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3 years ago

6

Jonah is going to the store to buy candles. Small candles cost $3.50 and large candles cost$5.00. He needs to buy at least 20 ca

ndles, and he can spend no more than $80.

1 answer:

mezya [45]3 years ago

3 0

He can buy 21 candels

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Find the probability that the person is frequently or occasionally involved in charity work.

Schach [20]

Given the table below which shows the result of a survey that asked 2,881 people whether they are involved in any type of charity work.

$\begin{tabular}
{|c|c|c|c|c|c|}
 &Frequently&Occassionally&Not at all&Total\\[1ex]
Male&227&454&798&1,479\\
Female &205&450&747&1,402\\
Total&432&904&1,545&2,881
\end{tabular}$

Part A:

If a person is chosen at random, the probability that the person is frequently or occassinally involved in charity work is given by

$P(being \ frequently \ involved \ or \ being \ occassionally \ involved)\\ \\= \frac{432}{2881} + \frac{904}{2881} = \frac{1336}{2881}=\bold{0.464}$

Part B:

If a person is chosen at random, the probability that the person is female or not involved in charity work at all is given by

$P(being
 \ female \ or \ not \ being \ involved)\\ \\= 
\frac{1402}{2881} + \frac{1545}{2881}-\frac{747}{2881} = 
\frac{2200}{2881}=\bold{0.764}$

Part C:

If a person is chosen at random, the probability that the person is male or frequently involved in charity work is given by

$P(being
 \ male \ or \ being \ frequently \ involved)\\ \\= 
\frac{1479}{2881} + \frac{432}{2881}-\frac{227}{2881} = 
\frac{1684}{2881}=\bold{0.585}$

Part D:

If a person is chosen at random, the probability that the person is female or not frequently involved in charity work is given by

$P(being
 \ female \ or \ not \ being \ frequently \ involved)\\ \\= 
\frac{1402}{2881} + \frac{904}{2881} + \frac{1545}{2881}-\frac{450}{2881}-\frac{747}{2881} = 
\frac{2654}{2881}=\bold{0.921}$

Part E:

The events "being female" and "being frequently involved in charity work" are not mutually exclusive because being a female does not prevent a person from being frequently involved in charity work.

Indeed from the table, there are 205 females who are frequently involved in charity work.

Therefore, the answer to the question is "No, because 205 females are frequently involved charity work".

4 0

2 years ago

Let $a$ and $b$ be nonzero real numbers such that

algol [13]

<h3>Answer: -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

4 0

1 year ago

Express as a difference: a+b, a+5

Tcecarenko [31]

Answer:

a - (-b), a - (-5)

Step-by-step explanation:

A double negative negative is a positive, so a - (-b) = a + b, and a - (-5) is a + 5. However, a double negative is still a difference, so this answer works.

6 0

2 years ago

Which value of x makes the equation 0.5(x + 16) = 3 + 0.25(x – 4) true?

Fynjy0 [20]

Answer:it is confusing

Step-by-step explanation:

5 0

3 years ago

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

8_murik_8 [283]

Hey!

-----------------------------------------------

Solution:

= -2.1 + 0.3 + -1.7 + -0.4

= -1.8 + -1.7 + -0.4

= -3.5 + -0.4

= -3.9

-----------------------------------------------

Answer:

a) -3.9

-----------------------------------------------

Hope This Helped! Good Luck!

5 0

2 years ago