All categories

2 years ago

Find the missing side lengths. Leave your answers as radicals in simplest form.

Mathematics

1 answer:

anzhelika [568]2 years ago

7 0

Answer:

x= 3sqrt2 y=3

Step-by-step explanation:

The triangle is isosceles triangle, which means 2 sides are congruent. Therefore, y =3

using the pythagorean theorem,

3^2+3^2=x^2

9+9=x^2

18=x^2

x=18 sqrt

3sqrt2

You might be interested in

Multiply. <br><br> 4 × 0.002 =

trapecia [35]

The answer to your question is 0.008

7 0

3 years ago

A rectangular parking lot has a perimeter of 384 meters. The length of the parking lot is 36 meters less than the width. Find th

-Dominant- [34]

Answer:

The length and width of the parking lot is 78 meters and 114 meters respectively.

Step-by-step explanation:

Given;

Perimeter of the parking lot = $384\ m$

Solution,

Let the width of the parking lot be x.

Then, according to question length = (x-36).

The perimeter of a rectangle is sum of all the sides of rectangle. Which is given by an expression;

$perimeter=2\times(length+width)$

Now substituting the values, we get;

$384=2\times(x-36+x)\\\frac{384}{2}=(2x-36)\\192=2x-36\\192+36=2x\\2x=228\\x=\frac{228}{2}= 114$

Width = $114\ m$

Length = $x-36=114-36=78\ m$

Hence the length and width of the parking lot is 78 meters and 114 meters respectively.

6 0

2 years ago

How much sale tax would be charged on $450 worth of merchandise if the sales tax rate is 8 3/4%?What is the final cost?

kotykmax [81]

Tax of $39.38
Total = $489.38

3 0

3 years ago

Read 2 more answers

Show how you round 1345/99 to the nearest integer

Naya [18.7K]

1345/99 = 13.585858

14

Rounding is easy, just look at the number in the tenths place. If the number is less than 5 round down and if the number is greater than or equal to 5 round up.

7 0

2 years ago

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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 normally distributed samples are 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.

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.

In this problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

3 years ago