All categories

3 years ago

If MQ also bisects angle ∠LMP, find the measure of ∠QMP and find the value of x. ∠QMP = (5x + 10)º

Mathematics

1 answer:

ANTONII [103]3 years ago

7 0

Answer:

Step-by-step explanation:

If MQ also bisects angle ∠LMP, then;

<LMQ + <QMP = <LMP

Also <LMQ = <QMP

The equation becomes <QMP + <QMP = <LMP

2<QMP = <LMP

Let <LMP be 8x+40° (This is an assumed value)

2(5x+10) = 8x+40

Open the parenthesis

10x+20 = 8x+40

10x-8x = 40-20

2x = 20

x = 20/2

x = 10

Find <QMP

Since <QMP = 5x+10

<QMP = 5(10)+10

<QMP = 50+10

<QMP = 60 degrees

Note that the angle <LMP was assumed. Any other function can be used depending on the question

You might be interested in

What is the value of the expression below? -4(2)

otez555 [7]

The value is -8 of the expression

4 0

3 years ago

An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concen

devlian [24]

Answer:

(a) A 95% confidence interval for the population mean is [433.36 , 448.64].

(b) A 95% upper confidence bound for the population mean is 448.64.

Step-by-step explanation:

We are given that article contained the following observations on degrees of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

420, 425, 427, 427, 432, 433, 434, 437, 439, 446, 447, 448, 453, 454, 465, 469.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = $\frac{\sum X}{n}$ = 441

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 14.34

n = sample size = 16

$\mu$ = population mean

Here for constructing a 95% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.131 < $t_1_5$ < 2.131) = 0.95 {As the critical value of t at 15 degrees of

freedom are -2.131 & 2.131 with P = 2.5%}

P(-2.131 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.131) = 0.95

P( $-2.131 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.131 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X -2.131 \times {\frac{s}{\sqrt{n} } }$ , $\bar X +2.131 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $441-2.131 \times {\frac{14.34}{\sqrt{16} } }$ , $441+2.131 \times {\frac{14.34}{\sqrt{16} } }$ ]

= [433.36 , 448.64]

(a) Therefore, a 95% confidence interval for the population mean is [433.36 , 448.64].

The interpretation of the above interval is that we are 95% confident that the population mean will lie between 433.36 and 448.64.

(b) A 95% upper confidence bound for the population mean is 448.64 which means that we are 95% confident that the population mean will not be more than 448.64.

6 0

3 years ago

Ratio Question:

netineya [11]

Answer:

i dont under stand but i will just ask for help to my father

Step-by-step explanation:

i dont wnow the answer!???

3 0

2 years ago

Read 2 more answers

2x – y=8

emmasim [6.3K]

Answer:

the answer is D no solution

5 0

2 years ago

How do i factor this?

Jet001 [13]

You need to watch a video on polynomials, that's how i learned to factor Polynomials

https://www.youtube.com/watch?v=5MA1eZVegg4 - click on the uploader and you'll find how to factor it.

i can't GIVE u the answers but YOU WILL LEARN IT :)

3 0

3 years ago