The average age of Elliot, Miya and Cara is 4 years more than the average
age of Elliot and Miya.
Cara is 9 years older than Elliot.
Four years ago, Elliot was double the age of Miya.
Work out the ages of Elliot, Miya and Cara.

Answers

Answer 1

Answer:

Elliot = 16 years old

Miya = 10 years old

Cara = 25 years old

Step-by-step explanation:

Define the variables:

x = Elliot's agey = Miya's agez = Cara's age

The average age of Elliot, Miya and Cara is 4 years more than the average age of Elliot and Miya:

[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y}{2}+4[/tex]

[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y+8}{2}[/tex]

[tex]\implies 2(x+y+z)=3(x+y+8)[/tex]

[tex]\implies 2x+2y+2z=3x+3y+24[/tex]

[tex]\implies 2z=x+y+24[/tex]

[tex]\implies x=2z-y-24[/tex]

Cara is 9 years older than Elliot:

[tex]\implies z = x + 9[/tex]

Four years ago, Elliot was double the age of Miya:

[tex]\implies (x - 4) = 2(y - 4)[/tex]

[tex]\implies x - 4 = 2y-8[/tex]

[tex]\implies x +4 = 2y[/tex]

[tex]\implies y=\dfrac{1}{2}x +2[/tex]

Substitute the equations for z and y into the equation for x and solve for x:

[tex]\implies x=2z-y-24[/tex]

[tex]\implies x=2(x+9)-\left(\dfrac{1}{2}x +2\right)-24[/tex]

[tex]\implies x=\dfrac{3}{2}x-8[/tex]

[tex]\implies \dfrac{1}{2}x=8[/tex]

[tex]\implies x=16[/tex]

Substitute the found value of x into the equation for z and solve for z:

[tex]\implies z = 16 + 9[/tex]

[tex]\implies z = 25[/tex]

Substitute the found value of x into the equation for y and solve for y:

[tex]\implies y=\dfrac{1}{2}(16) +2[/tex]

[tex]\implies y=8+2[/tex]

[tex]\implies y=10[/tex]

Therefore, the ages of Elliot, Miya and Cara are:

Elliot = 16 years oldMiya = 10 years oldCara = 25 years old


Related Questions

PLEASE HELP!! ALGEBRA 1 HW! I WILL GIVE BRAINLYEST​

Answers

Answer:

(0.5, 3)

Step-by-step explanation:

Just entered it into a desmos graphing calculator online

A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad.

The probability of drawing a bag with bad potatoes is less than 1.
True or False

The probability of drawing a bag with good potatoes is greater than 0.
True or False

What is the probability of drawing a bag with bad potatoes?


What is the expected probability of the complement of the event?

Answers

Answer:

The probability of drawing a bag with bad potatoes is less than 1. True

The probability of drawing a bag with good potatoes is greater than 0. True

What is the probability of drawing a bag with bad potatoes?

The probability of drawing a bag with bad potatoes is (2 bad bags) / (20 total bags) = 0.1 or 10%.

What is the expected probability of the complement of the event?

The complement of the event of drawing a bag with bad potatoes is drawing a bag with good potatoes. The probability of drawing a bag with good potatoes is (18 good bags) / (20 total bags) = 0.9 or 90%.

Uday Tahlan

Determine if the events are independent or dependent

Answers

Answer:

dependent

Step-by-step explanation:

there is no replacement

Answer:

Dependent

Step-by-step explanation:

The cards aren't replaced, so it depends on which ones are taken.

what is 900,000*9,000

Answers

Answer:

8,100,000,000

Step-by-step explanation:

I used a calculator lol

The director of special events for Sun City believed that the amount of money spent on fireworks displays for the Fourth of July was predictive of attendance at the Fall Festival held in October. She gathered the following data to test her suspicion.
4th of July ($000) Fall Festival (000)
10.6 8.8
8.5 6.4
12.5 10.8
9.0 10.2
5.5 6.0
12.0 11.1
8.0 7.5
7.5 8.4
9.0 9.5
10.0 9.8
7.5 6.6
10.0 10.1
6.0 6.1
12.0 11.3
10.5 8.8
1. Determine the regression equation
2. Complete the ANOVA table.

