Since you have two unknowns, you must formulate 2 equations in order to solve the system. Let x be the numbers of dimes and y be the number of quarters. The equations are:
x + y = 61
y = x + 3
Since a dime is 1/10 of a dollar and a quarter is 1/4 of a dollar,
(1/10)x + (1/4)y = 10.90
We made 3 equations. The system is overspecified. Let's just use the first two equations and apply it to the third for verification.
x + (x + 3) = 61
Solving for x,
x = 29
y = 29 + 3 = 32
Verifying,
(1/10)(29) + (1/4)(32) = 10.90
Hence, there are 29 dimes and 32 quarters.
For "less than or equal to" you can use <=
For "greater than or equal to" you can use >=
√(15(x−1)) / √(2x^2)
Value under square root must be ≥ 0
Value in denominator not = 0
15(x−1) ≥ 0
x−1 ≥ 0
x ≥ 1
2x^2 > 0
x^2 > 0
x ≠ 0
Combining both inequalities, we get:
x ≥ 1
Answer:
Step-by-step explanation:
a) Total number of people surveyed, n = 2500
Let X denote the number in the sample that say they support the increase. If 30% of all adults in Ohio support the increase, it means that the percentage of all adults in Ohio that did not support the increase is
100 - 30 = 70%
This is a binomial probability because there are only two possible outcomes. Therefore,
Probability of success, p = 30/100 = 0.3
Probability of failure, q = 1 - p = 1 - 0.3
q = 0.7
Standard deviation = √npq
Standard deviation = √(2500 × 0.3 × 0.7) = 22.91
b) The probability that x is at least 800 is expressed as
P(x ≥ 800)
We would determine the probability by using the binomial probability calculator. Therefore,
P(x ≥ 800) = 0.01577
b. about 0.015.
Answer: Table 3
A table of values x and y represents a linear function,
if the change in x is always proportional with the change in y:
For example:
x changes from 1 to 2, y changes from -3 to -5
that is, a change of 1 in the x-es, is a change of +2 in the y's.
x changes from 2 to 4, y changes from -5 to -9
that is, a change of 2 in x, is a change of +4 in the y's.
1, 2 and 2, 4 are proportional
Another way we can check that Table 3 is the only one representing a linear function, is the constant change in y:
as x takes the values : 1, 2, 3, 4, y becomes -3, -5, -7, -9
that is, a constant change of 1 in the x-es, means a constant change of +2 in the y's
Answer:
Answer: l = 82.5
Step-by-step explanation:
11/2 x 15 = 82.5.