Explanation:
The domain is the horizontal extent of the graph of the function. It is the set of all values of the independent variable for which the function is defined.
In a table or list of (x, y) or (x, f(x)) values the domain is the list of x-values.
On a graph, the domain is the horizontal extent of the graph, excluding any "holes" or vertical asymptotes. (The function is "undefined" at those places.)
__
For a polynomial, the domain is generally "all real numbers."
For rational functions, the domain always excludes any x-values that make any denominator be zero.
For functions such as logarithms or roots, the domain is the set of values for which the function is defined. Even roots (square root, 4th root, ...) are only defined for non-negative numbers. Logarithms are only defined for positive numbers.
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In some problems, a model is often used that is defined for all values of the independent variable. For example, a height function may be modeled using a quadratic: h(t) = -4.9t^2 +30t +6. This is defined for all values of t, but the "practical domain" is the set of values of t ≥ 0 and before h(t) = 0. That is, we don't care about negative time or negative height.
Which equation represents the circle shown?
A. (x − 3)2 + (y − 3)2 = 4
B. (x − 3)2 + (y − 3)2 = 16
C. (x + 3)2 + (y + 3)2 = 4
D. (x + 3)2 + (y + 3)2 = 16
E. (x + 4)2 + (y + 4)2 = 3
B. (x-3)2+(y-3)2=16
Equation of circle is
(x-a)2+(y-b)2=r2
Grouping 12x3 – 9x2 + 4x - 3?
[tex]12x^{3} - {9x}^{2} + 4x - 3 = \\ = 3 {x}^{2} (4x - 3) + 1(4x - 3) = \\ = (4x - 3)( {3x}^{2} + 1)[/tex]
Answer:4x+15
Step-by-step explanation: PEMDAS. First you multiply 12x3 and 9x2 so you get 36-18. Then you subtract 18 from 36 leaving you with 18. Then you combine 18 and -3, leaving you with 4x-15.
answer quick please (2x2 + 5x - 7) + (3 - 4x2 + 6x)
Answer:
[tex] \frac{8}{11} [/tex]
Step-by-step explanation:
(4+5x-7)+(3-8+6x)=0
(-3+5x)+(-5+6x)=0
-8+11x=0
x=8/11
Answer:
Step-by-step explanation:
Plz help me with my school work.
Answer:
∠HGB = 20°
∠ECD = 34°
∠GBH = 36°
∠FGH = 37°
Step-by-step explanation:
There are several useful rules regarding angles:
right angles are 90°the sum of angles in a triangle is 180°angles of a linear pair are supplementary (total 180°)vertical angles are congruentan exterior angle is equal to the sum of the remote interior anglesThis last observation is a consequence of the 2nd and 3rd observations.
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angle ECD
Using the last observation, ∠ECD = 124° -90° = 34°.
angle HGB
Again, using the last observation, ∠HGB = 110° -90° = 20°.
angle GBH
There are at least a couple of ways to find this one. We assume that lines FB and EC are parallel, so angles HBC and ECD are corresponding, hence congruent. Angle GBC is the supplement of of 110°, so is 70°. Then ...
∠GBH = 70° -34° = 36°
angle FGH
Again, this angle can be found multiple ways. Here, we'll use the sum of angles in triangle FGB.
∠FGB +∠GBF +∠BFG = 180°
(∠FGH +∠HGB) +∠GBF +∠BFG = 180°
∠FGH +20° +36° +87° = 180°
∠FGH = 180° -143° = 37°
__
Least to greatest, the angles are ...
∠HGB = 20°
∠ECD = 34°
∠GBH = 36°
∠FGH = 37°
Each person tries to balance his or her time between leisure and work. The tradeoff is that as you work less your income falls. Therefore each person has indifference curves which connect the number of hours of leisure, l, and income, s. If, for example, you are indifferent between 0 hours of leisure and an income of $1125 a week on the one hand, and 10 hours of leisure and an income of $750 a week on the other hand, then the points l = 0, s = 1125, and l = 10, s = 750 both lie on the same indifference curve.
