On a map, the distance from Los Angeles to San Diego is 6.35 cm. the scale is 1cm = 20 miles. What is the actual distance?

Answer:

286

Step-by-step explanation:

If the three-digit number is xyz, then:

x + y + z = 16

y = z + 2

z = 3x

Substitute the third equation into the second:

y = 3x + 2

Substitute this and the third equation into the first:

x + (3x + 2) + (3x) = 16

7x + 2 = 16

7x = 14

x = 2

y = 3x + 2 = 8

z = 3x = 6

The number is 286.

The three-digit number where the sum of its digits equal 16, the tens digit is two more than the unit's digit, and the unit's digit is triple the hundreds digit is 286.

The question involves finding a three-digit number where the sum of the digits is 16, the tens digit is two more than the unit's digit, and the unit's digit is triple the hundreds digit. Let's represent the hundreds digit as 'h,' the tens digit as 't', and the units digit as 'u'. According to the problem, we have three equations:

Substituting the third equation into the first, we get h + (3h + 2) + 3h = 16, which simplifies to 7h + 2 = 16, leading to h = 2. Thus, u = 3h = 6, and t = u + 2 = 8. Therefore, the three-digit number is 286.

1) 155.91 grams would be left after 10 years

2) The population would be 376,478 in 2040

Step-by-step explanation:

The form of the exponential function is [tex]y=a(b)^{x}[/tex] , where

1)

Scientists are studying a 500 grams sample of a radioactive element, which has an annual decay rate of 11%

∵ The initial amount is 500 grams

∴ a = 500

∵ The annual decay rate is 11%

∴ r = 11% = 11 ÷ 100 = 0.11

∵ b = 1 - r ⇒ decay

∴ b = 1 - 0.11 = 0.89

- We need to find how many grams of the sample would be left

  after 10 years

∴ x = 10

- Substitute all of these values in the form of the exponential function

∵ [tex]y=500(0.89)^{10}[/tex]

∴ y = 155.9085996

- Round it to 2 decimal places

∴ y = 155.91

155.91 grams would be left after 10 years

2)

In 2000, the population of an Ohio town was 140,212. The population is expected to grow at a rate of 2.5% each year

∵ The population of an Ohio town was 140,212

∴ a = 140.212

∵ The population is expected to grow at a rate of 2.5% each year

∴ r = 2.5% = 2.5 ÷ 100 = 0.025

∵ b = 1 + r ⇒ growth

∴ b = 1 + 0.025 = 1.025

- We need to find the population in 2040

∵ The number of years is 2040 - 2000 = 40 years

∴ x = 40

- Substitute all of these values in the form of the exponential function

∵ [tex]y=140212(1.025)^{40}[/tex]

∴ y = 376478.1709

- Round it to the nearest whole number

∴ y = 376,478

The population would be 376,478 in 2040

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15,567 because yeah i know math

Answer: x = -26

Step-by-step explanation:

3x-47

substitute x with 7: 3(7)-47

3(7) = 21 -47 = -26

Answer:

-26

Step-by-step explanation:

x=7

3 is being multiplied by X

replace X with 7 in your equation

Your equation should then look like this: 3(7)-47

The parentheses around the 7 indicate that the 7 is being multiplied by the 3 or in other words: (3*7)-47

multiply 3 and seven before subtracting 47

3*7= 21

Once you have your answer to that subtract 47, your answer should be a negative # because you are subtracting a larger # from a smaller #

21-47= -26

so if X equals 7.  3x-47= -26

Answer:

OPTION C

Step-by-step explanation:

If SOLUTION A has 4 cups then SOLUTION B has 2. If SOLUTION A has 8 then SOLUTION B has 4.

Note that for every 2 cups of Solution A, we have 1 cup of Solution B.

So, OPTION A is incorrect.

If there are 4 cups of Solution A, then there are 4 + 2 cups in total.

That means the ratio of cups of SOLUTION  A to the total number of cups is:

4 : 6 = 2 : 3

Similarly, 8 : 12 = 2 : 3

And, 12 : 18 = 2 : 3

And, 16 : 24 = 2 : 3

So, we see that the ratio is 2 : 3.

Therefore, OPTION C is the correct answer.

Answer:

kmjinhuygtfdrs

Step-by-step explanation:

Answer:

The total of Charlie's be $7.

Step-by-step explanation:

Given:

Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.

The regular ticket price was $9.00.

And the tax is 6%.

Now, to find Charlie’s total.

