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2 years ago

Find the value of f(3) for the function f(x) = -4(x+1)-2

Mathematics

1 answer:

lora16 [44]2 years ago

6 0

Answer:

f(3) = - 18

Step-by-step explanation:

To evaluate f(3) , substitute x = 3 into f(x) , that is

f(3) = - 4(3 + 1) - 2 = - 4(4) - 2 = - 16 - 2 = - 18

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Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula.

Goshia [24]

Answer:

$\sf 2^{(n+1)}$

Step-by-step explanation:

Explicit formula is used to represent all the terms of the geometric sequence using a single formula.

$\sf \boxed{\bf t_n=ar^{(n-1)}}$

Here, a is the first term.

r is the common ratio.

r = second term ÷ first term

4, 8,16,32,64,.....

a = 4

r = 8 ÷4 = 2

$\sf t_n =4*2^{(n-1)}$

$\sf = 4*2^n * 2^{(-1)}\\\\ = 4*2^n*\dfrac{1}{2}\\\\ = 2*2^n$

$\sf = 2^{(n+1)}$

4 0

1 year ago

PLEASE HURRY I NEED MY WORK TO BE SHOWN!!!!! 15 POINTS!!! CORRECT ANSWERS ONLY PLEASE!!!

Harlamova29_29 [7]

Answer:

f(-4) = 72, f(x + 5) = 3x² + 23x + 36

Step-by-step explanation:

f(-4) = 3(-4)² - 7(-4) - 4

= 48 - (-28) - 4

f(-4) = 72

f(x + 5) = 3(x + 5)² - 7(x + 5) - 4

= 3(x + 5)(x + 5) - 7(x + 5) - 4

= 3(x² + 10x + 25) - 7(x + 5) - 4

= 3x² + 30x + 75 - 7x - 35 - 4

f(x + 5) = 3x² + 23x + 36

4 0

3 years ago

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper

Korvikt [17]

Answer:

90.67% probability that John finds less than 7 golden sheets of paper

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it contains a golden sheet of paper, or it does not. The probability of a container containing a golden sheet of paper is independent of other containers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper containers.

This means that $p = 0.3$

14 of these containers of paper.

This means that $n = 14$

What is the probability that John finds less than 7 golden sheets of paper?

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{14,0}.(0.3)^{0}.(0.7)^{14} = 0.0068$

$P(X = 1) = C_{14,1}.(0.3)^{1}.(0.7)^{13} = 0.0407$

$P(X = 2) = C_{14,2}.(0.3)^{2}.(0.7)^{12} = 0.1134$

$P(X = 3) = C_{14,3}.(0.3)^{3}.(0.7)^{11} = 0.1943$

$P(X = 4) = C_{14,4}.(0.3)^{4}.(0.7)^{10} = 0.2290$

$P(X = 5) = C_{14,5}.(0.3)^{5}.(0.7)^{9} = 0.1963$

$P(X = 6) = C_{14,6}.(0.3)^{6}.(0.7)^{8} = 0.1262$

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0068 + 0.0407 + 0.1134 + 0.1943 + 0.2290 + 0.1963 + 0.1262 = 0.9067$

90.67% probability that John finds less than 7 golden sheets of paper

7 0

2 years ago

A desk is 39 inches wide. What is the width in yards

Stolb23 [73]

Answer:

1.0833 yd

Step-by-step explanation:

Inches Yards

37" 1.0278 yd

38" 1.0556 yd

39" 1.0833 yd

40" 1.1111 yd

Have a great day! :D

4 0

2 years ago

What is the volume of a hemisphere with a radius of 8.8 cm, rounded to the nearest

gizmo_the_mogwai [7]

Answer:

1427.3

Step-by-step explanation

just did it, got it right, don't listen to the mf above me.

4 0

2 years ago