9514 1404 393
Answer:
(f·g)(x) = 2x^3 +6x^2 -4x -12
Step-by-step explanation:
The distributive property is used to find the expanded form of the product.
(f·g)(x) = f(x)·g(x) = (x +3)(2x^2 -4) = x(2x^2 -4) +3(2x^2 -4)
= 2x^3 -4x +6x^2 -12
(f·g)(x) = 2x^3 +6x^2 -4x -12
Find the area of the triangle which the line 2x – 3y +6=0 forms with the coordinate axis.
2x-3y+6=0 has an x intercept of 2 and a y intercept of -3.
That means the 2 sides of the right triangle are 2 and -3
Area of triangle= 1/2×base×height
= 1/2×-3×2
=-3
∴ Area of the triangle=-3
The area of the asked triangle is 3 sq units.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a triangle is formed by the line 2x – 3y +6=0 and the coordinate axis.
When we plot the graph of the line, we get, y-intercept = 2 and x-intercept = -3
Hence, the height and base of the triangle will be 2 and 3 respectively.
Area of a triangle = 1/2 (base) (height)
Area = 1/2 (2)(3)
Area = 3
Hence, the area of the asked triangle is 3 sq units.
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Find the solution to 20 - (-3) - 10 - 6+3 - (-2) - 3.
O 10
0 -9
O -5
O 9
Answer:
O 9
Step-by-step explanation:
Subtracting a negative turns it into addition. So this becomes 20 + 3 - 10 - 6 + 3 + 2 - 3.
Going through this problem looks like this: 23 - 10, 13 - 6, 7 + 3, 10 + 2, 12 - 3. And you get 9.
Answer:
the answer is 9.
Step-by-step explanation:
If x = y, then x – a = y – a represents the ________ property of equality.
Answer:
Subtractive Property of equality
Step-by-step explanation:
Since x = y, When you subtract anything from x, you must do the same to y for them to stay equal.
Answer:
Subtraction property of equality
A scale drawing of a square desk is ¼ inch to 1 foot. The actual desk is 50 feet wide. What is the area of the desk in the model?
156.25 in2
40000 in2
625 in2
10000 in2
Answer:
Step-by-step explanation:
The edges of a rectangle solid have lengths 2x,3xand 5x.what is the total surface area of the solid ?
•30x^2
•60x^2
•62x^2
•30x^3
Answer:
30x³
Step-by-step explanation:
2x×3x=6x²
6x²×5x=30x³
The coordinates of A after the reflection are
The coordinates of A after the reflection are
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the coordinate of A is not given.
However, the rule to follow has been stated in the question.
i.e.
[tex](x,y) \to (-x,y)[/tex]
Assume that:
[tex]A = (2,5)[/tex]
After reflection, A will be:
[tex]A =(-2,5)[/tex]
Two more than four times a number.
2+4x=15
Answer:
13/4
Step-by-step explanation:
Subtract 2 from both sides. Now we have 4x=13. Divide by 4. We have our answer: x=13/4.
21. Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60%
solution. How many liters of each does he need make the needed 80 liters of 30% acid solution?
Gabe needs
liters of the 20% solution.
He also needs
liters of the 60% solution.
Let x be the amount (in liters) of 20% solution that Gabe uses, and y the amount (also in L) of the 60% solution.
He needs 80 L of 30% solution, so that
x + y = 80
0.20x + 0.60y = 0.30 (80) = 24
Solve for y in terms of x :
y = 80 - x
Substitute this into the second equation and solve for x :
0.20x + 0.60 (80 - x) = 24
0.20x + 48 - 0.60x = 24
24 = 0.40x
x = 60
Solve for y :
y = 80 - 60
y = 20
What is the constant of variation k of the direct variation y=KP through (-3, 2)
Answer:
isisis
Step-by-step explanation:
ISO’s
Answer:
-2/3
Answer: The constant of variation k for y = kx through (-3, 2) is k = -2/3.
