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3 years ago

9

Jenny’s Gift Shop sells candles in a variety of packages. The cost per candle is the same in every package. A package of 8 candl

es costs $12.96. Determine the cost of a package of 3 candles.

1 answer:

charle [14.2K]3 years ago

4 0

Answer:

8 candle = $12.96

1 candle =($12.96/8)

= $1.62

package of 3 candles =3×$(1.62)

: =$4.86

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A bag contains 4 blue marbles and 2 yellow marbles. Two marbles are randomly chosen (the first marble is NOT replaced before dra

VMariaS [17]

Answer:

0.4 = 40% probability that both marbles are blue.

0.0667 = 6.67% probability that both marbles are yellow.

53.33% probability of one blue and then one yellow

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

Step-by-step explanation:

To solve this question, we need to understand conditional probability(for the final question) and the hypergeometric distribution(for the first three, because the balls are chosen without being replaced).

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

What is the probability that both marbles are blue?

4 + 2 = 6 total marbles, which means that $N = 6$

4 blue, which means that $k = 4$

Sample of 2, which means that $n = 2$

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,6,2,4) = \frac{C_{4,2}*C_{2,0}}{C_{6,2}} = 0.4$

0.4 = 40% probability that both marbles are blue

What is the probability that both marbles are yellow?

4 + 2 = 6 total marbles, which means that $N = 6$

2 yellow, which means that $k = 2$

Sample of 2, which means that $n = 2$

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,6,2,2) = \frac{C_{2,2}*C_{4,0}}{C_{6,2}} = 0.0667$

0.0667 = 6.67% probability that both marbles are yellow.

What is the probability of one blue and then one yellow?

Total is 100%.

Can be:

Both blue(40%)

Both yellow(6.67%)

One blue and one yellow(x%). So

40 + 6.67 + x = 100

x = 100 - 46.67

x = 53.33

53.33% probability of one blue and then one yellow.

If you are told that both selected marbles are the same color, what is the probability that both are blue?

Conditional probability.

Event A: Both same color

Event B: Both blue

Probability of both being same color:

Both blue(40%)

Both yellow(6.67%)

This means that $P(A) = 0.4 + 0.0667 = 0.4667$

Probability of both being the same color and blue:

40% probability that both are blue, which means that $P(A \cap B) = 0.4$

Desired probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.4667} = 0.8571$

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

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3 years ago

Jake wants to surprise his parents with a small anniversary party at their favorite restaurant.

ch4aika [34]

Answer:

16 people

Step-by-step explanation:

35.75 times 16 is 572, times 17 is 607.75, he only has 600 and he cant have a fraction of a person, so he can have 16 people

4 0

3 years ago

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Solve 3x + 7 > -x - 9. Show each step of your work.

Kruka [31]

Answer:

x > -4

Step-by-step explanation:

Inequalities like these are solved the same way equations are solved, except when multiplying both sides you flip the less than/greater than sign:

3x + 7 > -x -9

3x + 7 - 7 > -x -9 -7 Subtract 7 from both sides

3x > -x -16

3x + x > -x -16 + x add x to both sides

4x > -16

$\frac{4x}{4}$ > $\frac{-16}{4}$ divide both sides by 4

x > -4

In this case the inequality sign did not have to be flipped since we never multiply both sides by a negative number.

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3 years ago

If f(x) = -x + 5 and g(x) = x^2, what is (g*f)(-1)

sasho [114]

Answer:

6

Step-by-step explanation:

(g × f)(x) = g(x) × f(x) = x²(- x + 5)

To evaluate (g × f)(- 1) substitute x = - 1 into the product

x²(- x + 5)

= (- 1)²(- (- 1) + 5)

= 1(1 + 5)

= 1 × 6 = 6

5 0

3 years ago

Find the equation of the line shown

yuradex [85]

Answer:

$y = 2x - 1$

Step-by-step explanation:

The line shown is a straight line its equation is of the form.

$y = mx + c$

Where m is the slope and c is the y-intercept.

From the graph, the slope is

$m = \frac{rise}{run}$

$m = \frac{2}{1} = 2$

The y-intercept from the graph is where the line intersects the y-axis, so c=-1

We substitute the values to get:

$y = 2x - 1$

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3 years ago