Answer: Point slope form is y-y1=m(x-x1)
Step-by-step explanation:
Here y1=4
x1=-11
m i.e slope=-2
And there you go.
To prove a polygon is a rectangle which of the properties listed must be included in the proof
Answer:
if the diagonals of a parallelogram are congruent, then it's a rectangle (neither the reverse of the definition nor the converse of a property). If a parallelogram contains a right angle, then it's a rectangle (neither the reverse of the definition nor the converse of a property).
Step-by-step explanation:
Please help!!! Which of the following is equal to the rational expression when x ≠ -2 or 3? x^2+5x+6/x^2-x-6
Answer:
see below
Step-by-step explanation:
These are always simplified by cancelling common factors from numerator and denominator. In order to do that, you have to factor the expressions. The restrictions on x give a clue as to the factors of the denominator.
[tex]\dfrac{x^2+5x+6}{x^2-x-6}=\dfrac{(x+3)(x+2)}{(x-3)(x+2)}=\boxed{\dfrac{x+3}{x-3}}[/tex]
The best possible statement to your question is x+3 / x-3
evaluate will give brainlist
Answer:
C. 1/25
Step-by-step explanation:
5^-2=5^(2*-1)
5^2=25
25^-1=1/25
Answer:
It is C 1/25 because it won't be -25 because a negative times a negative is a positive
Step-by-step explanation:
Employees at a company produced refrigerators on three shifts. Each shift recorded their quality stats below. A unit was considered defective if it at least one part was assembled wrong or was missing. Management believes that quality depends on the the shift it was produced. Test the claim that shifts are independent of quality using chi-square at alpha = 0.05. SHOW YOUR WORK
Answer:
Step-by-step explanation:
Hello!
So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.
Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.
The hypotheses are:
H₀: The variables are independent.
H₁: The variables are not independent.
α: 0.05
[tex]X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~X_{(r-1)(c-1)}[/tex]
r= total number of rows
c= total number of columns
i= 1, 2 (categories in rows)
j=1, 2, 3 (categories in columns)
To calculate the statistic you have to calculate the expected frequencies for each category:
[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]
[tex]O_{i.}[/tex] Represents the marginal value of the i-row
[tex]O_{.j}[/tex] Represents the marginal value of the j-column
[tex]E_{11}= \frac{O_{1.}*O_{.1}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{12}= \frac{O_{1.}*O_{.2}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{13}= \frac{O_{1.}*O_{.3}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{21}= \frac{O_{2.}*O_{.1}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{22}= \frac{O_{2.}*O_{.2}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{23}= \frac{O_{2.}*O_{.3}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]X^2_{H_0}= \frac{(7-7)^2}{7} + \frac{(5-7)^2}{7} + \frac{(9-7)^2}{7} + \frac{(33-33)^2}{33} + \frac{(35-33)^2}{33} + \frac{(31-33)^2}{33} = 1.385= 1.34[/tex]
Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:
[tex]X^2_{(c-1)(r-1);1-\alpha }= X^2_{2; 0.95}= 5.991[/tex]
Decision rule:
If [tex]X^2_{H_0}[/tex] ≥ 5.991, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 5.991, do not reject the null hypothesis.
The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.
At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.
I hope this helps!
A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?
O y=-4x + 5
y = 4x-5
2y = 8x - 10
-2y = -8x - 10
Answer:
[tex]4x -y = 5[/tex]
And if we rewrite this expression we got:
[tex] y= 4x -5[/tex]
If the system have just one solution then we need the slope different and for this reason we can discard the options:
y = 4x-5
-2y = -8x - 10 equivalent to y =4x+5
2y = 8x - 10 equivalent to y = 4x -5
And then the correct answer would be:
y=-4x + 5
Step-by-step explanation:
For this case we have the following equation given:
[tex]4x -y = 5[/tex]
And if we rewrite this expression we got:
[tex] y= 4x -5[/tex]
If the system have just one solution then we need the slope different and for this reason we can discard the options:
y = 4x-5
-2y = -8x - 10 equivalent to y =4x+5
2y = 8x - 10 equivalent to y = 4x -5
And then the correct answer would be:
y=-4x + 5
Answer:
A: y = –4x + 5
Step-by-step explanation:
I got it right on Edge
Solve for x. 6−x3=3 x=9 x=−9 x=27 x=−27
please help image attached!
