A zoo train ride costs $4 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who took the ride was 27, and the total money collected was $60. What was the number of children and the number of adults who took the train ride that day, and which pair of equations can be solved to find the numbers? 1) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 2) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 3) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60 4) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60

Answer:

"General Formulas" in mathematics is the general equation you can use for certain things, by just adding the numbers given to the equation so that you can solve the problem.

Form example:

The general formula to find the y-intercept: y=mx+b

Hope this helped!

Have a nice day:)

Answer:

"General Formulas" in mathematics is the general equation you can use for certain things, by just adding the numbers given to the equation so that you can solve the problem.

Step-by-step explanation:

Answer:

The number of years needed to repay the loan is 11.47 years or 11 years.

Step-by-step explanation:

The loan amount, Present value =  $14000

Annual repayment amount (annuity) = $1800

Interest rate = 7% per annum.

Now we have to find the number of years consumed to repay the loan amount. Below is the calculation.

Present value = (Annuity[1-(1+r)^-n] )/ r

14000 = (1800 × [1- (1+ 0.07 )^-n] )/ 0.07

14000 × 0.07 = 1800 × [1- (1+ 0.07 )^-n]

980 = 1800 × [1- (1+ 0.07 )^-n]

0.54 = [1- (1+ 0.07 )^-n]

n = 11.47  or 11  years.

Answer and Step-by-step explanation:

For the first part

Tara is incorrect as she practices the softball in 4 days in a week and she do each practice of minimum one hour

So we can conclude that she practices minimum hours in a week  

For the second part

Also in 4 days, she does practice [tex]1 \frac{1}{3}[/tex] hours per day i.e [tex]5 \frac{1}{3}[/tex]

Now convert [tex]1 \frac{1}{3}[/tex] this into a fraction which comes [tex]\frac{4}{3}[/tex]

For four days, it is

= [tex]4 \times \frac{4}{3} \\\\ \frac{16}{3} \\\\ 5 \frac{1}{3}[/tex]

Step-by-step explanation:

Without multiplying, explain how you know Tara is incorrect.

How long will Tara have softball practice this week? Write your answer as a mixed number.  

Each practice is [tex]1\frac{1}{3}[/tex] hours

Each practice is more than 1 hour. so 4 days of practice is more than 4 hours.

So Tara is incorrect

Practice for 4 days

[tex]1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}=4\frac{4}{3}=5\frac{1}{3}[/tex]

More than 5 hours .

Tara will have [tex]5\frac{1}{3}[/tex] softball practice this week

Answer:

Tara will have [tex]5\frac{1}{3}[/tex]  hours softball practice this week

Answer:

2/5

Step-by-step explanation:

There are 2 white and 4 yellow  = 6

P(yellow) = yellow /total = 4/6 = 2/3

We keep the ball

Now there are 2 white and 3 yellow  = 5

P(yellow) = yellow /total = 3/5

P ( yellow, keep, yellow) = 2/3 * 3/5 = 2/5

We are given 4 yellow balls and 2 white balls. In total, this adds up to 6.

Divide the number of yellow balls to the total number of balls:

4/6 -> 2/3

We are also given 3 yellow and 2 white.

Divide the number of yellow balls to the total number of balls:

3/5

Divide both fractions together:

3/5 * 2/3 = 6/15 = 2/5

Best of Luck!

Answer:

-1/3 sqrt(21)

Step-by-step explanation:

1/3 sqrt(21) - 2/3 sqrt(3)  * sqrt(7)

We know sqrt(a) * sqrt(b) = sqrt(ab)

1/3 sqrt(21) - 2/3 sqrt(21)

Factor out sqrt(21)

sqrt(21) (1/3-2/3)

sqrt(21) (-1/3)

-1/3 sqrt(21)

Answer: Choice A)  [tex]-\frac{1}{3}\sqrt{21}[/tex]

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

Work Shown:

I'm guessing that the x you wrote is to signify multiplication. If so, then one way to do the steps is shown in the attached image below.

In step 2, I used the rule that sqrt(x)*sqrt(y) = sqrt(x*y).

Answer:

Step-by-step explanation:

A. m∠4 = 180° - m∠3

   m∠1 = 180° - (m∠3 + m∠2)

  m∠3 < m∠3 + m∠2  ⇒  m∠4 >m∠1

B. m∠4 = 180° - m∠3

   m∠2 = 180° - (m∠3 + m∠1)

  m∠3 < m∠3 + m∠1  ⇒  m∠4 >m∠2

C. Not necessarily {could be but not always}

D.   m∠4 = 180° - m∠3

m∠1 + m∠2 + m∠3 = 180°  ⇒  m∠1 + m∠2 = 180° - m∠3 = m∠4

E.  m∠3 = m∠1 + m∠2  only if m∠3 = 90°

F.  Not necessarily. {Could be but also could not be. In the picture is, but we don't know if the diagram is accurate or just approximate.}

Answer:

C. The charge of each minute of a call is $0.40

Step-by-step explanation:

We look at the point (1, 0.4)

We know that our x = 1 is 1 minute of the call.

