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3 years ago

Find the volume of the triangular prism with height=9 cm, base=6cm, and altitude of triangles=8cm

Mathematics

2 answers:

telo118 [61]3 years ago

8 0

The answer is C

Multiply all of the measurements and divide by 2. Picture cutting the triangle in half from the top point, then use the measurements you have and multiply live it’s a rectangular prism.

saveliy_v [14]3 years ago

8 0

Answer:

The volume of the prism is $216\,cm^3$

Please notice that the number agrees with the third answer in the list of options, but the list contains errors in the units for the four options listed. Volumes shouldn't have units of square centimeters! there is a type in all the units. the exponent of the cm should be "3" not 2.

Step-by-step explanation:

Recall that the volume of a prism is given by the product of the area of its base (B) times its height (h) : $V=B\,h$

In our case, the base of the prism is a triangle of base 6 cm and height 8 cm. Then we can estimate the prism's base using the formula for the area of a triangle = base x height/2

triangle's area = $6\,cm*8\,cm/2=24\,cm^2$

Now we use this area in the volume formula:

$V=B\,h\\V=24\,cm^2\,*\,9\,cm\\V=216 \,cm^3$

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3 years ago

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

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These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

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Then the axis of symmetry is the line

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Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

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Answer:

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Read 2 more answers

A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occ

Shkiper50 [21]

Answer:

a) The mean number of cases is 0.14608 cases.

b) The probability that the number of cases is exactly 0 or 1 is 0.990.

c) The probability of more than one case is 0.010

d) No, because the probability of more than one case is very small

Step-by-step explanation:

We can model this problem with a Poisson distribution, with parameter:

$\lambda=r*t=0.000011*13,280=0.14608$

a) The mean amount of cases is equal to the parameter λ=0.14608.

b) The probability of having 0 or 1 cases is:

$P(k=0)=\frac{\lambda^0 e^{-\lambda}}{0!}=\frac{1*0.864}{1} =0.864\\\\ P(k=1)=\frac{\lambda^1 e^{-\lambda}}{0!}=\frac{0.14608*0.864}{1} =0.126\\\\P(k\leq1)=0.864+0.126=0.990$

c) The probability of more than one case is:

$P(k>1)=1-P(k\leq 1)=1-0.990=0.010$

d) The cluster of 4 cases can not be due to pure chance, as it is a very high proportion of cases according to the average rate. Just having more than one case has a probability of 1%.

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3 years ago