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lara31 [8.8K]
3 years ago
7

Shots invests $1000 in a certificate of deposit that earns interest. The investment’s value is multiplied by 1.02 each year

Mathematics
2 answers:
Slav-nsk [51]3 years ago
3 0

Answer:

1000 times 1.02

Here the answer will be 1020.

Step-by-step explanation:

1000 times 1.02= 1020

Aliun [14]3 years ago
3 0

Answer:

1000⋅1.02  ^5

Step-by-step explanation:

I just did this one

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If(x) = x + 2 and h(x) = x-1, what is f • h](-3)?
deff fn [24]

Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

x

) = 3(x

2 +

1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

4 0
2 years ago
a six sided number cube has faces with the numbers 1 through 6 marked on them. what is the probability that a number less than 2
iris [78.8K]

Solution:

we are given that

A six sided number cube has faces with the numbers 1 through 6 marked on them.

we have been asked to find the probability that a number less than 2 will occur on one toss of the number cube.

Since a number less than 2 is only one and that is "1" and total number of possible outcome is 6.

and as we know that probability is given using the formula

P(E)= \frac{n(E)}{n(S)}\\ \\

Substitute the values we get

P(E)= \frac{1}{6}

Hence the required probability is 1/6.

5 0
3 years ago
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Answer:

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4 0
2 years ago
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How to graph 5x+3y=15​
maxonik [38]

Answer:

Step-by-step explanation:

The number 2 goes into both 12 and 14.

Step-by-step explanation:

12 ÷ 2 is 6 and 14 ÷2 is 7 . You can't really simplify 14 by any other whole number besides 2 or 7 .

6 0
2 years ago
How many solutions does 2/3 (3x - 15) = x - 10 have?
irina1246 [14]

Answer:

2/3 [3x - 15] =x-10

open the brackets first

[2/3 x3x] -[2/3 x15 =x - 15

2x - 10 =x - 10

put the like terms together

2x -x =-10 +10

x=0

Step-by-step explanation:

6 0
2 years ago
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