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Damm [24]
3 years ago
14

Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for

$1.10/lb. How many pounds of lollipops are in the mixture?
Mathematics
1 answer:
dimulka [17.4K]3 years ago
4 0
L = pounds of lollipop
c = pounds of caramel candies

0.95l + 1.10c = 30 ($0.95/lb & $1.10/lb)
l + c = 30 (mixture sells for $1/lb)
c = 30 - l

0.95l + 1.10(30 - l) = 30 (Substitution)
0.95l + 33 - 1.10l = 30
-0.15l = -3 (move terms)
l = 20lbs

Hope this helps.
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A and b are positive integers and a-b=2. Evaluate the following:<br> 9^1/2b/3^a
OlgaM077 [116]

Answer:

\frac{1}{ 9 }

Step-by-step explanation:

\huge \frac{ {9}^{ \frac{1}{2}b } }{ {3}^{a} }  \\  \\  =  \huge \frac{ {( {3}^{2} )}^{ \frac{1}{2}b } }{ {3}^{a} } \\  \\  =  \huge \frac{ { {3}}^{2 \times  \frac{1}{2}b } }{ {3}^{a} }  \\  \\  \huge =  \frac{ {3}^{b} }{ {3}^{a} }  \\  \\  \huge =  \frac{1}{ {3}^{a - b} }  \\  \\   \huge=  \frac{1}{ {3}^{2} } \\  ( \because \: a - b = 2)\\  \\  \huge =  \frac{1}{ 9 }

5 0
3 years ago
The probability of tossing heads with a standard coin is 1/2, because it is one of two possible outcomes. The probability of tos
spayn [35]

Answer:

  a) 1/64

  b) 1/4096

Step-by-step explanation:

As you can tell from the example, the exponent of 1/2 is the number of heads in a row.

a) p(6 heads in a row) = (1/2)^6 = 1/(2^6) = 1/64

b) p(12 heads in a row) = (1/2)^12 = 1/(2^12) = 1/4096

_____

<em>Additional comment</em>

The probability of a head is 1/2 because we generally are concerned with a "fair coin." That is defined as a coin in which each of the 2 possible outcomes has the same probability, 1/2. Similarly, a "fair number cube" has 6 faces, and the probability of each is defined to be the same as any other, 1/6. Loaded dice and unfair coins do sometimes show up in probability problems.

3 0
2 years ago
Is 6.3 &gt; 6.04 reasonable yes or no Explain
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Answer:

Yes

Step-by-step explanation:

By rounding to the 10ths place, we can easily see that 6.3 is greater than 6.04. 6.3 is already rounded to the 10ths place, but 6.04 rounded to the 10ths place is 6.0.

6.3 is clearly more than 6.0, therefore 6.3 is greater than 6.04.

3 0
2 years ago
The business college computing center wants to determine the proportion of business students who have personal computers (PC's)
Anastasy [175]

Answer:

Option A) reject null hypothesis if z is greater than 1.645

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 250

p = 30% = 0.3

Alpha, α = 0.05

Number of women belonging to union , x = 75

First, we design the null and the alternate hypothesis  

H_{0}: p = 0.3\\H_A: p > 0.3

This is a one-tailed(right) test.

Rejection Region:

z_{critical} \text{ at 0.05 level of significance } = 1.645

So, the rejection region will be

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That is we will reject the null hypothesis if the calculated z-statistic is greater than 1.645

Option A) reject null hypothesis if z is greater than 1.645

6 0
3 years ago
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