Two towns are 6 inches apart on a map. If the scale for this map is 1 inch equals 100 miles, how many miles apart are the two towns?

Answer:

1350

Step-by-step explanation:

We can write a proportion to find the total amount in the school this year using the information given. A proportion is two equivalent ratios set equal to each other. If 10% has decreased, then 90% is now left.

[tex]\frac{10}{100}=\frac{y}{1500}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

10(1500)=100(y)

15000=100y

y=150

Y is the number of students who are now gone. We subtract 1500-150=1350

The simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The linear expression is:

= 5x - 5x + 3x - 3x

After simplification:

= 0 + 3x - 3x

= 0

All terms are canceled out,

Thus, the simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.

Learn more about the linear equation here:

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Answer: 4,050, 12,150, 36,450

Step-by-step explanation: multiply each following number by 3

Answer:

4050; 12150; 36450

Step-by-step explanation:

[tex]a_5 = 50.3^4 \\\ a_5 = 4050 \\\ a_6 = 50.3^5 \\\ a_6 = 12150 \\\ a_7 = 50.3^6 \\\ a_7 = 36450[/tex]

I hope I helped you.

Add 350 mL of the 90% alcohol mixture to obtain a 70% alcohol solution.

Let V be the volume of the 90% alcohol solution needed

Set up the equation

The final mixture volume will be 200 + V mL.

- The total amount of alcohol in the final mixture should be 70% of the total volume.

Calculate the total amount of alcohol

- Amount of alcohol from 200 mL of 35% solution: 0.35 * 200 = 70 mL.

- Amount of alcohol from V mL of 90% solution: 0.90 * V mL.

Total amount of alcohol in the final solution

- Total alcohol = 70 + 0.90V mL.

Set up the equation for the final concentration

- Final concentration: 70%

0.70 *(200 + V) = 70 + 0.90V

Solve the equation

0.70 * (200 + V) = 70 + 0.90V

140 + 0.70V = 70 + 0.90V

140 - 70 = 0.90V - 0.70V

70 = 0.20V

V = 70 / 0.20 = 350 mL.

Answer:

The gratuity  added is $28.2 .

Step-by-step explanation:

As given

A restaurant automatically charges a 20% gratuity if a party has 6 or more people.

The bill of the party is $141.

20% is written in the decimal form.

[tex]= \frac{20}{100}[/tex]

= 0.20

Gratuity is added to a party = 0.20 × 141

                                             = $28.2

Therefore the gratuity added is $28.2 .

Answer: The gratuity added is $28.2.

Answer:

2.1 yards of blue material will she need.

Step-by-step explanation:

As per the given statement:  Sue buys material for a costume she buys 1.75 yards of red material.

As she bought 1.75 yards of the red material.

For blue material she bought 1.2 times as much as yard of the red material.

"times" represents multiply

Blue material she will need =  [tex]1.2 \times 1.75 = 2.1 yards[/tex]

therefore, 2.1 yards of blue material will she need.

Answer: 11 and 6

Step-by-step explanation:

I think this is it because she is 5 years younger and last year she was half of his age so he was 10 then you have to add another year to their age because that was last year, 5+1=6, 10+1=11. but im not completely sure so if you can wait for someone else or if you agree go ahead and answer it.

We'll call the ages n and s

Nancy is 5 yrs younger than her brother Stan

n = s - 5

Last year she was half as old as he was

n - 1 = (1/2) ( s - 1 )

We substitute for n

s - 5 - 1 = (1/2) (s - 1)

2s - 12 = s - 1

s = 11

n = s - 5 = 6

Answer: Nancy is 6, Stan is 11

Check:

Clearly they're five years apart.  Last year they were 5 and 10, half, good.

The shaded region, which is approximately 251.74 cm².

For the area of the shaded region, we need to calculate the area of a trapezium and the area of two semicircles.

Given data: AB = 28 cm , DC = 12cm and h = 14 cm

The formula for the Area of Trapezium:
Area of trapezium = 1/2 × (AB + DC) × h
Substituting the given values:
Area of trapezium = 1/2 × (28 + 12) × 14 = 280 cm²

The formula for the Area of a Semicircle:
Area of semicircle = πr²/2
Given that the radius r is 3 cm:
Area of two semicircles = 2 × π × 3²/2 = 28.26 cm²

Area of the Shaded Region:
Area of shaded region = Area of trapezium - Area of two semicircles
Area of shaded region = 280 - 28.26 ≈ 251.74 cm²

Therefore, the area of the shaded region is approximately 251.74 cm².

Answer:

25/24 pounds of total meat processed.

Step-by-step explanation:

We have been given pounds of bologna and 3/8 pounds of ham and 2/4 pound turkey

And we need to find the total number of pounds of meat processed.

