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4 years ago

Write an exponential function y = ab" whose graph passes through (2,12) and (5,96).

Mathematics

1 answer:

motikmotik4 years ago

3 0

Answer:

y = 3 $(2)^{x}$

Step-by-step explanation:

Substitute the given points into the function and solve for a and b

Using (2, 12)

12 = ab² → (1)

Using (5, 96)

96 = a $b^{5}$ → (2)

Divide (2) by (1)

$\frac{ab^5}{ab^2}$ = $\frac{96}{12}$ , that is

b³ = 8 ( take the cube root of both sides )

b = $\sqrt[3]{8}$ = 2

Substitute b = 2 into (1) and solve for a

12 = a2² = 4a ( divide both sides by 4 )

3 = a

Thus

y = 3 $(2)^{x}$ ← is the exponential function

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write everything I know about similar figures. (what are they, how do you find the scale factor, how do you solve for x when giv

Dmitry [639]

Answer:

Suppose you have two similar figures , one larger than the other. The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Here, XYUV=123=4 . So, the scale factor is 4 .Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor .

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3 years ago

We roll two fair 6-sided dice. Each of the 36 possible outcomes is assumed to be equally likely. (a) Given that the roll results

boyakko [2]

Answer:

a) $\frac{1}{7}$

b) $\frac{2}{15}$

Step-by-step explanation:

Given : We roll two fair 6-sided dice. Each of the 36 possible outcomes is assumed to be equally likely.

The outcomes are :

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

(a) Given that the roll results in a sum of 3 or more, find the conditional probability that doubles (the first and the second rolls result in the same number) are rolled.

Let P(A) be the probability of event that the roll results in a sum of 3 or more.

Except (1,1) rest sum is 3 or greater than 3.

So, $P(A)=\frac{35}{36}$

Now, P(A and B) is that the roll results in a sum of 3 or more and that doubles (the first and the second rolls result in the same number) are rolled.

i.e. (2,2), (3,3), (4,4), (5,5), (6,6) - 5

$P(A\cap B)=\frac{5}{36}$