Answers

Tgwre is no attached ANOVA chart.

Answer:

y = 0.762x + 1.72

Step-by-step explanation:

Given the data above , the regression model obtained using a Pearson linear regression calculator is :

y = 0.762x + 1.72

The regression equation cloud be interpreted as follows :

Slope, which is the increase in the value of y per unit increase in x = 0.762

The intercwpt, which is the value of x when y = 0 is 1.72

x = amount of money spent in fireworks for 4th July

y = Attendance at the October fall festival.

Itzel purchased 18 pounds of oranges.
How many ounces of oranges did she
purchase?

Answers

Answer:

288

Step-by-step explanation:

1 pound is equal to 16 ounces

if Itzel purchases 18 pounds, to convert to ounces simply multiply 18 by 16.

Answer:

288

I wish you luck in your assignments.

(I just noticed someone got here in before me and answered WAY better. So I edited this to tell you to give them brainliest.)

4 is the slope of a line y - 4x = 0 true or false​

Answers

it is false but 4 is not y-4x=0

its 9/16 close to 0, 1/2 or 1 explain

Answers

Answer: It's closer to 1/2

Step-by-step explanation: It's closer to 1/2 and here's why:

So, 1/2 (exact) is 8/16

0 = 0

1 = 16/16

Since 9/16 is the closest to 8/16 or around 1/2 in this case, it'd be about 1/2. I hope this helps!

what is the sum of the IQR of the top data set and the IQR of the bottom data set

Answers

Answer:

IQR = 32 - 26 = 6

Step-by-step explanation:

Answer:

the answer is 11

Step-by-step explanation:

I took the algebra nation test

The measures of the angles of a triangle are shown in the figure below. Solve for x.
(5x-17)®
(7x-3)
56°

Answers

The measurement of three angles in the triangle are 43°, 81°, 56°.

What are the angles of a triangle?

A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it.

Given three angles,

∠A = (5x - 17)°

∠B = (7x - 3)°

∠C = 56°

We know that in a triangle ∠A + ∠B + ∠C = 180°

By substituting values,

(5x - 17) + (7x - 3) + 56 = 180

12x -20 + 56 = 180

12 x + 36 = 180

12x = 180 - 36

12x = 144

x = 144/12

x = 12

By substituting values of x we get,

∠A = (5x - 17)°

     = 5 x 12 - 17

     = 60 - 17

     = 43

∠A = 43°

∠B = (7x - 3)°

     = 7 x 12 - 3

     = 84 - 3

     = 81

∠B = 81°

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The quotient of s and 60

Answers

Answer:

60/s or s/60

Quotient means divide so you divide the following, s and 6 by each other.

Step-by-step explanation:

Hope it helps! =D

PLEASE HELP!
60 points!

Answers

Answer:

80*

Step-by-step explanation:

Answer: I found the answer!!!

Step-by-step explanation: enter this in bitly - 2SoXiJd


Of 1936 people so came into a blood bank to give blood, 200 people had high blood pressure. Estimate the probability that the next person who comes in to give
blood will have high blood pressure’s

Answers

Answer:

person has a 10% chance of having high bp

Step-by-step explanation:

200 out of 1936 equals about 10%

NO LINKS PLEASE! help me!

Answers

Answer:

it is b. she will have 99 bucks.

C
Because
650+110+225+950=1935 then 1935-2034= 99

Convert:
30 quarts
=
bushels
Round to the nearest hundredths.

Answers

Answer:

30 quarts= 0.8057 bushels

rounded to the nearest hundredths = 0.81

A pet shelter has 5 cats and 9 dogs.
Enter the ratios in the boxes.
ratio of cats to all animals:
ratio of dogs to cats:

Answers

The ratio of cats to all animals is 5:14

the ratio of dogs to cats is 9:5

Given-

Cats = 5

Dogs = 9

Total animals = cats+ Dogs

     5+9=14

so  the ratio of cats to all animals  = 5: 14

and dogs to the cats= 9:5

Ratio give the relation between quantities of to identies.

