For what values of them will the expression below be a perfect square? 9x^2+30x+m

1. Ruth Lockwood earns $2,917 a month as a supervisor for Acme

soldi70 [24.7K]

Answer:

a. 25%

b. $1560

c. $130

Step-by-step explanation:

a.

If 75% is paid by company, the rest is paid by Ruth.

Out of 100%, 75% is paid by company, so Ruth pays 100 - 75 = 25%

b.

Per year, the total amount paid is 6240, but Ruth pas 25% of this. So,

25% = 0.25

To get the answer, we multiply 0.25 with 6240.

0.25 * 6240 = 1560

So, $1560 is paid by Ruth annually.

c.

Since 1560 is paid annually (in 12 months), each month Ruth has to pay:

1560/12 = $130

Hence, $130 is deducted each month from her paycheck

6 0

3 years ago

Emily has nickels and quarters. She has 3 fewer

lawyer [7]

Answer:

Step-by-step explanation:

she has 3 quarters

4 0

3 years ago

Consider the equation 2(ax+3)=4x−3(4x+8). For what value of a is there no solution to the equation?

erastovalidia [21]

Answer:

the value of $a$ such that there is no solution to the equation is $a = -4$ .

Step-by-step explanation:

Let first simplify the expression presented on statement. The equation has no solution if and only if $a$ is eliminated in the process and an absurd is the result (i.e. $0 = 7$ ).

$2\cdot (a\cdot x + 3) = 4\cdot x -3\cdot (4\cdot x + 8)$

$2\cdot a\cdot x +6 = 4\cdot x -12\cdot x -24$

$2\cdot a \cdot x+6=-8\cdot x-24$

$2\cdot a\cdot x +8\cdot x = -30$

$2\cdot (a+4)\cdot x = -30$

$(a+4)\cdot x = -15$

To obtain an absurd, we need that $a+4 = 0$ . Hence, the value of $a$ such that there is no solution to the equation is:

$a = -4$

Let prove the certainty of the result. We find that an absurd exist: ( $a = -4$ )

$0 = -15$

5 0

3 years ago

Area of the polygon below

Dimas [21]

24×(23-7)+7×10=454u²

4 0

3 years ago

A company that produces fine crystal knows from experience that 13% of its goblets have cosmetic flaws and must be classified as

Kisachek [45]

Answer:

(a) The probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b) The probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c) The probability that at most five must be selected to find four that are not seconds is 0.9453.

Step-by-step explanation:

Let X = number of seconds in the batch.

The probability of the random variable X is, p = 0.31.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...$

(a)

Compute the probability that only one goblet is a second among six randomly selected goblets as follows:

$P(X=1)={6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=6\times 0.13\times 0.4984\\=0.3888$

Thus, the probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b)

Compute the probability that at least two goblet is a second among six randomly selected goblets as follows:

P (X ≥ 2) = 1 - P (X < 2)

$=1-{6\choose 0}0.13^{0}(1-0.13)^{6-0}-{6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=1-0.4336+0.3888\\=0.1776$

Thus, the probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c)

If goblets are examined one by one then to find four that are not seconds we need to select either 4 goblets that are not seconds or 5 goblets including only 1 second.

P (4 not seconds) = P (X = 0; n = 4) + P (X = 1; n = 5)

$={4\choose 0}0.13^{0}(1-0.13)^{4-0}+{5\choose 1}0.13^{1}(1-0.13)^{5-1}\\=0.5729+0.3724\\=0.9453$

Thus, the probability that at most five must be selected to find four that are not seconds is 0.9453.

8 0

3 years ago