Round off 65213 to the nearest tens
2 answers:
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Answer:
x =
x = -1
Step-by-step explanation:
The given equation is,
-2(bx - 5) = 16
Dividing by (-2) on both sides of the equation,
(bx - 5) = -8
By adding 5 on both the sides of the equation,
(bx - 5) + 5 = -8 + 5
bx = -3
Dividing by 'b' on both the sides of the equation,
x =
If b = 3,
x =
x = -1
Answer:
a) 0.34% probability that she goes three consecutive frames without a strike.
b) 1.91% probability that she her first strike in the third frame
c) 99.66% probability that she has at least one strike in the first three frames.
d) 14.22% probability that she bowls a perfect game.
Step-by-step explanation:
For each frame, there are only two possible outcomes. Either there is a strike, or there is not. The probability of a strike happening in a frame is independent of other frames. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
A certain bowler can bowl a strike 85 % of the time.
This means that
a) goes three consecutive frames without a strike?
This is when
. So
0.34% probability that she goes three consecutive frames without a strike.
b) makes her first strike in the third frame?
No strike during the first two(with a 15% probability)
Strike during the third(85% probability). So
P = 0.15*0.15*0.85 = 0.0191
1.91% probability that she her first strike in the third frame
c) has at least one strike in the first three frames?
Either there are no strikes, or there is at least one strike. The sum of the probabilities of these events is 100%.
From a), 0.34% probability that she goes three consecutive frames without a strike.
100 - 0.34 = 99.66
99.66% probability that she has at least one strike in the first three frames.
d) bowls a perfect game (12 consecutive strikes)?
This is when
. So
14.22% probability that she bowls a perfect game.
We need to determine whether is a terminating decimal or a repeating decimal.
Let's solve this question using the long division method
First, let's identify the divisor and dividend. The number to be divided is 11 hence this is the dividend, and it needs to be divided by 128 which is the divisor
Next, since the divisor (128) is greater than the dividend (11) it can not divide 11. Hence, we will introduce a decimal point in quotient, and append a 0 next to 11 and divide 110 by 128. Again, 128 is greater than 110 so we will introduce a 0 in the quotient, and append another 0 next to 110, and will divide 1100 by 128. We will see what multiple of 128 is less than or equal to 1100. That multiple is 8. So we write 8 in the quotient and multiply 128 with 8 and subtract the product (128*8 = 1024) from 1100. The remainder that we get is 76.
Next, we append a 0 to the remainder and divide 760 by 128. Now, we see what multiple of 128 is less than or equal to 760. That multiple is 5. So we write 5 next to the quotient and multiply 128 with 5 and subtract the product (640) from 760. Now, the remainder is 120.
Next, we append a 0 to the remainder and divide 1200 by 128. Now, we see what multiple of 128 is less than or equal to 1200. That multiple is 9. So we write 9 next to the quotient and multiply 128 with 9 and subtract the product (1152) from 1200. Now, the remainder is 48.
Next, we append a 0 to the remainder and divide 480 by 128. Now, we see what multiple of 128 is less than or equal to 480. That multiple is 3. So we write 3 next to the quotient and multiply 128 with 3 and subtract the product (384) from 480. Now, the remainder is 96.
Next, we append a 0 to the remainder and divide 960 by 128. Now, we see what multiple of 128 is less than or equal to 960. That multiple is 7. So we write 7 next to the quotient and multiply 128 with 7 and subtract the product (896) from 960. Now, the remainder is 64.
Next, we append a 0 to the remainder and divide 640 by 128. Now, we see what multiple of 128 is less than or equal to 640. That multiple is 5. So we write 5 next to the quotient and multiply 128 with 5 and subtract the product (640) from 640. Now, the remainder is 0.
Hence, we have solved the entire problem
Last, we look at the quotient i.e. 0.0859375, which is the solution to the problem. We see that the quotient has a definite number of digits in it, and terminates at 5. Hence, this is a terminating decimal.
A repeating decimal is one in which a particular pattern after the decimal point keeps re-occuring, which is not the case here. Hence, is a terminating decimal.
Please refer to the attached image for visualization