So ,we deduct the 25% off first:

[tex]\$9.00-25\%\ of\ \$9.00[/tex]

[tex]=9-\frac{25}{100} \times 9[/tex]

[tex]=9-\frac{225}{100}[/tex]

[tex]=9-2.25[/tex]

[tex]=\$6.75.[/tex]

Now, including tax :

[tex]\$6.75+6\%\ of\ \$6.75[/tex]

[tex]=6.75+\frac{6}{100} \times 6.75[/tex]

[tex]=6.75+0.06\times 6.75[/tex]

[tex]=6.75+0.405[/tex]

[tex]=\$7.155.[/tex]

Approximately = $7.

Therefore, the total of Charlie's be $7.

Answer:

[tex]g(x)=\frac{x}{4}-3[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4x+12[/tex]

Find the inverse

Let

y=f(x)

[tex]y=4x+12[/tex]

Exchange the variables (x for y and y for x)

[tex]x=4y+12[/tex]

Isolate he variable y

subtract 12 both sides

[tex]4y=x-12[/tex]

divide by 4 both sides

[tex]y=\frac{x}{4}-3[/tex]

Let

g(x)=y

[tex]g(x)=\frac{x}{4}-3[/tex] ---> inverse of the function f(x)

To find the calories in a 14 ounce drink, we first determine the calorie content per ounce from a 90 ounce drink. We find it to be about 9.89 calories per ounce. Multiplying this by 14 gives us approximately 138.46 calories in a 14 ounce drink.

To find the calories in a 14 ounce drink, we need to first determine the calorie content per ounce in the 90-ounce drink. This is found by dividing the total calories (890) by the total ounces (90). The number we get from this division (calories per ounce) can then be multiplied by the ounces in the smaller drink (14) to get the number of calories in that drink.

Therefore, a 14 ounce drink from this gas station would have approximately 138.46 calories.

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Answer:

Step-by-step explanation:

3,068 × 108

= 331344

Answer:

331,344

Step-by-step explanation:

Line up the numbers like how u would do it if adding or subtracting and multiply each digit in 108 by each digit in 3068 starting with 8*8. Then do the same with multiplying each digit in 3068 by each digit in 108 starting with 8*8

Answer:

The number of visit so that both plan cost same is 10 .

Both the plan has equivalent choice of benefit

Step-by-step explanation:

Given as :

A gym has two membership plans.

For Gold plan

The charge per month = $50  

The charge per visit = $3

For Platinum plan

The charge per month = $20  

The charge per visit = $6

Let The number of visit for which each plan be same = n visits

Now, According to question

∵ Each plan cost to be same

So,

The charge per month for gold plan+ The charge per visit × numbers of visit = The charge per month for platinum plan+ The charge per visit × numbers of visit

I.e $50 + $3 × n = $20 + $6 × n

Or, $50 - $20 =  $6 × n  -  $3 × n

Or, $30 = ($6 - $3) × n  

Or, $30 = $3 × n  

∴ n = [tex]\dfrac{30}{3}[/tex]

I.e n = 10

So, The number of visits = n = 10

Now, For Gold plan

The charge per month = $50  

The charge per visit = $3 × 10 = $30

So, Total charge for gold plan = $50 + $30 = $80

Similarly For Platinum plan

The charge per month = $20  

The charge per visit = $6×10 = $60

So, For Platinum plan ,total charge = $20 + $60 = $80

Hence, The number of visit so that both plan cost same is 10

and both the plan has equivalent benefit. Answer

Answer:

14

Step-by-step explanation:

If Jack puts 2 photos per page and there are 7 pages 2x7=14 or 2+2+2+2+2+2+2=14 on a number line it would jump two lines each time.

The number of photos that he uses to fill the photo album will be 14.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Jack puts 2 photos on each of the 7 pages of his photo album.

Then the number of photos that he uses will be given by the multiplication of the numbers 2 and 7.

⇒ 2 x 7

⇒ 14

Thus, the number of photos that he uses will be 14.

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Answer:

C

Step-by-step explanation: As you can see, the correlation goes up and down, this does not represent positive nor negative.  Therefore, C would be your final answer.

The shortest possible height of the tower is 24 cm

They used 4 blue blocks and 3 green blocks

Step-by-step explanation:

Tim and his brother are building towers out of blocks

We need to find the shortest possible height of the tower and how many of each color block they used

∵ Tim is using blue blocks that are 6 cm tall

∴ The height of his tower is a number divisible by 6

∵ His brother is using green blocks that are 8 cm tall

∴ The height of his tower is a number divisible by 8

∵ The heights of their towers are equal

∴ The height of the towers must be a number divisible by 6 and 8

Let us write some multiples of 6 and 8 to find the first common multiple of them

∵ The multiples of 6 are 6 , 12 , 18 , 24 , 30 , 36 , .........