The table below gives information on three indifference curves, I, II, and III.
Weekly Income Weekly Leisure Hours
I II III I II III
1125 1250 1375 0 20 40
750 875 1000 10 30 50
500 625 750 20 40 60
375 500 625 30 50 70
250 375 500 50 70 90
(a) On a sheet of paper, or using a calculator or other technology, graph the three indifference curves. (You will need these to answer part (d) of this problem.)(b) You have 95 hours a week available for work and leisure combined, and you earn $21.45/hour. Write an equation in terms of l and s which represents this constraint. (c) Graph this constraint with your graph of the indifference curves.(d) Estimate from the graph what combination of leisure hours and income you would choose under these circumstances. What is the corresponding number of hours per week you would work?
Answer:
.............gcg................
Evaluate how organizations can use one-sample hypothesis testing to determine if there are performance issues in the organization. Support your response with a specific example.
Answer:
Organizations can use one-sample hypothesis test to determine if there are performance issues in many ways.
It can be applied to the performance of a sector, a machine, a product, an advertising campaing, etc.
For example, we can take the example of a machine. It may be claimed that a specific machine performs significantly worse than the average.
This average would be the population mean: the average performance of the machines of the same type or process.
Then, a sample of the performance of the machine in study is taken and the hypothesis test can be performed to test the claim that this machine performs significantly worse.
Step-by-step explanation:
For example, we have an historic performance for this type of machine of 100 units a day. The machine A in study is sampled 14 days and have a performance of 92 units a day, with a sample standard deviation of 12 units/day. We have to test the claim that the machine A makes less units per day than the average.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]
The significance level is 0.05.
The sample has a size n=14.
The sample mean is M=92.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{14}}=3.2071[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{92-100}{3.2071}=\dfrac{-8}{3.2071}=-2.4944[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=14-1=13[/tex]
This test is a left-tailed test, with 13 degrees of freedom and t=-2.4944, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-2.4944)=0.0134[/tex]
As the P-value (0.0134) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that machine A produces significantly less units per day than the average.
Suppose I have a right trapezoid with base lengths of 4 and 16. Is there any way I can find out what the missing side is? (see image attached)
Answer:
no
Step-by-step explanation:
If you draw a line from the right end of the top base to the bottom base, parallel to the left side, you cut off a right triangle that has a bottom leg of 12 and two unknown sides (height, and slant length).
All you can say is that the unknown slant length is more than 12 units.
If you know the height, you can find the slant length (hypotenuse) using the Pythagorean theorem.
a. Use the one-mean t-interval procedure with the sample mean, sample size, sample standard deviation, and confidence level given below to find a confidence interval for the mean of the population from which the sample was drawn.
b. Obtain the margin of error by taking half the length of the confidence interval.
c. Obtain the margin of error by using the formula talpha/2. s/(n)^1/2.
x overbar = 20 n = 25 s = 4 confidence level = 98%
Answer:
a) (17.227, 22.773)
b) 2.773
c) 2.773
Step-by-step explanation:
Given:
Sample size, n = 25
Standard deviation, s = 4
Sample mean, x' = 20
Level of significance, a = 0.98 = 1 - 0.98 = 0.02
The degrees of freedom, df, for a t-distribution = n - 1 = 25 - 1 = 24
Using the t table, the Critical value = [tex] t_\alpha _/_2, _d_f = t_0_._0_2_/_2, _2_4 = t_0_._0_1_, _2_4 = 3.4668 [/tex]
Margin of error, E = [tex] t_\alpha _/_2, _d_f * \frac{\sigma}{\sqrt{n}} = 3.4668 * \frac{4}{\sqrt{25}} = 2.773 [/tex]
Limits of 98% confidence interval, we have:
Lower limit : x' - M.E = 20 - 2.773 = 17.227
Upper limit: x' + M.E = 20 + 2.773 = 22.773
Therefore, (17.227, 22.773) is 98% confidence interval.
b) Let's the margin of error by taking half the length of the confidence interval.