Calculate the mean of: 4.6, 3, 8.1, 9, 12, 3, 9, 3.5, 7, 3
A university professor asked his class of 42 students when they had studied for his class the previous weekend. There responses were. please answer part a, b and c
ANSWERS:
a) 16 students
b) 25 students
c) 2 students
STEP BY STEP:
There are 42 students in total. This question can be solved by "Principal of Inclusion and Exclusion"
Question a)
The students that studied on Sunday in total with overlaps is 30. To figure out the students that ONLY studied on Sunday you need to first minus the overlaps in the combos:
the combos:
3, 10, 6, 2
Since the last combo included all of the other dates, we need to minus it:
1, 8, 4, 2
Now we can use the total of Sunday and minus the combos that includes Sunday:
30 - (4 + 2 + 8) = 16 students
Question b)
To figure out all the students that only studied on ONE day, not 2 not 3, just one day. We need to figure out the students that studied for Saturday and Friday using the same method before for figuring out Sunday:
Friday: 9 - 4 - 1 -2 = 2 students
Saturday: 18 - 1 - 2- 8 = 7 students
and now add them all together: 2 + 7 + 16 = 25 students
That is the total number of students that studied on one day.
Question c)
Now for the numbers of students that didn't study... We can just use the total to minus everything else!
42 - (25 + 1 + 4 + 8 + 2) = 2 students!!!
And thats all done! If you still don't get it, please ask!
ASAP NEED HELP DESCRIBE AND GET CORRECT a) You are using the equation 4(p – 7) = 44 to determine how many pictures can be saved at one time to the photo stream on your cell phone. Describe the operations in the order that you will perform them to solve the equation. (3 points)a) You are using the equation 4(p – 7) = 44 to determine how many pictures can be saved at one time to the photo stream on your cell phone. Describe the operations in the order that you will perform them to solve the equation. (3 points)
Answer:
p = 18
Step-by-step explanation:
4(p – 7) = 44
Divide each side by 4, using the division property of equality
4(p – 7)/4 = 44/4
p-7 = 11
Add 7 to each side using the addition property of equality
p-7+7 = 11+7
p = 18
Answer:
he is right the guy above me
Step-by-step explanation:
15 POINTS PLS HELP MATHEMATICS
7(2e−1)−3=6+6e
Solve for e
Answer:
e=2
Step-by-step explanation:
7(2e−1)−3=6+6e
Distribute
14e -7 -3 = 6+6e
14e -10 = 6+6e
Subtract 6e from each side
14e-6e -10 = 6+6e-6e
8e -10 =6
Add 10 to each side
8e -10+10 = 6+10
8e = 16
Divide by 8
8e/8 = 16/8
e=2
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 82% confidence interval to 25 points, how many students should the administrator sample
Answer:
The appropriate solution is "259".
Step-by-step explanation:
According to the question,
[tex]\sigma = 300[/tex]
[tex]M.E=25[/tex]
At 82% CI,
[tex]\alpha = 0.18[/tex]
Critical value,
[tex]Z_c=1.341[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]
By substituting the values, we get
[tex]=(1.341\times \frac{300}{25} )^2[/tex]
[tex]=(1.341\times 12)^2[/tex]
[tex]=259[/tex]
Function: g(x) = 2x2 - 8
Answer:
f(x)= √ 1 2 x + 4 For x ≤ 0
Step-by-step explanation:
What are the coordinates grapging x=3 and y=-2x+1
From the figure, how many square units are the area of a triangle xwy when yw=zw?
A. 1.84
B. 1.42
C. 0.42
D. 0.84
Answer:
0.42
Step-by-step explanation:
→ Use Pythagoras to find YZ
√2.5² - 0.7² = 2.4
→ Half the answer to find YW
2.4 ÷ 2 = 1.2
→ Substitute the values into the formula for the area of a triangle
0.5 × 0.7 × 1.2 = 0.42
What is the point-slope form of a line with slope -3 that contains the point
(10, -1)?
Answer:
General equation of line:
[tex]{ \bf{y = mx + c}}[/tex]
Find y-intercept:
[tex]{ \tt{ - 1 = ( - 3 \times 10) + c}} \\ { \tt{c = 29}}[/tex]
Equation of line:
[tex]{ \bf{y = - 3x + 29}}[/tex]
7(x-9y) need an answer
Answer:
7x - 63y
Step-by-step explanation:
Given
7(x - 9y) ← multiply each term in the parenthesis by 7
= 7x - 63y
Henry rolls a fair dice 42 times.
How many times would Henry expect to roll an odd number?
