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2 years ago

5

Marie has 11 coins, all of which are quarters and nickels. In all, they're worth $1.15. How many of each kind of coin does Marie

have?

1 answer:

pickupchik [31]2 years ago

3 0

Answer:

Step-by-step explanation:

x + y = 11

.25x + .05y = 1.15

25x + 5y = 115

-25x - 25y = -275

-20y = -160

y = 8 nickels

x + 8= 11

x = 3 quarters

3 quarters and 8 nickels

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Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

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.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

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

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

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

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

So

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

Yochanan walked from home to the bus stop at an average speed of 5 km / h. He immediately got on his school bus and traveled at

kari74 [83]

Answer: 5 km walking and 30 km by bus

Step-by-step explanation:

Yochanan walked from home to the bus stop at an average speed of 5 km / h. He immediately got on his school bus and traveled at an average speed of 60 km / h until he got to school. The total distance from his home to school is 35 km, and the entire trip took 1.5 hours. How many km did Yochanan cover by walking and how many did he cover by travelling on the bus?

walking - 5km/h bus - 60km/h

distance walking - d₁ distance bus - d₂

time walking - t₁ time bus - t₂

d₁ + d₂ = 35

t₁ + t₂ = 1.5

v = d/t

vwalking = d₁/t₁

5 = d₁/t₁ ⇒ d₁ = 5t₁

vbus = d₂/t₂

60 = d₂/t₂ ⇒ d₂ = 60t₂

d₁ + d₂ = 35 ⇒ 5t₁ + 60t₂ = 35

_________________________

5t₁ + 60t₂ = 35

t₁ + t₂ = 1.5 (*-5)

5t₁ + 60t₂ = 35

-5t₁ -5t₂ = -7.5 (+)

__________________________

55t₂ = 27.5

t₂ = 27.5/55 = 0.5 h

t₁ + t₂ = 1.5 ⇒ t₁ = 1.5 - 0.5 = 1h

d₁ = 5t₁ ⇒ d₁ = 5.1 = 5 km

d₂ = 60t₂ ⇒ d₂ = 30.0.5 = 30 km

6 0

2 years ago

a beverage is made by mixing 3 parts of water with 5 parts of fruit juice how many parts of water are mixed with 1 part on fruit

Fittoniya [83]

Answer:

$\frac{3}{5}=0.6$

Step-by-step explanation:

Given the initial ratio of 3 parts water to 5 parts fruit juice, you can set up a proportion (equivalent ratios) to determine the amount of water needed with just 1 part of fruit juice:

$\frac{water}{fruit}=\frac{3}{5}=\frac{x}{1}$

cross multiply: 5x = 3

divide: 5x/5 = 3/5 or x = 3/5

3/5 = 0.6 parts water

7 0

3 years ago

Read 2 more answers

Im Starving!!!! I dont know what to eat. What should I eat? Im also Bored -w-"

Julli [10]

Answer:

umm id k sandwich ? eggs? cereal ? ice cream lol

Step-by-step explanation:

6 0

2 years ago

Can y'all help me please<br><br>n - 5.6 = 14.9

horrorfan [7]

Answer:

20.5

Step-by-step explanation:

n=14.9+5.6

n=20.5

3 0

3 years ago