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3 years ago

Subtract using the number line.

Mathematics

2 answers:

Nikitich [7]3 years ago

8 0

Answer:

−1 1/2

Step-by-step explanation:

i took the test <3

SIZIF [17.4K]3 years ago

7 0

Answer:

$-1\dfrac{1}{2}$

Step-by-step explanation:

A part of the number line ranging from -2 to 2 with an arrow on both ends and tick marks every $\dfrac{1}{6}$ is shown in attached diagram.

<u>Rules:</u>

To add a number using number line, we have to move to the right,
To subtract the number using number line, we have to move to the left.

To subtract $\dfrac{1}{6}$ using number line, you have to move to the left one mark (because the distance between two consecutive marks is $\dfrac{1}{6}$ ), so you'll be at point $-1\dfrac{1}{2}$

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The annual rainfall (in inches) in a certain region is normally distributed with mean 43.2 and variance 20.8. Assume rainfall in

Wittaler [7]

Answer:

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation(which is the square root of the variance) $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

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:

$\mu = 43.2, \sigma = \sqrt{20.8} = 4.56$

Probability that a year has rainfall of more than 50 inches.

pvalue of Z when X = 50. So

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

$Z = \frac{50 - 43.2}{4.56}$

$Z = 1.49$

$Z = 1.49$ has a pvalue of 0.9319

1 - 0.9319 = 0.0681

Find the probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

This is $P(X \leq 2)$ when $n = 15, p = 0.0681$ . So

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{15,0}.(0.0681)^{0}.(0.9319)^{15} = 0.3472$

$P(X = 1) = C_{15,1}.(0.0681)^{1}.(0.9319)^{14} = 0.3805$

$P(X = 2) = C_{15,2}.(0.0681)^{2}.(0.9319)^{13} = 0.1947$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3472 + 0.3805 + 0.1947 = 0.9224$

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

8 0

3 years ago

Read 2 more answers

Simplify 2 x squared-7x-15

Rina8888 [55]

Answer:

(x − 5) (2x + 3)

Step-by-step explanation:

2x² − 7x − 15

Factor using AC method.

2 × -15 = -30

Factors of -30 that add up to -7 are -10 and 3.

Divide by 2 and reduce: -10/2 = -5/1, 3/2

The factors are x − 5 and 2x + 3.

(x − 5) (2x + 3)

6 0

4 years ago

Fre.e po.ints have a great day

frozen [14]

Answer:

thanks and I like your pfp

8 0

3 years ago

Read 2 more answers

A sunflower grows to be 200cm tall. After four weeks, it was 30% of this height. How tall

hichkok12 [17]

Answer:

60cm

Step-by-step explanation:

200*3/10=20*3=60

6 0

2 years ago

Whar is 10.034 rounded to the nearest tenth

VLD [36.1K]

Answer: 10.0

Step-by-step explanation: In this problem, we are asked to round 10.034 to the nearest tenth. It's important to understand that the tenths place is 1 place to the right of the decimal point. So the digit in the rounding place is 0.

Next, look at the digit to the right of the rounding place which in this case is 3. Since the digit to the right of the rounding place, 3, is less than 5, we round down.

This means that the digit in the rounding place, 0, stays the same and we change all digits to the right of the rounding place to 0.

So 10.034 rounded to the nearest tenth is 10.000 or just 10<em>.</em>0 since we can drop zeroes at the end of a decimal.

8 0

4 years ago

Subtract ​​using the number line.

Subtract using the number line.