2x - the first and the smallest even integer
2x+2 - the second even integer
2x+4 - the third even integer
These three consecutive even integers are -54, -52 and -50.
Answer:
Step-by-step explanation:
1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)
Two numbers that work are -6 and +1
-6 x +1 = -6
-6 + -1 = -5
2. Split the middle term into the two numbers that you found.
3x^2 -6x +x -2 = 0
I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.
3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'
3x (x-2) +1 (x-2) = 0
4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.
(3x + 1) (x-2) = 0
5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.
3x + 1 = 0 x-2 = 0
3x = -1 x = 2
x = -1/3
6. The solutions to this equation are x = 2 and x = -1/3
Original number 21.4709
Rounded to the nearest hundredth 21.471
Step-by-step explanation:
the lines are all going through the origin (0, 0), so the y-intercept is the same (0) for all 4.
therefore, we only need to focus on the slope of the lines to see which two are identical.
the slope is the ratio "y coordinate change / x coordinate change" when going from one point to another on the line.
one point is for all 4 lines the origin, so the coordinate changes are the point coordinates themselves, and we only need to calculate y/x and see, which ones are equal.
105/15 = 7/1 = 7
150/12 = 50/4 = 25/2 = 12.5
120/10 = 12
96/8 = 12
so, C and D have identical slopes and therefore identical graphs, and have therefore the same costs of T-shirts.
Answer:
b) Fail to reject the null hypothesis with a sample of n = 23 participants
Step-by-step explanation:
Hello!
A "Repeated-measures t-test" is also known as "paired sample t-test" In this type of test you have only one sample and you measure two variables of interest to each experimental unit. Since both study variables are measured in the same units they are said to be dependent.
The most common example of this type of test is the "before-after treatment" experiment.
The degrees of freedom of this experiment are
, so if the test was conducted under a t₂₂ distribution, then the sample size was n= 23 experimental units. Remember if you use the p-value approach, to make a decision over the null hypothesis you have to compare it to the level of significance following the decision rule:
If the p-value ≤ α, you reject the null hypothesis.
If the p-value > α, you do not reject the null hypothesis.
In this example is specified that the p-value is greater than the level of significance, then the decision is to not reject the null hypothesis.
With all this in consideration, the correct option is b)
U hope you have a SUPER day!
