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Ludmilka [50]
3 years ago
12

Any help on this ? 30 pts

Mathematics
1 answer:
Vlad1618 [11]3 years ago
6 0
The perimeter is adding up all sides of a shape. Here we are told that the perimeter of the triangle is 41 inches. So we can make the equation:

\sf x+3x+7y=41

Combine like terms(x + 3x = 4x):

\sf 4x+7y=41

We are also told that the perimeter of the rectangle is 66 inches. The formula for the perimeter of a rectangle is:

\sf P=2(l+w)

Plug in what we know:

\sf 66=2(3x+7y)

Distribute 2 into the parenthesis:

\sf 6x+14y=66

So our system of equations is:

\sf 4x+7y=41
\sf 6x+14y=66

Let's use the substitution method to solve this system. Let's solve for 'x' in the second equation:

\sf 6x+14y=66

Subtract 14y to both sides:

\sf 6x=-14y+66

Divide 6 to both sides:

\sf x=-\dfrac{7}{3}y+11

Now let's plug this in for 'x' in the first equation:

\sf 4x+7y=41

\sf 4(-\dfrac{7}{3}y+11)+7y=41

Distribute:

\sf -\dfrac{28}{3}y+44+7y=41

Combine like terms:

\sf -\dfrac{7}{3}y+44=41

Subtract 44 to both sides:

\sf -\dfrac{7}{3}y=-3

Divide -7/3 to both sides or multiply by its reciprocal -3/7:

\sf y=\dfrac{9}{7}

So the solution to the system of equations is:

\sf (8,\dfrac{9}{7})

Plug these values in to find the length and width of the rectangle.

Length:

\sf 3x

\sf 3(8)

\boxed{\sf 24}

Width:

\sf 7y

\sf 7(\dfrac{9}{7})

\boxed{\sf 9}
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Suppose that the rate of return on stocks is normally dis-tributed with mean of 9% and a standard deviation of 3%. If I pick fiv
alisha [4.7K]

Answer:

The probability that at least two stocks will have a return of more than 12% is 0.1810.

Step-by-step explanation:

Let <em>X</em> = rate of return on stocks.

The random variable <em>X</em> follows a Normal distribution, N (9, 3²).

Compute the probability that a stock has rate of return more than 12% as follows:

P(X\geq 12)=1-P(X

**Use the <em>z</em> table for the probability.

The probability of a stock having rate of return more than 12% is 0.1587.

Now define a random variable <em>Y</em> as the number of stocks that has rate of return more than 12%.

The sample size of stocks selected is, <em>n</em> = 5.

The random variable <em>Y </em>follows a Binomial distribution.

The probability of a Binomial distribution is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2, ...

Compute the value of P (X ≥ 2) as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

              =1-{5\choose 0}(0.1587)^{0}(1-0.1587)^{5-0}-{5\choose 1}(0.1587)^{1}(1-0.1587)^{5-1}\\=1-0.4215-0.3975\\=0.1810

Thus, the probability that at least two stocks will have a return of more than 12% is 0.1810.

6 0
3 years ago
A shipment of 105 Otter box covers for I-phones has arrived. The total invoice (excluding tax, shipping, etc.) is $3,849.75.
bezimeni [28]
<span>3,849.75 </span>÷ 49.95 = 77 (Calculator)

Sense you would like it explained than the question is asking how many otter box Defender Covers where shipped in that price. So when you have that they want the amount of Otter Box Defenders than you divide the amount paid for the shipment with the amount of the otter box defender price.

I hope this is helpful.
3 0
3 years ago
What is a b c in 3x^2+4=5x
____ [38]

Answer:

a =3

b = -5

c = 4

Step-by-step explanation:

3x^2+4=5x

Subtract 5x from each side

3x^2-5x+4=5x-5x

3x^2-5x+4=0

The equation is in the form

ax^2 +bx+c =0

a =3

b = -5

c = 4

5 0
3 years ago
How many helmets must the company make and sell to break even? helmets
klio [65]

The sale the company must make and sell to break even is;

B=600

<h3>How many helmets must the company make and sell to break even?</h3>

Generally, the equation for the break even  is mathematically given as

In conclusion

B=y vertex/price of each

Therefore

B=15600/26

B=600

In conclusion, the company's  break even is

B=600

CQ

A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a  y-intercept of 8,400 and a vertex of (500, 15,900). How many helmets must the company make and sell to break even?

Read more about Arithmetic

brainly.com/question/22568180

#SPJ4

8 0
1 year ago
Read 2 more answers
The unit rate of 55 and 8
Hoochie [10]
55/8 or 55:8 will be the unit rate I think
4 0
2 years ago
Read 2 more answers
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