What’s the least common multiple of each group of numbers? A. 5 and 6 b. 2 and 9 c. 6 and 8 d. 2, 5, and 6
2 answers:
For this case we have that by definition, the LCM of two or more natural numbers is the smallest natural number that is a common multiple of all of them.
So:
A. 5 and 6
The LCM of 5 and 6 is the smallest positive integer that divides the numbers 5 and 6 without leaving a residue.
multiples:
5: 10,15,20,25,30,35,40,45
6: 12,18,24,30,36
B. 2 and 9
Multiplos:
2: 4,6,8,10,12,14,16,18
9: 18,27
C. 6 and 8
6: 12,18,24,30,36
8:16, 24
D. 2,5 and 6
Multiplos:
2: 4,6,8,10,12,14,16,18 ..., 30
5: 10,15,20,25,30,35,40,45
6: 12,18,24,30,36
Answer:
a.30
b.18
c.24
d.30
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1.The isosceles triangle has sides of length 14, y, y
2. According to the "triangle inequality" :
y+y>14
2y>14
y>14/2=7
(y is greater than 7)
3. Remark, check the figures:
the side lengths cannot be less than (neither equal to 7), because we cannot get a triangle in that case, check picture 2
In picture 1 wee see that the side lengths can be as large as we want. We can erect an altitude, as high as we want. Pick a point on the altitude, and join it to the endpoints of the base, and we get an isosceles triangle with base equal to 14.
2. According to the "triangle inequality" :
y+y>14
2y>14
y>14/2=7
(y is greater than 7)
3. Remark, check the figures:
the side lengths cannot be less than (neither equal to 7), because we cannot get a triangle in that case, check picture 2
In picture 1 wee see that the side lengths can be as large as we want. We can erect an altitude, as high as we want. Pick a point on the altitude, and join it to the endpoints of the base, and we get an isosceles triangle with base equal to 14.
Answer:
Step-by-step explanation:
A car traveled at a constant speed as shown in the graph.
Distance traveled is on the y-axis and duration of travel on the x-axis.
Point A(3.5, 210) shows,
Distance traveled = 210 miles
Time to travel = 3.5 hours
So the point (3.5, 210) shows the distance traveled by the car in 3.5 hours is 210 miles.
Slope of the line = speed of the car =
=
= 60 mph
Now we will find the speed of the car at another point B(1, 60).
If the speed of car is same as the point B as of point A, point B will lie on the graph.
Speed of the car at B(1, 60) =
=
= 60 mph
Hence, we can say that point B(1, 60) lies on the graph.
Answer:
The probability of getting a sample with 80% satisfied customers or less is 0.0125.
Step-by-step explanation:
We are given that the results of 1000 simulations, each simulating a sample of 80 customers, assuming there are 90 percent satisfied customers.
Let = <u><em>sample proportion of satisfied customers</em></u>
The z-score probability distribution for the sample proportion is given by;
Z = ~ N(0,1)
where, p = population proportion of satisfied customers = 90%
n = sample of customers = 80
Now, the probability of getting a sample with 80% satisfied customers or less is given by = P( 80%)
P( 80%) = P(
) = P(Z
-2.24) = 1 - P(Z < 2.24)
= 1 - 0.9875 = <u>0.0125</u>
The above probability is calculated by looking at the value of x = 2.24 in the z table which has an area of 0.9875.