2x-5y=5
x - y table
graphh

The age of Mrs. Lee when her 2 children's combined age is [tex]\frac{5}{11}[/tex] of her age will be [tex]44[/tex] yrs. old

As per the question statement, Mrs. Lee, who is 40, has a son who is twice as old as her daughter. Mrs. Lee will be thrice her son's age when her daughter is 12-year old. We are asked that how old Mrs Lee be when her two children's combined ages are 5/11 of her own age.

This question is a classic example of forming and solving linear equations.

When Mrs. Lee was 40, her son was twice her daughter's age.

Let d = her daughter's age when Mrs. Lee was 40.

Then her son was 2d yrs. old when Mrs. Lee was 40.

When her daughter is 12, Mrs. Lee will be three times her son's age.

This means [tex](12 - d)[/tex] years have passed since Mrs. Lee was 40.

So, if her daughter was 12 at this time, that means her son was [tex]2d + (12 - d)[/tex]

And, Mrs. Lee's age at this time was [tex]40 + (12 - d)[/tex]

Mrs Lee was thrice her son's age at this time:

[tex]40 + (12 - d) = 3(2d + 12 - d))[/tex]

[tex]40+12-d=6d+36-3d\\4d=16\\d=4[/tex]

So, Mrs. Lee's age when her daughter was 12 is [tex]40 + 12 - 4 = 48[/tex] yrs. old

Her daughter was 8 yrs. old 4 years earlier.

Thus, Mrs Lee's age when her daughter was 20 was [tex]48 - 4= 44[/tex] years old.

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Using translation concepts, the y-coordinate of R' will be of -10.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the rule is given by:

(x,y) -> (x + 4, y - 7)

y -> y - 7 means that for the image, the 7 is subtracted from the y-coordinate of the pre-image. The y-coordinate of R is of -3, -3 -7 = -10, hence the y-coordinate of R' will be of -10.

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Answer:

18

Step-by-step explanation:

∠BCD=2x (alternate interior angles)

∠BCD+∠CDE=180° (same side interior angles)

Thus, 10x=180, meaning x=18.

The solution to the give inequality is x < d-a/c

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given the inequality expression

d - cx < a

Make x the subject of formula to have:

-cx < a - d

Divide both sides by -c

-cx <(a-d)/-c
x < -(a-d)/c

x < d-a/c

Hence the solution to the give inequality is x < d-a/c

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Answer:

83/100

Step-by-step explanation:

You move 2 times to the right your answer will be 83/100  

Answer:

1st Question 24 ÷ (-6) = -4

2nd Question -15 ÷ 0.3 = -50

3rd Question -4 ÷ (-20) = 0.2

This should be correct. I used a calculator Lol. :3.

Answer:

7GB, $12

Step-by-step explanation:

I used subtraction to find the difference.

The value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1 is 10.

Expression

An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.

Given that:-

Expression : 5x -2y + 3z

x = 7, y = 11 , z = -1

We have to find the value of 5x - 2y + 3z

According to the data given in the question, we can write,

The value of the expression 5x - 2y + 3z is:-

5*(7) -2*(11) + 3*(-1) = 35 -22 - 3 = 35 - 25 = 10.

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Answer:

90 m

Step-by-step explanation:

a. Perimeter = 2( length + breadth) 2(x + y)

Answer: Perimeter:  2(x + y) = 420
or 2x + 2y = 420

Using the values given

b.

2x + 2y = 420 (perimeter p= 420)
2(120) + 2y = 420   (length x = 120)
240 + 2y = 420
2y =  420 - 240 = 180 (subtract 240 on both sides)

y = 190/2 = 90 m

The perimeter of a square is proportional to the sides of its length

The statement is given as

The perimeter of a square is four times as great as the length of any of the sides

The above statement can be represented as

P = 4L

Where P represents the perimeter and L represents the side length

A proportional equation is represented as

y = kx

Where k a constant

By comparing y = kx and P = 4L, we have

y = P, k = 4 and x = L

Hence, the perimeter of a square is proportional to the sides of its length

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Answer:

Hello yeily, I think and believe they are all rational..

Step-by-step explanation:

Hope it helps <=/

Answer:

[tex]12 > x[/tex]

Step-by-step explanation:

[tex]20 > .75x + 4[/tex]

Is the equation you need to set up.

Then you want to subtract four from both sides ehich ends up giving you

[tex]16 > .75x[/tex]

Then divide 16 by 4 (this gives you a fourth) you get four

Then multiple 4 by 3 to get .75 of 16 which is 12

Hope this helps!

If yoy have any other questions feel free to ask!

Answer:

Tanner can play 20 games in the arcade and will have 50 cents left over.

