please help!!!!


On a certain hot summer's day, 554 people used the public swimming pool. The
daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $1097.00.
How many children and how many adults swam at the public pool that day?


Answers

Answer 1

Answer:

Children= 384      Adults= 170

Step-by-step explanation:

First, write a system of algebraic equations:

[tex]1.75x+2.50y=1097[/tex]

[tex]x+y=554[/tex]

Second, use linear combination to eliminate one variable (I will eliminate x, or children.)

[tex]1.75x+2.50y=1097[/tex]

[tex]-1.75(x+y=554)[/tex]

[tex]1.75x+2.50y=1097[/tex]

[tex]-1.75x+-1.75y=-969.5[/tex]

[tex]0.75y=127.5[/tex]

Divide both sides by 0.75

[tex]0.75y=127.5[/tex]

[tex]/0.75[/tex]        [tex]/0.75[/tex]

[tex]y=170[/tex], there are 170 adults

Now, plug in 170 for [tex]x+y=554[/tex]

[tex]x+170=554[/tex]

Subtract 170 from both sides

[tex]x+170=554[/tex]

      [tex]-170[/tex]   [tex]-170[/tex]

[tex]x=384[/tex], there are 384 kids.

Hope this helps!!!

Answer 2

Answer:

384 children and 170 adults

Step-by-step explanation:

if x is children and y is adults

1.75x+2.5y=1097

x+y=554

1.75x=1097-2.5y

x=554-y

1.75x=1097-2.5y

1.75x=1.75(554-y)

1097-2.5y=969.5-1.75y

1097-969.5=2.5y-1.75y

127.5=0.75y

127.5/0.75=y

170=y

x+y=554

x=554-y

x=554-170

x=384

to prove these are correct just do 1.75(384)+2.5(170) and see if it equals 1097, and do 384+170 to see if its the amount of people

1.75(384)+2.5(170)

672+425

1097

384+170=554


Related Questions

The equation 3x² - 4x + 6 = 0 has the roots α and β . Find the new equation with the roots (α/β²) and (β/α²) .

Answers

Answer:

[tex]{ \tt{sum = \alpha + \beta = \frac{4}{3} }} \\ { \tt{product = \alpha \beta = \frac{6}{3} = 2}} \\ \\ new \: roots : \\ { \bf{sum = \frac{ \alpha }{ { \beta }^{2} } + \frac{ \beta }{ { \alpha }^{2} } }} \\ \\ { \bf{ = \frac{ { \beta }^{2} \alpha + { \alpha }^{2} \beta }{ { (\alpha \beta )}^{2} } }} \\ \\ = { \bf{ \frac{ \alpha \beta ( \alpha + \beta )}{ {( \alpha \beta )}^{2} } }} \\ \\ = { \tt{ \frac{2( \frac{4}{3}) }{2 {}^{2} } }} \\ \\ sum = \frac{2}{3} \\ \\ { \bf{product = \frac{1}{ \alpha \beta }}} \\ = \frac{1}{2} \\ \\ { \boxed{ \tt{equation : {2x}^{2} + \frac{4}{3} x + 1 }}}[/tex]

What is the vertex of the function f(x) = x2 + 12x?

(–6, –36)
(–6, 0)
(6, 0)
(6, –36)

Answers

Answer:

(- 6, - 36 )

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = x² + 12x ← is in standard form

with a = 1, b = 12, c = 0 , then

x = - [tex]\frac{12}{2}[/tex] = - 6

Substitute x = - 6 into f(x) for corresponding value of y

f(- 6) = (- 6)² + 12(- 6) = 36 - 72 = - 36

vertex = (- 6, - 36 )

Answer:

A: (-6, -36)

Step-by-step explanation:

This should be the right answer on edge,

please correct me if I'm wrong.

What is the explicit formula for this sequence?
2, 10, 50, 250, 1250, ...
O A. an = 2(5)(n-1)
O B. an = 5(2)(n-1)
O C. a, = 2 + (5)"
O D. an = 2(5)"

Answers

Answer:

O D. an = 2(5)"

Step-by-step explanation:

Given the expression/sequence below

2, 10, 50, 250, 1250, ...

