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2 years ago

The height of a parallelogram is 5 feet The base is 7 feet the length is 9 1/2 feet what is the area of the parallelogram

Mathematics

1 answer:

Pie2 years ago

8 0

Answer:

[10 ft.]

Step-by-step explanation:

It's being given that there is a paralleolgram.

Let the length of its base is x ft.

Therefore, length of height = (x+6) ft.

Also, area of paralleolgram = 160 sq.

ft.

Now, we know that,

Area of paralleolgram = base x height

Therefore, we will get,

=> x(x+6) = 160

=> x² + 6x - 160 = 0

=> x² + 16x - 10x - 160 = 0

=> x(x+16) - 10(x+16)=0

=> (x+16) (x - 10) = 0

=> x +16=0 or X- - 10-0

=> x=-16

X = 10

But, we know that, length can't ever be negative.

Therefore, x = 10

Hence, length of base = 10 ft.

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A triangle has side lengths of (2b+c)(2b+c) centimeters, (7b+4d)(7b+4d) centimeters, and (6d+2c)(6d+2c) centimeters. Which expre

Gnoma [55]

Answer:

(9b + 3c + 10d)cm

Step-by-step explanation:

Given the sides of a triangle expressed as (2b+c), (7b + 4d) and (6d+2c). The perimeter of the triangle is the sum of all the sides of the triangles.

Perimeter of the triangle = 2b+c + 7b+4d + 6d+2c

Perimeter of the triangle = 2b + 7b + c + 2c + 4d + 6d

Perimeter of the triangle = 9b + 3c + 10d

Hence the perimeter of the triangle is (9b + 3c + 10d)cm

3 0

3 years ago

Read 2 more answers

A sphere with a diameter of 30 inches is placed in a cube. The sphere touches the lateral faces

Nina [5.8K]

Answer:

a) 30 inches × 30 inches × 30 inches

b) 27,000 inches³

c) 14,130 inches³

d) 12,870 inches³

Step-by-step explanation:

Edge of the cube = diameter = 30 inches

Volume of cube = s³

30³ = 27000 inches³

Radius = 30/2 = 15

Volume of sphere:

(4/3) × 3.15 × 15³

14130 inches³

Difference:

27000 - 14130

12870 inches³

5 0

4 years ago

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

VikaD [51]

Complete Question

The complete question is shown on the first uploaded image

Answer:

$P(X = 8) = 0.0037$

$P(X < 5) = 0.805$

$P(X > 6) = 0.0206$

I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is $p = 0.267$

Generally data collected from this study follows binomial distribution because the number of trials is finite , there are only two outcomes, (covering , and not covering mouth when sneezing ) , the trial are independent

Hence for a randomly selected variable X we have that

$X \ \ \~ \ \ { B ( p , n )}$

The probability distribution function for binomial distribution is

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

Considering question a

Generally the the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as

$P(X = 8) = ^{12} C_8 * (0.267)^8 * (1- 0.267)^{12-8}$

Here C denotes combination

$P(X = 8) = 495 * 0.000025828 * 0.28867947$

$P(X = 8) = 0.0037$

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as

$P(X < 5 ) =[P(X = 0 ) + \cdots + P(X = 4)]$

=> $P(X < 5 ) =[ ^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0} + \cdots + ^{12} C_4 * (0.267)^4 * (1- 0.267)^{12-4} ]$

=> $P(X < 5 ) = 0.02406 + 0.10516 + 0.21067 + 0.25580 + 0.20964$

=> $P(X < 5) = 0.805$

Considering question c

Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

$P(X > 6) = 1 - p(X \le 6)$