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2 years ago

Now let the figure show a scale drawing of a park with the largest dimension equal to 63 meters. What is the scale

Mathematics

1 answer:

Strike441 [17]2 years ago

5 0

Let
x = scale
For this case you should count how many divisions there are in the longest dimension.
14
Then, as the longest dimendion of the park is 63 meters then, the scale is
14x = 63
x = 63/14
x = 4.5
answer
the scale is 4.5m

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The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your

Katyanochek1 [597]

Answer: 64 years

Step-by-step explanation:

Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

R1 = P(1.05)^t,

This means that after t years, the dealer would have the total amount of:

$P×1.05^t.

If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

R2 = $P(1 + 20).

The value of t which will make both returns equal, will be;

R1 = R2.

P×1.05^t = P(1+20)

P will cancel out

1.05^t = 21

Log both sides

Log1.05^t = Log21

tLog1.05 = Log21

t = Log21/Log1.05

t = 64 years

The best time to sell the wine is therefore 64years from now.

7 0

2 years ago

Given that a rectangle with length $3x$ inches and width $x + 5$ inches has the property that its area and perimeter have equal

scoray [572]

Answer:

First, we need to know how to calculate the area and the permiter of a rectangle.

To calculate the area, we multiply base by height and to calculate the perimeter, we sum all sides.

Knowing this, we can say that the area is 3x * (x+5) and the perimiter is 3x + 3x + x + 5 + x + 5, as we know both are the same, we write it as an equation:

$3x * (x+5) = 3x + 3x + x + 5 + x + 5$

Now we solve the equation:

$3x^2 +15x = 6x + 2x + 10$

$3x^2+15x =8x + 10$

$3x^2+15x-8x-10=0$

$3x^2+7x-10=0\\\\x_1=\frac{-10}{3}\\x_2 = 1$

As the negative result doesn't have sense, we only pick the second one: 1.

If x = 1, then area would be 3*6 = 18 square inches and perimeter 3+3+6+6 = 18 inches

7 0

2 years ago

Read 2 more answers

Each locker is shaped like a rectangular prism. Which has more storage space? explain/

seropon [69]

Locker 1 has more storage space because it has a greater volume.
The volume of locker 1 is 8,640 (48x15x12)
The volume of locker 2 is 7,200 (60x10x12)

I hope this helps.

4 0

2 years ago

A survey of the men in a certain town showed that 35% of the men have blond hair and 14% of them have blond hair and blue eyes.

natita [175]

If you are given he has blond hair, so the total probability will be 35%. And among them, he needs to have blue eyes, its probability is 14% among the 35%. So the final probability is 14%/35%=40%.

7 0

2 years ago

Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

Step-by-step explanation:

The random variable X and Y are defined as follows:

X = amount of ice cream in the box

Y = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

X + 3Y.

Compute the expected value of (X + 3Y) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (X + 3Y) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (X + 3Y) is:

$SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25$

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

X - Y.

Compute the expected value of (X - Y) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (X - Y) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (X - Y) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

7 0

2 years ago