Identify the domain and range of the relation. {(-9, 2), (-4, 2), (3, 2), (9, 2)}

Write an exponential function to model the situation. A population of 470 animals decreases at an annual rate of 12%.

Tamiku [17]

$\bf \qquad \textit{Amount for Exponential Decay}
\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &470\\
r=rate\to 12\%\to \frac{12}{100}\to &0.12\\
t=\textit{elapsed time}\\
\end{cases}
\\\\\\
A=470(1-0.12)^t\implies A=470(0.88)^t$

5 0

3 years ago

Point Q'Q ′ Q, prime is the image of Q(-7,2)Q(−7,2)Q, left parenthesis, minus, 7, comma, 2, right parenthesis under a translatio

Flauer [41]

Answer:

ikik

Step-by-step explanation:

just need points sorry

3 0

3 years ago

the plans for your 13th birthday party are well under way. your parents agree to your guest list of 400 people. you decided it w

diamong [38]

Answer:

11 people will get both the prizes.

Step-by-step explanation:

In this question we need to find common integral multiples of 5 and 7 under 400. As you can see in the figure 35th person is the first one to get both ipod and psp. The LCM (least common multiple) of 5 and 7 which is 35 (!!! I hope you know how to LCM of two integers ).

Therefore the integral multiples of 35 will be same as the common multiples of 5 and 7. So, figuring out the number of integral multiples of 35 under 400 will give the answer.

To do that divide the number 400 with 35. On performing the division the quotient will be 11 and the remainder will be 15.

Therefore 11 persons out of 400 will get both the prizes.

Similarly if you want to find the number of person getting ipod then divide 400 with 5. The quotient will be 80. ∴ 80 people will get ipod.

And for psp, divide 400 with 7. The quotient will be 57. ∴ 57 people will get psp.

In these divisions, consider just the quotient, here remainder is of no use.

5 0

2 years ago

Jerry King is a server in a restaurant that pays a salary of $43 per day. He also averages tips of 18% of his total gross food o

tatyana61 [14]

Answer:

His total gross pay for the week is $588.25.

Step-by-step explanation:

Consider the provided information.

Jarry has a salary of $43 per day and he worked for 4 days.

Thus, the salary of 4 days is:

4 × $43= $172

The average tips is 18% of his total gross food orders.

Last week he had total food orders of $2,312.5. Therefore, the total tips he received is:

$2312.5 \times(\frac{18}{100})$

$2312.5 \times(0.18)$

$416.25$

Total tips he received is $416.25.

His total gross pay for the week = The salary of 4 days + Total tips he received.

His total gross pay for the week = $172 + $416.25

His total gross pay for the week = $588.25

Hence, his total gross pay for the week is $588.25.

5 0

2 years ago

What is the solution to the system? 1. x-y + 2 z = -7 2. y + z =1 3. x-2 y - 3 z = 0

kvv77 [185]

You'd find this problem easier to understand and do if you'd please list the defining equations vertically and line up variables:

1. x - 1y + 2 z = -7

2. y + 1z = 1

3. x - 2 y - 3 z = 0 Now eliminate the line numbers:

x - 1y + 2 z = -7

1y + 1 z = 1

x - 2 y - 3 z = 0

Let's use the elimination method to eliminate variable z: Seeing that z = 1 - y, we transform the first equation into 1x - 1y + 2(1-y) = -7

and the third into x - 2y - 3(1-y) = 0.

Simplifying 1x - 1y + 2(1-y) = -7

and x - 2y - 3(1-y) = 0,

we get

1x - 2y - 3 + 3y) = 0 and 1x - 1y + 2 - 2y = -7

which in turn simplify to

1x + y = 3 and 1x - 3y = -9

Having eliminated the variable z, we now focus on eliminating x. Mult. the 1st equation by -1, obtaining -1x - 1y = -3. Add this result to 1x - 3y = -9:

0 - 4y = -12, which tells us that y = 3. Subbing 3 for y in 1x + 1y = 3 tells us that x = 0.

All we have left to determine is the vaue of z.

Borrowing Equation 3, from above, we get x - 2 y - 3 z = 0, and into this equation we substitute x = 0 and y = 3: 0 -2(3) - 3z = 0.

Thus, -3z = 6, and z = -2.

The solution set is (0, 3, -2). You should check this by substitution.

3 0

3 years ago