Since we are to use half the length of CI, we have:
[tex] M.E = \frac{22.773 - 17.227}{2} = 2.773 [/tex]
c)[tex] M.E = t_\alpha _/_2, _d_f *s/\sqrt{n} [/tex]
[tex] = t * \frac{s}{\sqrt{n}} = 3.4668 * \frac{4}{\sqrt{25}} = 2.773 [/tex]
The rental of the ice is $75, plus $3 per skater. Write an expression for the cost in dollars for n skaters.
Answer:
f(n)=75+(n*3)
Step-by-step explanation:
what is this equation x2 – 2x – 6 in vertex form?
Answer:
In vertex form, the parabola's equation is y=(x−1)^2 +5.
Step-by-step explanation:
when a number is decreased by 19% the result is 66 what is the original number to
the nearest tenth percent
Answer:
The original number is x = 66 .19
Step-by-step explanation:
Let 'x' be the number
Given data a number is decreased by 19% the result is 66
x - 19% = 66
x-0.19 = 66
Adding '0.19' on both sides , we get
x - 0.19 +0.19 = 66 +0.19
x = 66 .19
The original number is x = 66 .19
The original number is 66.19.
Given that,
The number is decreased by 19% the result is 66.
We have to determine,
What is the original number?
According to the question,
Let, the original number be x,
The number is decreased by 19% the result is 66.
[tex]x - \dfrac{19}{100} = 66\\\\x - 0.19 = 66\\\\x = 66 + 0.19\\\\x = 66.19[/tex]
Hence, The required original number is 66.19.
To know more about Linear inequality click the link given below.
https://brainly.com/question/8138166
A community is building a square park with side is that measure 120 m to separate the picnic area from the play area the park is split by a diagonal line what is the approximate length of the diagonal line
Answer:
(120^2+120^2)^0.5 = 169.705m
Step-by-step explanation:
Pythagorean Theorem
Use the figure to complete the statements.
The area of the base, B, of the pyramid is cm2.
The volume of the pyramid is cm3.asap
Answer:
The area of the base, B, of the pyramid is 96 cm2
he volume of the pyramid is 320 cm3.
Step-by-step explanation:
Answer:
96 320
Step-by-step explanation:
In a baseball tournament, teams get 5 points for a win, 3 points for a tie and 1 point for a loss Nathan’s team has 29 points how many different combinations of wins ties and losses can Nathan’s team have
Answer:
37 different combinations
Step-by-step explanation:
First of all, we will count the possible combinations that add up to 29.
-Losses only;
One possibility: 29 losses
-Ties & losses;
Nine possibilities: 1 tie and 26 losses; 2 ties and 23 losses; 3 ties and 20 losses;4 ties and 17 losses; 5 ties and 14 losses; 6 ties and 11 losses; 7 ties and 8 losses; 8 ties and 5 losses; 9 ties and 2 losses
-Wins & losses
Five possibilities: 1 win and 24 losses; 2 wins and 19 losses; 3 wins and 14 losses; 4 wins and 9 losses; 5 wins and 4 losses
Now, what we want to find from the question is number of possibilities for wins, ties, and losses all together. So, we will count up the ties and losses in the remainder for each case of a given number of wins.
Thus;
For 0 Wins: 0 ties and 29 losses; 1 tie and 26 losses; 2 ties and 23 losses; 3 ties and 20 losses;4 ties and 17 losses; 5 ties and 14 losses; 6 ties and 11 losses; 7 ties and 8 losses; 8 ties and 5 losses; 9 ties and 2 losses.
Which sums up to 10 possibilities
For 1 win; 0 ties and 24 losses; 1 tie and 21 losses........8 ties and 0 losses.
Which sums up to 9 possibilities
For 2 wins; 0 ties and 19 losses; 1 tie & 16 losses............ 6 ties and 1 loss.
Which sums up to 7 possibilities
For 3 wins; 0 ties and 14 losses; 1 tie and 11 losses ....... 4 ties and 2 losses.
