Answer:
.
Step-by-step explanation:
Let the unknown fraction be 
,
where, x and y both are prime numbers less than 20.
Now, it is given that adding 1 to both numerator and denominator will make the fraction 
.
Thus,
=
2(x + 1) = y + 1
2x + 2 = y + 1
2x + 1 = y.
Clearly if x will be any odd number , two times x will be odd and adding 1 to it will result in even number and y should be even number , which is not possible as only even prime is 2.
Thus , x should be the even prime which is 2.
And y will be 5.
Thus the required fraction is .
Answer:
93.32% probability of obtaining a value less than or equal to -7.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the likelihood of obtaining a value less than or equal to -7?
This is the pvalue of Z when X = -7.
So
has a pvalue of 0.9332.
So there is a 93.32% probability of obtaining a value less than or equal to -7.
Answer:
The speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
Step-by-step explanation:
Since a plane can fly 450 miles in the same time it takes a car to go 150 miles, if the car travels 100 mph slower than the plane, to find the speed (in mph) of the plane the following calculation must be performed:
450 to 150 is equal to 3: 1, that is, the plane travels three times the distance of the car.
Therefore, since 100/2 x 3 equals 150, the speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
By looking the given options, we can say that some of them are following pythagorean identities and pythagorean identities are
sin^2(x) + cos^2(x) =1, sec^2(x)-tan^2(x) =1,csc^2(x) -cot^2(x)=1
So out the four options, option a and option c are following pythagorean identity and option b and option d are not following pythagorean identity. And we have to find those options which are not identities .
So the correct options are
b) sec^{2} x+csc^{2} x=1 \ d) tan^{2} x + sec^{2} x =1
Answer:
Step-by-step explanation:
Question 6)
sin Y= m
sin Y = m/1
So, hypotenuse is 1
Since sine is opposite over hypotenuse
So XZ= m and YZ = 1
Similarly, cos Y = k
cos Y = k/1
So adjacent side of angle Y is k
So XY = k
cos z - sin z = 
cos z - sin z = 
cos z - sin z = m - k
Question 7)
the relationship between sine, cosine, and tangent.
tan(x) = sin(x)/cos(x) = (11/61)/(60/61)
tan(x) = 11/60
Question 8)
Start with where the shorter leg is. It must be opposite the smallest angle.
In a 30 - 60 - 90 degree triangle you have the hypotenuse to be twice as long as the shortest side. You have to read that a couple of times to make sure you understand it.
That being said, if the shortest side is x, the hypotenuse will be 2x.
Since in this case the shortest side is 11, the hypotenuse will be 2*11 = 22
The answer is 22
