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Umnica [9.8K]
2 years ago
11

Alison is buying binders for school. Small binders cost $3 each, and large binders cost $5 each. If Alison needs to buy at least

12 binders and has no more than $45 to spend, what is the maximum number of large binders she can buy?
a. 4

b 5

c 8

d 9
Mathematics
2 answers:
prisoha [69]2 years ago
8 0

Answer:

4 large folders     ( and 8 small folders....with $ 1 left over)

Step-by-step explanation:

x = small    y = large folders

x+y >= 12      x >=<u> 12-y </u>

3x + 5y <= 45

3 (12-y) + 5y <=45

36 -3y + 5y <= 45

    y <= 4.5               you cannot buy .5 of a large folder, so <u>4 large folders</u>

Mariulka [41]2 years ago
4 0

Answer:

9

Step-by-step explanation:

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Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$
Anna [14]

Answer:

\large\boxed{1\dfrac{1}{3}\ u^2}

Step-by-step explanation:

Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).

Let's calculate the common points:

x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1

The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.

We have integrals:

\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}

6 0
3 years ago
Find y: y − 4 = 6<br> A. 4<br> B. 10<br> C. 2<br> D. 6
aleksandrvk [35]

Answer:

Correct Answer is B

Step-by-step explanation:

y-4=6

+4. +4

y=10

7 0
2 years ago
Read 2 more answers
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gizmo_the_mogwai [7]
It is 0.53 hope this helps you.
7 0
3 years ago
Read 2 more answers
A farmer harvested some of his pecan crops on Friday and Saturday.what fraction of the pecan crop was harvested in two days
Sloan [31]

Answer:

Hence the 3.28 %or 2/61  of total work will be done .

Step-by-step explanation:

Given:

The pecan crops are harvested for  friday and saturday (2days)

To find :

What fraction these 2 days corresponds to the harvesting days?

Solution;

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and consider that in months of October and November  pecan crop becomes mature .

Hence the harvesting period is of 2 months considerably .

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Hence the Total days  of harvesting are 61 days.

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Now the farmer harvest for 2 days only .

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Depending upon the crop field and planting answer will vary

But 3.28 % of total work will be done in 2 days on harvesting

8 0
3 years ago
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Vesnalui [34]
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6 0
3 years ago
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