Miguel bought a bicycle at a 30% discount. he paid $122.50. what percent of the original price did Miguel pay

Answers

Answer 1

Answer: 70%

100% - 30% = 70%

The price is not needed

Answer 2

Answer:

Final answer:

Miguel paid 70% of the original price for the bicycle. The original price was calculated as approximately $175 by dividing the price Miguel paid ($122.50) by 70% (the remaining percentage after the 30% discount).

Explanation:

Miguel paid $122.50 for a bicycle which was discounted by 30%. So, the $122.50 represents the 70% of the original price (because 100% - 30% = 70%). To find out what 100% (the original price) is, we need to perform a calculation where we divide the price paid by Miguel ($122.50) by 70% (in decimal format, that's 0.70).

The formula would structure as below:

Original Price = Price Paid / Percentage of Original Price Paid

Substituting in the values provided, the equation would be:

Original Price = $122.50 / 0.70

Following through with this calculation, we find that the original price of the bicycle was approximately $175. Therefore, Miguel paid 70% of the original price, as that's the remaining percentage after the 30% discount.

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A builder needs to tile a 7-foot by8-foot room with one-foot square
tiles. How many tiles will she need?
56 tiles
15 tiles
30 tiles

Answers

Final answer:

To tile a 7-foot by 8-foot room with one-foot square tiles, the builder will need 56 tiles.

Explanation:

To find the number of tiles needed to tile a room, we can divide the area of the room by the area of each tile. The area of the room is 7 feet by 8 feet, which is 56 square feet. The area of each tile is 1 square foot. So, to find the number of tiles needed, we divide 56 by 1, which gives us 56 tiles.

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Data taken from a random sample of 60 students chosen from the student population of a large urban high school indicated that 36 of them planned to pursue post-secondary education. An independent random sample of 50 students taken at a neighboring large suburban high school resulted in data that indicated that 31 of those students planned to pursue post-secondary education. Do these data provide sufficient evidence at the 5% level to reject the hypothesis that these population proportions are equal

Answers

Answer:

No, these data do not provide sufficient evidence at the 5% level to reject the hypothesis that these population proportions are equal.

Step-by-step explanation:

We are given that data taken from a random sample of 60 students chosen from the student population of a large urban high school indicated that 36 of them planned to pursue post-secondary education.

An independent random sample of 50 students taken at a neighboring large suburban high school resulted in data that indicated that 31 of those students planned to pursue post-secondary education.

Let $p_1$ = population proportion of students of a large urban high school who pursue post-secondary education.

$p_2$ = population proportion of students of a large suburban high school who pursue post-secondary education.

So, Null Hypothesis, $H_0$ : $p_1-p_2$ = 0 {means that these population proportions are equal}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq$ 0 {means that these population proportions are not equal}

The test statistics that would be used here Two-sample z proportionstatistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{(\hat p_1(1-\hat p_1))/(n_1)+(\hat p_2(1-\hat p_2))/(n_2) } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of students of a large urban high school who pursue post-secondary education = $(36)/(60)$ = 0.60

$\hat p_2$ = sample proportion of students of a large urban high school who pursue post-secondary education = $(31)/(50)$ = 0.62

$n_1$ = sample of students of a large urban high school = 60

$n_2$ = sample of students of a large suburban high school = 50

So, the test statistics = $\frac{(0.60-0.62)-(0)}{\sqrt{(0.60(1-0.60))/(60)+(0.62(1-0.62))/(50) } }$

= -0.214

The value of z test statistics is -0.214.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that these population proportions are equal.

Given this table of values, what is the value of f(14)?

Answers

Answer:

f(14) = 14.6

Step-by-step explanation:

Form the table attached,

Values of 'x' represent the points on the x-axis of the graph of the given function 'f'.

Similarly, values of 'y' represent the points on the y-axis of the graph.

For every input value of x we get an output value 'y'.

f(10) = -12

f(-16) = 15.6

f(14) = 14.6

f(-18) = 14

Therefore, from the given table output value of f(14) will be 14.6

the cube of the sum of 4 and 9 times x divided by the product of 5 times x and the difference of x and 1

Answers

Answer:

Step-by-step explanation:

(4 + 9x)^3 represents "the cube of the sum of 4 and 9 times x"

and if we divide by "the product of 5 times x and the difference of x and 1," we get

(4 + 9x)^3

-----------------------

5x(x - 1)

What exactly do you need to know, or to do?

Which value of x is in the solution set of the inequality -2(x-5)<4

Answers

The value of X would be: x > 3

"India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution for the household size in India. Col1 Household Size 1 2 3 4 5 6 7 8 Col2 Probability 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 a. What is the probability that there are less than 5 members in a household in India"b. What is the probability that there are 5 or more members in a typical household in India? (Round your answer to 2 decimal places.)Probability
c. What is the probability that the number of members in a typical household in India is strictly between 2 and 5? (Round your answer to 2 decimal places.)

Probability

Answers

The probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively

Probability distribution

Given the probability distribution for the household size in India as shown;

X 1 2 3 4 5 6 7 8 Total

P 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 1.00

a) The probability that the number of members in a typical household in India is strictly less than 5 is given as:

P(X < 5) = P(X=1) + P(X=2) + P(X=3) + P(X=4)

P(X < 5) = 0.02+ 0.09 + 0.18 + 0.25

P(X < 5) = 0.54

b) The probability that the number of members in a typical household in India is greater or equal to 5 is given as:

P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8)

P(X ≥ 5) = 0.20 + 0.12 + 0.08 + 0.06

P(X ≥ 5) = 0.46

c) The the probability that the number of members in a typical household in India is strictly between 2 and 5

P(2 < X < 5) = P(X=3) + P(X=4)

P (2 < X < 5) = 0.18 + 0.25

P (2 < X < 5) = 0.43

Hence the probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively

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Answer:

0.54,0.46,0.43

Step-by-step explanation:

Given that India is the second most populous country in the world, with a population of over 1 billion people.

The pdf of household size say X in India varies from 1 to 8.

The distribution is shown as follows

X 1 2 3 4 5 6 7 8 Total

P 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 1.00

a) the probability that there are less than 5 members in a household in India

= $P(X<5)$