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Diano4ka-milaya [45]
3 years ago
11

For each give the correct METRIC unit of measure. Do NOT use the abbreviation. a. My foot is 21 (fill in blanks) long. b. My lar

ge aquarium holds 55 (fill in blank) of water. c. My dad drives 27 (fill in blank) to work each day. d. I just bought 12 (fill in blank) of carpet to cover my family room floor.
Mathematics
1 answer:
Nataly [62]3 years ago
7 0

Answer:

Inches

Gallons

Kilometers

Yards

Step-by-step explanation:

We are to proffer the appropriate unit of measurement for each scenario given below :

a. My foot is 21 inches long. (unit for measuring length which are usually small such a a person's foot)

b. My large aquarium holds 55 gallons of water. (volume measurement of liquid in a large container)

c. My dad drives 27 kilometers to work each day. (distance measurement which are moderately long)

d. I just bought 12 yards of carpet to cover my family room floor. (length measurement used for materials such as cloth, carpet, rugs e.t.c).

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
Which of the following is a statistical question? a.Who is your favorite fantasy author? b.Do you like fantasy novels? c.What is
Dovator [93]
I would say B. or c. but most likely B to make sure you can search up examples of statistical questions.
7 0
3 years ago
Consider this right triangle.<br> 21<br> 29<br> 20<br> Enter the ratio equivalent to s
AleksAgata [21]

Answer:

Part 1) sin(B)=\frac{21}{29}

Part 2) csc(A)=\frac{29}{20}

Part 3) cot(A)=\frac{21}{20}

Step-by-step explanation:

<u><em>The complete question is</em></u>

Consider this right triangle. 21 29 20 Write the ratio equivalent to: Sin B - CscA- Cot B

The picture of the question in the attached figure

Part 1) Write the ratio equivalent to: Sin B

we know that

In the right triangle ABC

sin(B)=\frac{AC}{AB} ----> by SOH (opposite side divided by the hypotenuse)

substitute the values

sin(B)=\frac{21}{29}

Part 2) Write the ratio equivalent to: Csc A

we know that

In the right triangle ABC

csc(A)=\frac{1}{sin(A)}

sin(A)=\frac{BC}{AB} -----> by SOH (opposite side divided by the hypotenuse)

substitute the values

sin(A)=\frac{20}{29}

therefore

csc(A)=\frac{29}{20}

Part 3) Write the ratio equivalent to: Cot A

we know that

In the right triangle ABC

cot(A)=\frac{1}{tan(A)}

tan(A)=\frac{BC}{AC} -----> by TOA (opposite side divided by the adjacent side)

substitute the values

tan(A)=\frac{20}{21}

therefore

cot(A)=\frac{21}{20}

4 0
3 years ago
The coordinates of rectangle ABCD are A(1, 2), B(4, 5),C(9, 0) and D(6, -3). What is the area of the rectangle? 18 square units
Natali5045456 [20]
In order to find the area of a rectangle, the formula is L*W (Length multiplied by Width). Our goal is to find these two measurements, so we will take the following steps:
1) Plot the coordinates on a graph (I have attached a visual guide)
2) Using the Pythagorean Theorem, or the Distance formula we can find the length and width: \sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}
3) We will use these values in the Area formula for a rectangle (L*W)
4) After solving the Area formula with the values retrieved from the Distance Formula we find that the area is roughly 30 units squared.

4 0
3 years ago
$500 at 4% for 3 years
dimaraw [331]
If you are trying to find the interest, it would be $60.00. To get this just multiply everything. Hope this helps!!! :)
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8 0
3 years ago
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