Answer:
45
Step-by-step explanation:
The order in which the items are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
How many possible subsets of 2 items can be chosen from this lot?
Combinations of 2 from a set of 10. So
Answer:
c =
Step-by-step explanation:
To make a perfect square
add ( half the coefficient of the x- term )² to x² + 5x
x² + 5x + ( )²
= x² + 5x +
= (x + )² ← a perfect square
Answer:
1.7 × 10⁻⁴
Step-by-step explanation:
The question relates to a two sample z-test for the comparison between the means of the two samples
The null hypothesis is H₀: μ₁ ≤ μ₂
The alternative hypothesis is Hₐ: μ₁ > μ₂
Where;
= 13.5
= 12
σ₁ = 2.5
σ₂ = 1.5
We set our α level at 0.05
Therefore, our critical z = ± 1.96
For n₁ = n₂ = 23, we have;
We reject the null hypothesis at α = 0.05, as our z-value, 3.5969 is larger than the critical z, 1.96 or mathematically, since 3.5969 > 1.96
Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day and the probability that Alyse has a larger time than Jocelyn is 0.99983
Therefore;
The probability that Alyse has a smaller time than Jocelyn is 1 - 0.99983 = 0.00017 = 1.7 × 10⁻⁴.
Answer:
The relation represents a growth when b>1 and a decay when 0<b<1
Step-by-step explanation:
Any function in the form , where a > 0, b > 0 and b not equal to 1 is called an exponential function with base b. If 0 < b < 1. It is an example of an exponential decay. The general shape of an exponential with b > 1 is an example of exponential growth. An exponential function is expressed in the form
The relation represents a growth when b >1 and a decay when 0<b<1.