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PLEASE ANSWER BOTH THANK U (if you can, look at my other questions and answer the other one. That would mean alot) tyyy

Answers

Answer:

1. Check all except for large pizza

2. how much Donna spent on one garlic bread

Step-by-step explanation:

Hope it helps :)

Solve the inequality:
4-3x<16

Answers

Answer:

x > -4

Step-by-step explanation:

This is solved just like as if it was an equation. Its a two-step equation (inequality) The only thing that's different is with an inequality, it is imperative that you flip the inequality symbol if you multiply or divide by a negative number.

Here, we'll subtract 4 from both sides. Then divide by -3 on both sides. Flip! the < to a >.

see image.

Answer:

x > -4.

Step-by-step explanation:

1. Write the expression.

[tex]4-3x < 16[/tex]

2. Subtract "4" from both sides of the equation.

[tex]4-3x-4 < 16-4\\ \\-3x < 12[/tex]

3. Divide both sides by "-3" and switch the inequality symbol.

[tex]\frac{-3x}{-3} < \frac{12}{-3} \\ \\x > -4[/tex]

Important. See that we switched the inequality symbol from "<" to ">", and this is because the symbol of the coefficient of variable "x" changed from negative to positive when it was divided by "-3". This rule will always be true, any time the symbol of the variable changed, the inequality symbol changes.

4. Verify.

If x >-4 is the correct answer, then substituting x by "-4" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).

[tex]4-3(-4) > 16\\ \\4-(-12) > 16\\ \\4+12 > 16\\ \\16 > 16[/tex]

That's correct! x > -4 is the correct answer.

In a class of 23 students, 9 play an instrument and 7 play a sport. There are 3 students who play an instrument and also play a sport. What is the probability that a student does not play an instrument given that they play a sport?

Answers

Answer:

There are 23 students

-- 9 students play neither sport

-- therefore, 23 - 9  =  14 students play at least one of the two sports; some play both sports.

Inclusive or:  the probability will be:  14 / 23 that a student chosen at random will play at least one of the two sports.

Exclusive or: we need to first find how many students play both sports.

Since 14 persons play sports and since 7 play basketball and 12 play baseball, this requires 7 + 12 = 19 students.

Subtracting  19 - 14 = 5 give the number of students who play both sports.

If we eliminate these 5 persons as well as the 9 who play neither sport, we have to eliminate 5 + 9  =  14 persons.

This gives 23 - 14 = 9 persons who play only one of the two sports.

The probability will be:  9/23 play a sport, but only one sport.

Step-by-step explanation:

The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

To find the probability that a student does not play an instrument given that they play a sport, we need to use conditional probability.

Let A be the event that a student plays a sport and B be the event that a student plays an instrument.

We want to find P(not B | A), which is the probability that a student does not play an instrument given that they play a sport.

We know that,

P(A) = 7/23, P(B) = 9/23, and P(A and B) = 3/23.

Using the formula for conditional probability, we have:

P(not B | A) = P(A and not B) / P(A)

We can find P(A and not B) by using the fact that,

P(A and B) = P(B) - P(A and not B).

P(A and not B)

= P(B) - P(A and B)

= 9/23 - 3/23

= 6/23

Substituting into the formula, we get:

P(not B | A) = (6/23) / (7/23) = 6/7

Therefore,

The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.

Learn more about probability here:

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Models come in different scales. A model of a G-scale railroad car has a scale ratio of 1:22.5, and the model is 3 in tall, how tall is the actual car?

Please help me answer this, this is due on Monday for me!!!

Answers

The actual car is 66.75 inches tall. The scale ratio of 22.5 means that for every 1 inch of the model, the actual car is 22.5 inches. Therefore, 3 inches of the model is equal to 66.75 inches of the actual car.

Hope this helps!

DB =4.3cm BC=6.7cm
How do I find x° ?​

Answers

Your answer is 40
x=40

Since angle DCB is 40, this means that angle ACD is 50 because DCB+ACD=90.
Now we just need to subtract 90 and 50 from 180 and the third angle (x) is 40
Hope this helps!

