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3 years ago

Solve for x. Then solve for the angle with the arrow.

Mathematics

1 answer:

ira [324]3 years ago

5 0

Answer:

132°

Step-by-step explanation:

The sum of interior angles of a pentagon is 540°

We sum all the angles and equate to 540.

91°+125°+92°+3x-5+4x-8=540°

This implies that:

295°+7x=540

7x=540-295

7x=245

x=35

The given angle is 4x-8

Substitute x=35

$4(35) - 8 = 132$

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lorasvet [3.4K]

2*10^-3 + 3*10^-3
(2+3)*10^-3
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0.005

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3 years ago

For the linear equation 3x + 7y = 42: a. Determine the slope: b. Determine y- intercept if it exists: c. Express equation in slo

algol13

Answer: The required answers are

(a) the slope of the given line is $-\dfrac{3}{7}.$

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is $y=-\dfrac{3}{7}x+6.$

Step-by-step explanation: We are given the following linear equation in two variables :

$3x+7y=42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to :

(a) determine the slope,

(b) determine the y-intercept, if exists

and

(c) express equation in slope-intercept form.

We know that

The SLOPE_INTERCEPT form of the equation of a straight line is given by

$y=mx+c,$ where m is the slope and c is the y-intercept of the line.

From equation (i), we have

$3x+7y=42\\\\\Rightarrow 7y=-3x+42\\\\\Rightarrow y=\dfrac{-3x+42}{7}\\\\\\\Rightarrow y=-\dfrac{3}{7}x+6.$

Comparing with the slope-intercept form, we get

$\textup{slope, m}=-\dfrac{3}{7},\\\\\\\textup{y-intercept, c}=6.$

Thus,

(a) the slope of the given line is $-\dfrac{3}{7}.$

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is $y=-\dfrac{3}{7}x+6.$

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3 years ago

A certain virus infects one in every 200 people. a test used to detect the virus in a person is positive 70% of the time when t

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We're told that

$P(A)=\dfrac1{200}=0.005\implies P(A^C)=0.995$

$P(B\mid A)=0.7$

$P(B\mid A^C)=0.05$

a. We want to find $P(A\mid B)$ . By definition of conditional probability,

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}$

By the law of total probability,

$P(B)=P(B\cap A)+P(B\cap A^C)=P(B\mid A)P(A)+P(B\mid A^C)P(A^C)$

Then

$P(A\mid B)=\dfrac{P(B\mid A)P(A)}{P(B\mid A)P(A)+P(B\mid A^C)P(A^C)}\approx0.0657$

(the first equality is Bayes' theorem)

b. We want to find $P(A^C\mid B^C)$ .

$P(A^C\mid B^C)=\dfrac{P(A^C\cap B^C)}{P(B^C)}=\dfrac{P(B^C\mid A^C)P(A^C)}{1-P(B)}\approx0.9984$

since $P(B^C\mid A^C)=1-P(B\mid A^C)$ .

4 0

3 years ago

12% of what number is 42?

Andreyy89

Answer:

350

Step-by-step explanation:

12% = 0.12

42 / 0.12 = 350

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3 years ago

the mean age of 5 people ina room is 32 years. A person enters the room.The mean age is now 34.What is the age of the person who

astraxan [27]

Answer:

Step-by-step explanation:

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2 years ago