∵ The multiples of 8 are 8 , 16 , 24 , 32 , 40 , .............

∵ The first common multiple of them is 24

∴ The shortest possible height of the tower is 24 cm

∵ The height of each blue block is 6 cm

- Divide the height of the tower by the height of the block to

   find the number of blue blocks

∵ 24 ÷ 6 = 4

∴ Time is using 4 blue blocks

∵ The height of each green block is 8 cm

- Divide the height of the tower by the height of the block to

   find the number of green blocks

∵ 24 ÷ 8 = 3

∴ His brother is using 3 green blocks

The shortest possible height of the tower is 24 cm

They used 4 blue blocks and 3 green blocks

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Answer:

73155 is the required 3rd number that will complete the sequence as: 88511, 16351, 73155 , 10251.

Step-by-step explanation:

So, let us consider 88511 and determine the pattern to find the next number and so on to complete the sequence.

Adding the first 2 digits in the number 88511 i.e.  8 + 8 = 16

Subtracting the 3rd digit from the 2nd digit i.e. 8 - 5 = 3

Multiplying the 3rd digit and 4th digit i.e. 5 × 1 = 5

Dividing the 4th digit by the 5th digit i.e. 1 ÷ 1 = 1

Hence, using these steps would get us the number 16351.

So, the next number would be obtained using same steps:

Adding the first 2 digits in the number 16351 i.e.  1 + 6 = 7

Subtracting the 3rd digit from the 2nd digit i.e. 6 - 3 = 3

Multiplying the 3rd digit and 4th digit i.e. 3 × 5 = 15

Dividing the 4th digit by the 5th digit i.e. 5 ÷ 1 = 5

Hence, using these steps would get us the number 73155.

So, the next number would be obtained using same steps:

Adding the first 2 digits in the number 73155 i.e.  7 + 3 = 10

Subtracting the 3rd digit from the 2nd digit i.e. 3 - 1 = 2

Multiplying the 3rd digit and 4th digit i.e. 1 × 5 = 5

Dividing the 4th digit by the 5th digit i.e. 5 ÷ 5 = 1

Hence, using these steps would get us the final number 10251.

So, from this pattern method, we determine that 73155 will be the 3rd number in the sequence: 88511,16351,?,10251.

So, the complete sequence would be: 88511, 16351, 73155, 10251.

Keywords: sequence, number

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Answer:

5

Step-by-step explanation:

Answer: the answer is 6

Step-by-step explanation: the hundredth place is 2 spaces behind the decimal.

The detailed answer explains how to simplify and solve the expression 8x + 3(x + 5) - 5(x - 4) = 2 step by step.

To find the equation equivalent to 8x + 3(x + 5) - 5(x - 4) = 2, we need to expand and simplify the expression step by step:

Answer:

E

Step-by-step explanation:

We will first find the percentage increase of 20 years. Then we will divide that by 20 to get the annual average percentage increase.

To get the percentage increase, we will find the increased amount and divide that by original population (2,000,000). Multiply that by 100 to get the percentage.

So,

Increased amount = 4,500,000 - 2,000,000 = 2,500,000

Now the percentage increase:

[tex]\frac{2,500,000}{2,000,000}*100=125[/tex]

So, in 20 years, the percentage increase is 125%

Per Year = 125/20 = 6.25% average per year

No correct answer in the answer choices from A through D, so E is the correct answer, None of These.

Using [tex](x-a)(x+a)=x^2-a^2[/tex] to obtain

[tex]4-(x^2-4)=4-x^2+4=8-x^2[/tex]

Hope this helps.

Answer:

Here's what I get  

Step-by-step explanation:

Let's assume that the sandwiches are circular (because I couldn't find a good rectangular fraction maker.

Toni ate ¾ of a medium sandwich (Figure below).

Mary Jo ate ⁶/₈ of a medium sandwich.

Mary Jo ate the same amount as Toni, because ¾ = ⁶/₈

Becky ate ¾ of a small sandwich and Toni ate ¾ of a medium sandwich.

Becky ate less than Toni, because ¾ of a small amount is less than ¾ of a large amount.

To find the probability of choosing a red card we need to add both the cards so we have a total amount of cards.

17 + 9 = 26

Since, the question is asking the probability of choosing a RED card then the probability is a 17/26 chance. The answer choices are written as ratios. The ratio that is the same to 17/26 is [ D. 17:26 ]

Best of Luck!

Answer:

The unit rate is 250 calories per servings.

Step-by-step explanation:

Given:

The ice cream has 1250 calories for 5 servings.