O D. an = 2(5)"

The explicit formula is C

a0= 2*5^0= 2

a1=2*5^1= 10

a2= 2*5^2= 50

a3=2*5^3= 250

a4=2*5^4= 1250

What is the value of the natural logarithm when x=0.5 is rounded to the nearest hundredth?

A.1.61

B.-0.30

C.-0.69

D.0.70

Answers

Yes the answers is b

Find three solutions of the equation.
y = -2x - 1

Answers

Step-by-step explanation:

three solutions of the equation:

y = -2x - 1

=>

1) (0, -1)

2) (1, -3)

3) ( -1, 1)


What will be the remainder when 6x + 4x4 - 27x³
- 7x² + 27x + 3/2 is divided by (2x² – 3)?

Answers

Answer: The remainder is 0.

Step-by-step explanation:

We are given:

Dividend polynomial = [tex]6x^5+4x^4-27x^3-7x^2+27x+\frac{3}{2}[/tex]

Divisor polynomial = [tex]2x^2-3[/tex]

We divide the dividend by the divisor using the long division method.

In this method, the final answer written in the bottom is considered as remainder and the uppermost polynomial is considered as the quotient.

The long division of the two polynomials is attached in the image below.

From the image, we can say that the remainder of the two is 0

Four spheres of radius 6 cm just fit inside a cylinder.

Calculate the volume inside the cylinder that is empty.

Leave your answer in terms of pi.

Answers

Answer:

1152\pi\

Step-by-step explanation:

which one is the smallest 4/5 1/6 2/3 1/5

Answers

Answer:1/6

Step-by-step explanation:

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{\dfrac{4}{5}=\boxed{\bf 0.80\ or\ 80\%}}\\\\\\\mathsf{\dfrac{1}{6}=\boxed{\bf 0.166667\ or\ 16.6667\% }}\\\\\\\mathsf{\dfrac{2}{3}=\boxed{\bf 0.666667\ or \ 66.6667\%}}\\\\\\\mathsf{\dfrac{1}{5}=\boxed{\bf 0.20\ or \ 20\%}}[/tex]

[tex]\large\textsf{After converting the fractions to decimals and percentages, we can}\\\large\textsf{now out them from descending (least) to ascending (greatest) order}\\\large\textsf{to determine your result to this question}[/tex]

[tex]\boxed{\mathsf{\dfrac{1}{6}, \ \dfrac{1}{5}, \ \dfrac{2}{3}, \& \ \dfrac{4}{5}}}[/tex]

[tex]\large\textsf{The SMALLEST one out of your set is: }\boxed{\mathsf{\bf \dfrac{1}{6}}}\large\checkmark[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{1}{6}}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Put these numbers in order from least to greatest.

1 1/8, 0.7, and 1.4

Answers

Answer:

1.4, 1 1/8, 0.7

Step-by-step explanation:

1 1/8 is equal to 1.125 which it makes it less than 1.4 but more than 0.7.

Answer:

[tex]0.7, \frac{11}{8},1.4[/tex]

Step-by-step explanation:

In order to understand what numbers are greater and what numbers are smaller, we need to make them have the same common denominator. So firstly, we turn all of these numbers into fractions, and we get...

[tex]0.7 = \frac{7}{10}\\\\1.4 = \frac{14}{10}\\\\\frac{11}{8 }= \frac{11}{8 }[/tex]

Now we, need to find the least possible number divisible by 10 and 8, to find the least common denominator. And we get, that the least common denominator is 40, and knowing this, now we have to take each fraction and turn it into an equivalent fraction with the denominator of 40. So we do...

[tex]\frac{11}{8}= \frac{(11)(5)}{(8)(5)}= \frac{55}{40}\\\\\frac{7}{10} = \frac{(7)(4)}{(10)(4)} = \frac{28}{40} \\\\\frac{14}{10} = \frac{(14)(4)}{(10)(4)} = \frac{56}{40}[/tex]

Now we can put these fractions in order from least to greatest...

[tex]\frac{28}{40} < \frac{55}{40}<\frac{56}{40}[/tex]

Therefore, we know that...