We know that y = 0.4 is the cost when 1 minute of the call has elapsed.

Therefore, our answer is C.

Answer:

Step-by-step explanation:

The answer is (c)

The price goes up $0.40 every minute Greg is on a call.

Answer:

B(-5, 1)

Step-by-step explanation:

We can test each value in the equation and see if the equation works out.

[tex]y > |x| - 6[/tex]

Let’s try A - (-1, -5).

[tex]-5 > |-1|-6\\\\-5 > 1-6\\-5>-5[/tex]

-5 is NOT greater than -5, it is equal so A doesn’t work.

Let’s try B, (-5, 1).

[tex]1 > |-5| -6\\1 > 5-6\\1 > -1[/tex]

1 IS greater than -1, so B works.

Let’s try C for fun.

[tex]-1 > |5| -6\\-1 > 5-6\\-1 > -1[/tex]

-1 is NOT greater than -1, it is equal, so it doesn’t work.

Hope this helped!

Answer:

B(-5,1)

Let us simply just write this in all scenarios.

A(-1,-5)

-5>|-1|-6

-5>-5

(False)

B(-5,1)

1>|-5|-6

1>-1

(True)

C(5, -1)

-1>|5|-6

-1>-1

False

The vertical distance through which the car rises is 16.7 m

"It is a triangle whose one of the angle is 90°."

In right triangle, for angle 'x',

sin(x) = (opposite side of angle x)/hypotenuse

For given example,

Consider the following figure for given situation.

A car travels 120 m along AC.

ΔABC is right triangle with hypotenuse AC.

∠C = 8°

Consider sine of angle C,

[tex]\Rightarrow sin(C)=\frac{AB}{AC}\\\\\Rightarrow sin(8^{\circ})=\frac{AB}{120}\\\\ \Rightarrow 0.1392=\frac{AB}{120}\\\\ \Rightarrow AB = 0.1392\times 120\\\\\Rightarrow AB = 16.70~ m[/tex]

Therefore, the vertical distance through which the car rises is 16.7 m

Learn more the sine angle here:

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Answer:

x = -1.5

Step-by-step explanation:

16x - 5 = 18x -2

Subtract 16x from each side

16x-16x - 5 = 18x-16x -2

-5 = 2x-2

Add 2 to each side

-5+2 = 2x-2+2

-3 = 2x

Divide by 2

-3/2 = 2x/2

-3/2 =x

Answer:

-3/2

Step-by-step explanation:

To solve this problem, start by moving all of your x's on to one side, and all of your constants on to the other as such:

16x-5=18x-2

     +2       +2

16x-3=18x

-16x    -16x

-3=2x

-3/2 = x

P.S. please give me brainliest. Thank you! :)

Answer:

the answer is 14

Step-by-step explanation:

you first add both side to 4 and get x=14

Answer: x = 14

Explanation: Our only step in solving the equation is to add 4 to both sides and the reason that we can add the same quantity to both sides of an equation is based on the addition property of equality.

So the solution to this equation is x = 14.

Surface area of sphere is what referred to as Total surface area or lateral surface area because here the surface is curved everywhere.

[tex] \large{ \boxed{ \rm{ \orange{Surface \: area \: of \: sphere = 4\pi {r}^{2} }}}}[/tex]

Total surface area of other 3-D shapes:

Lateral surface area of these shapes:

━━━━━━━━━━━━━━━━━━━━

Answer:

[tex]l = 28[/tex]

Step-by-step explanation:

Given

[tex]S = \sum (2k - 3); k = 4\ to\ l[/tex]

Required

What is l when S = 725

This can be solved using Sum of n terms of an AP;

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where

[tex]S_n = 725[/tex]

[tex]T_1 = first\ term[/tex]

To get T1; we substitute 4 for k in 2k - 3

[tex]T_1 = 2 * 4 - 3[/tex]

[tex]T_1 = 8 - 3[/tex]

[tex]T_1 = 5[/tex]

[tex]T_n = last\ term[/tex]

To get Tn; we substitute l for k in 2k - 3

[tex]T_n = 2 * l - 3[/tex]

