The oldest child in a family of four children is three times as old as the youngest. The two middle children are 19 and 23 years old. If the average age of the children is 28.5, how old is the youngest child?

Given the numbers:

355, 382, 383, 427, 500, 572, 601, 638, 669

Total numbers = 9

a) We find the mean:

Change 669 to 606:

Then:

Answer: It decreases by 7

b) We find median

Median: 355, 382, 383, 427, 500, 572, 601, 638, 669

Median = 500

669 changed to 606

Median: 355, 382, 383, 427, 500, 572, 601, 606, 638

Median = 500

Answer: It stays the same

For the function, f(x) =0, we have x = -6 and x =4

The given function is  f(x) = x² + 2x - 24

For f(x) = 0

f(x) = x² + 2x - 24 =0

x² + 2x - 24 =0

Middle Term Splitting is a method to solve quadratic equations of the form ax² + bx +c, In middle-term splitting, we split the middle term into the factors of the constant terms, then we take common multiples from the terms and then convert the equation into factors, we equate each factor to zero and we get the desired results.

By splitting the middle term, we have:

x² + 6x -4x - 24 =0

x( x + 6) -4(x+6) =0

( x + 6 ) ( x - 4 ) = 0

( x + 6 ) = 0 and ( x - 4 ) = 0

x = -6 and x = 4

Hence, for f(x) =0, we have x = -6 and x =4

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C. 6

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so

Step 1

given

a)let

b) now, replace and calculate

therefore, the answer is

C. 6

I hope this helps you

Given:

The dimension of square shape floor is 200 feet by 200 feet.

The area of the square is calculated as,

Now, given that the 1/2 bottle will cover approximately 2000 quare feet.

It gives,

So, the number of bottles required are,

Answer: option B)

INFORMATION:

We have the following options

And we must select the one that represents the explicit formula for a compound interest geometric sequence

STEP BY STEP EXPLANATION:

To select the correct one, we need to know that:

Finally, the correct one would be option A

ANSWER:

Solution:

Given the endpoints of the line;

The slope, m of the line is;

Thus;

CORRECT ANSWER:

s = 28π/3

The radius, r = 8

The angle, θ = 7π/6 radian

The length of the arc, s = rθ

s = 8 x 7π/6

s = 28π/3

Solution

We have the following:

5!= 5*4*3*2= 20*3*2= 60*2= 120

Compound interest - The amount in the account at the end of 1st year is $9720 and The amount in the account at the end of 2nd years is $10497.6

What is compound interest?
The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

We are given that the principal amount is $9000

An the interest is 8%

Hence after 1 year the amount will be

[tex]A=9000(1+0.08)\\A=9000(1.08)\\A=9720\\[/tex]

After 1 year the amount becomes $9720

Now After 2 years we will get interest on $9720

Hence the amount after 2 years will be

[tex]B=9720(1+0.08)\\B=9720(1.08)\\B=10497.6[/tex]

Therefore the amount after 2 years is $10497.6
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Part a

Remember that the linear equation in slope-intercept form is

y=mx+b

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

the equation is of the form

C=m(n)+b

where

m=8.50

b=350

therefore

Part b

A reasonable domain for n (number of cups)

Remember that the number of cups cannot be a negative number

so

the domain is the interval [0, infinite)

but a reasonable domain could be [0, 500]

Find out the range

For n=0 -----> C=350

For n=500 ----> C=8.50(500)+350=2,100 ZAR

the range is the interval [350,2,100]

Part c

calculate the cost

For n=100 cups ----> C=8.50(100)+350=1,200 ZAR

For n=200 cups ----> C=8.50(200)+350=2,050 ZAR

For n=400 cups ---> C=8.50(400)+350=3,750 ZAR

Part d

Average cost

Divide the total cost by the number of cups

For 100 cups ------> 1,200/100=12 ZAR per cup

For 200 cups ----> 2,050/200=10.25 ZAR per cup

For 400 cups ----> 3,750/400=9.38 ZAR per cup

Part e

it is better to order more cups, to reduce the initial ZAR 350 cost.

Part f

In this problem we have the ordered pairs

(200, 2150) and (400, 3750)

Find out the slope m

m=(3750-2150)/(400-200)

m=8 ZAR per cup

Find out the linear equation

C=mn+b

we have

m=8

point (200,2150)

substitute and solve for b

2150=8(200)+b

b=2150-1600

b=550

therefore

The linear equation is

Part g

A reasonable domain could be [0, 600]

Find out the range

For n=0 ------> C=550

For n=600 ----> C=8(600)+550=5,350

The range is the interval [550,5350]

Part h

The gradient is the same as the slope

so

slope=8

that means ----> the cost of each cup is 8 ZAR

Part i

For n=600

C=8(600)+550=5,350 ZAR

Part j

we have the inequality

8n+550 < 8.50n+350

Solve for x

550-350 < 8.50n-8n

200 < 0.50n

400 < n

Rewrite

n > 400

For orders more than 400 cups is more effective to order from Cupomatic

Verify

For n=401

C=8n+550=8(401)+550=3,758 ZAR

C=8.50n+350=8.5(401)+350=3,758.5 ZAR

the cost is less in CUPOMATIC, is ok

the answer is

Answer:

Explanation:

To solve compound inequalities, we do the same as in an equation or inequality: we need to do the same operation in all places.

We want to solve for x:

And that's the answer

First, calculate the total volume of alcohol in the gallon of windshield washer solution by calculating what is 6% of a gallon equal to. Since a gallon is equal to 128 ounces, then:

A quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.

Given that, the graph is passing through (2, 0), (10, 0) and (6, -4).

The standard form of a quadratic equation is given as:

ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.

