MATHEMATICS HIGH SCHOOL

A pro football team has 36,000 season ticket holders. Then the team wins the championship and the number of season ticket holders increases by 9,000. What is the percent of change in season ticket holders?20%
25%
33.3%
75%

Answers

Answer 1
Answer: Given:
36,000 season ticket holders (base number)
  9,000 increase in season ticket holders.

9,000 / 36,000 = 0.25
0.25 * 100% = 25%

The percentage change is an increase of 25%.

36,000 + 9,000 = 45,000 new number of season ticket holders.

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Answers

Answer:

6x-8=2x+4

6x-2x=8+4

4x=12

x=3

mike is taking a his social studies test . mike was only able to finish 1/6 of the test in 1/2 hour. how long will it take him to finish the test?

Answers

1-(1)/(6)=(5)/(6)\n\n\begin{array}{ccc}(1)/(6)\ of\ the\ test&-&(1)/(2)\ h\n\n(5)/(6)\ of\ the\ test&-&x\ h\end{array}\ \ \ \ |cross\ multiply\n\n\n(1)/(6)x=(1)/(2)\cdot(5)/(6)\n\n(1)/(6)x=(5)/(12)\ \ \ \ \ |multiply\ both\ sides\ by\ 6\n\n\boxed{x=(5)/(2)=2.5\ (h)}\leftarrow time\ he\ will\ have\ to\ do\ the\ test\n\n\ntotal\ test\ time:2.5\ h+0.5\ h=3\ h
1/2*6 = 3. It will take him 3 hours to finish his test if he continues on the same rate

Alex and Jackson are brothers who are selling mums for a football fundraiser. Together they have sold 37 mums. If Alex has sold 19 more mums than Jackson, how many mums has Jackson sold? Use X to represent the number of mums alex sold and y to represent the number of mums Jackson sold.

Answers

Jackson has sold 18, that’s the only possibility.

x = mums sold by Alex

y = mums sold by Jackson

\boxed{\begin{array}{llll} \stackrel{ \textit{together they've sold 37} }{x + y = 37} \n\n\n \stackrel{ \textit{Alex has sold}}{x} = \stackrel{ Jackson }{y} + 19 \end{array}}\hspace{5em} \begin{array}{llll} \stackrel{\textit{substituting on the 1st equation}}{(y+19)~~ + ~~y~~ = ~~37}\n\n 2y+19=37\n\n 2y=18\n\n y=\cfrac{18}{2}\n\n y=9 \end{array}

One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 215, find the numbers.

Answers

Answer:

23, 69 and 123

Step-by-step explanation:

let the first number be x then the second number is 3x ( 3 times the first) and the third number is x + 100 ( 100 more than the first number)

The sum of the three numbers is

x + 3x + x + 100 = 215

5x + 100 = 215 ( subtract 100 from both sides )

5x = 115 ( divide both sides by 5 )

x = 23

The 3 numbers are

x = 23, 3x = 3 × 23 = 69 and x + 100 = 23 + 100 = 123

Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest and gives him the ability to make ATM withdrawals from that bank’s ATMs. Putting the money in an online savings account will earn him 4.85% annual interest, but he will be charged $3 every time he makes an ATM withdrawal. Assuming that Gareth’s ATM withdrawals do not affect the amount of interest he earns, roughly how many ATM withdrawals must Gareth make every year for the local savings account to be a better deal than the online savings account?

Answers

Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest.

Interest earned in local bank = 2000 * 22.2% = 2000 * 0.022 = 44

Putting the money in an online savings account will earn him 4.85% annual interest

Interest earned in online account = 2000 * 4.85% = 2000 * 0.0485 = 97

He will be charged $3 every time he makes an ATM withdrawal.

In online account, the interest is 97 . If he withdraws 18 times then

Total ATM fee is 18 * 3= 54 . so 97 - 54 = 43

43 is lower than 44 that is interest of local account.

Therefore, 18 ATM withdrawals make local savings account to be a better deal than the online savings account every year.

Answer:

Gareth should make 18 ATM withdrawals every year for better deal.

Step-by-step explanation:

Consider the provided information.

Gareth has $2,000 to invest and local bank will earn him 2.2% annual interest.

The amount earned by local bank is: \$2000* (2.2)/(100)=\$44

The money in an online savings account will earn him 4.85% annual interest, but he will be charged $3 every time he makes an ATM withdrawal.

The amount earned by online account \$2000* (4.85)/(100)=\$97

Savings account has no ATM withdrawal charges but online savings account charge $3.00 per withdrawal.

Let x is the number of times he withdrawal money.

97-3x=44\n3x=53\nx=17.67\approx 18

Hence, Gareth should make 18 ATM withdrawals every year for better deal.

The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?

Answers

This one is a bit confusing but I'll try to answer. Since the sum is given and one of the addend is given, we need to perform subtraction to get the other addend.

     8d⁵ - 3c³d² + 5c²d³ - 4cd⁴ + 9  ⇒ SUM
-    2d⁵ -   c³d²              + 8cd⁴ + 1  ⇒ 1ST ADDEND
     6d⁵ - 2c³d² + 5c²d³ -12cd⁴ - 8 ⇒ 2ND ADDEND

Answer:

A which is 6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8
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