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3 years ago

Help please i don’t understand

Mathematics

1 answer:

Monica [59]3 years ago

7 0

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Triangles are similar ,

Thus :

$\frac{9}{3} = \frac{6}{x} \\$

$3 = \frac{6}{x} \\$

$\frac{6}{x} = 3 \\$

Inverse both sides

$\frac{x}{6} = \frac{1}{3} \\$

Multiply sides by 6

$6 \times \frac{x}{6} = 6 \times \frac{1}{3} \\$

$x = 2 \times 3 \times \frac{1}{3} \\$

$x = 2$

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A half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of

Ainat [17]

Answer:

99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.

Step-by-step explanation:

We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.

Also, a samples of 21 of today's women in their 20's have been taken.

Let $\bar X$ = sample mean heights

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean height of women = 64.7 inches

$\sigma$ = standard deviation = 2.07 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the sample of 21 of today's women in their 20's have mean heights of at least 65.86 inches is given by = P( $\bar X$ $\geq$ 65.86 inches)

P( $\bar X$ $\geq$ 65.86 inches) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{65.86-64.7}{\frac{2.07}{\sqrt{21} } }$ ) = P(Z $\geq$ -2.57) = P(Z $\leq$ 2.57)

= 0.99492 or 99.5%

The above probability is calculated by looking at the value of x = 2.57 in the z table which has an area of 0.99492.

Therefore, 99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.

3 0

3 years ago

Write an equation to match each graph. I already tried y=[x] that didn’t work

UkoKoshka [18]

Answer:

y=|x|

Step-by-step explanation:

We know

general modulus function passes through origin as |0| is 0

And it's symmetric on both sides of y axis .

As it's not one -one function

Means

f(-1)=|-1|=1
f(1)=|1|=1

So the graph is y=|x|

6 0

2 years ago

Read 2 more answers

A solution initially contains 200 bacteria. 1. Assuming the number y increases at a rate proportional to the number present, wri

GuDViN [60]

Answer:

1. $\frac{dy}{dt}=ky$

2.543.6

Step-by-step explanation:

We are given that

y(0)=200

Let y be the number of bacteria at any time

$\frac{dy}{dt}$ =Number of bacteria per unit time

$\frac{dy}{dt}\proportional y$

$\frac{dy}{dt}=ky$

Where k=Proportionality constant

2. $\frac{dy}{y}=kdt$ ,y'(0)=100

Integrating on both sides then, we get

$lny=kt+C$

We have y(0)=200

Substitute the values then , we get

$ln 200=k(0)+C$

$C=ln 200$

Substitute the value of C then we get

$ln y=kt+ln 200$

$ln y-ln200=kt$

$ln\frac{y}{200}=kt$

$\frac{y}{200}=e^{kt}$

$y=200e^{kt}$

Differentiate w.r.t

$y'=200ke^{kt}$

Substitute the given condition then, we get

$100=200ke^{0}=200 \;because \;e^0=1$

$k=\frac{100}{200}=\frac{1}{2}$

$y=200e^{\frac{t}{2}}$

Substitute t=2

Then, we get $y=200e^{\frac{2}{2}}=200e$

$y=200(2.718)=543.6=543.6$

e=2.718

Hence, the number of bacteria after 2 hours=543.6

4 0

4 years ago

A grading machine can grade 48 tests in 1 minute. How

S_A_V [24]

$\bf \begin{array}{ccll}
tests&minutes\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
48&1\\
300&m
\end{array}\implies \cfrac{48}{300}=\cfrac{1}{m}\implies m=\cfrac{300\cdot 1}{48}$

3 0

3 years ago

20% of the people in a village own a dog, 30% own goats and 40% own cattle, 5% own both a dog and goats, 4% own both a dog and c

lana66690 [7]

Answer:

37 %

Step-by-step explanation:

here..

only Dog = 20- 5 - 4 - 1 = 10

only goats = 30 - 5 - 3 - 1 = 21

only cattle = 40 - 4 - 3 - 1 = 32

then ... since the maximum percentage is 100 %

people who don't own any animal = 100% - 10% - 21% - 32% = 37 %

3 0

3 years ago