Answer:
The unit circle centered at the origin in the Euclidean plane is defined by the equation:
[tex]x^2+y^2=1\\[/tex]
Given an angle , there is a unique point P on the unit circle at an angle θ from the x-axis, and the x- and y-coordinates of P are:
[tex]x=cos \theta \\y = sin \theta[/tex]
Consequently, from the equation for the unit circle:
[tex]cos^2\theta+sin^2\theta=1[/tex]
the Pythagorean identity.
What is the additive inverse of the complex number 9-4i?
Answer:
[tex] \frac{1}{9 - 4i} [/tex]
I'm not sure
A U.S.-based Internet company offers an online proficiency course in basic accounting. Completing this online course satisfies the "Fundamentals of Accounting" course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. Region Enrollment 1 45 2 60 3 30 4 40 5 50 6 55 7 35 The CEO looked at the data presented and said no they are not equal. It is obvious, since the enrollment in one region is 60 and another 30. However, the CFO said that using a Chi-Square Goodness of Fit Test with a 1% significance level, the frequencies in the regions are not significantly different. Which one is correct? Use statistics to support your answer.
Answer:
[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]
[tex]Expected \ mean = \dfrac{315 }{7}[/tex]
Expected mean = 45
The Chi - Square Value = 15.556
Conclusion:
We conclude that there is equal number of average interest in the course across all regions.
Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.
Step-by-step explanation:
From the question; Let state our null hypothesis and alternative hypothesis
Null Hypothesis
[tex]\mathbf{H_0:}[/tex]There is equal number of average interest in the course across all regions.
Alternative Hypothesis
[tex]\mathbf{H_a:}[/tex] At least one of the region differs in average number of interest in the course.
The table can be better structured as :
Region Enrollment
1 45
2 60
3 30
4 40
5 50
6 55
7 35
From above; we know the number of sample = 7
Then our expected mean can be calculated as :
[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]
[tex]Expected \ mean = \dfrac{315 }{7}[/tex]
Expected mean = 45
SO, let's construct our Chi-Square Statistics Test Table as follows:
Observed Expected Expected (O-E)² [tex]\dfrac{(O-E)^2}{E}[/tex]
(O) (E) proportion
45 45 0.142857 0 0
60 45 0.142857 225 5
30 45 0.142857 225 5
40 45 0.142857 25 0.556
50 45 0.142857 25 0.556
55 45 0.142857 100 2.222
35 45 0.142857 100 2.222
15.556
The Chi - Square Value = 15.556
Degree of freedom = n- 1
Degree of freedom = 7 - 1
Degree of freedom = 6
Level of significance ∝ = 1% = 0.01
The Critical value of Chi Square test statistic at df = 6 and 0.01 significance level is 16.812
The Decision rule is to reject the Null hypothesis if The Chi Square test statistic X² > 16.812
Thus , since the Chi Square test statistic is lesser than the critical value,
i.e 15.556 < 16.812 ,we accept null hypothesis [tex]\mathbf{H_0}[/tex]
Conclusion:
We conclude that there is equal number of average interest in the course across all regions.
Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.
Consider the polynomial 9x2 – 16.
Answer: 2
Step-by-step explanation:
9 × 2 - 16
18 - 16
2
A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 2010 to 2012. The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q1 + 1.28 Q2 + 0.617 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise Using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 2013?A. The quarterly growth rate in the number of contracts is significantly different from 100% (? = 0.05).
B. The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05).
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
D. The quarterly growth rate in the number of contracts is not significantly different from 100% (? = 0.05).
There is a missing content in the question.
After the statements and before the the options given; there is an omitted content which says:
Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?
Answer:
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
Step-by-step explanation:
From the given question:
The resulting regression equation can be represented as:
[tex]\hat Y = 3.37 + 0.117 X - 0.083 Q_1 + 1.28 Q_2 + 0.617Q_3[/tex]
where;
the estimated number of contracts in a quarter X is the coded quarterly value with X = 0
the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise
Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise
Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise
Our null and alternative hypothesis can be stated as;
Null hypothesis :
[tex]H_0 :[/tex] The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05)
[tex]H_a:[/tex] The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
The decision rule is to reject the null hypothesis if the p-value is less than 0.05.
From the missing omitted part we added above; we can see that the t-statistics value = 9.08 and the p-value = 0.000 .
Conclusion:
Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
Use the compound interest formulas A = Pert and A = P(1 + ) to solve. Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually? Show your work
Answer:
Continuously
Step-by-step explanation:
Compounded continuously:
A = Pe^(rt)
A = 11,000 e^(0.0625 × 10)
A = 20,550.71
Compounded semiannually (twice per year):
A = P(1 + r)^t
A = 11,000 (1 + 0.063/2)^(2×10)
A = 11,000 (1 + 0.0315)^20
A = 20,453.96
What is the mode of this set of data?
