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myrzilka [38]
3 years ago
8

2

Mathematics
1 answer:
Tju [1.3M]3 years ago
8 0

Answer:

<em>x + y ≤ 40</em>

<em>10x + 12 y ≥ 400</em>

<em>x ≥ 0</em>

<em>y ≥ 0</em>

Step-by-step explanation:

<u>System of Inequalities</u>

In order to model the situation stated in the problem, we'll call the following variables:

x = number of hours Sarah spends in the office

y = number of hours Sarah spends babysitting

She works for a maximum of 40 hours per week. This condition leads us to the inequality:

x + y ≤ 40

Her office job pays $12 per hour and her babysitting job pays $10 per hour.

She needs to make at least $400 per week in order to cover her expenses, thus:

10x + 12 y ≥ 400

Two obvious conditions could be added to the set of inequalities:

x ≥ 0

y ≥ 0

The system of inequalities is:

x + y ≤ 40

10x + 12 y ≥ 400

x ≥ 0

y ≥ 0

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Peter, Jan, and Maxim are classmates. Their total score for the last test was 269. Peter's score was more than the sum of Jan's
Goshia [24]

Answer:

135

Step-by-step explanation:

Given that :

Total score obtained by Peter, Jan and Maxim = 269

Let :

Peter's score = x

Jan's score = y

Maxim's score = z

x + y + z = 269

x > (y + z)

For x to be greater Than y + z ;

Then x > (269 / 2) ; x > 134.5

The least possible x score is 135

Hence, Peter's least possible score is 135.

5 0
3 years ago
Could someone solve this for me.
Studentka2010 [4]
The answer is 7.6 units
5 0
2 years ago
what is the equation of a line that passes through the point (1,3) and is parallel to a line with a slope of -2?
natta225 [31]

Answer:

Step-by-step explanation:

y - 3 = -2(x - 1)

y - 3 = -2x + 2

y = -2x + 5

3 0
3 years ago
In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that
attashe74 [19]

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let <em>X</em> = number of soldiers killed by horse kicks in 1 year.

The random variable X\sim Poisson(\lambda = 0.62).

The probability function of a Poisson distribution is:

P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,...

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

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

             =1-\frac{e^{-0.62}(0.62)^{0}}{0!}-\frac{e^{-0.62}(0.62)^{1}}{1!}\\=1-0.54335-0.33144\\=0.12521\\\approx0.1252

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: \lambda=7\times0.62=4.34

Compute the probability of no deaths in a corps over 7 years as follows:

P(X=0)=\frac{e^{-4.34}(4.34)^{0}}{0!}=0.01304\approx0.0130

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

6 0
3 years ago
A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the res
julia-pushkina [17]

Money earned by restaurant on Friday=$1073

Money earned by restaurant on Saturday=$1108

Let Money earned by restaurant on Sunday=$x

Average=$1000

\text { average}=\frac  { sum of all the observation}{total number of observation}

Number of observation=3

                           ⇒  3×  1000=1073+1108+x

                            ⇒3000=     2 181+x

                              ⇒3000-2181=x

                            ⇒x=819

The restaurant needs to earn on Sunday to average $1000 per day over the three-day period=$819


6 0
3 years ago
Read 2 more answers
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