What is the surface area of this prism?<br> 5 yd<br> 5 yd<br> 11 yd<br> 6 yd

A caterer is preparing a dinner for a party. Shecharges an initial fee of $16 and $8.25 per person. How manypeople can attend a

Dafna1 [17]

Answer:

The nomber of people can attend a dinner that costs $131. 50 is 14.

Step-by-step explanation:

With the information provided, it can be said that the total cost of a dinner would be equal to the initial fee plus the result of multiplying the price per person for the number of people, which can be expressed as:

c=16+8.25x, where:

c is the total cost of he dinner

x is the number of people

Now, you can replace c with 131.50 that is the cost of a dinner and solve for x to find the number of people that can attend:

131.50=16+8.25x

131.50-16=8.25x

115.50=8.25x

x=115.50/8.25

x=14

According to this, the answer is that the nomber of people can attend a dinner that costs $131.50 is 14.

7 0

3 years ago

Karen, Trey, and Dante have a total of 75 in their wallets. Karen has 5 more than Trey. Dante has 2 times what Karen has. How mu

Taya2010 [7]

Answer: Karen has 20, Trey has 15, Dante has 40

Step-by-step explanation:

Karen=x+5 Trey=x Dante=2x+10

x+x+5+2x+10=75

4x+15=75

4x=60

x=15

5 0

3 years ago

In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban po

Sedbober [7]

Answer:

City @ 2017 = 8,920,800

Suburbs @ 2017 = 1, 897, 200

Step-by-step explanation:

Solution:

- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:

0.94*p_c + 0.04*p_s = p_c'

0.06*p_c + 0.96*p_s = p_s'

- Assuming 6% moved while remaining 94% remained settled at the time of migrations.

- The matrix representation is as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] = \left[\begin{array}{c}p_c'\\p_s'\end{array}\right]$

- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1$

- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1$

- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o$

- Where,

$x_o = \left[\begin{array}{c}10,000,000\\800,000\end{array}\right]$

- The population in 2017 x_2 would be:

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right]$