Which sums up to 5 possibilities
For 4 wins; 0 ties & 9 losses; 1 tie and 6 losses....... 3 ties and 0 losses
Which sums up to 4 possibilities
For 5 wins; 0 ties and 4 losses; 1 tie and 1 loss
Which sums up to 2 possibilities
Thus;
Total number of possibilities of combinations of wins, ties and losses = 10 + 9 + 7 + 5 + 4 + 2 = 37
You can type 36 words per 18 minute. How many words can you type in 2 minutes?
Answer:
4 words in 2 minutes
Step-by-step explanation:
36 / 18 = 2
2 words per minutes
2 x 2 = 4
You can type 4 words in two minutes
Step-by-step explanation:
So if you can type 36 word in 18 minutes then divide 36 by 18 to get 2 words per minute. Now multiply 2 words by 2 minutes to get 4 words per minute, your answer.
Given the inequality -10x + y > 25, determine whether the following two ordered pairs are included in the solution set.
(0, 25)
(-4, 10)
Which of the following statements is true?
Question 5 options:
The point (0, 25) is a solution, but the point (-4, 10) is not a solution.
The point (0, 25) is not a solution, but the point (-4, 10) is a solution.
Both (0, 25) and (-4, 10) are solutions.
Both (0, 25) and (-4, 10) are not solutions.
Answer:
The point (0, 25) is not a solution, but the point (-4, 10) is a solution.
Step-by-step explanation:
You can graph the inequality and check. The first point (0, 25) is on the boundary line, but that line is NOT part of the solution set. The second point (-4, 10) is well inside the solution space.
(0, 25) is not a solution
(-4, 10) is a solution
_____
You can put the values into the inequality and see if a true statement results.
-10(0) +(25) > 25 . . . . False
-10(-4) +(10) > 25 . . . . true
The first point is NOT a solution; the second point IS a solution.
what makes an equation true?
Answer:
Step-by-step explanation:
An equation is true when certain values are able to be substituted for the variable which is most of the time "x", the values that make an equation true is when the answer has a solution.
What is the determinant of A = [ -2 2 -5 4 -1 -2 1 3 -5]
Answer:
-51
Step-by-step explanation:
[tex]\begin{vmatrix}-2&2&-5\\4&-1&-2\\1&3&-5\end{vmatrix}=\\=\mathsf{-10-4-60-5+40-12}=\\=\mathsf{-91+40}=\\=\mathsf{-51}[/tex]
Answer:
-51
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}-2&2&-5\\4&-1&-2\\1&3&-5\end{array}\right] =1*\left[\begin{array}{ccc}2&-5\\-1&-2\end{array}\right] +(-3)*\left[\begin{array}{ccc}-2&-5\\4&-2\end{array}\right] +(-5)*\left[\begin{array}{ccc}-2&2\\4&-1\end{array}\right] =-9+(-72)+30=-9-72+30=-51[/tex]
A freshman English class at a certain college has 49 women and 20 men. If 5 students are randomly selected, what is the probability that they are all men? Round to five decimal places.
Answer:
0.00138
Step-by-step explanation:
Cuanto es 32256 dividido para 25 con proceso
Answer:
49905 dividido por 81 = 616.11
32256 dividido por 25= 1290.24
58308 dividido por 64= 911.06
9218 dividido por 768= 12.0026.
Select one of these options to each of these 6 question thar apply to
A .Slope formula
B. Given
C. Perpendicular lines intersect to form right angles.
D. Multiply.
E. Definition of right triangle
F. If the product of the slopes of two nonvertical lines is −1
the lines are perpendicular.
Answer:
1) Given
2) Slope Formula
3) Multiply
4) If the product of the slopes of two non vertical lines is -1, then the lines are perpendicular
5) Perpendicular lines intersect to form right angles
6) Definition of right triangle
Plz I need a lot of help plz solve the answer with an explanation
Step-by-step explanation:
Each roll has 6 possible outcomes, so two rolls have 36 possible sums. We can make a table showing what these sums are:
[tex]\left[\begin{array}{ccccccc}&\textbf{1}&\textbf{2}&\textbf{3}&\textbf{4}&\textbf{5}&\textbf{6}\\\textbf{1}&2&3&4&5&6&7\\\textbf{2}&3&4&5&6&7&8\\\textbf{3}&4&5&6&7&8&9\\\textbf{4}&5&6&7&8&9&10\\\textbf{5}&6&7&8&9&10&11\\\textbf{6}&7&8&9&10&11&12\end{array}\right][/tex]
Of the 36 sums, 10 are greater than 8, and 18 are odd.