Answer:
The mode is 15
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).
Answer:
The mode of this set is 15.
Step-by-step explanation:
the mode is 15 bcoz 15 is repeated two times where as other numbers aren't repeated..
Use z scores to compare the given values. Based on sample data, newborn males have weights with a mean of 3259.6 g and a standard deviation of 722.4 g. Newborn females have weights with a mean of 3031.2 g and a standard deviation of 495.9 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g? Since the z score for the male is zequals nothing and the z score for the female is zequals nothing, the female female male has the weight that is more extreme.
Answer:
Since the z score for the male is z=-2.1589 and the z score for the female is z=-2.6844, the female has the weight that is more extreme.
Step-by-step explanation:
To find the z score, we use the following equation:
[tex]z=\frac{x-m}{s}[/tex]
Where m is the mean and s is the standard deviation.
So, the z score for a male who weighs 1700 g is:
[tex]z=\frac{1700-3259.6}{722.4}=-2.1589[/tex]
At the same way, the z score for a female who weighs 1700 g is:
[tex]z=\frac{1700-3031.2}{495.9}=-2.6844[/tex]
Finally, -2.6844 is farther from zero than -2.1589, so the female has the weight that is more extreme.
What value of x makes 3(x + 4) = 3x + 4 true?
Well lets see.
[tex]3(x+4)=3x+4\implies 12 = 4\implies x\notin\mathbb{C}[/tex].
There are no such x-es that satisfy the equation.
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2013?
Answer: The population will be 408,000 people.
Step-by-step explanation:
So in 2000 there were 200,000 people and it started to grow 8% every year so up to 2013.
so find 8% of 200,000 and then multiply it by the the number of years.
8% * 200,000 = 16,000
Find the difference between the years.
2013 - 2000 = 13 years
13 * 16000 = 208000 This is the amount of new people from 2000 to 2013 so add it to the original population.
208,000 + 200,000 = 408,000
Which of the following is the perimeter of a triangle with side lengths of 18 cm, 26 cm, and 32 cm?
Answer:
76 cm
Step-by-step explanation:
To find the perimeter, add up all of the side lengths.
18 cm + 26 cm + 32 cm = 76 cm
I hope this helps :))
which is the domain of f(x) = 4^x
will give brainlist!
Answer:
all real numbers
Step-by-step explanation:
The domain is the input values
All values for x are valid as inputs to the function
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.
60
25
Answer:
65
Step-by-step explanation:
C^2= A^2 + B^2
C^2 = (60)^2 + (25)^2
C^2 = 4225
Take the square root of C
C = 65
Answer:
65
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
I'm assuming that '60' and '25' are measures of the legs, since the question asks to find the hypotenuse.
[tex]60^2+25^2=c^2\\\rightarrow 60^2=3600\\\rightarrow 25^2 = 625\\3600+625=c^2\\4225=c^2\\\sqrt{4225}=\sqrt{c^2}\\\boxed{65=c}[/tex]
The hypotenuse should measure 65 units.
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
PLEASE HELP
Answer: [tex]y=\frac{3}{2} x - 3[/tex]
Step-by-step explanation:
Looking at the graph we could locate the y intercept at point (0,-3) and we can locate another point (4,3) which also passes through the line. So using these coordinates we already know the the y-intercept as -3 but we need to find the slope to write it in slope intercept form.
To find the slope, we will need to find the difference in the y values and divide it by the difference in the x values.
(0,-3)
(4,3)
-3 - 3 = -6
0-4 = -4
-6 /-4 = 3/2 so now we know that the slope is 3 over 2
so we could write the equation as y = 3/2x -3
Answer: Thank you (nermay7)
Step-by-step explanation: They are correct!!!!!!!
Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards. A sample of 20 cards are selected from the lot without replacement for functional testing. (a) If 20 cards are defective, what is the probability that at least one defective card appears in the sample
Answer:
The probability that at least one defective card appears in the sample
P(D) = 0.9644 or 96.44%
Step-by-step explanation:
Given;
Total number of cards t = 140
Number of defective cards = 20
Number of non defective cards x = 140-20 = 120
The probability that at least one defective card = 1 - The probability that none none is defective
P(D) = 1 - P(N) ........1
For 20 selections; r = 20
-- 20 cards are selected from the lot without replacement for functional testing
The probability that none none is defective is;
P(N) = (xPr)/(tPr)
P(N) = (120P20)/(140P20)
P(N) = (120!/(120-20)!)/(140!/(140-20)!)
P(N) = (120!/100!)/(140!/120!) = 0.035618370821
P(N) = 0.0356
The probability that at least one defective card appears in the sample is;
P(D) = 1 - P(N) = 1 - 0.0356 = 0.9644
P(D) = 0.9644 or 96.44%
Note: xPr = x permutation r
Which of the following linear equations has the steepest slope?
A. Y = -2x +11
B. y=+x+4
C. y - x +7
D. y - 7+2
Answer:
A --- unless d is supposed to be "y= -7x + 2"
Step-by-step explanation:
The slope is m in y=mx + b
So:
a. y= -2x + 11 slope= -2
b. y= x + 4 slope= 1
c. y= -x + 7 slope= -1
d. y= -7 + 2 (I don's see an x but if there were an x I assume that the slope would equal -7)
The higher the m value, the steeper the slope because it is m/1
So, -2/1 is steeper than 1/1 or -1/1
1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
[tex]\dfrac{1}{216}^{-2/3}+\dfrac{1}{256}^{-3/4}+\dfrac{1}{243}^{-1/5}= \\\\\\\sqrt[3]{216^2}+\sqrt[4]{256^3}+\sqrt[5]{243}=\\\\\\6^2+4^3+3=\\\\\\36+64+3=\\\\\\103[/tex]
Hope this helps!
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
1/2
Step-by-step explanation:
Find two points on the line
(2,0) and (4,1)
The slope is given by
m= (y2-y1)/(x2-x1)
=(1-0)/(4-2)
= 1/2
Mai deposited $4000 into an account with 4.8% interest, compounded quarterly. Assuming that no withdrawals are made, how much will she have in the
account after 7 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
5,586.17
Step-by-step explanation:
A = $ 5,586.17
A = P + I where
P (principal) = $ 4,000.00
I (interest) = $ 1,586.17
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
Step-by-step explanation:
The complete question is:
There are 103 students in a physics class. The instructor must choose two students at random.
Students in a Physics Class
Academic Year Physics majors Non-Physics majors
Freshmen 17 15
Sophomores 20 14
Juniors 11 17
Seniors 5 4
What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Solution:
There are a total of N = 103 students present in a Physics class.
Some of the students are Physics Major and some are not.
The instructor has to select two students at random.
The instructor first selects a senior Physics major and then a sophomore Physics major.
Compute the probability of selecting a senior Physics major student as follows:
[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]
[tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]
Now he two students are selected without replacement.
So, after selecting a senior Physics major student there are 102 students remaining in the class.
Compute the probability of selecting a sophomore Physics major student as follows:
[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]
[tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]
Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:
[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]
[tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]
Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.
8b-ab=7a, .subtracted from 3a-9ab+b
Answer: You can't. Read explanation.
Step-by-step explanation:
You can't subtract an expression from an equation. If you said something like subtract 8b-ab+7a from 3a-9ab+b that would work, but not here.
Let's just assume You mean it as 8b-ab-7a, then (3a-9ab+b)-(8b-ab-7a) = -8ab + 10a - 7b.
Hope that helped,
-sirswagger21
A card is drawn from a standard deck of 5252 playing cards. What is the probability that the card will be a heart and not a club? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
The probability of choosing a heart and not a club is
P = 0.1875
Step-by-step explanation:
There are 13 hearts in a deck of 52 cards. The probability that the chosen card will be a heart is given by
Probability = favorable outcome/ Total number of outcomes
P= 13/52= 1/4
There are 13 clubs in a deck of 52 cards.
The probability of not choosing a club would be
P = 52-13/52= 39/52= 3/4
So the combined probability of choosing a heart and not a club is
P = 1/4 * 3/4= 0.25 * 0.75= 0.1875
A machine part consist of a half sphere and a cylinder, as shown in the figure.the total volume of the part is blank pi c
Answer:
Volume of the machine part = 114π inches³
Step-by-step explanation:
Volume of the machine part = Volume of cylinder + Volume of hemisphere
Volume of cylinder = [tex]\pi r^{2}h[/tex]
Where r = radius of the cylinder
h = height of the cylinder
Volume of the cylinder = [tex]\pi(\frac{6}{2})^{2}(12)[/tex]
= 108π inches³
Volume of the hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]
= [tex]\frac{2}{3}\pi (3)^{3}[/tex]
= 6π inches³
Total area of the machine part = 108π + 6π
= 114π inches³
I NEED HELP PLEASE HELP ME
Answer:
3
Step-by-step explanation:
Solving the inequality
2x-1>=5
2x>=6
x>=3
The graph should have a shaded circle on 3 and a line pointing to values increasing.
