Answer:
x = 8
z = 65
Step-by-step explanation:
Through various rules, we are able to assert: (6x + 67)° = 115°.
Now, we want to solve for x:
6x + 67 = 115
6x = 48
x = 8
We know that z° is equal to the complement of (6x + 67)°, and together these must sum to 180°. Therefore, we can simply take 180° - 115° to find that z° = 65°.
Answer:
Y = 0.4925X - 22.26 ;
(-12.413, 13.398) ;
Yes, there is
Step-by-step explanation:
X = IQ Score ; Y = musical aptitude
The regression equation from the table given using the slope and intercept coefficient :
Y = 0.4925X - 22.26
0.4925 = slope ; Intercept = - 22.26
The 95% confidence interval of the slope :
Confidence interval = b ± Tcritical*SE
Tcritical at 95%, df = n - 2 = (20 - 2) = 18
Tcritical = 2.1009
b = slope Coefficient = 0.4925
S.E = 6.143
Hence, we have :
Confidence interval = 0.4925 ± (2.1009 * 6.143)
Confidence interval = 0.4925 ± 12.9058287
Lower boundary = 0.4925 - 12.9058287 = - 12.413
Upper boundary = 0.4925 + 12.9058287 = 13.398
(-12.413, 13.398)
There is a significant relationship between IQ score and musical aptitude because, 0 is within the confidence interval obtained.
Answer:
C
Step-by-step explanation:
Not 100% sure
Answer:
a. Cosine is an even function
b. Sine is an odd function
c. cos(x) = sin(x + pi/2)
Step-by-step explanation:
See the plot attached.
a. In the figure it can be seen that, for example, cos(pi/2) = cos(-pi/2); therefore, cosine is even.
b. In the figure it can be seen that, for example, sin(pi/2) = 1; sin(-pi/2) = -1; therefore, sine is odd.
c. Function displacements along x-axis are made adding (or subtracting) values to x; i. e., f(x + a), where a is a constant, displace the function f(x) a steps to the left. It can be seen in the figure that sine is cosine but displaced pi/2 values to the right. So, sin(x + pi/2) will displace sine pi/2 values to the left, where cosine is placed.
To solve this problem, there are a couple things we need to do. First of all, we need to figure out how much more she's running every day. On day 1, she ran 3/16 of a mile. On day 2, she ran 3/8 of a mile. On day 3, she ran 9/16 of a mile.
How much are we adding each time? To find that out, we need all of our fractions to have the same denominator so we can compare. Let's give 3/8 a denominator of 16. 8*2=16. What you do on one side of the fraction bar, you MUST do to the other: 3*2=6. So, 3/8 = 6/16.
Day 1: 3/16. Day 2: 6/16. Day 3: 9/16. Now do you see the pattern? Every day, she runs 3/16 of a mile more. That's the answer to part 1: 3/16.
So, how long will it take her to get over 1 mile? Let's continue. Day 3: 9/16. Day 4: 9+3=12, so that's 12/16. Day 5: 15/16. Day 6: 18/16! Since the numerator is bigger than the denominator, guess what? That's more than one mile!! So on the 6th time she runs, she ran 18/16 miles. Keep in mind that 18/16 = 9/8 = 1 1/8 miles.
Answers: 3/16; 6th; 1 1/8 (or 9/8)
