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GarryVolchara [31]

3 years ago

8

Bell goes for tutoring at a is for algebra tutoring. They charge a registration fee of $57 and $34 an hour for tutoring. If bell

s parents budget is $300 for tutoring. What is the maximum number of hours of tutoring she can afford?

1 answer:

Makovka662 [10]3 years ago

3 0

Answer:

7

Step-by-step explanation:

The expression is 57+34h is less than or equal to 300. So 300-57 is 243. 243/34 is 7.147... so you round. So you get 7 hours without going over

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Every day your friend commutes to school on the subway at 9 AM. If the subway is on time, she will stop for a $3 coffee on the w

Shtirlitz [24]

Answer:

1.02% probability of spending 0 dollars on coffee over the course of a five day week

7.68% probability of spending 3 dollars on coffee over the course of a five day week

23.04% probability of spending 6 dollars on coffee over the course of a five day week

34.56% probability of spending 9 dollars on coffee over the course of a five day week

25.92% probability of spending 12 dollars on coffee over the course of a five day week

7.78% probability of spending 12 dollars on coffee over the course of a five day week

Step-by-step explanation:

For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so $p = 0.6$

The week has 5 days, so $n = 5$

She spends 3 dollars on coffee each day the train is on time.

Probabability that she spends 0 dollars on coffee:

This is the probability of the train being late all 5 days, so it is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102$

1.02% probability of spending 0 dollars on coffee over the course of a five day week

Probabability that she spends 3 dollars on coffee:

This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768$

7.68% probability of spending 3 dollars on coffee over the course of a five day week

Probabability that she spends 6 dollars on coffee:

This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304$

23.04% probability of spending 6 dollars on coffee over the course of a five day week

Probabability that she spends 9 dollars on coffee:

This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456$

34.56% probability of spending 9 dollars on coffee over the course of a five day week

Probabability that she spends 12 dollars on coffee:

This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592$

25.92% probability of spending 12 dollars on coffee over the course of a five day week

Probabability that she spends 15 dollars on coffee:

Probability that the subway is on time all days of the week, so $P(X = 5)$ .

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.6)^{5}.(0.4)^{0} = 0.0778$

7.78% probability of spending 12 dollars on coffee over the course of a five day week

8 0

3 years ago

Carrie has 40 more nickels than Joan has dimes. They both have the same amount of money. How many coins does each girl have? Wha

LuckyWell [14K]

Answer:

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Step-by-step explanation:

Let be $x$ and $y$ the amounts of nickels and dimes that Carrie and Joan have, as $c$ the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.

The following equations are constructed after a careful reading on statement:

Carrie's amount of money:

$0.05\cdot x = c$ (Eq. 1)

Joan's amount of money:

$0.10\cdot y = c$ (Eq. 2)

Relation between amounts of coins:

$x = y+40$ (Eq. 3)

First we eliminate $c$ by equalizing (Eq. 1) and (Eq. 2):

$0.05\cdot x = 0.10\cdot y$

Then, we reduce the resulting formula by (Eq. 3):

$0.05\cdot (y+40) = 0.10\cdot y$

$y+40 = 2\cdot y$

$y = 40$

And rest of variable are now determined:

$x = 40+40$

$x = 80$

$c = 0.05\cdot (80)$

$c = 4$

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

5 0

3 years ago

∆ABC m∠B = 90° AB = 4 BC = 3<br> Find AC

lutik1710 [3]

Step-by-step explanation:

In ∆ABC, m∠B = 90°

Therefore ∆ABC is a right angled triangle with sides AB = 4 & BC = 3. AC is the hypotenuse.

Hence, by Pythagoras theorem:

$AC^2 = AB^2 +BC^2 \\ \\ \therefore \: AC = \sqrt{AB^2 +BC^2 } \\ = \sqrt{ {4}^{2} + {3}^{2} } \\ = \sqrt{16 + 9} \\ = \sqrt{25} \\ = 5 \\ \\ \huge \red{ \boxed{ \therefore \: AC = 5 \: units}}$

8 0

3 years ago

-3(x+3)-3(x - 1)+8x = 4

Leviafan [203]

Answer:

Step-by-step explanation:

(distribute)

-3x -9 -3x + 3 + 8x = 4

(simplify)

2x -6 = 4

x=5

3 0

3 years ago

I need help!!!!!!!!!!!

Keith_Richards [23]

3. well you know to get the perimeter of a rectangle, you add together 2L and 2W. A way you could write this is-- 2x + 2(x+5). You would just need to simplify it--2x + 2x+10 --4x+10.
4. To find out how much they have in all, you just need to add them together--x+24.50 + 7x-52.34. Now you need to simplify the problem by putting the values together. x+7x + 24.50-52.34-- you can do that.
5. To do this one, look back at 3. and just change the numbers. Drawing a picture may help. The sides are x+y and the top and bottom are 5y+12.
6. same as 5.
7. I think this one is just solving for x first. make Tom and his brother's equations equal to zero and get x by itself. Tom's equation would be 8x-30=0 ----His brother's would be 5x+10. You need to find out what x equals then plug it back into the equations. To plug it in, have x's value take x's place then find the number of candies they have.
8. The easiest way to start is by writing the same values together. 4x+3x-5x-5-7+2---then just add the x's together and add the numbers together.
9. Multiply the outer numbers to both of the values in the parentheses. 2(x-4) would turn out to 2x-8. then do the same as 8. and put the same values together to simplify.
10. get x by itself. Start by multiplying 3 by x and 4 in the parentheses. simplify the numbers then subtract it from both sides to get x alone.

7 0

3 years ago

Read 2 more answers