MATHEMATICS HIGH SCHOOL

How many ways are there to distribute three different teddy bears and nine identical lollipops to four children (a) Without restriction? (b) With no child getting two or more teddy bears? (c) With each child getting three ""goodies""?

Answers

Answer 1

Answer:

Answer:a) 14080, b) 5280, c) 64.

Step-by-step explanation:

Since we have given that

Number of teddy bears = 3

Number of identical lollipops = 9

Total number of things = 3+9 =12

Number of children = 4

(a) Without restriction?

Number of ways would be

$4^3* ^(12)C_3\n\n=14080$

(b) With no child getting two or more teddy bears?

$4* 3!* ^(12)C_9\n\n=5280$

(c) With each child getting three ""goodies""?

$4^3=64$

Hence, a) 14080, b) 5280, c) 64.

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Each week, you drive 150 miles. Your car gets 25 miles to the gallon, and gas prices are $3 per gallon. How much gas money will you spend on gas each week?

Answers

$18

Further explanation

Given:

Every week drive 150 miles.
The car gets 25 miles to the gallon.
Gas prices are $3 per gallon.

Question:

How much gas money will you spend on gas each week?

This is properly a simple multiplication problem that however has to pay attention to the units carefully.

Let's find out how many gallons we need to drive over 150 miles.

$\boxed{ \ = 150 \ miles * (1 \ gallon)/(25 \ miles) \ }$

Units of miles crossed out.

$\boxed{ \ = 150 * (1 \ gallon)/(25) \ }$

$\boxed{ \ = (150)/(25) \ gallon \ }$

Therefore, we need 6 gallons to drive over 150 miles.

And now let's calculate how much gas money will be spent each week.

$\boxed{ \ = 6 \ gallons * (\$ 3)/(1 \ gallon) \ }$

Units of gallon crossed out.

$\boxed{ \ = 6 * \$ 3 \ }$

$\boxed{ \ = $ 18 \ }$

Hence, we will spend $18 on gas each week.

If it's already straightforward in understanding, then we can arrange multiplication operations at once.

$\boxed{ \ = 150 \ miles * (1 \ gallon)/(25 \ miles) * (\$3)/(1 \ gallon) \ }$

$\boxed{ \ = (150)/(25) * \$3 \ }$

150 and 25 can be divided by 25.

$\boxed{ \ = 6 * \$3 \ }$

Once again, we will spend $18 on gas each week.

Learn more

A similar problem and associated with currency exchange rates brainly.com/question/3959122
About unit conversion factor brainly.com/question/5009365
About the simplification of polynomial operations brainly.com/question/1394854

Keywords: each week, you drive 150 miles, car, 25 miles to the gallon, gas prices are $3, per gallon, how much, money will you spend, multiplication, the units

The amount of money spent on gas each week is $\fbox{\begin\n\ \bf \$18\n\end{minispace}}$

Further explanation:

As given in the question $150$ miles of distance is covered by the car each week.

To cover a distance of $25$ miles, $1$ gallon of gas is required for the car and the price for the gas is $\$3$ per gallon.

The objective is to determine the amount of money spent on gas each week.

It is given that to travel $25$ miles, $1$ gallon of gas is required so, for $1$ mile of distance $\left((1)/(25)\right)^(th)$ gallon of gas is required.

This implies that in $\left((1)/(25)\right)^(th)$ gallon of gas the car runs for $1$ mile of distance.

Now if in $\left((1)/(25)\right)^(th)$ gallon of gas $1$ mile of distance is covered so, for $150$ miles of distance the amount of fuel required is calculated as follows:

$\fbox{\begin\n\ (1)/(25)* 150=6\n\end{minispace}}$

From the above calculation it is concluded that with $6]$ gallon of gas $150$ miles of distance is covered.

The price for the gas is $3 per gallon so, the price of 6 gallon of gas is calculated as follows:

$\fbox{\begin\n\ 6* 3=18\n\end{minispace}}$

From the above calculation it is concluded that the cost of $6$ gallon of gas is $\$18$ .

Therefore, the amount of money spent on the gas each week is $\fbox{\begin\n\ \bf \$18\n\end{minispace}}$ .

Summary:

$25\ \text{miles}\rightarrow1\ \text{gallon}\n1\ \text{mile}\rightarrow((1)/(25))^(th)\ \text{gallon}\n150\ \text{miles}\rightarrow((1)/(25)* 150)=6\ \text{gallons}\n1\ \text{gallon}\rightarrow\$3\n6\ \text{gallons}\rightarrow\fbox{\begin\n\ \bf \$18\n\end{minispace}}$

Learn more:

1. A problem on composite function brainly.com/question/2723982

2. A problem to find radius and center of circle brainly.com/question/9510228

3. A problem to determine intercepts of a line brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Simplification

Keywords: Simplification, multiplication, miles, distance, price, gas, $3, each week, drives 150 miles, money spent each week, 25 miles per gallon.

Divide: (x^2-10x+30)/(x-5)A. x-10-6
B. x-5- 5/x-5
C. x-10- 30/x-5
D. x-5+ 5/x-5

Answers

Answer:

Option D is correct.

Step-by-step explanation:

$(x^(2) -10x+30)/(x-5)$

Solving this we get:

$x+(-5x+30)/(x-5)$

Quotient = x remainder = -5x+30

Now dividing, $(-5x+30)/(x-5)$ , we get

$-5+(5)/(x-5)$

quotient = -5 and remainder = 5

So, the answer is :

$x-5+(5)/(x-5)$

Therefore, option D is correct.

Jasmine wants to use her savings of $1128 to buy video games and music CDs. The total price of the music CDs she bought was $72. The video games cost $43 each. What is the maximum number of video games that Jasmine can buy with her savings?

Answers

Answer

Find out the number of video games that Jasmine can buy with her savings .

To proof

Let us assume that the number of video games Jasmine can buy be x .

As given

Jasmine wants to use her savings of $1128 to buy video games and music CDs.

The total price of the music CDs she bought was $72. The video games cost $43 each.

Than the equation becomes

72 + 43× x = 1128

simplify

72 + 43x = 1128

43x = 1128 - 72

43x = 1056

$x = (1056)/(43)$

x = 24.6 (approx)

Take

x = 24

Therefore the maximum number of video games that Jasmine can buy with her savings be 24 .

Hence proved

she can buy 24 video games
1128-72=1056
1056/43=24

Which of the following ratios are equivalent to 6:8?9:12
12 to 16
24:36
16 to 24

Answers

12 to 16 should be the only one.
i looked over ti and 9/12 is also equivalent.
if you multiple by 1.5 that gets you 9/12

Nina walked 3.7 miles everyday for one month how many miles in all did she walk in 31 days

Answers

Nina walked 114.7 miles in 31 days. All you have to do is multiply 3.7 by 31

A ball is thrown straight up from the top of a 40 feet tall building with an initial speed of 24 feet per second. The height of the ball as a function of time can be modeled by what function h(t) = _________________ 1. after how many seconds the ball hit the ground. 2.What is the maximum height of the ball? 3.How long did it take for the ball to reach its maximum height?