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Lesechka [4]
2 years ago
14

A triangular prism is 40 millimeters long and has a triangular face with a base of 24 millimeters and a height of 35 millimeters

. The other two sides of the triangle are each 37 millimeters. What is the surface area of the triangular prism?
Mathematics
1 answer:
abruzzese [7]2 years ago
7 0

Answer:

26,508

Step-by-step explanation:

To find out how to solve this is that we first need to know that Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.

Also: To find the total surface area of a prism, you need to calculate the area of two polygonal bases, the top face and bottom face. And then calculate the area of lateral faces connecting the bases. Add up the area of the two bases and the area of the lateral faces to get the total surface area of a prism.

The top= 12 x 24 x 35 = 10,080

The lateral faces: 12 x 37 x 37 = 16,428

Surface Area= 10,080 + 16,428 = 26,508

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Resistors. An electrical engineer has two boxes of resistors, with four resistors in each box. The resistors in the first box ar
Dafna11 [192]

Answer:

A. Sample Space = S = {(9, 18),(9, 19),(9, 20),(9, 21),(10, 18),(10, 19),(10, 20),(10, 21),(11, 18),(11, 19),(11, 20),(11, 21),(12, 18),(12, 19),(12, 20),(12, 21)}

B.  {(9, 18),(10, 18),(11, 18),(12, 18)}

C. {(9, 18),(9, 19),(10, 18)}

D.  {(9, 18),(9, 19),(10, 18),(11, 18),(12, 18)}

E. B(complement) ∩C =  {(9, 19)}

Step-by-step explanation:

The Sample Space would contain each element of the box A associated with each element of the box B.

A. Sample Space = S = {(9, 18),(9, 19),(9, 20),(9, 21),(10, 18),(10, 19),(10, 20),(10, 21),(11, 18),(11, 19),(11, 20),(11, 21),(12, 18),(12, 19),(12, 20),(12, 21)}

B.  Let the Outcomes in the event B, the event that the second resistor has a resistance less than 19 be denoted by J then

J=  {(9, 18),(10, 18),(11, 18),(12, 18)}

C. Let the outcomes in the event C, the event that the sum of the resistances is equal to 28 be denoted by L then

L =  {(9, 18),(9, 19),(10, 18)}

D. The  outcomes in B∪C contains all the elements of B and C

B∪C=J∪L= {(9, 18),(9, 19),(10, 18),(11, 18),(12, 18)}

E. B complement contains those elements of the Sample Space which are not the elements of Set B.

B complement= S-B=  {(9, 19),(9, 20),(9, 21),(10, 19),(10, 20),(10, 21),(11, 19),(11, 20),(11, 21),(12, 19),(12, 20),(12, 21)}

B(complement) ∩C contains those elements of B and C which are common to both B complement and C.

B(complement) ∩C =  {(9, 19)}

4 0
2 years ago
Three businesswomen are trying to convene in Northwest Arkansas for a business meeting. The first (Woman 1) is arriving on a fli
boyakko [2]

Answer:

a) The probability mass function of X is then presented in the table below.

X | probability P(X=x) or p

0 | 0.001

1 | 0.032

2 | 0.283

3 | 0.684

b) The cumulative distribution function of X

Cdf = Σ pdf = P(X=0) + P(X=1) + P(X=2) + P(X=3)

= 1.000

c) The probability that at least two businesswomen arrive on time

P(X ≥ 2) = P(X=2) + P(X=3) = 0.967

d) Expected value of X = E(X) = 2.65

e) Standard deviation = 0.545

Step-by-step explanation:

The probability that the woman coming from Atlanta arrives on time = P(A) = 0.90

The probability that the woman coming from Atlanta DOES NOT arrive on time = P(A') = 1 - 0.90 = 0.10

The probability that the woman coming from Dallas arrives on time = P(B) = 0.95

The probability that the woman coming from Dallas DOES NOT arrive on time = P(B') = 1 - 0.95 = 0.05

The probability that the woman coming from Chicago arrives on time = P(C) = 0.80

The probability that the woman coming from Chicago DOES NOT arrive on time = P(C') = 1 - 0.80 = 0.20

Since X is the random variable that represents how many women arrive on time,

To evaluate the probability function, we will first obtain the probability that the number of women that arrive in time = 0, 1, 2, and 3.

