Answer:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]
And we can use one of the points in order to find the intercept like this:
[tex] -3= \frac{2}{3} (-3) +b[/tex]
[tex] b =-3 +2=-1[/tex]
And the equation would be given by:
[tex] y= \frac{2}{3}x -1[/tex]
Step-by-step explanation:
We want an equation given by:
[tex] y=mx+b[/tex]
where m i the slope and b the intercept
We have the following two points given:
[tex] (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)[/tex]
We can find the slope with this formula:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]
And we can use one of the points in order to find the intercept like this:
[tex] -3= \frac{2}{3} (-3) +b[/tex]
[tex] b =-3 +2=-1[/tex]
And the equation would be given by:
[tex] y= \frac{2}{3}x -1[/tex]
(a^2-b^2) (c^2-d^2) +4abcd
[tex]a^{2} {c}^{2} - {a}^{2} {d}^{2} - {b}^{2} {c}^{2} + {b}^{2} {d}^{2} + 4abc[/tex]
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:
A store, on average, has 500 customers per day.
a) what can be said about the probability that it will have at least 700 customers on a given day?
from now on, suppose in addition that the variance of the numbers of customers per day is 100.
b) what can be said about the probability that it will have at least 700 customers on a given day?
c) what can be said about the probability that there will be more than 475 and less than 525 customers on a given day?
Answer:
a) We can not estimate the probability.
b) Zero probability.
c) There is a probability between 95% and 99% that they have between 475 and 525 customers on a given day.
Step-by-step explanation:
a) We can not said nothing because we only know the average of customers per day. We need to know the probability distribution of the amount of customers per day to answer this question.
b) Now that we know that the variance is 100, although we do not know the exact distribution of the values, we can use the empirical rules to estimate the probability of having at least 700 customers on a given day.
If the variance is 100, the standard deviation is √100=10.
Applying the empirical rule (68-95-99.7 rule), we know that there is probability 0.15% of having at least 500+3*10=530 customers per day (more than 3 deviations from the mean).
Then, we can conclude that the probability of having at least 700 customers per day is zero.
c) To estimate this probability, we have to calculate how many deviations from the mean this values represent:
[tex]\Delta_1=475-500=-25=2.5\sigma\\\\\Delta_2=525-500=25=2.5\sigma[/tex]
We have an interval that have a width of ±2.5 deviations from the mean.
For 2 deviations from the mean, it is expected to have 95% of the data.
For 3 deviations from the mean, it is expected to have 99.7% of the data.
Then, for the interval 475 to 525, we can estimate a probability between 95% and 99%.
Could someone please help me with the steps for this problem? Factor by grouping: w²+3w+w+3
Answer:
Please see steps below
Step-by-step explanation:
In order to factor by grouping, we divide the four terms given into two groups, and extract on each group any common factor we can.
In our example, we can select the terms: [tex]w^2[/tex] and [tex]w[/tex] as one of our groups, and [tex]3w[/tex] and 3 in the other group. Then we re-organize the expression as:
[tex](w^2+w)+(3x+3)[/tex]
Now we extract from the first binomial group, the factor [tex]w[/tex] as a common factor of both terms, and from the second group we extract the factor "3" as common factor of those two terms:
[tex](w^2+w)+(3x+3)\\w(w+1)+3(w+1)[/tex]
We notice now that after the extraction, we are left with two exactly equal binomial factors [tex](w+1)[/tex] that appeared in the first group and in the second group. We proceed then to extract it as common factor for the two groups:
[tex]w(w+1)+3(w+1)\\(w+1)(w+3)[/tex]
this last product of two binomials ([tex](w+1)\,(w+3)[/tex] is the result of factoring the original expression.
A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank.
Required:
a. Write a formula that expresses v in terms of t.
b. As t increases from 3 to 6, v varies from _________ to _________
Answer:
a) [tex]V(t) = 24 - 2t[/tex]
b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Step-by-step explanation:
The volume of the tank in terms of the time can be described by the following equation:
[tex]V(t) = V(0) - at[/tex]
In which V(0) is the initial volume and a is the hourly decrease rate.
a. Write a formula that expresses v in terms of t.
The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]
Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]
Then
[tex]V(t) = V(0) - at[/tex]
[tex]V(t) = 24 - 2t[/tex]
b. As t increases from 3 to 6, v varies from _________ to _________
[tex]V(t) = 24 - 2t[/tex]
[tex]V(3) = 24 - 2*3 = 18[/tex]
[tex]V(6) = 24 - 2*6 = 12[/tex]
So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
15 POINTS & BRAINLIEST!!!
How do you find the axis of symmery in the form f(x) = 3(x - 4)^2 + 5?
Answer:
so the axis of symmetry is x=4
Answer: X = 4
Explanation: Hope it helps you♡
The area of a circle is 497 squared meters.
What is the radius, in meters?
Answer: r= 12.58m
Step-by-step explanation:
100% SURE
What is the y-intercept of a line that has a slope of -3 and passes through point (0, -7)?
Answer:
Step-by-step explanation:
line equation: y=mx + C
substitute given values
-7 = -3*0 + C
C=y= -7 ANS
When writing expressions for complex numbers, what does i represent?
