Answer:
Carlos and Pamela drove 120 miles on the first day, 240 miles on the second day, and 290 miles on the third day.
Step-by-step explanation:
Let x be the number of miles driven on the first day.
Then they drove twice as many miles, or 2x on the second day
and 50 miles more than the second day's, so 2x + 50
The total is 650 across all three days, so we'll take the sum.
x + 2x + (2x + 50) = 650
Combine like terms on the left
5x + 50 = 650
Subtract 50 on both sides
5x = 600
Divide by 5 on both sides
x = 120
Check work:
120 + 2(120) + 2(120) + 50 = 650
120 + 240 + 240 + 50 = 650
600 + 50 = 650
650 = 650
So they drove 120 miles on the first day
2*120 = 240 miles on the second day
and 2*120 + 50 = 240 + 50 = 290 miles on the third day
Answer: s, v, w, & x = 13 y = 20 z = 20 + 13√3
<u>Step-by-step explanation:</u>
First, you need to understand the side lengths of each special triangle in the drawing.
A 45°- 45°- 90° triangle has corresponding sides of a - a - a√2
A 30°- 60°- 90° triangle has corresponding sides of b - b√3 - 2b
The hypotenuse of the 45-45-90 triangle is 13√2, so its legs are 13.
So A F = 13 → s = 13 and w = 13
FB = 13 → x = 13
EC = 13 → v = 13
Since the x-value of C is 20, then the x-value of E is also 20 → y = 20
ED is opposite of the 60° angle of the 30-60-90 triangle so ED is EC√3. Since EC = 13, then ED = 13√3.
AE + ED = AD
20 + 13√3 = AD → z = 20 + 13√3
Answer:
a. The sample has more than 30 grade-point averages.
Step-by-step explanation:
Given that a researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample
We are asked to find the conditions under which that sample mean can be treated as a value from a population having a normal distribution
Recall central limit theorem here
The central limit theorem states that the mean of all sample means will follow a normal distribution irrespective of the original distribution to which the data belonged to provided that
i) the samples are drawn at random
ii) The sample size should be atleast 30
Hence here we find that the correct conditions is a.
Only option a is right
a. The sample has more than 30 grade-point averages.
Your first answer will be: 115
Your second answer will be: 135
180 - 98 - 27 = 55 there you go
