Gary buys a skateboard for<br> $145. What's the total cost<br> including 6% sales tax?

Marsha had $4.00 in her pocket in the morning, and Mark had $0.50. Marsha sells her sweets for $0.25 each, and Mark sells his fo

Karo-lina-s [1.5K]

They would both have to sell 14 candy

4 0

2 years ago

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John took all his money from his savings account. He spent $88 on a radio and 1/4 of what was left on presents for his friends.

gayaneshka [121]

Answer:

$968

Step-by-step explanation:

x= the money John originally had in his savings account

The statement says that John spent $88 on a radio and 1/4 of what was left on presents for his friends. This means that the remaining money is 3/4 of the total amount minus the money spent on the radio:

3/4(x-88)

Then, it says that of the money remaining, John put 4/11 into a checking account and the last remaining $420 was left to charity. Since, he spent 4/11 of the remining 3/4(x-88), the remaining is 7/11 of that and that remaining is equal to $420 that was the money left at the end:

7/11(3/4(x-88))= 420

21/44(x-88)=420

21/44x-42=420

21/44x=462

x=968

According to this, the money that John originally had in his savings account was $968.

He spent $88 on a radio: 968-88= 880

1/4 of what was left on presents for his friends: 880/4= 220

880-220=660

Of the money remaining, John put 4/11 into a checking account: 660*(4/11)=240

the last remaining $420 was left to charity: 660-240= 420

6 0

3 years ago

(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice

vesna_86 [32]

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

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.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that $\mu = 100, \sigma = 15$

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{107.5 - 100}{15}$

$Z = 0.5$

$Z = 0.5$ has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{130 - 100}{15}$

$Z = 2$

$Z = 2$ has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

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

In which

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

$P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549$

$P(X \geq 1) = 1 - P(X = 0) = 0.0451$

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

8 0

2 years ago

What is the perimeter of the rectangle with length of 2x + 3 and width of 5x – 5? Explain your process to find the perimeter.

Furkat [3]

Answer:

14x-4

Step-by-step explanation:

length:2x+3

width:5x-5

perimeter of rectangle:2(l+b)

:2(2x+3+5x-5)

:2(7x-2)

:14x-4

•••The perimeter of rectangle(p)=14x-4

5 0

3 years ago

Robert climbed 775 steps and 12 1/2 minutes. How many steps did he average per minute?

UNO [17]

Answer:

Since the question requires you to give the answer in terms of steps/minute, the first step would be to convert hours to minutes: 12.5 hours = 750 minutes. Next, if he took 775 steps in 750 minutes, how many would he take in 1 minute? This requires you to set up the question as a proportion: (775 steps/ 750 minutes) = (x steps/1 minute)

Step-by-step explanation:

7 0

3 years ago

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Gary buys a skateboard for $145. What's the total cost including 6% sales tax?