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oksano4ka [1.4K]

3 years ago

10

A courtyard in the shape of a right triangle is set in the middle of three square office buildings, with one office building alo

ng each side. Which statement is true about the three office buildings?

1 answer:

oksian1 [2.3K]3 years ago

3 0

Answer:

The area of Building C minus the area of Building B equals the area of Building A.

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When Carson runs the 400 meter dash, his finishing times are normally distributed with a mean of 63 seconds and a standard devia

Gnom [1K]

Answer: in 95% of races, his finishing time will be between 62 and 64 seconds.

Step-by-step explanation:

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 63 seconds and the standard deviation is 5 seconds.

2 standard deviations = 2 × 0.5 = 1

63 - 1 = 62 seconds

63 + 1 = 64 seconds

Therefore, in 95% of races, his finishing time will be between 62 and 64 seconds.

6 0

3 years ago

In a population of similar households, suppose the weekly supermarket expense for a typical household is normally distributed wi

Rina8888 [55]

Answer:

P(Y ≥ 15) = 0.763

Step-by-step explanation:

Given that:

Mean =135

standard deviation = 12

sample size n = 50

sample mean $\overline x$ = 140

Suppose X is the random variable that follows a normal distribution which represents the weekly supermarket expenses

Then,

$X \sim N ( \mu \sigma)$

The probability that X is greater than 140 is :

P(X>140) = 1 - P(X ≤ 140)

$P(X>140) = 1 - P( \dfrac{X-\mu}{\sigma} \leq \dfrac{140-135}{12})$

$P(X>140) = 1 - P( \dfrac{X-\mu}{\sigma} \leq \dfrac{5}{12})$

$P(X>140) = 1 - P( Z\leq0.42)$

From z tables,

$P(X>140) = 1 - 0.6628$

$P(X>140) = 0.3372$

Similarly, let consider Y to be the variable that follows a binomial distribution of the no of household whose expense is greater than $140

Then;

$Y \sim Binomial (np)$

$Y \sim Binomial (50,0.3372)$

∴

P(Y ≥ 15) = 1- P(Y< 15)

P(Y ≥ 15) = 1 - ( P(Y=0) + P(Y=1) + P(Y=2) + ... + P(Y=14) )

$P(Y \geq 15) = 1 - \begin {pmatrix} ^{50}_0 \end {pmatrix} (0.3372)^0 (1-0,3372)^{50} + \begin {pmatrix} ^{50}_1 \end {pmatrix} (0.3372)^1 (1-0,3372)^{49} + \begin {pmatrix} ^{50}_2 \end {pmatrix} (0.3372)^2 (1-0,3372)^{48} +... + \begin {pmatrix} ^{50}_{50{ \end {pmatrix} (0.3372)^{50} (1-0,3372)^{0}$

P(Y ≥ 15) = 0.763

7 0

3 years ago

Three high school basketball teams measured the heights of all of their basketball players: The Derby Dragons have a mean height

sweet [91]

Answer:

The Ballwin Bears are taller on average, and the Aviston Aces have players whose heights are more consistent.

Step-by-step explanation:

for derby dragon;

mean height = 72 inches

standard deviation = 1.2 inches

for aviston aces:

mean height = 70.8

standard deviation = 0.7 inches

for balwin bears;

mean height = 73 inches

standard deviation = 1.0 inches

the mean height of aviston aces < mean height of derby < mean height of balwin bears

So on average the balwin bears are taller.

The standard deviation of derby dragon is > that of balwin bears > aviston aces.

So the more consistent height is that of aviston aces players.

6 0

3 years ago

if i am 57 years old and i have known someone for 6 and a half years what percentage of my life have i known that person

Mekhanik [1.2K]

Answer: 11.4%

Step-by-step explanation:

100% of your life is 57 years

?% will be 6.5 years?

this is a simple ratio problem:

57 --> 100%

6.5 ---> (6.5 x 100)/57 ≅ 11.4%

You have known the person for about 11.4% of your life.

4 0

3 years ago

A taxi charges $5 plus $1.95 per mile to drive up to 6 people. If a family of 4 wants to take a taxi from the airport to their h

nataly862011 [7]

Pretty sure it’s y= 5 + 1.95x
I don’t think that the number of people matters because the cost doesn’t vary based on the number of people

5 0

3 years ago