Step-by-step explanation:

20 = 4.50 + 0.75x

Subtract 4.5 from both sides.

15.5 = 0.75x

Plug in numbers for x until it is equal more that 15.5

x = 20

0.75(20) = 15

0.75(21) = 15.75 < too much

3/13              least

1/7

1/4               greatest

The length of hypotenuse is 4.5 meters.

The length of hypotenuse can be calculated using Pythagoras theorem. Writing the Pythagoras theorem below -

Hypotenuse² = Base² + Perpendicular²

The given other two sides will be base and perpendicular. So, keeping the values in mentioned equation of Pythagoras theorem to find the value of Hypotenuse.

Hypotenuse² = 2² + 4²

Taking square of the numbers to find the value of Hypotenuse

Hypotenuse² = 4 + 16

Performing addition to find the value of Hypotenuse

Hypotenuse² = 20

Hypotenuse = [tex]\sqrt{20}[/tex]

Taking square root to find the value of Hypotenuse

Hypotenuse = 4.5 meters

Hence,  the length in meters of a right triangle's hypotenuse is 4.5 meters

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The difference between the area of the square and the area of the circle is C. 9x²(4 - π).

The area of the square will be:

= Side ×Side

= 6x × 6x

= 36x²

The area of the circle will be:

= πr²

= 3.14 × (3x)²

= π × 9x²

= 9πx²

The difference will be:

= 36x² - 9πx²

= 9x²(4 - π)

Therefore, the correct option is C.

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The difference between the area of the square and the area of the circle is 9x²(4 - π)

area of circle = πr²

where

Therefore,

area of a square = l²

where

The circle is inscribed in the square.

Therefore, the difference in area of the square and circle is as follows:

area of circle = π × (3x)² = 9x²π

area of the square = (6x)² = 36x²

Hence,

difference in area = 36x² - 9x²π

difference in area = 9x²(4 - π)

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Answer:

6 x 10^7

Step-by-step explanation:

(2x3)(10^4 x 10^3)

6 x 10^4+3

6 x 10^7

The number of people working on that day are 107 people in the staff.

According to the statement

We have to find that the number of people were working that day.

So, For this purpose, we know that the

A percentage is a number or ratio expressed as a fraction of 100.

From the given information:

a hospital day staff consists of 25 registered nurses, 75 unlicensed assistants, five phlebologists, six receptionists and office staff, and 45 physicians. one summer day the staff was at only 68% strength.

Then

Total number of staff = 25+75+5+6+45

Total number of staff = 156

Then

the staff was at strength = 68%

And then

Number of people working on that day = 68% of 156

And

Number of people working on that day = 68/100 *156

Number of people working on that day = 0.68*156

Number of people working on that day = 106.08

Approximate 107 people.

So, The number of people working on that day are 107 people in the staff.

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The eight machines can be arranged in the three available spaces in 336 ways.

Here we have 8 screw machines with 3 spaces. To find the different way, permutation will help.

Different ways = 8 P 3

= 8! / (8! -3!)

= 8! / 5!

= 8 x 7 x 6 x 5! / 5!

= 6x7x8 = 336.

Therefore, in 336 different ways the eight machines be arranged in the three spaces available.

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Answer:niamh gets 15 and jack gets 35

Step-by-step explanation:

think of the raito 3:7 as 3x:7x. then we can do: 3x + 7x = 50, which means 10x = 50. then we can find x by dividing 50 by 10, so x is 5. then we can find 3x, whihc is 3x5 = 15. then find 7x, so 7x5 = 35. so niamh gets 15 and jack gets 35

Answer: See diagram below

Scale factor = 3

============================================================

Explanation:

The given L shape has a perimeter of 3+1+2+1+1+2 = 10 units. I added up the exterior sides of this shape.

We want the perimeter to be 30 units, so we scale it by a factor of 3. Since 30/10 = 3.

This means we'll triple each side

The vertical side on the left originally 3 units long is now 3*3 = 9 units. The bottom side that is 2 units long is now 2*3 = 6 units. And so on.

See the diagram below.

Notice in the red figure the sides add to 9+3+6+3+3+6 = 30 to help confirm our answer.

The percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.

The normal distribution, also recognized as that of the Gaussian distribution, would be a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far away from the mean. The normal distribution is represented graphically as a "bell curve."

Now, according to the question;

The formula for finding the z-score is;

z = (x - μ)/σ

where,

x is the score

μ is the mean

σ is the standard deviation.

Summer vacation costs $1,755 for the average local family.

The distribution is normal, with a standard deviation of $390.

We need to figure out what percentage of families took vacations less than $1200.

