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ser-zykov [4K]
2 years ago
8

Condense the expression to the logarithm of a single quantity.​

Mathematics
1 answer:
vladimir1956 [14]2 years ago
7 0

Answer:

\log _3\left(\frac{x^{\frac{1}{2}}}{\left(y+8\right)^2}\right)

Step-by-step explanation:

-> Apply log rules

\log _3\left(x^{\frac{1}{2}}\right)-2\log _3\left(y+8\right)

->

\log _3\left(x^{\frac{1}{2}}\right)-\log _3\left(\left(y+8\right)^2\right)

-> Apply basic math rules

\log _3\left(\frac{x^{\frac{1}{2}}}{\left(y+8\right)^2}\right)

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You have 4 cards, 2 black and 2 red. You play a game where during each round you draw a card. If it's black, you lose a point. I
sineoko [7]

Answer: The expected value of this game is 2/3

Step-by-step explanation:

Give that

If it's black, you lose a point. If it's red, you gain a point. 

And then you can stop at any time. But you should never stop when you are losing because that can guarantee 0 by drawing all the cards.

Assuming you should stop after three cards when you are +2.

The only question is whether to draw if you are +1 on the first draw.

If you draw red first, You have 1/3 chance of drawing red again and this will give you +2 points

1/3 chance of drawing two blacks and earn zero point, chance of drawing black-red and earn +1. This gives +1, so it doesn't matter whether you draw or not.

From the beginning, If you draw red (probability 1/2 you end +1. If you draw black and then draw two reds (probability 1/6 you end +1) Otherwise you break even with probability 1/3. Overall, the value is 2/3

8 0
3 years ago
Order these numbers from least to greatest.<br> 1.4, 1.103, 1.1322, 1.13
hodyreva [135]

Answer:

1.103,1.13,1.1322,1.4

Step-by-step explanation:

find the decimal places and u can figure out with they are greater than this decimal or less

8 0
3 years ago
Read 2 more answers
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes
Komok [63]

Answer:

a. The probability of completing the exam in one hour or less is 0.0783

b. The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. The number of students will be unable to complete the exam in the allotted time is 8

Step-by-step explanation:

a. According to the given we have the following:

The time for completing the final exam in a particular college is distributed normally with mean (μ) is 77 minutes and standard deviation (σ) is 12 minutes

Hence, For X = 60, the Z- scores is obtained as follows:

Z=  X−μ /σ

Z=60−77 /12

Z=−1.4167

Using the standard normal table, the probability P(Z≤−1.4167) is approximately 0.0783.

P(Z≤−1.4167)=0.0783

Therefore, The probability of completing the exam in one hour or less is 0.0783.

b. In this case For X = 75, the Z- scores is obtained as follows:

Z=  X−μ /σ

Z=75−77 /12

Z=−0.1667

Using the standard normal table, the probability P(Z≤−0.1667) is approximately 0.4338.

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is obtained as follows:

P(60<X<75)=P(Z≤−0.1667)−P(Z≤−1.4167)

=0.4338−0.0783

=0.3555

​

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. In order to compute  how many students you expect will be unable to complete the exam in the allotted time we have to first compute the Z−score of the critical value (X=90) as follows:

Z=  X−μ /σ

Z=90−77 /12

Z​=1.0833

UsING the standard normal table, the probability P(Z≤1.0833) is approximately 0.8599.

Therefore P(Z>1.0833)=1−P(Z≤1.0833)

=1−0.8599

=0.1401

​

Therefore, The number of students will be unable to complete the exam in the allotted time is= 60×0.1401=8.406

The number of students will be unable to complete the exam in the allotted time is 8

6 0
3 years ago
Please show your work and check!!
ad-work [718]

Step 1. Add 6 to both sides

a ≥ 1 + 6

Step 2. Simplify 1 + 6 to 7

a ≥ 7

4 0
3 years ago
Read 2 more answers
Help me please!!! :(
Archy [21]

Answer:

There is no solution because the graphs do not intersect

Step-by-step explanation:

Both of theses equations do intersect with one another when graphed. In conclusion, there is no solution.

6 0
3 years ago
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