[tex]0.7 < \frac{11}{8} < 1.4[/tex]

due in 1 hour ok help

Answers

Answer:

x = 13.2

Step-by-step explanation:

We know that

sin theta = opp / hyp

sin 27 = y/x

sin 27 = 6/x

x sin 27 =6

x = 6/sin 27

x=13.21613559

Rounding to 1 decimal place

x = 13.2

What is the domain of function g if g(x)= f(x)-12?

Answers

Using translation concepts, it is found that the domain of g(x) = f(x) - 12 is the same domain of f(x).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x) - 12, that is, g(x) is a shift down of 12 units of f(x).

The domain of a function is the set that contains all possible input values for the function. A shift down does not add any restriction to the function, hence the domain of f(x) and g(x) are the same.

More can be learned about translation concepts at https://brainly.com/question/4521517

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The city of Plainview is building a new sports complex. The complex includes eight baseball fields, four soccer fields, and three buildings that have


concessions and restrooms. Arrange the structures in the sports complex using translations, reflections, and rotations so that the final


arrangement satisfies each of these criteria:


. All the fields and buildings fit on the provided lot.


• Each field is adjacent to at least one building for ease of access.


. Two or more fields can be adjacent, but no two fields should share the same boundary (e.g., a sideline or a fence.)


• For safety reasons, no baseball field should have an outfield (the curved edge) pointed at the side (the straight edges) of another baseball


field.

Answers

Answer:

See Explanation

Step-by-step explanation:

(Please Find Diagram in the attachment)⇒Answer Drawing is Given There.

According to the question,  

Given that, The city of Plainview is building a new sports complex. The complex includes eight baseball fields, four soccer fields, and three buildings that have concessions and restrooms. Now, Arrange the structures in the sports complex using translations, reflections, and rotations so that the final arrangement satisfies each of these criteria: All the fields and buildings fit on the provided lot. Each field is adjacent to at least one building for ease of access. Two or more fields can be adjacent, but no two fields should share the same boundary (e.g., a sideline or a fence.) For safety reasons, no baseball field should have an outfield (the curved edge) pointed at the side (the straight edges) of another baseball field

Jessica filled the birdbath in her yard with 4 liters of water. How many milliliters of water did she put in the birdbath?

Answers

Answer:

4,000 milliliters

Step-by-step explanation:

There are 1,000 millililters in one liter. 4*1,000=4,000.

Answer:

4,000 mL

Step-by-step explanation:

there are 1,000 mL in one liter so there are 4,000 mL in four liters


Find the sum of the series
{1875 + 750 + 300+...
+3.072}

Answers

Answer:

Find the indicated sum for each geometric series.

{1875+750+300+⋯+3.072}

Answer: 3122.952

Step-by-step explanation:

{1875+750+300+⋯+3.072}

r=0.4 3.072=1875(0.4)n−1

0.0016384=(0.4)n−1

7=n−1→n=8

Sn=1875(1−(0.4)8)1−0.4=3122.952

I think is like this.

P={x:x is a natural number,x<9​

Answers

Answer:

x:x = 1 so it is a natural number

Step-by-step explanation:

it can be any negative number because: -x<9

and any number from 1 to 8

(x cannot be 0, because you cannot do 0/0 = 1)

This question is incomplete and cannot be answered.
There are 8 natural numbers less than 9. (1, 2, 3, 4, 5, 6, 7, 8)
but we don’t know how large the set is we are choosing from.

Determine whether the given equation has one solution, no solution, or infinitely many solutions. 2/3 x=9-2(-1/3x+3)

infinitely many solutions
no solution
cannot be determined
one solution

Answers

The answer is no solution

rotation,
glide reflection,
reflection,
translation.

Answers

Answer:

it appears to have TRANSLATED

we want to factor the following expression (x-3)^2-10(x-3)+25 which pattern can we use to factor the expression

Answers

Answer:

This question is asking for the pattern , not the factoring of it...

this is the [tex](a+b)^{2} pattern = a^{2} + 2ab + b^{2}[/tex]

Step-by-step explanation:

Answer:

(x - 8)²

Step-by-step explanation:

This is in the form of a perfect square, that is

(x + b)² = x² + 2bx + b²

with x = x - 3 and by comparison of like terms

2b = - 10 ⇒ b = - 5

Then

(x + b)²

= (x - 3 - 5)²

= (x - 8)² ← in factored form

Need help on this!!! 10 points!!!