P(A) = 10/36 = 5/18
P(B) = 18/36 = 1/2
The Darnells are having a swimming pool installed. The pool has a radius of 14 feet and a height of 4 feet. What is the volume of the pool? Use 3.14 for Pi.
cylinder. height 4 feet. radius 14 feet
a
351.68 cubic feet
b
703.36 cubic feet
c
2,461.76 cubic feet
d
615.44 cubic feet
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
y = x² - 8x + 17
Step-by-step explanation:
Recall this formula:
y = a(x-h)² + k
Original equation was y = x², which in this form looks like
y = 1(x - 0)² + 0
If the shape of the graph didn't change, that means that a (the compressor/intensifier) stayed the same (a - value) meaning we can write the equation as..
y = (x-h)² + k
Remember, (h, k) is the vertex, which looking from your graph is at (4, 1)
y = (x - 4)² + 1
y = x^2- 8x + 16+1
y = x² - 8x + 17
Find the average rate of change of g(x)=2x^4 + 7/x^2 on the interval [-2,4]
Answer:
79.78125
Step-by-step explanation:
The average rate of change (m) on an interval [a, b] is found as ...
m = (g(b) -g(a))/(b -a)
Here, that is ...
m = (g(4) -g(-2))/(4 -(-2))
g(-2) = 2(-2)^4 +7/(-2)^2 = 32+7/4 = 33.75
g(4) = 2(4^4) +7/(4^2) = 512 +7/16 = 512.4375
Then ...
m = (512.4375 -33.75)/6 = 478.6875/6 = 79.78125
The average rate of change of g(x) on [-2, 4] is 79.78125.
_____
The attached graph verifies the calculation and shows the line with that slope goes through the endpoints of the interval.
This Venn diagram shows the pizza topping preferences for 9 students let event A= The student likes pepperoni let event B= the student likes olives
What is P(a or b)
Answer:
B. 5/9
Step-by-step explanation:
There are 5 names listed in the circles representing pepperoni and olives, so of the 9 students, 5 like pepperoni or olives.
P(A or B) = 5/9
What is the area of circle with a diameter of 22 ft? (use 3.14 for pi; show your work in numbers)
The right answer is 379.94 ft^2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex]379.94 {in}^{2} [/tex]
Step-by-step explanation:
[tex]d = 2r \\ 22 = 2r \\ \frac{22}{2} = \frac{2r}{2} \\ \\ r = 11ft[/tex]
[tex]area = \pi {r}^{2} \\ = 3.14 \times 11 \times 11 \\ = 379.94 {ft}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
x^3+3y-xy' = 0
dy/dx = xy^3-xy
Answer:
dy/dx = xy^3-xy =
y = ± √2 = ± 1.4142
x = 0
y = 0
Step-by-step explanation:
Step 1 : Simplify y/d
Step 2 : See below
Step 3 : See below
Pulling out like terms
Trying to factor as a Difference of Squares
Answer:
y = ± √2 = ± 1.4142
x = 0
y = 0
Hope this helps.
Complete the equation of the line whose slope is -2 and y-intercept is (0,-8).
y =
Answer:
y = -2x - 8
Step-by-step explanation:
The slope is the number in front of the x. If it is a whole number then the slope is number/1. Then the slope is rise over runs. Then the y-intercept is the number after the x. Sometimes there isn't y-intercept. In this one the y-intercept is -8.
Who ever answers this correctly will get Brainliest, but be quick because I don’t have all the time.
If you cannot see PLEASE PLEASE PLEASE zoom in. I cannot stress this enough. Thank you in advance. Giving out 30 points too!
Answer:
please refer tp the photo . It s D. 101 in2
Step-by-step explanation: