2) 200 mL
3) 0.2 kg
Step-by-step explanation:
2)
In this problem, we know that:
- With 1 liter of juice, we can fill a total of 5 cups
So we know that the total volume of 5 cups is equal to
V = 1 L
This means that the volume of each cup is equal to the total volume divided by the number of cups (5), therefore:
And keeping in mind the equivalence between liters and milliliters:
1 L = 1000 mL
This means that the capacity of each cup is
3)
Here we want to find the mass contained in each cup.
We know that the mass of a substance is related to each volume by the equation
where
d is the density
m is the mass
V is the volume
In this problem, we have:
V = 0.2 L is the volume of juice in each cup
is the density of juice (assuming it is the same as the density of water)
So, the mass of juice in one cup is:
R = m - v + 2, where r = faces, v = vertices, and m = edges
r = 28 - 13 + 2
r = 15 + 2
r = 17, so the first answer is correct.
7. The surface area of a cone is A = pi*r*sqrt(r^2 + H^2)
A = pi*(7)(sqrt(49 + 1849)
A = pi*(7)(43.57)
A = pi*305 = 959 m^2, so the first answer is correct.
13. The volume of the slab is V = HLW
V = (5 yards)(5 yards)(1/12 yards)
V = 25/12 cubic yards
So it costs $46.00*(25/12) = $95.83 of total concrete. The third answer is correct.
21. First, find the volume of the rectangular prism. V = HLW
V = (15 cm)(5 cm)(7 cm)
V = 525 cm^3
Next, find the volume of the pyramid. V = 1/3(BH), where H is the height of the pyramid and B is the area of the base of the pyramid. Note that B = (15 cm)(5 cm) = 75 cm^2
V = (1/3)(75 cm^2)(13 cm)
V = 325 cm^3
Add the two volumes together, the total volume is 850 cm^3. The fourth answer is correct.
22. The volume of a square pyramid is V = 1/3(S^2)(H), where S is the side length and H is the height.
V = (1/3)(20^2 in^2)(21 in)
V = 2800 in^3
Now that we know the volume of this pyramid, and that both pyramids have equal volume, we plugin our V to the equation for the volume.
2800 = (1/3)(84)(S^2)
2800 = 28S^2
100 = S^2
<span>
10 in = S, so we have a side length of 10 in, and the first answer is correct. </span>
Recall that
d/dx sech(x) = - sech(x) tanh(x)
d/dx tan⁻¹(x) = 1/(1 + x²)
Then by the chain rule,
dy/dx = - sech(x) tanh(x) / (1 + x²)
1000/7 = <span>142.857142857
Because this is not an even number we take "142", then times it by 7 teachers.
142*7= 994
1000 - 994 = 6 Pencils left</span>
The answer is: [D]: " 2.6 " .
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Given: a = - 2.6 ; What is the value of "-a "?
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So, what is the value of " - (-2.6)" ?
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The opposite of a negative is a positive;
so, " - (-2.6) = 2.6 " ; which is: "Answer choice: [D] " .
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