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2 years ago

A store sells a package of 25 trading cards for 5.25. What is the cost of one trading card

Mathematics

2 answers:

Reil [10]2 years ago

8 0

Answer:

21 cents

Step-by-step explanation:

25 (number of cards)

5.25 (price)

5.25/25=price per card, which equals .21

andreev551 [17]2 years ago

5 0

Answer: 21 cents

Step-by-step explanation:

25 trading cards, for $5.25

5.25 ÷ 25 = 0.21

The cost of one trading card is 21 cents.

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From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh

Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

Step-by-step explanation:

Volume = height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V= 4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so, 4 (3x² - 60x +225)=0

3x² - 60x+225=0 (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5 (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

7 0

3 years ago

Sin 75°(cot 75° + cot 60°)<br><br>help me simplify this

leva [86]

(square root of 6)/ 3

7 0

2 years ago

Charlotte has been working for her company for x years. Travis has been working for the same company exactly 3 years longer than

shtirl [24]

Question:

Charlotte has been working for her company for x years. Travis has been working for the same company exactly 3 years longer than Charlotte. What is the range of the relationship?

A- y>0

B- y>3

C. y<3

D. 0

Answer:

y > 3

Step-by-step explanation:

Number of years Charlotte has worked = x

Number of years Travis has worked = y. ie, y = 3+x

Let's assume the function reaches its lowest point at 3. There could also be a higher value for this function.

We now have:

f(x) = y > 3

Since Travis has been working for the same company exactly 3 years longer than Charlotte the range of the relationship is y>3

5 0

3 years ago

An art history professor assigns letter grades on a test according to the following scheme.A: Top 5% of scoresB: Scores below th

adoni [48]

Answer:

Grade B score:

$76 \leq x \leq 89$

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 73.3

Standard Deviation, σ = 9.7

We are given that the distribution of score on test is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

B: Scores below the top 5% and above the bottom 62%

We have to find the value of x such that the probability is 0.62

$P( X > x) = P( z > \displaystyle\frac{x - 73.3}{9.7})=0.62$

$= 1 -P( z \leq \displaystyle\frac{x - 73.3}{9.7})=0.62$

$=P( z \leq \displaystyle\frac{x - 73.3}{9.7})=0.38$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 73.3}{9.7} = 0.305\\\\x = 76.26$

We have to find the value of x such that the probability is 0.05

$P(X < 0.95) = \\\\P( X < x) = P( z < \displaystyle\frac{x - 73.3}{9.7})=0.95$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 73.3}{9.7} = 1.645\\\\x = 89.26$

Thus, the numerical value of score to achieve grade B is

$76 \leq x \leq 89$

7 0

3 years ago

The question is asking to determine which statement is true?

Advocard [28]

Answer:

the answer is true which

7 0

2 years ago