Refer to the figure in the picture to determine
the measure of each given angle.

Answers

Check the picture below.

The sum of any three different even numbers is odd.

Answers

Answer:
The sum of three odd numbers is odd same thing goes for three even numbers which would be even but A even number divided by two would leave a remainder of zero

Solve the triangle. Round to the nearest tenth.
39°
16
84°
B

Answers

Answer:

A. m<C = 57 degrees, a = 12, b = 19

Step-by-step explanation:

First we can start by calculating Angle C by using the rule that all interior angles of a triangle always add to 180 degrees:

180 - (39+84) = C

180 - 123 = C

C = 57

Now let's calculate side a. We can do this by using the sin rule: [tex]\frac{sin A}{a}=\frac{sin C}{c}[/tex]

According to the diagram we know that Angle A is 39 degrees, Angle C is 57 degrees, and side c is 16 so we can substitute these values into the formula and solve:

[tex]\frac{sin39}{a} =\frac{sin 57}{16} \\\\\frac{0.629320}{a} =\frac{0.838671}{16}\\\\0.629320=0.052417a\\0.629320/0.052417=a\\a= 12[/tex]

We can use the same method to solve for side b:

[tex]\frac{sin84}{b} =0.052417 \\0.994522=0.052417b\\0.994522/0.052417=b\\b= 19[/tex]

We now have the following values:

Angle C = 57 degrees, a = 12, b = 19

We can now see that A/Number 1 is the correct option.

Hope this helped!

Graph: y - 3 = 1/2 (x + 2)

Answers

Answer:

Slope: [tex]\frac{1}{2}[/tex]

Y-intercept: (0,4)

Step-by-step explanation:

Put the equation into y = mx + b form, which is y = [tex]\frac{1}{2}[/tex] +4. Then create a table.

X: -2, -1, 0, 1, 2

Y: 3, [tex]\frac{7}{2}[/tex], 4, [tex]\frac{9}{2}[/tex], 5

7 movie tickets for $56 -help please lol-

Answers

Answer:

8

Step-by-step explanation:

If 7 tickets equals 56

56/7=8

Answer:

8 Dollars

Step-by-step explanation:

If the question you are asking is how much is a ticket, if 7 tickets cost a total of 56 dollars, then the answer is 8. This is because you would divide the total cost bu how many there are, which would look like 56 / 7 = 8.

Help me with this !!!!!

Answers

Answer:

3. 30

4. 46

5. 55

Step-by-step explanation:

7. (a) A homeowner wishes to replace the three identical steps leading to her front door with a ramp. Each step is 10 cm high and 35 cm long. Find the length of the ramp. Give your answer correct to one decimal place.​

Answers

Answer: To replace the three steps with a ramp, the height of the ramp must be equal to the total height of the steps. Since each step is 10 cm high, the total height of the three steps is 3 * 10 = 30 cm.

The length of the ramp must be equal to the length of the steps, since the ramp is replacing them. Since each step is 35 cm long, the total length of the three steps is 3 * 35 = 105 cm.

So the length of the ramp to replace the three steps leading to the front door is 105 cm, correct to one decimal place.

Step-by-step explanation:

Which statement is true for log3(x+1)=2?

Answers

log₃ (x+1) = 3
It could be written:
(x+1)= 3³==> x+1 = 27 ==> x =27-1 =26

HOPE THIS HELPS

Answer:

It is A: A: x+1=3^2 on EDG

Step-by-step explanation:

Find the missing side lengths. Leave your answers as radicals in simplest form.
Please help!!!! Due today

Answers

Answer:

B) x = 5sqrt2, y = 5

Step-by-step explanation:

(y) is equal to 5 because both angles are 45 degrees.

From here you can use the Pythagorean theorem to find (x):

a^2+b^2 = c^2

5^2+5^2 = c^2

25+25 = c^2

50 = c^2

sqrt50 = c

5sqrt2 = c (c is x in this case)

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