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Katarina [22]
3 years ago
14

A supermarket finds that the number of boxes of a new cereal sold increases each week. In the first week, only 26 boxes of the c

ereal were sold. In the next week, 57 boxes of the cereal were sold and in the third week 88 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence. What is the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n?
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
4 0

If the pattern goes 26, 57, 88 you can find the difference between each number to see how much it's going up by each time. 57 - 26 = 31 and 88 - 57 = 31

That means each week the number of boxes of a new cereal increases by 31, or +31

You might be interested in
George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his t
nikdorinn [45]

Answer:

a. B+S = 1

0.06B+0.1S \geq 0.075

B \geq 0.3

Objective function:

R=0.06B+0.1S

b) See Attached picture

30% in bonds and 70% in stocks

Step-by-step explanation:

a.

In order to solve the first part of the problem we need to take into account that the problem wants us to determine the percentage that should be allocated to each of the possible investment alternatives. In that case, the sum of the percentages must be equal to 1 (which means that we will have 100 of the trust fund)

so that gives us our first restriction for the problem.

B+S=1

Next, the problem tells us that the projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. It also states that he wants to select a mix that will enable him to obtain a total return of at least 7.5%, so we can take this information and get the second restriction from it:

0.06B+0.1S \geq 0.075

Next, the problem tells us that whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund, so that's where the last restriction comes from:

B \geq 0.3

now, the idea is to optimize the investment, this is get the greatest amount of money out of the trust fund, so the objective function is:

R=0.06B+0.1S

which represents the return on the investment.

b)

For part b we can start by graphing each of the restrictions:

B+S = 1

This will be a single line, you can draw the line by setting B=0 first so you get:

0+S=1

S=1

So the first point to plot will be (0,1)

next, we can set s=0 to get:

B+0=1

B=1

so the second point to plot will be (1,0)

so you can plot the two points and connect them with a straight line. This is the green line on the uploaded graph.

Next we can graph the second restriction:

0.06B+0.1S \geq 0.075

we can use the same procedure we used for the previous graph, in this case the points would be:

(0 , 0.75) and (1.25, 0)

and again connect the two points with a straight line. Next we need to decide which region of the graph to shade for which we can pick two arbitrary points on each side of the line, for example we can pick:

(0,0) and (2,2) and see which one makes the inequality true:

for (0,0) we get:

0.06B+0.1S \geq 0.075

0.06(0)+0.1(0) \geq 0.075

0 \geq 0.075

Which is false, therefore we need to shade the other region of the graph:

for (2,2) we get:

0.06B+0.1S \geq 0.075

0.06(2)+0.1(2) \geq 0.075

0.32 \geq 0.075

Which is true, so we shade the region of the graph that contains that point. (see red graph)

now we graph the third restriction:

B \geq 0.3

In order to graph this third restriction we just need to draw a vertical line at B=0.3 and shade everything to the right of that line. (Blue graph)

Now, we can analyze the graph, in this case we need to locate the points where the green line crosses the red and the blue line which gives us the following coordinates:

(0.3, 0.7) and (0.625, 0.375)

these two points can be found by setting the first restriction equal to each of the other two restrictions if you are to do it algebraically. If you are using a graphing device, you can directly read them from the graphs.

So once we got those points, we can see which one gives us the greatest percentage of return.

let's test the first point (0.3, 0.7)

R=0.06B+0.1S

R=0.06(0.3)+0.1(0.7)

R=0.088

so this distribution gives us 8.8% in return, let's test the second point:

(0.625, 0.375)

R=0.06B+0.1S

R=0.06(0.625)+0.1(0.375)

R=0.075

so this distribution gives us 7.5% in return.

In this case the best distribution for us is 30% in bonds and 70% in the stock fund to get a return of 8.8%

6 0
3 years ago
The length of a rectangle is 12 in. and the perimeter is 56 in. Find the width of the rectangle.
yuradex [85]

Answer:

W = 16 in

Step-by-step explanation:

P = 2L + 2W

56 = 2(12) + 2W

56 = 24 + 2W

56-24 = 2W

32 = 2W

W = 32/2

W = 16 in

Best regards

7 0
3 years ago
+4<br> What is the solution of 2x-15<br> - &lt;0?<br> • -45x51<br> 0 -4 -45<br> -4
soldier1979 [14.2K]

Answer:

alto 5.340040 to costco

Step-by-step explanation:

7 0
3 years ago
There are two spinners. Each spinner has 10 equal sectors labeled with the numbers 1 through 10.
Reika [66]

Answer: Second option is correct.

Step-by-step explanation:

Since we have two spinners,

Each spinner has 10 equal sectors labeled with the numbers from 1 to 10.

Primes numbers from 1 to 10 is given by

\{2,3,5,7\}

So, number of outcomes shows a  primes number from 1 to 10 = 4

Similarly ,

Composite numbers from 1 to 10 is given by

\{4,6,8,9,10\}

So, number of outcomes shows a composite number from 1 to 10 =5

∴ Total outcomes show a prime number on the first spinner and a composite number on the second spinner is given by

4\times 5=20\\

Thus, Second option is correct.


3 0
3 years ago
30 points!!<br> What is the sum of the first six terms of the series?<br> 48 - 12 + 3 - 0.75 +...
Lunna [17]

Answer:

The sum of the first six terms is 38.39

Step-by-step explanation:

This is a geometric sequence since the common difference between each term is -\frac{1}{4}

Thus, r=-\frac{1}{4}

To find the sum of first six terms, we need to find the fifth and sixth term of the sequence.

To find the fifth term:

The general form of geometric sequence is a_{n}=a_{1} \cdot r^{n-1}

To find the fifth term, substitute n=5 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{5} &=(48) \cdot\left(-\frac{1}{4}\right)^{5-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{4} \\&=(48)\left(\frac{1}{256}\right) \\a_{5} &=0.1875\end{aligned}

To find the sixth term, substitute n=6 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{6} &=(48) \cdot\left(-\frac{1}{4}\right)^{6-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{5} \\&=(48)\left(-\frac{1}{1024}\right) \\a_{5} &=-0.046875\end{aligned}

To find the sum of the first six terms:

The general formula to find Sn for |r| is S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}

\begin{aligned}S_{6} &=\frac{48\left(1-\left(-\frac{1}{4}\right)^{6}\right)}{1-\left(-\frac{1}{4}\right)} \\&=\frac{48\left(1-\frac{1}{4096}\right)}{1+\frac{1}{4096}} \\&=\frac{48(0.95)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{47.9904}{5} \\&=38.39\end{aligned}

Thus, the sum of first six terms is 38.39

5 0
3 years ago
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