Now, the equation passes through (2, 0)

y = ax² + bx + c

0 = 4a + 2b + c  ----------------(1)

The equation passes through (6, -4)

y = ax² + bx + c

-4= 36a + 6b + c ----------------(2)

The equation passes through (10, 0)

y = ax² + bx + c

0 = 100a + 10b + c ----------------(3)

Using the Gauss elimination method to solve the system of equations we get,

a = 1/4, b = -3, and c = 5

The quadratic equation will be:

y = ax² + bx + c

y = (1/4) x² - 3x + 5

Therefore, a quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.

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Answer: [tex]k < 8.48[/tex]

Step-by-step explanation:

[tex]\frac{k}{-1.6} > -5.3\\\\k < (-5.3)(-1.6)\\\\k < 8.48[/tex]

For the point 1)

- The domain will be: (note that this is not an interval, it is a set of two points)

-The range is the set R of all real numbers (since the line extends to infinite)

-The first graph is NOT a function

For the point 2)

-The domain will be the interval

-The range is the interval:

-The second graph is a function.

the expression is

(a+b)^2=a+b^2

substitute a=1 and b=1

(1+1)^2 = 1+1^2

4=2

that is not possible. so these are the values of a and b that is not counterpart example to the conjecture.

now substitute a=0, b=1

(0+1)^2 = 0+1^2

1=1

so this is true for the above expression.

now for a=-1, b=1

(-1+1)^2 = -1+1^2

0=0

this is true.

now for a=-1, b=2

(-1+2)^2 = -1+2^2

1=3

that is not possible

so a=1, b=1 and a=1,b=2 is the values that not counterpart example to the conjecture.

ANSWER :

49f and 7(f + 6f)

EXPLANATION :

From the problem, we have :

When multiplied, it will be 49f

When breaking it down, 7f is equal to f + 6f. Then it will be 7(f + 6f)

The next options f + 14 and f + 49 has two terms, so it will not be equivalent to the given expression with one term.

So the only expressions that are equivalent to the given expression are 1 and 2

The Solution:

Let's solve with the Factoring Method:

Solving by the Completing the Square:

Take the square root of both sides.

Therefore, the answers is:

Given:

Required:

To identify the horizontal and vertical asymptotes, and to point the graph.

Explanation:

Now the graph of the given function is

To find the horizontal asymptotes apply the limit

Looking at the graph, we will the following:

The portion ab is increasing

The portion bc is decreasing

The portion cd is decreasing

The portion de is increasing

The portion ef is increasing

The portion fg is decreasing

The portion beyond g is increasing

In the interval x = y to x = ∞, we will observe that the graph is positive & increasing

Hence, the first option is correct (it is positive and increasing)

To eliminate the coefficient divide each side by 3

Now solve the two step equation

3g - 5 = 17

3g = 17 + 5 = 22

then g= 22/3

Now solve 9 = 4a + 13

9 -13 = 4a

-4 = 4a then -1= a

a= -1

Answer

It will take 2 hours to fill the daily quota if all the machines are running.

Explanation

To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:

Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines

We have to find the vertical and horizontal lines that passes through the point (3,6).

A vertical line will be defined as x = constant. If it passes trough a point (x,1,y1), the line will be defined as a x=x1, so the point (x1,y1) belongs to the line.

The same goes for horizontal lines, but in this case the line is defined as y = constant.

For a point (x1,y1), the horizontal line that pass through the point will be y = y1.

Then, for point (x,y)=(3,6), the vertical and horizontal lines as:

x=3 and y=6.

Answer:

Vertical line: x = 3

Horizontal line: y = 6.

2+7x=15

Explanation

Step 1

Let

x represents the number

seven times a number = 7x

two more = +2 or 2+, you need to add 2

is = "="

Step 2

replace,

"Two more than seven times a number is fifteen"

I hope this helps you

Given data:

The weight of man and daughter = 90

The weight of man and cat is = 70

The weight of cat and daughter = 40 .

The man weights 60 kg.

then daughter weight = 90-60 = 30.

Thus the daughter weight is 30kg.

therefore the cat weight iwith daughter, 40-30 = 10 .

also with father, 70-60 = 10 .

Thus, the father weight is 60 kg.

The daughter weight is 30 kg and

The cat weight is 10 kg.

She walked 3 1/4 miles per day.

Given,

Jane walked 9 3/4 miles in the course of 3 days.

If we calculate this mixed number into a fraction,

We get:

9 3/4 miles = {(9×4)+3} / 4 miles

=39/4 miles.

So, Jane walks 39/4 miles in 3 days.

Therefore, in one day she walked:

(39/4 ÷ 3) miles

= 13/4 miles per day

Let's now convert this fraction into a mixed number:

when 13 is divided by 4 we get the remainder as 1 and the quotient as 3.

So, a mixed number is given by:

quotient remainder/divisor

Hence 13/4 = 3 1/4.

So, Jane walked 3 1/4 miles per day.

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SOLUTION:

We want to know the scale factor of the transformation from;

We do this by taking ratios of corresponding sides, they should be the same in either case;

Thus , the scale factor is;

Thus, the scale factor is 2.

D= {-2,0,1, 2,3,4}

1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state

- The lowest value for that is given by x=-2

- The highest value for that is x= 4

- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)

2) So, we can write the set, the Domain, after examining the options as:

D= {-2,0,1, 2,3,4}

Notice that we're considering the x-coordinates

3) So the answer is D= {-2,0,1, 2,3,4}

For this problem, we are given the dimensions of a rectangular prism and are asked to determine its volume.

The volume of a rectangular prism is given by the product of the three dimensions, therefore we have:

The correct answer is 328.02 cubic centimeters.