How many vertices does the following shape have

KengaRu [80]

Answer:

x=4.77

Angle 3=98.32 degrees

Angle 6= 81.68 degrees

Step-by-step explanation:

(Assuming these are parallel lines), Angle 3 and angle 5 are equal because they are alternate Angles. Therefore we can write the following equation to solves for x:

16x+22=3x+84 (angle 3=angle5)

Which we can now solve:

16x +22 - 22 - 3x=3x-3x+84-22

13x=62

13x/13=62/13

x=4.77 (2dp)

We can then use this x to calculate angle 3:

16(4.77)+22

76.33+22=98.32 degrees

Finally,

Angle 6 and angle 3 are interior angles, so they add up to 180 degrees.

So to find angle 6,we can just subtract angle 3 from 180:

180-98.32=81.68 degrees.

Hope this helped!

6 0

3 years ago

The length of a rectangle is 4 ft longer than its width.

son4ous [18]

Answer:

96

Step-by-step explanation:

40=4x+8

32=4x

x=8

other side x+4 is 12

area is 12×8

96

6 0

2 years ago

Use synthetic division to divide (x^3 +12x^2 +48x +26) / (x+4)

deff fn [24]

Answer:

The correct option is C

Step-by-step explanation:

(x^3 +12x^2 +38x +26) / (x+4)

Use the coefficients of dividend.

And the divisor is -4:

Bring down 1 and multiply it by -4 and add to 12

12-4 = 8

Now multiply 8 by -4 = -32

48-32 = 6

Now multiply 6 by -4 = -24

26-24= R2

1 12 38 26

-4 -32 -24

_______________

1 8 6 R2

Thus the correct option is C ....

6 0

3 years ago

By selling a chair for Rs. 1440 a shopkeeper loses 10%.At what price did he buy it?

Dvinal [7]

Selling price of the chair = 1440 rupees
Percentage of loss made by the shopkeeper = 10%
Let us assume the price at which the shopkeeper bought the chair = x
Then
90% * x = 1440 rupees
(90/100) * x = 1440 rupees
9x/10 = 1440 rupees
9x = 1440 * 10 rupees
9x = 14400 rupees
x = 14400/9 rupees
= 1600 rupees
So the price at which the shopkeeper bought the chair was 1600 rupees. I hope the procedure is clear enough for you to inderstand.

5 0

3 years ago

Read 2 more answers

Scores at a local high school on the American College Testing (ACT) college entrance exam follow the normal distribution with a

san4es73 [151]

Answer:

a) The mean is 18 and the standard deviation is 1.79.

b) The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

c) 0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 18 and a standard deviation of 8.

This means that $\mu = 18, \sigma = 8$

Sample of 20:

This means that $n = 20, s = \frac{8}{\sqrt{20}} = 1.79$

(a) Calculate the mean and standard deviation of the sampling distribution of x¯.

By the Central Limit Theorem, the mean is 18 and the standard deviation is 1.79.

(b) Interpret the standard deviation from part (a).

The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

(c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.

This is 1 subtracted by the pvalue of Z when X = 19.5. So

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

By the Central Limit Theorem

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

$Z = \frac{19.5 - 18}{1.79}$

$Z = 0.84$

$Z = 0.84$ has a pvalue of 0.7995

1 - 0.7995 = 0.2005

0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

7 0

2 years ago

How many vertices does the following shape have​

How many vertices does the following shape have