Answer:
see below
Step-by-step explanation:
i is the imaginary number and it represents the square root of -1
A farmer knows that every 50 eggs his chickens lay, only 45 will be marketable. If his
chickens lay 1000 eggs in a week, how many of them will be marketable?
Answer:
900 eggs
Step-by-step explanation:
45/50 are marketable
divide the top and bottom by 5
9/10
Multiply this fraction by the 1000 eggs laid
9/10 *1000
900 eggs will be marketable
Answer:
900
Step-by-step explanation:
Please help . I’ll mark you as brainliest if correct !
Answer:
4 ( a+2)
Step-by-step explanation:
The average rate of change is
(f(a) - f(2))/(a-2)
f(a) = 4a^2 -8
f(2) = 4*2^2 -8 = 4*4 -8 = 16-8 = 8
(4a^2 - 8 - 8))/(a-2)
(4a^2 -16) / (a-2)
Factor the numerator
4( a^2 -4) / (a-2)
4( a-2)(a+2) / (a-2)
Cancel
4 ( a+2)
In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 65 inches. The probability that the study participant selected at random is less than 65 inches tall is nothing. (Round to four decimal places as needed.)
Answer:
The probability that a study participant has a height that is less than 65 inches is 0.1103.
Step-by-step explanation:
We are given that the heights in the 20-29 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches.
A study participant is randomly selected.
Let X = heights in the 20-29 age group.
So, X ~ Normal([tex](\mu=69.9,\sigma^{2} =4.0^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean height = 69.9 inches
[tex]\sigma[/tex] = standard deviation = 4.0 inches
Now, the probability that a study participant has a height that is less than 65 inches is given by = P(X < 65 inches)
P(X < 65 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{65-69.9}{4}[/tex] ) = P(Z < -1.225) = P(Z [tex]\leq[/tex] 1.225)
= 1 - 0.8897 = 0.1103
The above probability is calculated by looking at the value of x = 1.225 in the z table which lies between x = 1.22 and x = 1.23 which has an area of 0.88877 and 0.89065 respectively.
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.
I want the answer of this question
[tex]the \: answer \: is \: 10 \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]
Answer:
10 is the answer for this question.
The relationship between ttt and rrr is expressed by the equation 2t+3r+6=02t+3r+6=02, t, plus, 3, r, plus, 6, equals, 0. If rrr increases by 444, which of the following statements about ttt must be true?
Question:
The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?
Answer:
The value of t is reduced by 6 when the value of r is increased by 4
Step-by-step explanation:
Given
[tex]2t + 3r + 6 = 0[/tex]
Required
What happens when r is increased by 4
[tex]2t + 3r + 6 = 0[/tex] -------- Equation 1
Subtract 2t from both sides
[tex]2t + 3r + 6 - 2t = 0 - 2t[/tex]
[tex]3r + 6 = - 2t[/tex] --- Equation 2
When r is increased by 4, equation 1 becomes
[tex]2T + 3(r+4) + 6 = 0[/tex]
Note that the increment of r also affects the value of t; hence, the new value of t is represented by T
Open bracket
[tex]2T + 3r+12 + 6 = 0[/tex]
Rearrange
[tex]2T + 3r+6 +12 = 0[/tex]
Substitutr -2t for 3r + 6 [From equation 2]
[tex]2T -2t +12 = 0[/tex]
Make T the subject of formula
[tex]2T = 2t - 12[/tex]
Divide both sides by 2
[tex]\frac{2T}{2} = \frac{2t - 12}{2}[/tex]
[tex]T = t - 6[/tex]
This means that the value of t is reduced by 6 when the value of r is increased by 4
Alex has a bag of stuffed animals containing nine bears, six lions, and three monkeys. The probability that Alex will randomly pull out a bear and then a lion is . Using this probability, determine if the event of pulling out a bear and the event of pulling out a lion was independent, dependent, both, or neither.
Answer:
P = 0.1764
The events are dependent
Step-by-step explanation:
We have a total of 9 + 6 + 3 = 18 stuffed animals.
The probability of the first animal pulled being a bear is:
P(bear) = N(bear) / N(total)
P(bear) = 9 / 18 = 0.5
Then, for the second animal, we now have only 17 stuffed animals in total.
So the probability of the second animal pulled being a lion, given the first animal was a bear, is:
P(lion | bear) = N(lion) / N(total)
P(lion | bear) = 6 / 17 = 0.3529
So the final probability is the product of these probabilities:
P = P(bear) * P(lion | bear) = 0.5 * 0.3529 = 0.1764
To find if the events are dependent or independent, let's find the probability of the first pick being a lion:
P(lion) = N(lion) / N(total)
P(lion) = 6 / 18 = 0.3333
The probability of picking a lion is different from the probability of picking a lion given we already picked a bear, so the events are dependent.
A battery with 20 percent of its full capacity is connected to a charger. Every minute that passes, an additional 5% , percent of its capacity is charged.
Answer:
y = 5x + 20
Step-by-step explanation:
The initial percent is 20.
