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Diano4ka-milaya [45]
2 years ago
3

Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wa

nts the number of pencils to be greater than or equal to the square of 3 less than the number of pens. Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Mathematics
1 answer:
pav-90 [236]2 years ago
6 0
Let <em>x</em> be the number of pens she buys and <em>y</em> be the number of pencils she buys.  Our first inequality is
<em>x</em> + <em>y</em> ≤ 25.  When we graph this, it might be helpful to have <em>y</em> isolated.  To do this, subtract <em>x</em> from both sides:
<em>x</em> + <em>y</em> - <em>x</em> ≤ 25 - <em>x</em>
<em>y</em> ≤ 25 - <em>x</em>
Our second inequality is
<em>y</em> ≥ (<em>x</em> - 3)²
This is the same as <em>y</em> ≥ (<em>x</em> - 3)(<em>x</em> - 3); multiplying we have <em /><em>y</em> ≥ <em>x</em>² - 3<em>x</em> - 3<em>x</em> + 9 or <em>y</em> ≥ <em>x</em>² - 6<em>x</em> + 9.
Graphing these in the graphing calculator will give you the graph pictured in the screenshots.  We can see that the minimum value for <em>x</em> (pens) would have to be 0, in which case she could purchase 25 pencils.  The maximum value for <em>x</em> that works would be 7, in which case she could purchase 18 pencils.

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A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical
Korolek [52]

Answer:

78% probability that a randomly selected online customer does not live within 50 miles of a physical​ store.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Total outcomes:

100 customers

Desired outcomes:

A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. So the number of desired outcomes is 78 customers.

Using this​ estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical​ store?

p = \frac{78}{100} = 0.78

78% probability that a randomly selected online customer does not live within 50 miles of a physical​ store.

4 0
2 years ago
What are the coordinates of vertex J of the pre-image?(14 POINTS. PLS HELP, GEOMETRY)
DaniilM [7]
If we look at where it is now, we would have multiplied the x and y values by 1/2. since we are working backwards, lets multiply by 2 instead...giving us the vertex for the pre-image....

J is now (0, -2)      multiply by 2
J was     (0, -4)
5 0
2 years ago
Read 2 more answers
You have a function that takes in an X value and produces a Y value. The Y value equals 24 times the X value, plus 4?More. What'
guapka [62]

Answer:

100

Step-by-step explanation:

The function takes in an X value and produces a Y value.

The Y value equals 24 times the X value plus 4 more.

This means that:

Y = 24X + 4

When the X value equals 4, the Y value will be:

Y = 24(4) + 4

Y = 96 + 4

Y = 100

When the X value is 4, the Y value is 100.

7 1
2 years ago
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The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2
dangina [55]

Answer:

irrational

Step-by-step explanation:

A = s^2

s^2 = 24,200

s = \sqrt{24200}

s = \sqrt{242 \times 100}

s = \sqrt{100 \times 121 \times 2}

s = 10 \times 11\sqrt{2}

s = 110\sqrt{2}

P = 4s

P = 4 \times 100 \sqrt{2}

P = 440 \sqrt{2}

The perimeter is irrational.

3 0
2 years ago
You save $5,000.00 and invest 60% of it in stocks while leaving the rest in a savings account earning a 4.9% APR. The stock incr
Angelina_Jolie [31]

Answer:

5,340

Step-by-step explanation:

Hi there:)

Amount invested in stock

=5000×0.6=3000

Amount invested in a saving account

5000-3000=2000


The stock increases 9% in the first year

3,000×(1+0.09)=3,270

and loses 4% of its value the second year

3,270×(1−0.04)=3,139.2

Amount of a saving account after two years

2,000×(1+0.049)^(2)=2,200.8


the total amount gained during the 2 years

3,139.2+2,200.8=5,340...answer


Hope it helps




8 0
2 years ago
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