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3 years ago

Choose all true statements.

Mathematics

2 answers:

gogolik [260]3 years ago

6 0

Answer:

B. Some rational numbers are natural numbers.

D. All whole numbers are integers.

E. Some integers are natural numbers.

Step-by-step explanation:

serious [3.7K]3 years ago

3 0

Answer:

Some rational numbers are natural numbers

All whole numbers are integers

Some integers are natural numbers.

Step-by-step explanation:

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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0

3 years ago

Four friends go to an amusement arcade.

galben [10]

Answer:

The rule is:

T(x) = 8x + 20

Explanation:

We are given that:

The rule for the amount that one friend pays is:

C(x) = 2x + 5

Now, we know that:

Each of the four friends will pay the entry fee which is $5 per person

The 4 friends will play the same number of games represented by x

This means that:

We can simply get the rule for the total amount to be paid by the four friends (T(x)) by multiplying the amount paid by each friend by 4

This means that:

T(x) = 4 * C(x)

T(x) = 4(2x + 5)

T(x) = 8x + 20

Hope this helps :)

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3 years ago

Jessica is asked to write a quadratic equation to represent a function that goes through the point (8, –11) and has a vertex at

Kitty [74]

Answer: c

Step-by-step explanation:

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3 years ago

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A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of

inessss [21]

That is an annuity and use the attached formula.

Total = 300 * [(1.055)^11 -1] / .055 -300
Total = 300 * 1.8020924036 -1 /.055 -300
Total = 300 * .8020924036 / .055 - 300
Total = 300 * 14.5834982473 -300
Total = 4375.0494741818 -300
Total = 4075.05

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3 years ago

Huang eats a salad for breakfact,a burger for lunch,then a saled for dinner.how many burger has Huang eaten if he had 71 salads

sweet [91]

35 because if you half the amount of salads he's eaten (seeing as he eats one burger for every two salads) then the extra one is the first salad in the cycle.

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