[tex]T_n = 2l - 3[/tex]

n = the number of terms;

Since k = 4 to l, then

[tex]n = l - 4 +1[/tex]

[tex]n = l - 3[/tex]

Substitute these values in [tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]725 = \frac{l-3}{2}(5 + 2l - 3)[/tex]

Collect Like Terms

[tex]725 = \frac{l-3}{2}(2l + 5- 3)[/tex]

[tex]725 = \frac{l-3}{2}(2l + 2)[/tex]

Open the bracket

[tex]725 = \frac{l-3}{2} * 2l + \frac{l-3}{2} * 2[/tex]

[tex]725 = (l-3) * l + (l-3)[/tex]

[tex]725 = l^2-3l + l-3[/tex]

[tex]725 = l^2-2l -3[/tex]

Subtract 725 from both sides

[tex]725 - 725 = l^2-2l -3 - 725[/tex]

[tex]l^2-2l -3 - 725 = 0[/tex]

[tex]l^2-2l - 728 = 0[/tex]

[tex]l^2 + 26l - 28l - 728 = 0[/tex]

[tex]l(l + 26) - 28(l + 26) = 0[/tex]

[tex](l - 28)(l + 26) = 0[/tex]

[tex]l - 28 = 0[/tex] or [tex]l + 26 = 0[/tex]

[tex]l = 28[/tex] or [tex]l = -26[/tex]

But l must be positive;

Hence, [tex]l = 28[/tex]

Answer:

£23.96

Step-by-step explanation:

Area to be painted:

3.6 m * 8.3 m = 29.88 m^2

The area to be painted is 29.88 m^2.

A tin of paint covers 8 m^2. We divide to find the number of tins needed.

29.88/8 = 3.735

Since full tins must be bought, the smallest number of tins needed is 4.

Now we find the price of 4 tins. 1 tin costs £5.99, so 4 tins cost:

4 * £5.99 = £23.96

Answer:

35

Step-by-step explanation:

it's the same value each side

Answer:

a^2 × a^4

= a^2+4

= a^6

Remember:

a^n × a^m= a^n+m

Hope it helps

if u have any question let me know in comments ^_^

Answer:

[tex]a^2 * a^4 = \\a^{(2 + 4)} = \\a^6[/tex]

Step-by-step explanation:

Hope it helps!

Answer:

Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of room  because

1. It specifically talks about green roof's

2. Unlike the blog post, the .org/.gov is not attempting to sell a product that may change how the article is written.

Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms because It talks explicitly about green roofs.

A survey is research done by any company or an organisation on the group of people or their activity or on any other data like their sells etc to find out the valuable information from that data.

Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms.

1. It specifically talks about green roofs

2. Unlike the blog post, the .org/.gov is not attempting to sell a product that may change how the article is written.

Therefore Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms because It talks explicitly about green roofs.

To know more about surveys follow

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Answer:

p= 25/100 = 180/x

Step-by-step explanation:

In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.

Answer:

0.75p=p-180

Step-by-step explanation:

0.75p=p-180 is your answer

Answer:

P(NOT printed page) = 3/38

Step-by-step explanation:

Total pages = 27+8+3=38

Types of pages that satisfy requirement(s)= 3

Therfore, P(NOT printed page) = 3/38

Answer:

-8.58

Step-by-step explanation:

p = 9.7

=> -3.28 - (-4.4) + (-p)

=> -3.28 - (-4.4) + (- (9.7))

=> -3.28 - (-4.4) + (-9.7)

=> -3.28 - (-4.4) -9.7

=> -3.28 +4.4 -9.7

=> -12.98 +4.4

=> -8.58

Answer:

The evaluated answer for this equation is -8.58

Step-by-step explanation:

We are given a value of p so we will use this value for the equation.

-3.28 - (-4.4) + (-p)

Replace p with 9.7

-3.28 - (-4.4) + (-9.7)

Since there is a double negative in front of 4.4, then that means that we are going to be adding -3.28 to 4.4

1.12 + (-9.7)

Subtract 1.42 from 9.7 because there is negative sign in front of 9.7

-8.58

Answer:99

Step-by-step explanation:(11×9)×1=99

Answer:

Step-by-step explanation:

(a x b) x c

a = 11, b = 9, and c = 1

In order to solve substitute the values of a , b and c into the above expression

That's

( 11 × 9) × 1

Solve the terms in the bracket first

99 × 1

We have the final answer as

Hope this helps you

Answer:

Felix

Step-by-step explanation:

The graph contains 3 segments,

first one is for the first 4minutes,

second one is for the next 2 minutes (standing still)

third one is for the last 2 minutes.

Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end. (e.g., from 4 to 6 is 2 minutes).

The student that most accurately described Roy's motion is Felix.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

We need to find the student that most accurately described Roy's motion.

Here we can see that the graph contains 3 segments, first one is for the first 4 minutes, Second one is for the next 2 minutes (standing still) and the third one is for the last 2 minutes.

Now, Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end.

Therefore, the student that most accurately described Roy's motion is Felix.

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Answer:

see explanation

Step-by-step explanation:

Since (k, 3) lies on each of the lines, the point satisfies the equations.

Substitute x = k, y = 3 into each and solve for k

y = 3x + 1

3 = 3k + 1 ( subtract 1 from both sides )

2 = 3k ( divide both sides by 3 )

k = [tex]\frac{2}{3}[/tex]

-------------------------------------------------------

y = 4x - 2

3 = 4k - 2 ( add 2 to both sides )

5 = 4k ( divide both sides by 4 )

k = [tex]\frac{5}{4}[/tex]

--------------------------------------------------------

y = [tex]\frac{1}{2}[/tex] x

3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )

k = 6

---------------------------------------------------------

2x + 3y = 4

2k + 3(3) = 4

2k + 9 = 4 ( subtract 9 from both sides )

2k = - 5 ( divide both sides by 2 )

k = - [tex]\frac{5}{2}[/tex]

Answer:

  7 seconds

Step-by-step explanation:

We assume h(t) represents the height above ground, so that h(t) = 0 will be the point where the ball hits the ground.

The factored form of the equation tells us ...

  h(7) = -16(7 -7)(7 +2) = 0

So, the baseball will land on the ground when t=7, seven seconds after first being thrown into the air.

_____

The other value of t that makes h(t) = 0 is -2. Since we only count time after the ball is thrown, t=-2 is an extraneous solution.

Answer:

dicontinuity at (-4.-2)zero at (-2.0)

Step-by-step explanation:

answer c

this shoud be correct

Answer:

I hope this will help!

Step-by-step explanation:

Answer:

Hey there!

X+Y=0.

For example, two numbers that are equally far from the 0 on a number line are -2 and 2.

-2+2=0

Hope this helps :)

Answer:

x + y = 0

Step-by-step explanation:

Since the two values are the same distance from zero on the number line (i.e., they are equivalent in distance) and one is in the negative direction, and the other is in the positive direction, then the sum of both will be zero.

Since they are the same distance, just opposite in direction, it requires the same amount of "hops" for both values to reach zero, hence they will cancel each other out when added together.

Consider, -1 and 1.  Both are the same distance from 0; however, if you add them together (-1 + 1) you'll get the sum to be 0.

Cheers.

Answer:

Step-by-step explanation:

Let (a, b) represent the coordinates of point Q on line x -2y -4 = 0. Then we know that ...

  a -2b -4 = 0

  a -2b = 4

__

If P is the midpoint of QR, then ...

  R = 2P -Q = 2(1, 1) -(a, b) = (2 -a, 2 -b)

We know this point satisfies the equation for the other line:

  x + y = 5

  (2 -a) +(2 -b) = 5

  a + b = -1 . . . . . . . . . . . rearrange to standard form

__

To find the solution to these two equations, we can subtract the first from the second:

  (a +b) -(a -2b) = (-1) -(4)

  3b = -5

  b = -5/3

  a = -1 -1b = -1 -(-5/3) = 2/3

The point Q is (a, b) = (2/3, -5/3).

The point R is ...

  R = (2 -a, 2 -b) = (2 -2/3, 2 -(-5/3)) = (4/3, 11/3)

The exact coordinates of Q and R are ...

  Q(2/3, -5/3), R(4/3, 11/3)

_____

Comment on the GeoGebra solution

The points can be found by reflecting either line across point P. Where that reflected line intersects the other line is one of the points of interest. Of course, the other is its reflection in P. You may recognize the equation for line b' (hidden in the diagram) as matching the second equation we derived above.

Answer:

[tex]\frac{1}{256}[/tex]

Step-by-step explanation:

(¼)²=√x

√x=1/16

x=(1/16)²

x= 1/256

Answer:

Reserve rate = 3%

Step-by-step explanation:

Reserve Ratio = Reserve Maintained with Central Bank / Deposit Liabilities × 100

Reserve maintained = $6,000

Deposit liabilities = $200,000

Reserve Rate = Reserve Maintained with Central Bank / Deposit Liabilities × 1000

=$6,000 / $200,000 × 100

=0.03 × 100

r=0.03 × 100

=3%

Therefore,

Reserve Rate =3%