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2 years ago

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The height of trapezoid VWXZ is 8 StartRoot 3 EndRoot units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle

theorem to find the length of YX.
Once you you know the length of YX, find the length of the lower base, ZX.
A.14 units
B.10 + 4 StartRoot 3 EndRoot units
C.18 units
D.10 + 8 StartRoot 3 EndRoot units

1 answer:

vredina [299]2 years ago

4 0

Answer:

C. 18 units.

Step-by-step explanation:

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Ms. Corley wants to take her class on a trip to either the nature center or the zoo the nature center charges $4 per student plu

lianna [129]

X- class members
y-total cost of a trip
The nature center: y=4$*x+95$
The zoo: y=9$*x+75$
4x+95=9x+75⇒5x=20⇒x=20/5
x=4, y=111
<span>If Ms. Corley has 22 students in her class, cost for nature center would be 4$*22+95$=183$ and for the zoo 9$*22+75$=273$.
The zoo would cost less.
</span>

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1 year ago

Read 2 more answers

A car travels 180 miles in 4 hours. Find the car’s speed in feet per minute. (There are 5,280 ft in 1 mile)

FinnZ [79.3K]

Given :

Distance travelled , d = 180 miles.

Time taken , t = 4 hours.

To Find :

Speed in feet per minutes.

Solution :

Distance in feet is , d = 180×5280 = 950400 feet.

Time taken , t = 4×60 = 240 minutes.

Speed is given by , $s=\dfrac{Distance}{Time \ Taken}$

$S=\dfrac{950400}{240}\ ft/min\\\\S=3960\ ft/min$

Hence, this is the required solution.

4 0

1 year ago

In 1970 the population of the United States was 203 million. Ten years later, in 1980, the population of the United States was 2

andrezito [222]

Answer:

The exponential function for the US population is:

$y = 203\cdot e^{0.0107\cdot t}$

Step-by-step explanation:

Let be supposed that US population can be modelled by means of the following exponential function:

$y = A \cdot e^{B\cdot t}$

Where:

$t$ - Time, measured in years. Where t = 0 for 1970.

$A$ - Initial population, in millions inhabitants.

$B$ - Exponential rate constant, in years.

$y$ - Population, in millions inhabitants.

Each constant is found hereafter:

A

$203 = A \cdot e^{B\cdot 0}$

$203 = A \cdot 1$

$A = 203$

B

$226 = 203\cdot e^{B\cdot 10}$

$\frac{226}{203} = e^{10\cdot B}$

$10\cdot B = \ln \frac{226}{203}$

$B = \frac{1}{10}\cdot \ln \frac{226}{203}$

$B = 0.0107$

The exponential function for the US population is:

$y = 203\cdot e^{0.0107\cdot t}$

4 0

2 years ago

Point b has coordinates (3,-4) and lies on the circle whose equation is x^2 + y^2= 25. If angle is drawn in a standard position

lakkis [162]

<span>Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:
</span>
<span> $BO^2=AO^2+AB^2 \\ BO^2=3^2+4^2 \\ BO^2=9+16 \\ BO^2=25 \\ BO=5$ .
</span>
{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
<span>The sine of the angle BOA is</span>
$\sin \angle BOA= \dfrac{AB}{BO} = \dfrac{4}{5} =0.8$

Since point B is placed in the IV quadrant, the sine of the angle that is <span> drawn in a standard position with its terminal ray will be </span>
<span /><span>
</span><span>
</span> $\sin \theta=-0.8$ .

3 0

1 year ago

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

Sati [7]

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

Step-by-step explanation:

When the distribution is normal, we use 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.

If X is two standard deviations from the mean or more, it is considered unusual.

In this question:

$\mu = 128, \sigma = 23$

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

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

$Z = \frac{135 - 128}{23}$

$Z = 0.3$

$Z = 0.3$ has a pvalue of 0.6179

1 - 0.6179 = 0.3821

38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the pvalue of Z when X = 141.

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

$Z = \frac{141 - 128}{23}$

$Z = 0.565$

$Z = 0.565$ has a pvalue of 0.7140

71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So

X = 125

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

$Z = \frac{125 - 128}{23}$

$Z = -0.13$

$Z = -0.13$ has a pvalue of 0.4483

X = 120

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

$Z = \frac{120 - 128}{23}$

$Z = -0.35$

$Z = -0.35$ has a pvalue of 0.3632

0.4483 - 0.3632 = 0.0851

8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

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

$1.28 = \frac{X - 128}{23}$

$X - 128 = 1.28*23$

$X = 157.44$

So

157.44mmHg

6 0

2 years ago