Answer:
The remainder is 4.
Step-by-step explanation:
Note: This question is not correctly stated. It is therefore correctly restated before answering the question as follows:
When 17 is divided by k; where k is a positive integer less than 17, the remainder is 3. What is the remainder when the sum of the possible values of k is divided by 17?
The explanation of the answer is now given as follows:
Since k < 17, it implies that the possible values of k must be from between 1 and 16 inclusive.
Between 1 and 16, only 7 or 14 will give a remainder of 3 when either of them is used to divide 17. Therefore, 7 and 14 are the possible values of k.
Therefore, we have:
Sum of the possible values of k = 7 + 14 = 21
Also, we have:
Sum of the possible values of k divided by 17 = 21 / 17 = 1 with a remainder of 4.
Therefore, the remainder is 4 when the sum of the possible values of k is divided by 17.
The distance around the pool is 43.96 m.
Solution:
The distance across the circle is <em>diameter</em>.
The distance around the circle is <em>circumference</em>.
The value of π = 3.14
Diameter of the circle = 14 m
Circumference of the circle = πd
= 3.14 × 14 m
Circumference of the circle = 43.96 m
The distance around the pool is 43.96 m.
Each hour she works, she earns

dollars.
The first day, she worked 6 hours, so she'd earn

dollars.
The second day, she worked 8, so she'd earn

.
Together, she'd have earned

dollars.
You could add the number of hours she worked first and then multiply by

to get the same result. This would look like

.
Answer:
Two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.
Step-by-step explanation:
We are given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.65 millimeters and a standard deviation of 0.07 millimeters.
<em>Let X = diameters of bolts produced in a machine shop</em>
So, X ~ N(
)
The z score probability distribution is given by;
Z =
~ N(0,1)
where,
= population mean
= standard deviation
<u>Now, we have to find the two diameters that separate the top 4% and the bottom 4%.</u>
- Firstly, Probability that the diameter separate the top 4% is given by;
P(X > x) = 0.04
P(
>
) = 0.04
P(Z >
) = 0.04
<em>So, the critical value of x in z table which separate the top 4% is given as 1.7507, which means;</em>
= 1.7507
= 5.65 + 0.122549 = 5.77
- Secondly, Probability that the diameter separate the bottom 4% is given by;
P(X < x) = 0.04
P(
<
) = 0.04
P(Z <
) = 0.04
<em>So, the critical value of x in z table which separate the bottom 4% is given as -1.7507, which means;</em>
= -1.7507
= 5.65 - 0.122549 = 5.53
Therefore, the two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.
Answer:
y = -1/3x - 5
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes, so the line is:
y = -1/3x + b
Finding the value of b, using the given point (-9, -2)
-2 = -1/3*(-9) + b
-2 = 3 + b
b = -2 - 3
b = -5
The line is
y = -1/3x - 5
Hopefully, this helps!