We will be using the Angle Addition Postulate in this problem.
This states that if <em>c</em> is on the interior
of <ABD, then m<ABC + m<CBD = m<ABD.
Since m<ABC is 4x + 2, m<CBD is 3x - 7, and m<AVD is 100,
our equation will be 4x + 2 + 3x - 7 = 100.
Solving from here, we first simplify the left side to get 7x - 5 = 100.
Now add 5 to both sides to get 7x = 105.
Dividing both sides by 7, we find that <em>x = 15</em>.
Now we can use the value of x to help us find m<ABC.
Since the m<ABC is 4x + 2, we can substitute a 5 in for x.
This gives us 4(15) + 2 or 60 + 2 which is 62.
So m<ABC is 62°
First, we can find that the kitten runs 4 meters per second because 2/3 of 6 is 4
Now we can find how far the puppy will go in 15 seconds
If he goes 6 meters in one second, we do 6*15 to get 90 meters
If the kitten goes 4 meters in one second, we do 4*15 to get 60 meters
So to find the distance between them we do 60+90 to get 150 meters
42
Step-by-step explanation:
you plug in -4 into x and multiply
ex: (-4)2-3(-4)+2
Answer:
D) He calculated the joint relative frequency of female students who prefer playing sports. The conditional relative frequency for female students who prefer playing sports is 34%.
Step-by-step explanation:
The table is given as:
Playing sports Dancing Row totals
Male students 18 16 34
Female students 18 35 53
Column totals 36 51 87
- We know that the joint relative frequency of an outcome is calculated as dividing the frequency of the outcome by the grand total.
Hence, when we divide the frequency of the female students who prefer playing sports i.e. 18 by the grand total i.e. 87 ; we obtain:
18/87=0.20689
which is approximately equal to 21%.
- Hence, in order to calculate the conditional relative frequencies she should have divided the required frequency by the row total;.
Hence, here we divide the frequency of the female students who prefer playing sports i.e. 18 by the row total i.e. 53 ; we obtain:
18/53-0.3396
which is approximately equal to 34%.
Hence, option: D is correct.
