Factor completely, the expression: 2x^3-2x^2-12x show work please.
Answers
2x(x^2-x-6).
Factor out x^2-x-6:------------------>must factors must multiply to -6 and add to -1
-3 and 2 fit the criteria therefore
x^2-x-6 factors out to (x-3)(x+2).
But dont forget to put it all back together. The 2x is part of the expression so the full factored expression is:
2x(x-3)(x+2)
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A population has a mean of 300 and a standard deviation of 70. Suppose a sample of size 125 is selected and is used to estimate . Use z-table. What is the probability that the sample mean will be within +/- 8 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.) What is the probability that the sample mean will be within +/- 17 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)
Answers
In the provided data, the categorical variables are gender and car.
In the given data set, the categorical variables are characteristics that can be divided into distinct categories or groups, without considering numerical values.
1. **Gender:** Gender is a categorical variable as it consists of distinct categories such as Male and Female, indicating the driver's gender.
2. **Car:** The type of car each driver uses is also a categorical variable. It includes categories like Truck, Van, SUV, and Sports car, representing different types of vehicles.
These variables are categorical because they represent qualitative characteristics without numerical significance. They provide information about the driver's gender and the type of car they use for delivery.
In contrast, numerical variables such as Age, Average Time, and Average Distance are quantitative and represent measurable quantities.
Age is measured in years, and both Average Time and Average Distance are measured in minutes and miles, respectively. Numerical variables can be further classified into discrete (countable) or continuous (measurable on a scale) variables, but they are not considered categorical as they represent quantities rather than categories.
For more such questions on categorical variables
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y + 5 ≤ 4
B.
y + 5 < 4
C.
y + 5 ≥ 4
D.
y + 5 > 4
Answers
3x –y = 7
Answers
Let's write both equations in the standard form of [ y = mx + b ],
and then see what we can tell about their graphs.
First equation: x + 3y = 9
Subtract 'x' from each side: 3y = -x + 9
Divide each side by 3: y = -1/3 x + 3
This line crosses the y-axis at y=3, and it has a slope of -1/3 .
Second equation: 3x - y = 7
Subtract 3x from each side: -y = -3x + 7
Multiply each side by -1 : y = 3x - 7
This line crosses the y-axis at y=-7, and it has a slope of 3 .
-- The two lines have different slopes, so they're not parallel.
They must intersect somewhere.
-- They're not the same line, so they can't 'intersect' everywhere.
-- They have slopes of -1/3 and 3 . Their slopes are negative reciprocals,
so the lines are perpendicular.
All of this says that the two equations can't have no solution, and they can't have
infinitely many solutions. They must have one and only one solution.
I guess that means that it's our job to find it now.
============================================
For each equation, the "mx + b" form is equal to 'y' . Since these two things are
equal to the same thing, they must be equal to each other, and we can write:
-1/3 x + 3 = 3x - 7
Multiply each side by 3 : -x + 9 = 9x - 21
Add 'x' to each side: 9 = 10x - 21
Add 21 to each side: 30 = 10x
Divide each side by 10 : 3 = x
The intersection/solution is some place where x=3 .
Let's put that back into the first equation:
x + 3y = 9
3 + 3y = 9
Subtract 3 from each side: 3y = 6
Divide each side by 3 : y = 2
And there's your solution: x = 3
y = 2
On the graph, the two lines intersect at the point (3, 2) .
We used the first equation to get part of the solution, so we can't use
the same equation to check the solution. We'll put our solution into the
second equation, and see whether it checks there:
3x - y = 7
3(3) - (2) = 7
9 - 2 = 7
7 = 7 yay !
The two equations have one and only one solution,
and it is definitely x = 3, y = 2 .
Substitution or Elimination
im using substitution
1. solve for variable for one of the equation
x + 3y = 9
x = 9 - 3y
2. Substitute the variable into one of the equation
3 (9-3y) - y = 7
27 - 9y - y = 7
27 - 10y = 7
-10y = 7 - 27
-10y = -20
y = 2
3. sub y = 2 into any equation to find x
3x - 2 = 7
3x = 7 -2
3x = 5
x = 5/3
X+3(2) = 9
x + 6 = 9
x = 9-6
x= 3
therefore there are two solutions x = 3 and x= 5/3
Answers
Since you are given 2 points. You will plug the points into this formula. X2-X1/Y2-Y1. This will get you your slope. Then you will plug one of the points given and your slope into point slope form. This form is Y-Y1=m(X-X1). Then you to get your final answer you want to get Y to be by itself.
Your problem:
5-(-1)/1-(-1)
5+1/1+1
=6/2 =3
m=3
Y-(-1)=3(X-(-1))
Y+1=3(X+1)
Y+1=3X+3
Y=3X+2
Answers
13.20 ÷ 6 = 2.20
$2.20 per bowl
CHECK OUR WORK:-
2.20 × 6 = 13.20
we were RIGHT!!
So, the unit rate in dollars for, Melinda bought 6 bowls for $13.20 is, $2.20 per bowl.
Hope I helped ya!! xD
also you could , 2.20*6=13.20 , thats still 13.20 (2.20)
all together this means the unit rate in dollar is 2.20 for bowl , per bowl. for Melinda because she bought them for 13.20
i hope this helps.
Answers
Answer:
2 2/5 or 12/5
Step-by-step explanation:
First, you change the mixed number in the equation to an improper fraction; 8/5 divided by 2/3. 8/5 divided by 2/3 equals 8/5x3/2, simply multiply the numerators and the denominator, and simply the fraction.
Hope this helps!