Step-by-step explanation:
Consider the provided information.
Consider the figure 1:
We need to give an example of a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.
Alternate interior angles: If a transversal cuts two parallel line then pair of angles on the inner side of lines but on opposite sides of the transversal are know as the alternate interior angle:
For example: ∠3 and ∠6 are alternate interior angle another pair are ∠4 and ∠5.
Corresponding angles: If a transversal cuts two parallel line then the angles in same corner are called corresponding angles.
For example: ∠1 and ∠5 are corresponding angle another pair are ∠4 and ∠8.
Alternate exterior angles: If a transversal cuts two parallel line then the pair of angles on the outer side of lines but on opposite sides of the transversal are known as the alternate exterior angles.
For example: ∠1 and ∠8 are alternate exterior angle another pair are ∠2 and ∠7.
Answer:
To find c you know that angles on a straight line equal 180° (supplementary angles). So 70+30+∠C=180.
Now we can solve this.
100+c=180.
Move the 100 over to the other side.
100-100+c=180-100
Simplify.
∠C=80°
Because we know that the two lines with double arrows are parallel, we can use the rule that alternate interior angles are congruent. This means that ∠E=70.
∠E=70°
Since the total sum of the angles in a triangle are equal to 180°, we know that ∠D+∠C+∠E=180. Because we already know ∠C and ∠E we can put those numbers in for them. 80°+70°+∠D=180°. Now we can solve this.
80+70+D=180
Simplify this.
150+D=180
Now we move the 150 over to the other side to get D by itself.
150-150+D=180-150
Simplify.
D=30
∠D=30°
Now we can find the vertical angle opposite ∠A by using the alternate interior angles rule again this time using the parallel lines with only one arrow on them. The vertical angle opposite ∠A=30°. Since vertical angles are congruent ∠A=30°.
∠A=30°
We are going to use the alternate angles rule one more time to solve for ∠B (this rule is very important when dealing with parallel lines), we could also use the corresponding angles rule but for simplicity we will just stick with the alternate angles rule. Because the vertical angle opposite ∠A is equal to 30°, we can see that the supplementary angle opposite ∠B=30°. Because this angle is supplementary with B we know that 30+B=180.Now we can solve this.
30+B=180
Now we move the 30 over to the other side.
30-30+B=180-30
Simplify.
B=150
∠B=150°
I hope this helps!
Answer:the probability that exactly five customers make a purchase is 0.033
Step-by-step explanation:
The formula for binomial distribution is expressed as
P(x = r) = nCr × q^(n - r) × p^r
Where
p = probability of success
q= probability of failure
n = number of sample
From the information given,
39 percent of all customers who enter a store will make a purchase. It means that the probability of success, p = 39/100 = 0.39
The probability of failure q, would be 1 - p = 1 - 0.39 = 0.61
n = 6
The probability that exactly five customers make a purchase is expressed as
P(x = 5) = 6C5 × 0.61^(6 - 5) × 0.39^5
P(x = 5) = 6 × 0.61× 0.39^5 = 0.033
Answer: x + y = z
Example:
Lets say if x 5 and y is 10 then z would equal 15.
5 + 10 = 15
Hope this helped! :)
