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lina2011 [118]
3 years ago
10

William is taking the 25-question, multiple choice American Mathematics Competition. Each question has five answer choices. Will

iam guesses random answers for the last four questions. What is the probability that he will get at least one of these final four questions right?
Mathematics
1 answer:
o-na [289]3 years ago
7 0
Given that <span>William guesses random answers for the last four questions and that e</span><span>ach question has five answer choices.</span><span>

The probability that he gets an answer correct </span>is 1 / 5.

The probability that he did not get an answer correct is 4 / 5.

The probability that he will not get any of the 4 questions correctly is

\left( \frac{4}{5} \right)^4= \frac{256}{625}

Therefore, the probability that he gets at least one of the 4 questions correctly is

1-\frac{256}{625}= \frac{369}{625} =0.59=59\%
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one a windy moring a hot air balloon starts ascending and flying away from the too of a hill the alritude h(x) in feet of the ba
makkiz [27]

The greatest common factor of all the coefficients is of 8.

<h3>What is the greatest common factor?</h3>

The greatest common factor between multiple terms is the largest value for which all terms are divisible.

In this problem, the equation is:

h(x) = -16x^2 + 56x + 96

The terms are 16, 56 and 96. Hence, to find the gcf, we have to keep factoring them by prime factors while all can be factored by the same value, hence:

16 - 56 - 96|2

8 - 28 - 48|2

4 - 14 - 24|2

1 - 7 - 12

There are no terms by which both 7 and 12 are divisible, hence the procedure is stopped and:

gcf(16, 56, 96) = 2³ = 8.

You can learn more about the greatest common factor at brainly.com/question/26140769

3 0
2 years ago
Find the non-extraneous solutions of the square root of the quantity x plus 6 minus 5 equals quantity x plus 1.
denis23 [38]
(x+6)^(1/2)-5=x+1
(x+6)^(1/2)=x+6
((x+6)^(1/2))^2=(x+6)^2
x+6=x^2+12x+36
0=x^2+11x+30
(-11+(11^2-4(1)(30))^(1/2))/2
(-11+((1)^(1/2))/2
(-11+1)/2=-5
(-11-1)/2=-6
((-6)+6)^1/2-5=(-6)+1
(0^(1/2))-5=-5
-6 is non-extraneous
((-5)+6)^1/2-5=(-5)+1
(1^1/2)-5=-4
1-5=-4
-4=-4
-5 is non-extraneous

3 0
3 years ago
find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B
SashulF [63]

Answer:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3

|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

\theta = cos^{-1} (\frac{ab}{|a| |b|})

If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

3 0
2 years ago
Pls explanation me the question ı know the ase but ı dıdnt understand it
lara [203]
It's just asking of all the number of wings that were left behind in bucket which one is the smallest number which is 1.
7 0
3 years ago
John walks 3 miles in 5 hours<br>for his exercise routine. Find<br>the Unit rate​
Brilliant_brown [7]

John walks 0.6 miles in 1 hour.

Step-by-step explanation:

Distance walked by John = 3 miles

Time period = 5 hours

5 hours = 3 miles

Unit rate is the ratio of two measurements, in which one measurement is one, therefore,

1 hour = \frac{3}{5}\ miles

1\ hour=0.6\ miles

John walks 0.6 miles in 1 hour.

Keywords: ratio, distance

Learn more about distances at:

  • brainly.com/question/3456442
  • brainly.com/question/3503862

#LearnwithBrainly

3 0
3 years ago
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