x = 176.05[/tex]  

A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.

c) My family spends on average $130 dollars on groceries.

P(less than $130)

[tex]P( x < 130) = P( z < \displaystyle\frac{130 - 155}{25}) = P(z < -1)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]

Thus, my family percentile is 15.87%

a) 21.2%
b)  $176.05 or more
c) 15.87%    

We are given the following information in the question:
Mean, μ = $155
Standard Deviation, σ = $25
We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_(score) = \displaystyle(x-\mu)/(\sigma)[/tex]
a) P(spends more than $175 per week on groceries)
[tex]P(x > 175)P( x > 175) = P( z > \displaystyle(175 - 155)/(25)) = P(z > 0.8)= 1 - P(z \leq 0.8)[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%\\[/tex]

b) [tex]P(X > x) = 0.2[/tex]
We have to find the value of x such that the probability is 0.2
[tex]P(X > x) \\P( X > x) = P( z > \displaystyle(x - 155)/(25))=0.2 \\= 1 -P( z \leq \displaystyle(x - 155)/(25))=0.2 \\=P( z \leq \displaystyle(x - 155)/(25))=0.8[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(z < 0.842) = 0.8\\\displaystyle(x - 155)/(25) = 0.842\n\nx = 176.05[/tex]
A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.

c) My family spends on average $130 dollars on groceries.
P(less than $130)
[tex]P( x < 130) = P( z < \displaystyle(130 - 155)/(25)) = P(z < -1)[/tex]
Calculation the value from standard normal z table, we have,  
[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]
Thus, my family percentile is 15.87%

Answer:question 1)$6.66.67

Question2) Rent and expenses =$760

Rent and expenses are too high for the budget

Step-by-step explanation:

1)$2000×(1/3)= $666.67

2)Rent and expenses =$(650+60+10+20+20)= $760

$2100×(1/3)= $700

Rent and expenses should not exceed one third of $2100, which is $700 but it exceeded by$60. Therefore budget is too high.

Final answer:

These Mathematics questions involve calculating budgets to manage income and expenses. For budgeting housing costs, the recommendation is not to exceed one-third of income. A budget table is used to track all monthly expenses against income to determine savings potential and necessary adjustments.

Explanation:

The subject of these questions is Mathematics, specifically focusing on budgeting and personal finance. In these scenarios, students are learning to apply mathematical operations to real-life situations involving income, expenses, and budget planning.

For question 1, you would calculate the maximum amount you should spend on housing from a $2,000 monthly budget by dividing $2,000 by 3, which gives you $666.67. This is because it's recommended to spend no more than one-third of your income on housing.

For question 2, adding together the rent and housing expenses ($650 + $60 + $10 + $20 + $20), you get a total of $760. If you have an income of $2,100, you should not spend more than $700 on housing (which is one-third of your income), so $760 is indeed too high for the budget.

Creating a budget table is an essential skill for financial literacy. When constructing one, you list your monthly income and subtract all your expenses, including housing, utilities, groceries, and any other costs, to see what is left for savings and discretionary spending. For example, with an after-tax monthly income of $2,589.10, if you spend $790 on rent, $75 on a cell phone, and have other listed expenses, you'd subtract all these from your income to see if you can save the desired 10%.