All categories

3 years ago

LMNO is a parallelogram. If NM = x + 33 and OL = 4x + 9, find the value of x and then find NM and OL.

Mathematics

1 answer:

anyanavicka [17]3 years ago

7 0

Because these are on opposite sides of the parallelogram, x + 33 = 4x + 9.

This gives you x = 8; OL = 41, NM = 41.

You might be interested in

Information about the proportion of a sample that agrees with a certain statement is given below. Use StatKey or other technolog

lara31 [8.8K]

Answer:

$SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048$

If we replace the values obtained we got:

$0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443$

The 95% confidence interval would be given by (0.257;0.443)

Step-by-step explanation:

Notation and definitions

$X=35$ number of people that agree.

$n=100$ random sample taken

$\hat p=\frac{35}{100}=0.35$ estimated proportion of people that agree

$p$ true population proportion of peopl that agree

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The standard error is given by:

$SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048$

If we replace the values obtained we got:

$0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443$

The 95% confidence interval would be given by (0.257;0.443)

6 0

3 years ago

Read 2 more answers

The area of Jackson’s rectangular garden is 64 square ft. If the length of the garden is 16 ft, what is the width of the garden?

zlopas [31]

Answer:

Step-by-step explanation:

1,280 it ez bro

6 0

3 years ago

There are 35 more musicians in the String section of a city Symphony Orchestra than in its Brass section. There are 29 musicians

blagie [28]

X = string section
y = brass section

x = y + 35
y = 29 .....there are 29 in the brass section

x = 29 + 35
x = 64...there are 64 in the string section

for a total of : 64 + 29 = 93 total musicians <==

3 0

3 years ago

Find the Slope:

AveGali [126]

Answer:

4) slope= 0

5) $slope = - \frac{1}{7}$

Step-by-step explanation:

$\boxed{ slope = \frac{y _{2} - y_1 }{x_2 - x_1} }$

4) Slope

$= \frac{10 - 10}{ - 10 - 3}$

$= \frac{0}{ - 13}$

= 0

The slope is zero as the line is a horizontal line (since both points have the same y-coordinate of 10).

5) Slope

$= \frac{5 - 4}{2 - 9}$

$= \frac{1}{ - 7}$

$= - \frac{1}{7}$

Since you have taken (x₁, y₁) to be (9, 4), the value of x₁ should be 9 instead of 2.

6 0

2 years ago

Read 2 more answers

Jamie's older brother and his three friends want to split the cost of lunch they also want to leave a 15% tip how much should ea

goldfiish [28.3K]

Answer:
$22.43

Explanation:
We can start by finding the amount that they should tip. The total bill is $78, so we should take 15% of 78 and add it to the total.
0.15 * 78 = 11.7
78 + 11.7 = 89.7
This means that the total cost of the bill, with a tip, is $89.70.
Since there are 4 people, we have to split this total into 4 if they all want to pay equally.
89.70 / 4 = 22.425 = $22.43 !

Hope this helps

4 0

3 years ago