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Harrizon [31]
3 years ago
14

The larger of two numbers is one more than twice the smaller. Four times the larger is the same as less than nine times the smal

ler. What's the larger number
Mathematics
1 answer:
Lostsunrise [7]3 years ago
4 0

Answer:

9

Step-by-step explanation:

Let larger number be L

and

smaller number be S

The larger is 1 more than twice smaller, so we can write:

L = 1 + 2S

4 times larger is 9 times smaller, so we can write:

4L = 9S

Let's put 1st equation in 2nd and solve for S first:

4L = 9S

4(1 + 2S) = 9S

4 + 8S = 9S

S = 4

Now,

L = 1 + 2S

L = 1 + 2(4)

L = 9

The larger number is, thus, equal to 9

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You decide to work part-time at a local veterinary hospital. The job pays $9.50 per hour and you work 20 hours per week. Your em
nadezda [96]

Answer:

a. Weekly Gross pay:

= 9.50 * 20

= $190

b. Federal tax withheld:

= 10% * 190

= $19

c. FICA Tax withheld:

= 5.65% * 190

= $10.74

d. State tax withheld:

= 5% * 190

= $9.50

e. Weekly net pay

= Gross pay - taxes

= 190 - 19 - 10.74 - 9.50

= $150.76

f. Percentage withheld for taxes:

= (19 + 10.74 + 9.50) / 190 * 100%

= 20.7%

8 0
2 years ago
Factor x^4 + x y^3 + x^3 + y^3 completely. Show your work.
andrey2020 [161]
\bf x^4+xy^3+x^3+y^3\impliedby \textit{now let's do some grouping}
\\\\\\
(x^4+xy^3)~~+~~(x^3+y^3)\implies x(x^3+y^3)~~+~~(x^3+y^3)
\\\\\\
\stackrel{\stackrel{common}{factor}}{(x^3+y^3)}(x+1)\\\\
-------------------------------\\\\
\textit{now recall that }\qquad \qquad \textit{difference of cubes}
\\ \quad \\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
a^3-b^3 = (a-b)(a^2+ab+b^2)\\\\
-------------------------------\\\\
(x+y)(x^2-xy+y^2)(x+1)
5 0
3 years ago
A quiz in statistics course has four multiple-choice questions, each with five possible answers. A passing grade is three or mor
nekit [7.7K]

Answer:

a) 0.0016

b) 0.0224

Step-by-step explanation:

If every question has 5 possible answers, the probability of getting the correct answer by guessing would be 0.20. The probability of getting an incorrect answer would be 0.80.

a)Find the probability she lucks out and answers all four questions correctly.

To do this, Allison would have to guess right the first, second, third AND fourth answers. Therefore, we have to multiply the probabilities:

0.20 x 0.20 x 0.20 x 0.20 = 0.0016

The probability that she answers all 4 questions correctly is 0.0016.

b) Find the probability that she passes the quiz.

To pass the quiz, she has to have three OR 4 correct answers:

  1. The probability that she has 3 correct answers is: 0.20 x 0.20 x 0.20 x 0.80 (since she has to have 1 correct answer and 1 incorrect one) = .0064.
  2. We already calculated the probability that she guesses 4 answers correctly: 0.0016.

Now, we have to sum up these two scenarios:

0.0064 + 0.016 = 0.0224.

Thus, the probability that she passes the quiz is 0.0224

3 0
3 years ago
Factor.
Blababa [14]

Answer:

Step-by-step explanation:

Are these the only choices?

A would equal 5x^2-32xi+64

B would equal 25x^2-6561

c would equal 25x^2+1024

D would equal 64x^2+25

If there is an option for (5x+8i)(5x-8i) this would be the answer

8 0
2 years ago
Estimate 43% of 117. (2 points)<br> Show your work to
finlep [7]

Answer:

Let's say 50

Step-by-step explanation:

40% of 100 is 40

50% of 117 is about 59

so number should be a somewhere in between.

8 0
2 years ago
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