MATHEMATICS HIGH SCHOOL

Evaluate the expresson when n=8 The product of one fourth and a number increased by 3

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Substitute the n for 8 in

( $(1)/(4)$ times n)+3

product means multiply, so

( $(1)/(4)$ times 8)+3

First multiply $(1)/(4)$ by 8 to get 2

$(1)/(4)$ · 8 = 2

Then add 2 and 3

2+3=5

I hope this helps :)

Given

The graph of the parent squareroot function is;

$\rm y= √(x) +2$

What is the horizontal shift?

The horizontal shift is obtained by determining the change being made to the x-value. The horizontal shift is C.

If the horizontal shift is positive, the shifting moves to the right.

If the horizontal shift is negative, the shifting moves to the left.

The square root parent function is,

$\rm y= √(x) +2$

There is a shift in positive x-direction 2 units.

When the constant is negative the shift is to the right in c units, and when the constant is positive (like in this case) the shift is to the left in c units.

Hence, the graph is a horizontal shift of the function two units to the left.

To know more about Horizontal Shift-click the link given below.

brainly.com/question/8740413

which of the following best describes the relationship between (x+1) and the polynomial -3x^3-2x^2+1 a) (x+1) is a factor b) (x+1) is not a factor c) it is impossible to tell whether (x+1) is a factor

Answers

Answer:

I will solve this problem by factor theorem.

If , (x+1) is a factor of the polynomial , $f(x)=-3 x^3-2 x^2 +1$ then ,if we substitute,x= -1 in f(x), then, f(-1)=0.

Now,

$f(-1)= -3* (-1)^3-2 * (-1)^2+1\n\n f(-1)=-3 * (-1)-2 * 1+1\n\n f(-1)=3 -2+1\n\n f(-1)=2$

As, f(-1)≠ 0

Option B: (x+1) is not a factor of the polynomial , $f(x)=-3 x^3-2 x^2 +1$ .

Hello,

3x^3+2x²-1=(x-1)(3x²-x+1)+2
remainder is 2
(x+1) is not a factor of 3x^3+2x²-1 nor of -(3x^3+2x²-1)= -3x²-2x²+1.

Answer B

A certain bacteria population is known to quadruples every 150 minutes. Suppose that there are initially 200 bacteria. What is the size of the population after t hours?

Answers

This is a geometric progression
The size of the population afeter t hours will be=a₁*r^n

a₁= the first term =200
r=common ratio=4

150 minutes=150 minutes * (1 hour /60 minutes)=2.5 hours.

In this case:
the size of the populatation after t hours=200*4^t/2.5=200*4^0.4t

To check
t=0⇒ the size will be=200*4⁰=200*1=200
t=2.5 hours=150 minutes; the size will be =200*4¹=800
t=5 hours; the size will be=200*4²=200*16=3200

Answer: the size will be= 200*4^(0.4t)

Final answer:

The growth of the bacteria is represented by the exponential growth equation. Given the initial population, the four-fold increase, and the time interval for the increase, we can find the population after any given time by using the equation P = 200 * 4^(t/2.5).

Explanation:

The problem given is an example of an exponential growth problem. For these types of problems, we use the formula P = P0 * e^(kt), where P is the final population, P0 is the initial population, k is the growth rate, and t is time. However, in this case, we were given that the bacteria quadruples, meaning 'quadrupling' is not a continuous rate, so we use a slightly different form of the equation: P = P0 * (b)^(t/t0), where b is the times increase and t0 is the time interval for the b-fold increase.

Given that the initial population P0 is 200 bacteria, b is 4 because the population quadruples every 150 minutes, and time t0 is 150 minutes or 2.5 hours. We need to find the population P after t hours. Substituting these values into our equation gives us: P = 200 * 4^(t/2.5).

So, after t hours, the population of the bacteria will be given by the equation P = 200 * 4^(t/2.5).

Learn more about Exponential Growth here:

brainly.com/question/12490064

#SPJ2

Need the answer to this

Answers

Answer:

4.5 per package

Step-by-step explanation:

Though they give us 4 different pairs of values on the table, we only need 1 pair to solve this question. For simplicity, lets chose the pair of whole numbers:

54 : 12

This is the ration of servings to packages, or the servings per package.

To get our answer, we must find how many servings per 1 package, so we need to divide by 12:

$(54)/(12) : (12)/(12)$

4.5 : 1

This means that there are 4.5 servings per 1 package!

Hope this helps!

The function t(x) = x + 6 determines how many cans of soup a food truck needs to stock, where x is the number of shifts the crew is going to work in the truck. The crew uses c(t(x)) to find the amount of money to spend on soup. The function c(x) = 2x + 4. Solve for how much money must be spent when the crew is going to work 4 shifts.(A. 24; B. 28; C. 30; D. 34)

Answers

Answer:

Option A is correct.

The amount of money must be spent when the crew is going to work 4 shifts is, 24

Step-by-step explanation:

Given the function: $t(x) = x+6$ .....[1] ; where x represents the number of shifts the crew is going to work in the truck.

Also, the crew uses c(t(x)) which represents the amount of money to spend on soup.

The function is given as:

c(x) = 2x + 4 .....[2]

To find c(t(x)) i.e, the money must be spent when the crew is going to work 4 shifts.

⇒ x = 4

First substitute the value of x in [1] to find t(x);

$t(4) = 4+6 = 10$

Then;

For x=4 ,

c(t(4)) = 2(t(4)) +4 [Using equation [2]]

Substitute the value of t(4) = 10 we have;

c(t(4)) = 2(10) +4 = 20 + 4 = 24

Therefore, the amount must be spent when the crew is going to work 4 shifts is, 24

First, you have to solve t(x) when x=4, because the crew is working 4 scripts. Which is t(x)=4+6
t(x)=10
Then, you plug in t(x) to c(x).
c(x)=2(10)+4
c(x)=24

Megan is trying to remember her password for her computer. All she can remember is that it is 2 letters followed by 3 digits.How many possible combinations are there for Megan's password?

A. 1,560

B. 1,676

C. 468,000

D. 492,804

E. 676,000

Answers

The number of permutations possible is 468000.

What is permutation?

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

The first two places are occupied by letters.

The last 3 places are occupied by numbers.

The permutation for the first 2 places is: $26P_2$