Real World Problems with Rational Numbers

In a basketball game Anya makes 14 baskets. Some of these baskets were worth 2-points and others were worth 3-points. In total s

Tems11 [23]

Answer:

She made 12 two point basket.

Step-by-step explanation:

Assuming the number of 2 point basket is x and that of 3 point basket is y.

Based on the question the total numbers of basket is 14, that is x + y = 14 , and the total numbers of points is 30, which helps us with our second equation 2(x) +3(y)=30.

x + y = 14 eqn 1

2(x) +3(y)=30 eqn 2

Using elimination method multiplying eqn 1 by -3 and adding it to equation 2

-3x-3 y = -42 adding to eqn 2 gives

-x= -12

x=12. Which gives the number of the 2 points basket she made .

7 0

3 years ago

What is the value of 5 in 673,512

hammer [34]

500 because it is in the hundredths place

6 0

3 years ago

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According to survey data, the distribution of arm spans for males is approximately Normal with a mean of 71.4 inches and a stan

Gekata [30.6K]

Answer:

a) 89.97% of men have arm spans between 66 and 76 inches.

b) The z-score for this person's arm span is 5.68. 0% of males have an arm span at least as long as this person

Step-by-step explanation:

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 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.

Mean of 71.4 inches and a standard deviation of 3.1 inches.

This means that $\mu = 71.4, \sigma = 3.1$

a. What percentage of men have arm spans between 66 and 76 inches?

The proportion is the pvalue of Z when X = 76 subtracted by the pvalue of Z when X = 66. The percentage is the proportion multiplied by 100.

X = 76

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

$Z = \frac{76 - 71.4}{3.1}$

$Z = 1.48$

$Z = 1.48$ has a pvalue of 0.9306

X = 66

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

$Z = \frac{66 - 71.4}{3.1}$

$Z = -1.74$

$Z = -1.74$ has a pvalue of 0.0409

0.9306 - 0.0409 = 0.8997

0.8997*100% = 89.97%

89.97% of men have arm spans between 66 and 76 inches.

b. A particular professional basketball player has an arm span of almost 89 inches. Find the z-score for this person's arm span. What percentage of males have an arm span at least as long as this person?

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

$Z = \frac{89 - 71.4}{3.1}$

$Z = 5.68$

The z-score for this person's arm span is 5.68.

Z = 5.68 has a pvalue of 1

1 - 1 = 0

0% of males have an arm span at least as long as this person

8 0

3 years ago

2,000 water bottles are being labeled and boxed. Each box holds 6 water bottles. How many bottles will be left over?

Lostsunrise [7]

Answer:

2 left out, with 333 boxes

Step-by-step explanation:

2000/6=333.333333 ( $\frac{1}{3}$ )

$\frac{1}{3}$ of 6 is 2. Therefore, there would be 333 boxes, with two left unboxed.

4 0

3 years ago

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If two angles are complements, then they are both acute. Which is the hypothesis?

GalinKa [24]

Answer:

the hypothesis is "two angles are complements"

Step-by-step explanation:

In the given statement, the hypothesis is "two angles are complements".. While the conclusion is that "they are both acute".

The hypothesis of the two angles being complements is what led to the conclusion that they are both acute since sum of 2 complementary angles is 90° and acute angle is any angle that measures less than 90°.

5 0

3 years ago