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2 years ago

Each week, Darin's Lawn Service mows 90 lawns in 45 hours at a housing c

Mathematics

1 answer:

sweet [91]2 years ago

4 0

9514 1404 393

Answer:

6 h

Step-by-step explanation:

The bottom number in the table is half the top number. The missing value is 6 (hours).

I like to put the variable in the numerator of a proportion. Here, we can write it as ...

t/12 = 45/90

Multiplying by 12 gives ...

t = 12(45/90) = 12(1/2) = 6

It will take Darin 6 hours to mow 12 lawns.

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Y=-3x+6 and y=5x-2 for y

andriy [413]

Answer:

The first one is x=2 and the second one is x=2/5 or 0.4

Step-by-step explanation:

4 0

3 years ago

How does the Binomial Theorem’s use Pascal’s triangle to expand binomials raised to positive integer powers?

MrMuchimi

Answer:

There are ways for quickly multiply out a binomial that's being raised by an exponent. Like

(a + b)0 = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = (a + b)(a + b)2 = (a + b)(a2 + 2ab + b2) = a3 + 3a2b + 3ab2 + b3

and so on and so on

but there was this mathematician named Blaise Pascal and he found a numerical pattern, called Pascal's Triangle, for quickly expanding a binomial like the ones from earlier. It looks like this

1 1

2 1 2 1

3 1 3 3 1

4 1 4 6 4 1

5 1 5 10 10 5 1

Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)n, where n is the row of the triangle.

Hope this helps!

5 0

2 years ago

Assume that a policyholder is four times more likely to file exactly two claims as to file exactly three claims. Assume also tha

kykrilka [37]

Answer:

1.3125

Step-by-step explanation:

Given that our random variable $X$ follows a Poisson distribution $P(X=k)=\frac{\lambda^k e^-^p}{k!} \ \ \ \ \ \ \ \ p=\lambda$

Evaluate the formula at $k=2,3:$

$P(X=2)=0.5\lambda^2e^{-\lambda}\\\\P(X=3)=\frac{1}{6}\lambda^2e^{-\lambda}$

#since

$4P(X=2)=P(X=3);\\\\0.5\lambda^2e^{-\lambda}=4\times\frac{1}{6}\lambda^3e^{-\lambda}\\\\0.5\lambda^2=\frac{2}{3}\lambda^3\\\\0.75=\lambda$

The mean and variance of the Poisson distributed random variable is equal to $\lambda$ :

$\mu=\lambda=0.75\\\sigma ^2=\lambda=0.75$

#By property variance:

$\sigma ^2=V(X)=E(X^2)-(E(X))^2=E(X^2)\\\\E(X^2)=\sigma^2+\mu^2=0.75+0.75^2=1.3125$

The expectation is 1.3125

4 0

3 years ago

The area of a soccer field is ( 24x^2 + 100x + 100) m^2. The width of the field is (4x + 10)m. What is the length?

Firdavs [7]

The answer should be (12x + 20) (2x + 5)

4 0

3 years ago

Eric and Linda are paid 52.25 for they're work. Eric worked 3.5 hours, and Linda worked 2 hours. They split the money according

Ne4ueva [31]

Answer:

$33.25

Step-by-step explanation:

Taking Eric's hours as a ratio to the total hours :

3.5 : 3.5 + 2
3.5 : 5.5
3.5 x 2 = : 5.5 x 2
7 : 11

Multiply the ratio into the amount paid :

52.25 x 7/11
4.75 x 7
$33.25

Eric's share of the money is $33.25

4 0

2 years ago

Read 2 more answers