The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certainday, 252 people entered the park, and the admission fees collected totaled 728 dollars. How many childrenand how many adults were admitted?Your answer isnumber of children equalsnumber of adults equalso

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:

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

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)

The value of the expression 7+[9÷(9x1 to the second power)] is 64/9

A fraction can be described as the part of a whole set or element.

There are several types of fractions, which includes;

Some examples of these fractions are given as;

Simple fractions: 1/5, 1/6

Mixed fractions: 2 1/8, 3 1/4

Proper fractions: 2/3, 4/5

Improper fractions; 4/1, 6/3

Given the expression;

7+[9÷(9x1 to the second power)]

This is expressed as;

7 + ( 9 ÷ (9)^2

Find the square

7 + ( 9 ÷ 81)

find the ratio

7 + 1/9

Find the common multiple

63 + 1 /9

64/9

Hence, the value is 64/9

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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)

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

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

Given the following expression:

Remember that we have the following general rule:

this rule is called the distributive property, which is used on our given expression.

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

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

Solution

We have the following:

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

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.

Answer:

Domain: [3, ∞)

Range: [1, ∞)

Step-by-step explanation:

The domain represents the x-axis

The point starts at 3 and points to what can assume to be infinity

Since the dot is close it is included.

In interval notation:

[3, ∞)

The range represents the y-axis

The point starts at 1 and goes to infinity

The dot is included so we use a bracket

Interval notation

[1, ∞)

I hope this helps!

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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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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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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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:

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

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

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.

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]

We have that the general exponential formula is:

In this case, we have:

the term b on the exponential formula is also known as the growth factor. Therefore, in this case the growth factor is b=3/2

Solution:

Given the endpoints of the line;

The slope, m of the line is;

Thus;

CORRECT ANSWER:

The slope of the line passing through the coordinates (9, 9) and (6, 7) is 2/3.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( 9, 9 )

Point 2( 6, 7 )

To determine the slope, plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 7 - 9 )/( 6 - 9 )

Slope m = ( -2 )/( -3 )

Slope m = ( 2 )/( 3 )

Slope m = 2/3

Therefore, the slope of the line is 2/3.

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The slope of the required line is 2/3 which passes through points (9, 9) and (6, 7).

The slope is simply expressed as an inclination of the line in the coordinate system.

Slope m = (y₂ - y₁) / (x₂ - x₁)

Given that the line that passes through two points (9, 9) and (6, 7)

Let x₁ = 9, y₁ = 9 and x₂ = 6, y₂ = 7

The slope of the required line is

m = (y₂ - y₁ )/( x₂ - x₁ )

Substitute the values in the formula to get the slope of the line,

m = ( 7 - 9 )/( 6 - 9 )

m = ( -2 )/( -3 )

m = ( 2 )/( 3 )

m = 2/3

Therefore, the slope of the line would be 2/3.

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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

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

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.

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

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.