The total number will be calculated by finding their sum of all the meats which is

1/6+3/8+2/4

Taking LCM of (6,8,4)=24 hence, we get:

1/6+3/8+2/4= 25/24

Final answer:

Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.

Explanation:

Phyllis Doran worked a total of two different shifts across Monday and Tuesday. On Monday, she worked for 7 1/2 hours. On Tuesday, she started at 8:00 a.m. and finished at 1:00 p.m., which is a 5-hour shift.

To find the total number of hours Phyllis worked, we add the hours from both days together.

Monday: 7.5 hours
Tuesday: 5 hours (since 1:00 p.m. is 5 hours after 8:00 a.m.)

Now, we sum these up:
Total hours worked = 7.5 hours + 5 hours = 12.5 hours.

So, Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.

Answer:

A

Step-by-step explanation:

The expansion of (x +y)⁴ is ...

... x⁴ +4x³y +6x²y² +4xy³ +y⁴

The expansion coefficients are 1, 4, 6, 4, 1; the sum of exponents is always 4, and there are 5 terms.

Answer:

B

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The units are stokes per hole or strokes / hole

Jordan had the lowest number of strokes / hole followed by Rickie and finally Rory.

Answer:

Jordan had the lowest number of strokes per hole

Step-by-step explanation:

1) Total holes played by Rory = 9

Total strokes of Rory = 42

Number of stroke per hole: Rory

[tex]\frac{42 strokes}{9 hole}=4.667 strokes/hole[/tex]

2)Total holes played by Jordan = 18

Total strokes of Jordan = 79

Number of stroke per hole: Jordan

[tex]\frac{79 strokes}{18 hole}=4.389 strokes/hole[/tex]

3) Total holes played by Rickie  = 27

Total strokes of Rickie = 123

Number of stroke per hole: Rickie  

[tex]\frac{123 strokes}{27 hole}=4.556 strokes/hole[/tex]

4.667 strokes/hole > 4.556 strokes/hole > 4.389 strokes/hole

Rory > Rickie > Jordan

Jordan had the lowest number of strokes per hole

Answer:

Might not be congruent

Step-by-step explanation:

You don't have enough information

Answer with explanation:

It is given that,In ΔABC and Δ DEF

  ∠C =∠F⇒⇒[Given]

To prove that two triangles are similar, we can use following Similarity axiom which are

a.→ AA

b.→S AS

c.→SSS

→Ratio of sides of two triangles should be proportional while proving similarity of two triangles.

But, Here between two triangles , only one angle is congruent ∠C and ∠F.So, we can't conclude that these two triangles that is, ΔABC and Δ DEF are similar.

Option D:→ Not

6 hours

The two hoses together take 1/3 the time (4/12 = 1/3), so the two hoses together are equivalent to 3 of the first hose.

That is, the second hose is equivalent to 2 of the first hose. Two of the first hose could fill the vat in half the time one of them can, so 6 hours.

The second hose alone can fill the vat in 6 hours.

_____

The first hose's rate of doing work is ...

... (1 vat)/(12 hours) = (1/12) vat/hour

If h is the second hose's rate of doing work, then working together their rate is ...

... (1/12 vat/hour) + h = (1/4 vat/hour)

... h = (1/4 - 1/12) vat/hour = (3/12 -1/12) vat/hour = 2/12 vat/hour

... h = 1/6 vat/hour

so will take 6 hours to fill 1 vat.

The second hose can fill the vat alone in 6 hours, calculated by subtracting the work rate of the first hose from their combined work rate.

The question is about the time it would take for the second hose to fill the large vat alone, given that the first hose takes 12 hours alone, but together they take 4 hours. We are not given any info about the hose size or flow rate, so those don't need to be involved here.

We can analyze this problem in terms of work done. We know that one hose can fill the vat in 12 hours, so its work rate is 1/12 of the vat per hour. When we add the second hose, the vat is filled in 4 hours. The combined work rate of both hoses is 1/4 of the vat per hour.

To find the work rate for the second hose, we subtract the work rate of the first hose from the combined work rate: 1/4 - 1/12 = 1/6. This means the second hose can fill the vat in 6 hours alone.

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Answer:

x is greater than or equal to 358

Step-by-step explanation:

1. Subtract 100 from 18,000

2. Divide by 50 to get your number of seven letter words

[tex]h(x+5)=3x+18\\\\h(x)=mx+b\to h(x+5)=m(x+5)+b=mx+5m+b\\\\\text{Therefore we have}\ m=3\ \text{and}\\\\5m+b=18\to5(3)+b=18\\\\15+b=18\qquad\text{subtract 15 from both sides}\\\\b=3\\\\Answer:\ \boxed{h(x)=3x+3}[/tex]

To find the function h(x) when given h(x+5)=3x+18, we substitute x with (x-5) in 3x+18 to make h(x) = 3x+3.

