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3 years ago

What is the volume of the prism below?

Mathematics

2 answers:

julia-pushkina [17]3 years ago

6 0

Answer: D. $168\ m^3$

Step-by-step explanation:

We know that the volume of a prism is given by :-

$V=\dfrac{1}{2}*\text{base area*height}$

Now, from the given picture, the dimensions of the base of the prism = $7\ m\times8\ m$

Thus, Base Area = $7\times8=56\ m^2$

Height of prism = 6 m

Therefore, the volume of the prism is given by ;-

$V=\dfrac{1}{2}*56\times6=168\ m^3$

Hence, Volume of the given prism = $168\ m^3$

ASHA 777 [7]3 years ago

5 0

The answer is D. 168 units^3

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Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. J(2,

MAVERICK [17]

Applying a dilation centered at the origin with scale factor $k$ has the effect of multiplying both coordinates of a point by $k$ :

$(x,y)\mapsto (kx,ky)$

So, in your case, the coordinates of the points double:

$J'=(4,8),\quad K'=(8,8),\quad P'=(6,4)$

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3 years ago

5x + 14 = K solve for K

siniylev [52]

Flip the equation.k=5x+14

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3 years ago

Read 2 more answers

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

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

=> $P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)]$

=> $P(X > 6)=1 - [^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 * (0.267)^6 * (1- 0.267)^{12-6} ]$

=> $P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ]$

=> $P(X > 6) = 0.0206$

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

8 0

3 years ago

Factorize 9(a+1)^2-81

Lunna [17]

Answer:9a^2+18a-72

Step-by-step explanation:

9(a+1)^2-81

9(a+1)(a+1)-81

Open brackets

9(a^2+a+a+1)-81

9(a^2+2a+1)-81

9a^2+18a+9-81

9a^2+18a-72

5 0

3 years ago

Please solve both of these with how you solved them.

Paladinen [302]

Answer:

a. (2,5)

b. (14,15.5)

Step-by-step explanation:

y=4x-3

y=-2x+9

Set both equations equal to each other to solve for x.

4x-3=-2x+9

6x=12

x=2

Plug in x to solve for y.

y=4x-3

y=4(2)-3

y=8-3

y=5

(2,5)

y=(5/4x)-2

y=(-1/4x)+19

Set both equations equal to each other to solve for x.

(5/4x)-2=(-1/4x)+19

4((5/4x)-2=(-1/4x)+19)

5x-8=-x+76

6x=84

x=14

Plug in x to solve for y.

y=(5/4x)-2

y=(5/4(14))-2

y=17.5-2

y=15.5

(14,15.5)

6 0

3 years ago