Which pair of expressions is equivalent using the Associative Property of Multiplication?

Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find

natka813 [3]

Answer:

The width of the football field is 160 feet.

The length of the football field is 360 feet.

Step-by-step explanation:

Let w represent width of the football field.

We have been given that the length is 200 ft more than the width, so the length of the field would be $w+200$ .

We are also told that the perimeter is 1,040 ft. We know that football field is in form of rectangle, so perimeter of field would be 1 times the sum of length and width. We can represent this information in an equation as:

$2(w+w+200)=1040$

Let us solve for w.

$2(2w+200)=1040$

$4w+400=1040$

$4w+400-400=1040-400$

$4w=640$

$\frac{4w}{4}=\frac{640}{4}$

$w=160$

Therefore, the width of the football field is 160 feet.

Upon substituting $w=160$ in expression $w+200$ , we will get length of field as:

$w+200\Rightarrow 160+200=360$

Therefore, the length of the football field is 360 feet.

7 0

3 years ago

Vector V is in standard position and makes an angle of 50° with the positive x-axis. Its magnitude is 15. Write V in component f

Scilla [17]

Answer:

a=9.641, b=11.49

Vector will be 9.641 i + 11.49 j

Step-by-step explanation:

We have given that vector V has the magnitude of 15

And it makes an angle of 50 $^{\circ}$ with positive x axis

Now let the x component of vector V is a and y component of vector V is b

So $a=Vcos\Theta =15\times cos50^{\circ}=9.641$

$b=Vsin\Theta =15\times sin50^{\circ}=11.49$

In vector form 9.641 i+11.49 j

8 0

3 years ago

Assume that in a particular military exercise involving two units, Red and Blue, thereis a 60 % chance that the Red unit will su

Marysya12 [62]

Answer: a) There are 42% chances that both units will meet their objectives.

b) There are 88% chances that one or the other but not both of the units will be successful.

Step-by-step explanation:

Since we have given that

Probability that the Red unit will successfully meet its objectives = 60% = P(R)

Probability that Blue unit will successfully meet its objectives = 70% = P(B)

Probability that only Red unit will be successful = P(only Red) = 18%

As we know that

$P(only\ red)=P(R)-P(R\cap B)\\\\0.18=0.60-P(R\cap B)\\\\0.18-0.60=-P(R\cap B)\\\\-0.42=-P(R\cap B)\\\\P(R\cap B)=42\%$

Hence, there are 42% chances that both units will meet their objectives.

the probability that one or the other but not both of the units will be successful is given by

$P(R\cup B)=P(R)+P(B)-P(R\cap B)\\\\P(R\cup B)=0.60+0.70-0.42\\\\P(R\cup B)=0.88\\\\P(R\cup B)=88\%$

Hence, there are 88% chances that one or the other but not both of the units will be successful.

6 0

2 years ago

M/

satela [25.4K]

<h3>Answer: C) 2.47 cm</h3>

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Explanation:

We have 81 cm^3 of clay. Divide this among the 20 students and each gets 81/20 = 4.05 cm^3 of clay

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The volume of a cone is

V = (1/3)*pi*r^2*h

Solving for h gets us

3V = pi*r^2*h

(3V)/(pi*r^2) = h

h = (3V)/(pi*r^2)

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The diameter is 2.5 cm which cuts in half to 1.25 cm, so this is the radius.

We'll plug this radius in, along with V = 4.05 and pi = 3.14

h = (3V)/(pi*r^2)

h = (3*4.05)/(3.14*(1.25)^2)

h = 2.4764

This value is approximate. Rounding down to the nearest hundredth gets us 2.47

We round down because rounding up to 2.48 will lead to a volume larger than 4.05

7 0

2 years ago

William wants to invest $30,000 in a mutual fund.

Natali [406]

Answer:

He will have $39,750 at the end of five years.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$T = E + P$