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Nataly_w
2 months ago
10

Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppin

gs from a list of hot fudge, strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find B'.
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
{vanilla, hot fudge, sprinkles, whipped cream}
{chocolate, strawberries, peanuts}
{chocolate, strawberries}
{vanilla, strawberries, peanuts}
Mathematics
1 answer:
zzz [12.3K]2 months ago
4 0
{chocolate, strawberries, peanuts} Explanation: Given three sets, let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}, let B = {vanilla, hot fudge, sprinkles, whipped cream}, and let C = {chocolate, hot fudge, peanuts, whipped cream}. Thus, the universal set U = A ∪ B ∪ C = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}. B' consists of the elements found in U but not in B, which results in: {chocolate, strawberries, peanuts}.
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An investment of $7,650 earns interest at the rate of 5% and is compounded quarterly. What is the accumulated value of the inves
zzz [12365]
FV = P(1 + r/t)^nt, where P denotes the principal amount, r is the interest rate, t is the frequency of compounding per year, and n is the total number of years.

Calculating: FV = 7650(1 + 0.05/4)^(9 x 4) = 7650(1 + 0.0125)^36 = 7650(1.0125)^36 = 7650(1.564) = $11,964.17

8 0
3 months ago
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One similar figure has an area that is nine times the area of another. The larger figure must have dimensions that are times the
Svet_ta [12734]
T<span>he area of a figure signifies the measure of space within a two-dimensional shape, typically expressed as square units based on the figure's dimensions.

For instance, with a shape having dimensions of k, its area can be given by k^2.
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<span>Consider that one similar figure possesses an area nine times that of another.

As these figures are similar, their areas correspond to the proportionality of their dimensions.

Let the smaller shape's dimensions be k, while the larger is p times the dimensions of the smaller shape. The smaller shape's area is k^2 and the larger shape's area is (pk)^2.

Now, knowing the larger figure's area is nine times the area of the smaller figure, we have:
\frac{(pk)^2}{k^2} = \frac{9}{1} \\ \\ \frac{p^2k^2}{k^2} =9 \\ \\ p^2=9 \\ \\ p= \sqrt{9} \\ \\ p=3
</span>
Thus, the dimensions of the larger figure must be 3 times those of the smaller figure.
3 0
1 month ago
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What is the product? (5r − 4)(r2 − 6r + 4)
Zina [12379]
(5r - 4)(r² - 6r + 4)

uses the distributive property for multiplication.

This expands to 5r(r² - 6r + 4) - 4(r² - 6r + 4)
which results in 5r³ - 30r² + 20r - 4r² + 24r - 16

as you combine like terms and simplify.

The outcome is 5r³ - 30r² - 4r² + 20r + 24r - 16

leading to a final expression of 5r³ - 34r² + 44r - 16. Choice A.
5 0
2 months ago
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