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3 years ago

In solving the following problem for x, how do we get the bases to be the same? 2^x-4= 4

Mathematics

1 answer:

Gala2k [10]3 years ago

5 0

Answer:

2^x-4=4

add 4 to both sides

2^x=8

8 is equal to 2*2*2 or 2^3

2^x=2^3

The bases are now both 2 and you can find x.

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Ests show that the first photo detector isacceptable with probability 3/5. When the first photo detector is acceptable, the seco

vredina [299]

Answer:

The probability that exactly one photo detector of a pair is acceptable is $\frac{19}{25}$ .

Step-by-step explanation:

Let the A = first photo detector is acceptable and B = second photo detector is acceptable .

The information provided is:

$P(A) = \frac{3}{5} \\P(B|A)=\frac{4}{5}\\ P(B|A^{c})=\frac{2}{5}$

The law of total probability states that:

$P(X)=P(X|Y)P(Y)+P(X|Y^{c})P(Y^{c})\\$

Using the law of total probability determine the probability of B as follows:

$P(B)=P(B|A)P(A)+P(B|A^{c})P(A^{c})\\=(\frac{4}{5}\times\frac{3}{5} )+(\frac{2}{5}(1- \frac{3}{5}))\\=\frac{12}{25}+\frac{4}{25}\\ =\frac{16}{25}$

The addition rule of probability is:

$P(Y\cup X) = P(Y) + P(X) - P(Y\cap X)\\$

Compute the probability that exactly one photo detector of a pair is acceptable using the addition rule of probability as follows:

$P(A\cup B) = P(A) + P(B) - P(A\cap B)\\=P(A) + P(B) - P(B|A)P(A)\\=\frac{3}{5} +\frac{16}{25} -[\frac{4}{5}\times\frac{3}{5}] \\=\frac{3}{5} +\frac{16}{25}-\frac{12}{25}\\=\frac{15+16-12}{25}\\= \frac{19}{25}$

Thus, the probability that exactly one photo detector of a pair is acceptable is $\frac{19}{25}$ .

3 0

3 years ago

Avery wants to put blueberry muffins in a display case for the breakfast crowd. There are 60 muffins and 40% are blueberry. How

Alexxandr [17]

$60 \times \frac{40}{100} = 24$

3 0

3 years ago

17. Oranges cost 25 cents for 1/2 kilogram. How much would 8 kilograms of ornages cost? Show all of your work. Make sure to incl

Debora [2.8K]

9514 1404 393

Answer:

$4.00

Step-by-step explanation:

We assume the price is proportional to the quantity of oranges. If p is the desired price in dollars, we want ...

p/8 = 0.25/(1/2)

p = 8(0.50) = 4.00 . . . . multiply by 8, simplify

8 kg of oranges would cost $4.00.

5 0

3 years ago

The measure of an angle is 8 degrees less than three times the measure of another angle. If the two angles are supplementary, wh

OLga [1]

Let x and y be the angles
X= 3•y-8
X+ y = 180
Substitute first relationship in second
3y-8+y=180
4y=180+8
Y =188/4= 47 degrees
X= 180-47=133 degrees
The measure of the large angle is
133 degrees

4 0

4 years ago

Give me the answer for 2 1/5 times 4

Korvikt [17]

2 1/5* 4
= (11/5) * 4
= 44/5
= (40+ 4)/5
= 40/5+ 4/5
= 8+ 4/5
= 8 4/5

The final answer is 8 4/5~

6 0

4 years ago

Read 2 more answers

In solving the following problem for x, how do we get the bases to be the same? 2^x-4= 4​

In solving the following problem for x, how do we get the bases to be the same? 2^x-4= 4