Now, to find the unit rate.

So, by using unitary method:

If the 5 servings of ice cream has 1250 calories.

Then, to get the calories in 1 servings we divide number of calories by the number of servings:

= [tex]Number\ of\ calories \div number\ of\ servings[/tex]

[tex]=1250\ calories\div 5\ servings[/tex]

[tex]=250\ calories.[/tex]

Thus, in 1 servings there are 250 calories.

Therefore, the unit rate is 250 calories per servings.

Answer:

-8

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

Negative reciprocal of 1/8 is -8.

The slope of a line that is perpendicular to y = 1/8x - 9 is -8. This is because perpendicular lines have slopes that are negative reciprocals of each other.

In Mathematics, particularly in algebra, the slope of a line is a measure of the steepness of the line. It's also a central part of the line's equation. In the equation you provided, y = 1/8x - 9, the slope of this line is 1/8.

The property of perpendicular lines is that their slopes are negative reciprocals of each other. The negative reciprocal of 1/8 is found by flipping the fraction to get 8/1 and changing the sign to get -8. Therefore, the slope of a line that is perpendicular to y = 1/8x - 9 is -8.

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Answer:

x > 14

Step-by-step explanation:

10.5x > 147   (divide both sides by 10.5)

x > 147 / 10.5

x > 14

Inequalities help us to compare two unequal expressions. The solution to the inequality 10.5x > 147 is 14.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The solution of the inequality can be solved as shown below,

[tex]10.5x > 147\\\\x>\dfrac{147}{10.5}\\\\x>14[/tex]

Thus, the solution to the inequality 10.5x > 147 is 14, which means the value of the x must be greater than 14.

Hence, the solution to the inequality 10.5x > 147 is 14.

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Answer:

non linear

Step-by-step explanation:

linear means a straight line graph. This type is quadratic since it has a parabola.

Answer:

Step-by-step explanation:

When we talk about linear and nolinear funciton, we can distinguish them by using their graphs.

A linear function has a linear behaviour, that means it's representes by a straight line.

A nonlinear function doesn't have a straight line behaviour.

That's the easiest way to distinguish wether is a linear function or nonlinear.

Therefore, in this case, you can observe that the graph is not a straight line, that means the function is nonlinear.

Answer:

The total number of pages in the e-book is 240.

Step-by-step explanation:

Given:

Logan has completed 75%

Logan has read 180 pages

To Find:

The total number of pages in the e-book= ?

Solution:

Let X be the total number of pages on the e-book

then

=> 75% of X = 180

Now lets find the value of X

X = [tex]\frac{180}{75\%}[/tex]

X = [tex]\frac{180}{\frac{75}{100}}[/tex]

X = [tex]\frac{180}{0.75}[/tex]

X = 240

The total number of pages in the e-book is 240.

To find the total number of pages in the e-book, we can set up a proportion based on the information given. Logan has read 75% of the e-book, which corresponds to 180 pages. We can represent this as:

 75% of total pages = 180 pages

To find the total number of pages, we can express the percentage as a fraction and solve for the total number of pages (let's denote this as P):

[tex]\(\frac{75}{100} \times P = 180\)[/tex]

Now, we can solve for P:

[tex]\(P = \frac{180 \times 100}{75}\)[/tex]

[tex]\(P = \frac{180}{0.75}\)[/tex]

[tex]\(P = 240\)[/tex]

Therefore, the total number of pages in the e-book is 240.

Answer:

1/2 of a yard

Step-by-step explanation:

Here you have to find 2/3 of 3/4.

In this case "of" means multiplication.

2/3 × 3/4 = 2×3 / 3×4 = 6/12 = 1/2

Answer:BC=11.77 mi

Step-by-step explanation:

cosα=5.71mi/AC

cos61°=5.71mi/AC

0.485=5.71mi/AC

AC=11.77mi

Answer:

BC=10.28

Step-by-step explanation:

Answer:

Step-by-step explanation:

If x = 1;        x  + 3 = 1 + 3 = 4  (≠ 7)

If x = 2;       x  + 3 = 2 + 3 = 5  (≠ 7)

If x = 3;       x  + 3 = 3 + 3 = 6  (≠ 7)

If x = 4;       x  + 3 = 4 + 3 = 7  ( =7)

x + 3 = 7 is true when x = 4

Answer:

Step-by-step explanation:

10

Answer:

27

Step-by-step explanation:

To find the answer to this, you need to divide the 15 slices of pizza by 5/9. 15/(5/9) is 15*9/5 (multiply both the top and the bottom by 9 and you cancel out the 9 in the 5/9 fraction) and you get 135/5 = 27