To find the function h(x), we need to replace (x+5) in the equation with x. The given equation is h(x+5)=3x+18.

We know that if we substitute x+5 with x in h(x+5), we must also substitute the x in 3x+18 with (x-5) to keep the equation and function consistent.

So, we replace x with (x-5) in 3x+18, and our new equation will be 3(x-5)+18.

This simplifies to 3x - 15 + 18, which further simplifies to 3x+3.

Consequently, the function h(x) = 3x+3.

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For this case we must factor the following expression: [tex]6x ^ 2-9x-6[/tex]

We test the options:

Option A:

[tex]3 (2x + 1) (x-2) =[/tex]

We apply distributive property for the first parenthesis:

[tex](6x + 3) (x-2) =[/tex]

We apply distributive property of the form:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

[tex]6x ^ 2-12x + 3x-6 =[/tex]

Different signs are added and the sign of the major is placed.

[tex]6x ^ 2-9x-6[/tex]

So, [tex]3 (2x + 1) (x-2) = 6x ^ 2-9x-6[/tex]

Answer:

Option A

Answer:

[tex]f(t)=43,200-7200t[/tex]

Step-by-step explanation:                      

We have been given that a delivery company purchased a new delivery truck for $43,200. The depreciated value of the truck can be estimated by the number of t years in service. The truck depreciates at a rate of $7,200 per year.

This means that after t years truck will depreciate 7200t. To find the truck's depreciated value after t years we will subtract 7200t from the cost of new delivery truck (43,200).  

[tex]f(t)=43,200-7200t[/tex]          

Therefore, the function [tex]f(t)=43,200-7200t[/tex] could be used to estimate the truck's depreciated value after t years.

The depreciated value of the truck after t years can be estimated by the linear function ƒ(t) = 43200 - 7200t, reflecting a straight-line depreciation method at a rate of $7,200 per year.

To estimate the depreciated value of the delivery truck after t years, we can use a linear equation which reflects a straight-line depreciation method. Since the truck cost $43,200 and depreciates at a rate of $7,200 per year, the equation representing the depreciated value of the truck after t years would be ƒ(t) = 43200 - 7200t. This equation starts with the initial value of the truck and subtracts the depreciation cost multiplied by the number of years the truck has been in service.

Depreciation is a way businesses can allocate the cost of a physical asset over its useful life. In this case, each year the truck is in service, it loses $7,200 in value. After one year, the value of the truck would be $43,200 - $7,200, which equals $36,000, and you would continue to subtract $7,200 for each additional year to determine the truck's value at any given time.

Answer:

$ 25.31 finance charges  he can save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle

Step-by-step explanation:

In the beginning of Month ,  ADB will be on the total amount of balance and the purchase that means ADB = 0.21 (2360 + 1500)/12

= $ 67.55

ADB at the end of the month  

Part of 2360 for 27 days = (2360 x 27)/28 = $ 2275.71

Part of 3860 for 1 day = (3860 x 1)/28 = $ 137.85

So the total becomes $ 2275.71 + $ 137.85 = $ 2413.56

So , ADB will be $ 2413.56 x (0.21)/12

= $ 42.23  

Difference in the finance charges at the beginning and at the end of the month is  

$ 67.55 - $ 42.23

= $ 25.31

Answer:

it would be 20%

Step-by-step explanation:

out of 100% you would subtract the 23%, 30%, 15% and, 12% and you would get 20%

Answer:

The opposite of Carlos's elevation would be +12ft.

Step-by-step explanation:

This question is using positive and negative integers to represent elevation and descending.  The surface of the pool would represent an elevation of 0, where we are level.  However, when Carlos descends (swims to the bottom) of the pool, he is at an elevation of -12 because he is below the surface.  The opposite of -12 would be +12.  So the opposite of where Carlos is -12ft below the surface of the water would be +12 foot above the surface of the water.  

Answer:

9

Step-by-step explanation:

45/5 = 9

Answer:

[tex]x^3-3x^2+2x-\frac{3}{2}[/tex]

Step-by-step explanation:

We can divide polynomials by other polynomials by dividing each term by the denominator. Remember, when we divide a variable by itself, we must change the exponent in our answer according to exponent rules.

[tex]\frac{ (2x^4-6x^3+4x^2-3x)}{2x}=\frac{2x^4}{2x} -\frac{6x^3}{2x} +\frac{4x^2}{2x} -\frac{3x}{2x} =x^3-3x^2+2x-\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

11.73%

Step-by-step explanation: