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SCORPION-xisa [38]

3 years ago

8

The length of the table is 9 feet . Express the length in inches

2 answers:

a_sh-v [17]3 years ago

8 0

Answer:

The answer is 108 inches

Step-by-step explanation:

To convert feet to inches, we multiply the numbers of feet by 12, that is

1 ft = 12 inches

∴ 9 ft = 9×12 inches

= 108 inches

diamong [38]3 years ago

4 0

Answer:

the length of the table is 108 inches

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What do you mean?
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2 years ago

Which expression illustrates the associative property of addition? (3 19) – 12 = (3 12) – 19 3 (19 – 12) = 3 (19 12) (3 19) – 12

Gre4nikov [31]

Answer:

Associative Property

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1 year ago

As a financial consultant, the CFO of a major television company has shared the profit function P(x) = −x4 - 2x3 + 21x2 + 22x −

drek231 [11]

Answer:

The company will break even at x=1 and x=4.

Step-by-step explanation:

The given profit function is

$P(x)=-x^4-2x^3+21x^2+22x-40$

Where, x is number of commercials.

Use synthetic division or long division to find the factors of the function.

$P(x)=(x-1)(x^3+3x^2-18x-40)$

$P(x)=(x-1)(x+2)(x^2+x-20)$

$P(x) = -(x - 4) (x - 1) (x + 2) (x + 5)$

Equate P(x)=0, to find the break even points.

$-(x - 4) (x - 1) (x + 2) (x + 5)=0$

Use zero product property and equate each factor equal to zero.

$x=4,1,-2,-5$

Therefore the zeros of the function P(x) are 4, 1, -2 and -5. Since x is number of commercials, therefore the value of x must be positive. Therefore the company will break even at x=1 and x=4.

The higher degree of the function is even and the leading coefficient is negative. So,

$P(x)\rightarrow -\infty \text{ as }x\rightarrow \infty$

$P(x)\rightarrow -\infty \text{ as }x\rightarrow -\infty$

Since the value of x must be positive, therefore the left end point is y-intercept of the graph, i.e., (0,-40).

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The graph of the function is given below.

7 0

2 years ago

How many randomly chosen guests should I invite to my party so that the probability of having a guest with the same birthday as

dimulka [17.4K]

Answer:

At least 401 chosen guests

Step-by-step explanation:

Represent those with same birth day with Same

So:

$P(Same) > \frac{2}{3}$

Represent number of people with n

There are 365 days in a year and 364 days out of these days is not your birthday.

So, there the probability that n people do not share your birthday is $(\frac{364}{365})^n$

i.e.

$P(none) = (\frac{364}{365})^n$

Solving further, we have that:

$P(same) + P(none) = 1$

$P(same) + (\frac{364}{365})^n = 1$

$P(same) = 1 - (\frac{364}{365})^n$

We're calculating the probability that $P(Same) > \frac{2}{3}$ .

So, we have:

$1 - (\frac{364}{365})^n > \frac{2}{3}$

Collect Like Terms

$1 - \frac{2}{3}> (\frac{364}{365})^n$

$\frac{3-2}{3}> (\frac{364}{365})^n$

$\frac{1}{3}> (\frac{364}{365})^n$

$3^{-1} > (\frac{364}{365})^n$

Take natural logarithm (ln) of both sides

$ln(3^{-1}) > ln((\frac{364}{365})^n)$

$-ln\ 3 > n\ ln\ (\frac{364}{365})$

Apply laws of logarithm

$-ln\ 3 > n\ (ln(364) - ln(365))$

Multiply through by -1

$ln\ 3 < n\ (ln(365) - ln(364))$

Solve for n

$\frac{ln\ 3}{(ln(365) - ln(364))} < n$

Reorder

$n > \frac{ln\ 3}{(ln(365) - ln(364))}$

$n > \frac{1.09861228867}{(5.89989735358 - 5.89715386764)}$

$n> \frac{1.09861228867}{0.00274348594}$

$n > 400.443928891$

$n > 400$ (approximated)

This implies that n = 401, 402, 403 .....

i.e

$n \geq 401$

So, at least 401 people has to be invited

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3 years ago

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oksian1 [2.3K]

Answer:

m = $\frac{13}{3}$

Step-by-step explanation:

Given

$\frac{1}{12}$ = $\frac{m-4}{4}$ ( cross- multiply )

12(m - 4) = 4 ( divide both sides by 12 )

m - 4 = $\frac{4}{12}$ = $\frac{1}{3}$ ( add 4 to both sides )

m = 4 $\frac{1}{3}$ = $\frac{13}{3}$

7 0

2 years ago