The mean is $1,755

∴ μ = $1,755

∵ The standard deviation is $390

∴ σ = 390

∵ The vacation cost is under $1200

∴ x = $1200

Substitute the values in the formula of z score.

z-score = (1200 - 1,755)/390 = -1.42

Use the negative normal distribution table of z

P(z < 1,200) = 0.07782

P(x < 1,200) = P(z < 1,200)

P(x < 1,200) = 0.07782

P(x < 1,200) = 7.78%

Therefore, the percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.

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The complete question is -

International travel is usually more expensive than domestic travel. A recent survey found that the average per-person cost of a 12-day international vacation is  $1,755. This includes transportation, food, lodging, and entertainment.

a. if the data are normally distributed with standard deviation $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.

Answer:

96

Step-by-step explanation:

It is a straight linek so it adds up to 189.

53+31 = 84

180-84=96

yay brainliest :D

[tex]0.7\times10^{-2}[/tex] times as long as the small virus cell is the white blood cell.

Given that, the length of a white blood cell is [tex]1.4\times10^{-5}[/tex] meter and the length of a small virus cell is [tex]2.0\times10^{-7}[/tex] meter.

We need to find how many times as long as the small virus cell is the white blood cell.

To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.

Now, [tex]\frac{1.4\times10^{-5}}{2.0\times10^{-7}}[/tex]

=[tex]0.7\times10^{-2}[/tex]

Therefore, [tex]0.7\times10^{-2}[/tex] times as long as the small virus cell is the white blood cell.

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The number of times that blue will be expected will be 100 times.

It should be noted that from the information given, the spinner is divided into four equal sections labeled yellow, green, red, and blue.

It simply means that each color has a 1/4 chance for each scenario.

Therefore, the number of times that blue will be expected will be:

= 1/4 × 400

= 100 times

Therefore, the number of times that blue will be expected will be 100 times.

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A spinner is divided into four equal sections labeled yellow, green, red, and blue. If the spinner is spun 400 times, how many times would you expect to get blue?

Answer:

Step-by-step explanation:

Givens

Let the Length = L

Let the width = w

w = 2*L - 3

Area = L * w

Area = 193

Solution

Area = 193

193 = L*(2L - 3)

193 = 2L^2 - 3L       Subtract 193 from both sides.

2L^2 - 3L - 193 = 0

You have to use the quadratic formula get the answer. Without going through all all that, I will tell you that the only value you can use for L is 10.6

L = 10.6

w = 2* 10.6 - 3 = 18.4

But you want the diagonal. Use the Pythagorean Theorem to get it.

Diagonal^2 = L^2 + w^2

Diangonal^2 = 10.6^2 + 18.4^2

Diagonal^2 = 450.92                   Take the square root of both sides

√diagonal^2 = √450.92

Answer

The diagonal is 21,23

We need to know about logic statements to solve this problem. The solution of the logic statements are 0 and 1 respectively.

Logical operators are used to form logical statements, logical operators compute result based on boolean values true and false or binary 1 and 0. The common logical operators are AND and OR. AND is represented by ^ symbol and OR is represented by v symbol, ' means negation of the value, which means that true becomes false and vice versa. For AND operator, it works like multiplication, 0 and 1 yield 0, 1 and 1 yields 1 and 0 and 0 yields 0. For OR operator it works like addition, 0 and 1 yields 1, 1 and 1 yields 1 and 0 and 0 yields 0. For the logical statements given in the question we need to first compute the logical statement inside the bracket and then compare the inner result with the outer value.

(1'^0)^1 =(0^0)^1=0^1=0

(1v0')^(0v1)=(1v1)^(0v1)=1^1=1

Therefore we found the values of the logical statements to be 0 and 1 respectively.

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Answer: 8 tacos

Step-by-step explanation: To turn 15 into 3 students you would divide 15 by 5. You would also have to divide 40 by 5 too so that would be 8 tacos.

The least amount of money you can spend to buy the same number of candles and mints is $125.

The prime factorization of 12 and 15 is:

12= 2*2*3

15= 2*5*5

Now the factor of both appears in both number's factorization so least common multiple is:

LCM of 12 and 15 = 2*2*3*5*5=300

It is given that candies come in packs of 12 and mints in packs of 50.

Hence, the total quantity of packs of each thing is:

Candles: 300÷12=25

Mints: 300÷50=6

The least amount of money to be spent is:

25×$3.50 + 6×$6.25= $87.5 + $37.5= $125

Thus, the least amount of money you can spend to buy the same number of candles and mints is $125.

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Answer:125

Step-by-step explanation: no explanations sorry but it is right thank me later