Helppppppp please:( and thank you

Suppose r(140°, P)(A) = B and (RPD←→∘RPC←→)(A) = B, what is m∠CPD?

NISA [10]

An angle bisector divides an angle into two equal halves.

The measure of angle $\angle CPD$ is 70 degrees

The complete question is an illustrates the concept of angle bisector;

Where:

$\angle RPD = 140^o$ , and line PC bisects $\angle RPD$

Because line PC bisects $\angle RPD$ , then it means that the measure of RPD is twice the measure of CPD:

So, we have:

$\angle RDP = 2 \times \angle CPD$

Substitute $\angle RPD = 140^o$

$140^o = 2 \times \angle CPD$

Divide both sides by 2

$70^o = \angle CPD$

Apply symmetric property of equality:

$\angle CPD = 70^o$

Hence, the measure of angle $\angle CPD$ is 70 degrees

Read more about angle bisectors at:

brainly.com/question/12896755

5 0

2 years ago

The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probab

kolezko [41]

Answer:

(a) 0.6579

(b) 0.2961

(c) 0.3108

(d) 240

Step-by-step explanation:

The random variable X can be defined as the number of particles in a suspension.

The concentration of particles in a suspension is 50 per ml.

Then in 5 mL volume of the suspension the number of particles will be,

5 × 50 = 250.

The random variable X thus follows a Poisson distribution with parameter, λ = 250.

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.

The mean of the approximated distribution of X is:

μ = λ = 250

The standard deviation of the approximated distribution of X is:

σ = √λ = √250 = 15.8114

Thus, $X\sim N(250, 250)$

(a)

Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:

$P(235$

$=P(-0.95$

Thus, the value of P (235 < X < 265) = 0.6579.

(b)

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

$P(48$

$=P(-0.28$

Thus, the value of $P(48$ .

(c)

A 10 mL sample is withdrawn.

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

$P(48$

$=P(-0.40$

Thus, the value of $P(48$ .

(d)

Let the sample size be n.

$P(48$

$0.95=P(-z$

The value of z for this probability is,

z = 1.96

Compute the value of n as follows:

$z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241$

Thus, the sample selected must be of size 240.

5 0

3 years ago

12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

never [62]

Answer:

Part a) Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Domain of f+g = {-1, 0, 1, 2, 3}

Part d) Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

Part a) Determining the domain of f

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Determining the domain of g

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Determining the domain of f+g

When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.

As,

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

Domain of g : {-1, 0, 1, 2, 3, 4}

As when there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains

So, the domain of f+g = {-1, 0, 1, 2, 3}

Part d) List the ordered pairs of f-g

As

f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = f(-1) - g(-1) = 14 - 4 = 10

(f - g)(x) = f(0) - g(0) = 7 - 5 = 2

(f - g)(x) = f(1) - g(1) = 4 - 6 = -2

(f - g)(x) = f(2) - g(2) = 5 - 1 = 4

(f - g)(x) = f(3) - g(3) = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords: domain, function, f+g, f-g

Learn more about domain, and ordered pairs from brainly.com/question/11422136

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7 0

3 years ago

A line segment has more then one midpoint true or false

Anika [276]

Answer:

false

Step-by-step explanation:

any line segment or distance has only one midpoint.

there is only one middle to everything.

how would that look like, if something had 2 middles ?

then they would not be a middle, and the middle between these 2 middles would then be the real middle ...

6 0

1 year ago

Read 2 more answers

Can I please get help? Find M1 and M2

marishachu [46]

Answer:

m∠1 = 110° and m∠2 = 70°

Step-by-step explanation:

m∠1 = 110° since vertical angles

To find m∠2, m∠1 and m∠2 must add to 180°

m∠1 + m∠2 = 180°

110° + m∠2 = 180°

m∠2 = 70°

8 0

2 years ago