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frez [133]
3 years ago
9

What is the distance between points A(3, 8) and B(-3, 4)?

Mathematics
1 answer:
max2010maxim [7]3 years ago
8 0

Answer:

About 7.2 OR (7.211102551)

Step-by-step explanation:

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Step-by-step explanation:

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What’s the value of n in the equation-1/2(2n+4)+6=-9+4(2n+1)
klemol [59]

Answer:

n=13/7

Step-by-step explanation:

2n+4+6*2=-9*2+8(2n+1)

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16+18=16n-2n+8

34=14n+8

34-8=14n

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n=13/7

8 0
2 years ago
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Describe the effect an increase in i, the interest rate applied to the present value, has on the monthly payment P in the formul
VARVARA [1.3K]

Answer:

B. An increase in i, the interest rate, will create an increase in P, the monthly payment.

Step-by-step explanation:

We have the formula for the monthly payment as,

P=\frac{i \times PV}{1-(1+i)^{-n} },

where P = monthly payment, i = rate of interest, PV = present value and n = time period.

Now, as i increase we get that (1+i) increases and so (1+i)^{n} increases.

This gives us that, \frac{1}{(1+i)^{n} } decreases and so 1-\frac{1}{(1+i)^{n}} decreases

Therefore, \frac{1}{1-(1+i)^{-n} } increases.

So, we get that as i increases , the value of P will increase.

Hence, option B is correct.

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The answer would be 400
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3 years ago
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Based on the number of voids, a ferrite slab is classified as either high, medium, or low. Historically, 5% of the slabs are cla
AnnyKZ [126]

Answer:

(a) Name: Multinomial distribution

Parameters: p_1 = 5\%   p_2 = 85\%   p_3 = 10\%  n = 20

(b) Range: \{(x,y,z)| x + y + z=20\}

(c) Name: Binomial distribution

Parameters: p_1 = 5\%      n = 20

(d)\ E(x) = 1   Var(x) = 0.95

(e)\ P(X = 1, Y = 17, Z = 3) = 0

(f)\ P(X \le 1, Y = 17, Z = 3) =0.07195

(g)\ P(X \le 1) = 0.7359

(h)\ E(Y) = 17

Step-by-step explanation:

Given

p_1 = 5\%

p_2 = 85\%

p_3 = 10\%

n = 20

X \to High Slabs

Y \to Medium Slabs

Z \to Low Slabs

Solving (a): Names and values of joint pdf of X, Y and Z

Given that:

X \to Number of voids considered as high slabs

Y \to Number of voids considered as medium slabs

Z \to Number of voids considered as low slabs

Since the variables are more than 2 (2 means binomial), then the name is multinomial distribution

The parameters are:

p_1 = 5\%   p_2 = 85\%   p_3 = 10\%  n = 20

And the mass function is:

f_{XYZ} = P(X = x; Y = y; Z = z) = \frac{n!}{x!y!z!} * p_1^xp_2^yp_3^z

Solving (b): The range of the joint pdf of X, Y and Z

Given that:

n = 20

The number of voids (x, y and z) cannot be negative and they must be integers; So:

x + y + z = n

x + y + z = 20

Hence, the range is:

\{(x,y,z)| x + y + z=20\}

Solving (c): Names and values of marginal pdf of X

We have the following parameters attributed to X:

p_1 = 5\% and n = 20

Hence, the name is: Binomial distribution

Solving (d): E(x) and Var(x)

In (c), we have:

p_1 = 5\% and n = 20

E(x) = p_1* n

E(x) = 5\% * 20

E(x) = 1

Var(x) = E(x) * (1 - p_1)

Var(x) = 1 * (1 - 5\%)

Var(x) = 1 * 0.95

Var(x) = 0.95

(e)\ P(X = 1, Y = 17, Z = 3)

In (b), we have: x + y + z = 20

However, the given values of x in this question implies that:

x + y + z = 1 + 17 + 3

x + y + z = 21

Hence:

P(X = 1, Y = 17, Z = 3) = 0

(f)\ P{X \le 1, Y = 17, Z = 3)

This question implies that:

P(X \le 1, Y = 17, Z = 3) =P(X = 0, Y = 17, Z = 3) + P(X = 1, Y = 17, Z = 3)

Because

0, 1 \le 1 --- for x

In (e), we have:

P(X = 1, Y = 17, Z = 3) = 0

So:

P(X \le 1, Y = 17, Z = 3) =P(X = 0, Y = 17, Z = 3) +0

P(X \le 1, Y = 17, Z = 3) =P(X = 0, Y = 17, Z = 3)

In (a), we have:

f_{XYZ} = P(X = x; Y = y; Z = z) = \frac{n!}{x!y!z!} * p_1^xp_2^yp_3^z

So:

P(X=0; Y=17; Z = 3) = \frac{20!}{0! * 17! * 3!} * (5\%)^0 * (85\%)^{17} * (10\%)^{3}

P(X=0; Y=17; Z = 3) = \frac{20!}{1 * 17! * 3!} * 1 * (85\%)^{17} * (10\%)^{3}

P(X=0; Y=17; Z = 3) = \frac{20!}{17! * 3!} * (85\%)^{17} * (10\%)^{3}

Expand

P(X=0; Y=17; Z = 3) = \frac{20*19*18*17!}{17! * 3*2*1} * (85\%)^{17} * (10\%)^{3}

P(X=0; Y=17; Z = 3) = \frac{20*19*18}{6} * (85\%)^{17} * (10\%)^{3}

P(X=0; Y=17; Z = 3) = 20*19*3 * (85\%)^{17} * (10\%)^{3}

Using a calculator, we have:

P(X=0; Y=17; Z = 3) = 0.07195

So:

P(X \le 1, Y = 17, Z = 3) =P(X = 0, Y = 17, Z = 3)

P(X \le 1, Y = 17, Z = 3) =0.07195

(g)\ P(X \le 1)

This implies that:

P(X \le 1) = P(X = 0) + P(X = 1)

In (c), we established that X is a binomial distribution with the following parameters:

p_1 = 5\%      n = 20

Such that:

P(X=x) = ^nC_x * p_1^x * (1 - p_1)^{n - x}

So:

P(X=0) = ^{20}C_0 * (5\%)^0 * (1 - 5\%)^{20 - 0}

P(X=0) = ^{20}C_0 * 1 * (1 - 5\%)^{20}

P(X=0) = 1 * 1 * (95\%)^{20}

P(X=0) = 0.3585

P(X=1) = ^{20}C_1 * (5\%)^1 * (1 - 5\%)^{20 - 1}

P(X=1) = 20 * (5\%)* (1 - 5\%)^{19}

P(X=1) = 0.3774

So:

P(X \le 1) = P(X = 0) + P(X = 1)

P(X \le 1) = 0.3585 + 0.3774

P(X \le 1) = 0.7359

(h)\ E(Y)

Y has the following parameters

p_2 = 85\%  and    n = 20

E(Y) = p_2 * n

E(Y) = 85\% * 20

E(Y) = 17

8 0
2 years ago
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