Answers

Number 2: B
Hope this helps :))

The bus seats 36 people. The van seats 12 people. What portion of seats are van seats?

Answers

24
reason: 36-12=24
ez dubs

Please help me as soon as possible!
36 - 2s² + t²
S = 2
T = 8

Answers

Answer:

i think its 20

Step-by-step explanation:

On the last day of a Shakespeare class, an English teacher asked her students which play
they liked the best, and she recorded the results to date.
2 liked Hamlet
8 liked Twelfth Night
2 liked a Midsummer Night's Dream
What is the experimental probability that the next student to respond likes Hamlet best?
Write your answer as a fraction or whole number

Answers

Answer:

ok so if we add this up we get that there is 14 kids in the class who have been polled and 2/14 or 1/7 likes hamlet so the chance is 1 out of 7

The experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .

Concept:Probability = [tex]\frac{Favourable \ Outcomes }{Total \ Outcomes}[/tex]To find total outcomes, we will add all the students.To find the favorable outcomes, we will count the number of students that likes hamlet.

How to solve the given question?Probability = [tex]\frac{Favourable \ Outcomes }{Total \ Outcomes}[/tex]Total Outcomes = 2 + 8 + 2 = 12Favorable outcomes = 2∴ [tex]P(E) = \frac{Favourable \ Outcomes }{Total \ Outcomes} = \frac{2}{12} =\frac{1}{6}[/tex]

Thus, the experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .

Learn more about Probability here:

https://brainly.com/question/15161940

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Help is appreciated:)

Answers

Answer:

252 in^3

Step-by-step explanation:

7*3*12 = 252

252*.04 = $10.08


A triangle has vertices (-1, 2), (3, 1), and (7.2). What is the approximate perimeter of the triangle? Round your answer to the nearest hundredth

Answers

Answer

16.25

Step-by-step explanation: To The Nearest Hundredth

(-1, 2), (3, 1)

√17

(3, 1), (7, 2)

√17

(3, 1), (7, 2)

√8

So our answer is =

8 + √17 + √17 = 16.25

hope it works for you!

Given 1x) = 10-2x, find f(7).

Answers

Step-by-step explanation:

Given that,

f(x) = 10 - 2x

We are asked to calculate the value of f(7).

Substitute the value of x as 7 in the polynomial to find the value of f(7).

→ f(7) = 10 - 2(7)

→ f(7) = 10 - 14

f(7) = -4

Therefore, 4 is the required answer.

3x + 14 < 38
Please show work

Answers

3x + 14 < 38

Subtract 14 from both sides:

3x < 24

Divide both sides by 3:

X < 8

Martina read that the average graduate student is 33 years old. She wanted to estimate the mean age of graduate students at her large university, so she took a random sample of 30 graduate students. What is Martina's margin of error?

Answers

Answer: Martina's margin of error is 1.5.

Step-by-step explanation:

Given: Average graduate student (upper limit) = 33

Random sample graduate student (lower limit) = 30

Formula to calculate margin of error is as follows.

Margin of error = [tex]\frac{upper limit - lower limit}{2}[/tex]

Substitute the values into above formula as follows.

[tex]Margin of error = \frac{upper limit - lower limit}{2}\\= \frac{33 - 30}{2}\\= \frac{3}{2}\\= 1.5[/tex]

Thus, we can conclude that Martina's margin of error is 1.5.

Larry works at the Gap Clothing Store. He works 15 hours week. If his manager cuts all employee hours by 20%, how many hours a week will Larry work now.

Answers

Answer:

12 hours

Step-by-step explanation:

Find 20% of 15 hours

15 * 20%

15 * .2

3

Subtract this because his hours are cut

15-3

12

What is the same as 3(4 + 5 + 6)?

Answers

Answer:

45

Step-by-step explanation:

3(4 + 5 + 6)

= 3(15)

= 3 × 15

= 45 (Ans)

Subtract the second equation from the first. 4x+3y = 17 (4x + y 9)

A. -8x = 26
B. 4y= 8
C. 8x = 26
D. 2y = 8​

Answers

Answer:

D

Step-by-step explanation:

4x+3y -4x -y = 17 -9

<=> 2y =8

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