Answer:
You should get 21 odds
Step-by-step explanation:
There are 6 possible outcomes on a fair die
1,2,3,4,5,6
3 of the outcomes are odd
1,3,5
P(odd) = odd outcomes/ total = 3/6 =1/2
Rolling 42 times
number of times * P(odd)
42*1/2 = 21
You should get 21 odds
What is the radius of the circle if the circumference is 18 pi centimeters
Answer:
9cm
Step-by-step explanation:
Circumference formula = 2piR
To calculate radius
The equation becomes
2piR = 18pi
R = 18pi/2pi
= 9cm
A university financial aid office polled a random sample of 670 male undergraduate students and 617 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 388 of the male students and 323 of the female students said that they had worked during the previous summer. Give a 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer. Construct the 90 % confidence interval.
Answer:
The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Male undergraduates:
670, 388 were employed. So
[tex]p_M = \frac{388}{670} = 0.5791[/tex]
[tex]s_M = \sqrt{\frac{0.5791*0.4209}{670}} = 0.0191[/tex]
Female undergraduates:
Of 617, 323 were employed. So
[tex]p_F = \frac{323}{617} = 0.5235[/tex]
[tex]s_F = \sqrt{\frac{0.5235*0.4765}{617}} = 0.0201[/tex]
Distribution of the difference:
[tex]p = p_M - p_F = 0.5791 - 0.5235 = 0.0556[/tex]
[tex]s = sqrt{s_M^2+s_F^2} = \sqrt{0.0201^2 + 0.0191^2} = 0.0277[/tex]
Confidence interval:
The confidence interval is given by:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.0556 - 1.645*0.0277 = 0.01[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.0556 + 1.645*0.0277 = 0.1012[/tex]
The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).
Can someone please help me with this.
Household Size Probability 1 0.04 2 0.09 3 0.14 4 0.20 5 0.29 6 0.14 7 0.08 8 0.02 a. What is the probability that there are less than 5 members in a household in India
Given:
Probability distribution table is:
Household Size : 1 2 3 4 5 6 7 8
Probability : 0.04 0.09 0.14 0.20 0.29 0.14 0.08 0.02
To find:
The probability that there are less than 5 members in a household in India.
Solution:
Let x be the number of members in a household. The probability that there are less than 5 members in a household in India is:
[tex]P(x<5)=P(x=1)+P(x=2)+P(x=3)+P(x=4)[/tex]
[tex]P(x<5)=0.04+0.09+0.14+0.20[/tex]
[tex]P(x<5)=0.47[/tex]
Therefore, the probability that there are less than 5 members in a household in India is 0.47.
consider the absolute value function f(x)=a|x|
Answer:
huh
Step-by-step explanation:
what's the question? i've taken the function into consideration, and determined that i have absolutely no clue what you're asking. "a" is a coefficient, or what "|x|" is being multiplied by.
Solve for X. Round to the nearest tenth, if necessary. Please help
Answer:
X=1.2/1.3
answérica is 1.25, depends on how you want to round
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The given composite shape has an area of (72,78,66,84) cm2 and a perimeter of (42,47,40,33) cm.
Answer:
78 cm²
42 cm
Step-by-step explanation:
To obtain the area of the shape given :
The figure is divide into three different rectanglular parts :
Recall, area of a rectangle = Length x width :
Rectangle 1 : 9* 6 = 54 cm²
Rectangle 2 = 6 * 2 = 12 cm²
Rectangle 3 = 4 * 3 = 12 cm²
Total area = (54 + 12 + 12). = 78 cm²
Perimeter = sun of the exterior sides of the shape
Perimeter = (9 + 8 + 3 + 4 + 3 + 6 + 3 + 6) = 42 cm
Given the functions below, find f(x) - g(x) f(x) = 3x^2 + 2x + 1 g(x) = x^2 - 6x + 3
Answer:
Here is your answer.....
Hope it helps....
The value of given function f(x) - g(x) is 2x² + 2x + 1.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.Given,
f(x) =3x² + 2x + 1
g(x) = x² - 6x + 3
f(x) - g(x) = ( 3x² + 2x + 1) - ( x²- 6x + 3)
= 3x² + 2x +1 - x² + 6x - 3
= 2x² +8x - 2
Therefore , the value of given function f(x) - g(x) is 2x² + 2x + 1.
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In a tram, 12% of the passengers go without a ticket. What can be the largest number of passangers in the tram, if its not greater than 60
45 POINTS
(9,2) and (5,-4) find the slope of the line containing the pair of points
Answer:
3/2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= ( -4-2)/(5-9)
= -6/-4
=3/2