First probability; that no woman arrives on time. X = 0

P(X=0) = P(A') × P(B') × P(C')

= 0.10 × 0.05 × 0.20

P(X=0) = 0.001

Second probability; that only one of the women arrive on time. X = 1

P(X=1) = [P(A) × P(B') × P(C')] + [P(A') × P(B) × P(C')] + [P(A') × P(B') × P(C)]

= [0.90 × 0.05 × 0.20] + [0.10 × 0.95 × 0.20] + [0.10 × 0.05 × 0.80]

= 0.009 + 0.019 + 0.004

P(X=1) = 0.032

Third probability; that only two women arrive on time. X = 2

P(X=2) = [P(A) × P(B) × P(C')] + [P(A) × P(B') × P(C)] + [P(A') × P(B) × P(C)]

= [0.90 × 0.95 × 0.20] + [0.90 × 0.05 × 0.80] + [0.10 × 0.95 × 0.80]

= 0.171 + 0.036 + 0.076

P(X=2) = 0.283

Fourth probability; that all 3 women arrive on time. X = 3

P(X=3) = P(A) × P(B) × P(C)

= 0.90 × 0.95 × 0.8

P(X=3) = 0.684

The probability mass function of X is then presented in the table below.

X | probability P(X=x) or p

0 | 0.001

1 | 0.032

2 | 0.283

3 | 0.684

b) The cumulative distribution function of X

Cdf = Σ pdf = P(X=0) + P(X=1) + P(X=2) + P(X=3)

= 0.001 + 0.032 + 0.283 + 0.684 = 1.000

c) The probability that at least two businesswomen arrive on time

P(X ≥ 2) = P(X=2) + P(X=3) = 0.283 + 0.684 = 0.967

d) Expected value of X

Expected value is given as

E(X) = Σ xᵢpᵢ

E(X) = (0)(0.001) + (1)(0.032) + (2)(0.283) + (3)(0.684) = 0 + 0.032 + 0.566 + 2.052 = 2.65

e) What is the standard deviation of X?

Standard deviation = √(variance)

Variance = Var(X) = Σx²p − μ²

μ = E(X) = 2.65

Σx²p = (0²)(0.001) + (1²)(0.032) + (2²)(0.283) + (3²)(0.684)

= (0)(0.001) + (1)(0.032) + (4)(0.283) + (9)(0.684)

= 0 + 0.032 + 1.132 + 6.156

= 7.32

Variance = Var(X) = 7.32 - 2.65² = 7.32 - 7.0225

Var(X) = 0.2975

Standard deviation = √(variance) = √0.2975

Standard deviation = 0.545

Hope this Helps!!!

8 0
2 years ago
What is the equation for the hyperbola shown?
castortr0y [4]

Answer:

\frac{x^{2} }{3600} - \frac{y^{2} }{121} = 1

Step-by-step explanation:

Since the hyperbola opens left and right with a center at the origin, then

\frac{x^{2} }{^{2} } - \frac{y^{2} }{b^{2} } = 1

In the graph a = 60 and b = 11

So

\frac{x^{2} }{60^{2} } - \frac{y^{2} }{11^{2} } = 1.

\frac{x^{2} }{3600} - \frac{y^{2} }{121} = 1

7 0
2 years ago
If x - 3 Is a factor P(x) = x ^ 3 - 7x ^ 2 + 15x - 9, which of the following represents the complete factorization for P(x) ?
sattari [20]

the answer is c, i just got this question

3 0
2 years ago
There are 16 girls and 20 boys in the school band. Express an equivalent ratio of boys to total number of students in the school
Alex17521 [72]

Answer:

4:5

Step-by-step explanation:

half of 16 is 8, and half of 8 is 4

and half of 20 is 10, and half of 10 is 5

hope i helped man

8 0
2 years ago
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