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ICE Princess25 [194]
3 years ago
14

Mr. Nelson has a class of 16 students. He can spend $22 on each student to buy math supplies for the year. He first buys all of

his students calculators, which costs a total of $117.76. After buying the calculators, how much does he have left to spend on each student?
Mathematics
2 answers:
Nuetrik [128]3 years ago
6 0

Answer:

$14.64

Step-by-step explanation:

First, find how much he spent on the calculators

Divide the amount spent on calculators by the number of students

calculator cost/students

117.76/16=7.36

So, he spent 7.36 on each student so far.

To find how much he still has left to spend, subtract the amount he has spent from the total he can spend

total-$ spent on calculators

22-7.36=14.64

He can still spend $14.64 on each student

Hope this helps! :)

Yuri [45]3 years ago
3 0
If he can spend $22 per student, that means he can spend a total of $352 when you multiply 22 times 16. Because he spent $117.76, that means he has a remainder of $234.24 to spend on his students. Because he has 16 students and needs to divide the money among them equally, 234.24/16 means there is $14.64 to spend on each student.
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Natali [406]
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8 0
3 years ago
The total number of people at a football game was 5600. Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.
rewona [7]

Answer:

1100 field-side tickets and 4500 end-zone tickets.

Step-by-step explanation:

Let x represent number of field side tickets and y represent number of end-zone tickets.

We have been given that the total number of people at a football game was 5600. We can represent this information in an equation as:

x+y=5600...(1)

y=5600-x...(1)    

We are also told that Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

Cost of x field side tickets would be 40x and cost of y end-zone tickets would be 20y.

The total amount of money received for the tickets was $134000. We can represent this information in an equation as:

40x+20y=134000...(2)

Upon substituting equation (1) in equation (2), we will get:

40x+20(5600-x)=134000

40x+112000-20x=134000

20x+112000=134000

20x+112000-112000=134000-112000

20x=22000

\frac{20x}{20}=\frac{22000}{20}

x=1100

Therefore, 1100 field side tickets were sold.

Upon substituting x=1100 in equation (1), we will get:

y=5600-1100

y=4500

Therefore, 4500 end-zone tickets were sold.

3 0
3 years ago
Kathy has $2 less than 3 times the amount of money jason has. Together, they have a total of $34. How much money does Kathy has?
Paul [167]
3j-2=34 Then add two to both sides 3j=36 Then divide three by both sides and get J=12
7 0
3 years ago
A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru
Viktor [21]

Answer:

1) S = 2\cdot w\cdot l - 8\cdot x^{2}, 2) The domain of S is 0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}. The range of S is 0 \leq S \leq 2\cdot w \cdot l, 3) S = 176\,in^{2}, 4) x \approx 4.528\,in, 5) S = 164.830\,in^{2}

Step-by-step explanation:

1) The function of the box is:

S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)

S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w

S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x

S = 2\cdot w\cdot l - 8\cdot x^{2}

2) The maximum cutout is:

2\cdot w \cdot l - 8\cdot x^{2} = 0

w\cdot l - 4\cdot x^{2} = 0

4\cdot x^{2} = w\cdot l

x = \frac{\sqrt{w\cdot l}}{2}

The domain of S is 0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}. The range of S is 0 \leq S \leq 2\cdot w \cdot l

3) The surface area when a 1'' x 1'' square is cut out is:

S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}

S = 176\,in^{2}

4) The size is found by solving the following second-order polynomial:

20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}

20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}

8\cdot x^{2} - 164\,in^{2} = 0

x \approx 4.528\,in

5) The equation of the box volume is:

V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x

V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x

V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}

V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}

V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}

The first derivative of the function is:

V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}

The critical points are determined by equalizing the derivative to zero:

12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0

x_{1} \approx 4.952\,in

x_{2}\approx 1.548\,in

The second derivative is found afterwards:

V'' = 24\cdot x - 78\,in

After evaluating each critical point, it follows that x_{1} is an absolute minimum and x_{2} is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

x \approx 1.548\,in

The surface area of the box is:

S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}

S = 164.830\,in^{2}

4 0
2 years ago
The tens digit is 2 less than the one's digit and the sum of the digits is 8
Basile [38]

it going to be 18 because the number is two less than ones digits and the sum of the digit is 8

4 0
2 years ago
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