Every minute, the percent goes up 5%, so the slope is 5.
So the equation of the line is y = 5x + 20.
what is the name of the shape graphed by the function: r=2cos theta
Answer:
Circle
Step-by-step explanation:
r = 2 cos θ
Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular.
x² + y² = 2x
x² − 2x + y² = 0
Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
This is a circle with center (1, 0) and radius 1.
The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
Given function is r = 2 cos θ
Now, Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular form;
x² + y² = 2x
x² − 2x + y² = 0
Using Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
Hence, This is a circle with a center (1, 0) and radius of 1.
Learn more about circle here;
brainly.com/question/12512221
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Which of the following is NOT a requirement of the Combinationsâ Rule, Subscript n Baseline Upper C Subscript requalsStartFraction n exclamation mark Over r exclamation mark (n minus r )exclamation mark EndFraction â, for items that are allâ different?
a. That r of the n items are selectedâ (without replacement).
b. That there be n different items available.
c. That order is not taken into accountâ (consider rearrangements of the same items to be theâ same).
d. That order is taken into accountâ (consider rearrangements of the same items to be differentâ sequences).
Answer:
d. That order is taken into account (consider rearrangements of the same items to be different sequences).
Step-by-step explanation:
Given the combination rule:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
A major difference between permutation and combination is the order of the items in the selection. If the order does not matter then we have a combination. If on the other hand, the order of the items matter, then it is a permutation.
Therefore, that which is not a rule for combination is Option D since, in combination, we do not consider rearrangements of the same items to be different sequences.
Find the area of the circle. Use pialmost equals 3.14. Radius equals19 yd
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 80 businesses at random. Of these, 46 return the questionnaire mailed by the committee.
a) What is the population for this sample survey?
The population in this situation is _______ (none, some, most, or all) of the __________(local business or college students) .
b) What is the sample?
The sample is the ______(enter exact number) of ___________ (local business or college students) selected.
c) What is the rate (percent) of nonresponse?
Answer:
a) The population population in this situation is all the local business
b) The sample is the 80 of local business selected.
c) The rate of nonresponse is 42.5%.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
The population for this survey is all New York State residents, while the sample are the 1000 New York State residents.
From telephone book listings, the committee chooses 80 businesses at random.
Survey: 80 businesses.
Population: All businesses in the college town.
Then
a) What is the population for this sample survey?
The population population in this situation is all the local business
b) What is the sample?
The sample is the 80 of local business selected.
c) What is the rate (percent) of nonresponse?
80 - 46 = 34 non-responses, out of 80
34/80 = 0.425
0.425*100 = 42.5%
The rate of nonresponse is 42.5%.
3/11 ÷ 3/11
and
9/10 ÷ 3/5
PLZ HELP ME
Answer:
3/11 divided by 3/11 is 1
9/10 divided by 3/5 is 1 1/2 (1.5)
Step-by-step explanation:
Answer:
1
1.5
Step-by-step explanation:
3/11 ÷ 3/11 = 1
9/10 ÷ 3/5 = 3/2 ≈ 1.5
g(-4)
Please help!!
Answer:
1
Step-by-step explanation:
g(-4) means what is the y value when x is -4.
Find x=-4, and when x=-4. y=1
Answer:
1
Step-by-step explanation:
luke is 5 years younger than 3 times sydenys age, s in this situation what does 3s represent
3s represents three times Sydney's age. Sydney's age is symbolized with an S.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. (f - g)(x) = [tex]3^x-2x+14[/tex]
Step-by-step explanation:
→Set it up, like so:
[tex](3^x+10)-(2x-4)[/tex]
→Distribute the -1 to (2x - 4):
[tex]3^x+10-2x+4[/tex]
→Add like terms (10 and 4):
[tex]3^x-2x+14[/tex]
45 units and is centered at
A circle has a radius of
(-2.4, -4.8).
What is the equation of this circle?
The correct question is:
A circle has a radius of 45 units and is centered at (-2.4, -4.8).
What is the equation of this circle?
Answer:
Equation of the circle is;
(x + 2.4)² + (y + 4.8)² = 2304
Step-by-step explanation:
The standard equation of a circle is;
(x - a)² + (y - b)² = r²
where;
(a,b) is the center of the circle and r is the radius of the circle
Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45
Thus, plugging those values into the standard form of equation of a circle, we have;
(x - (-2.4))² + (y - (-4.8))² = 48²
This gives;
(x + 2.4)² + (y + 4.8)² = 2304
Simplify (4.5)(5)(-2)
Answer:
[tex] - 45[/tex]
[tex]2.25( - 2) = - 45 \\ - 45[/tex]
The list of ordered pairs below represents a relation. {(−6,10),(−5,4),(−1,−9),(9,−4)} Find the range of the relation.
Answer:
The range is simply all the y values of the ordered pairs in the relation so the answer (in increasing order) is -9, -4, 4, 10.
What is the simplified value of the exponential expression 27 1/3
1/3
1/9
3
9
Answer:
I think its 1/9
Answer:
B
Step-by-step explanation:
Jose predicted that he would sell 48 umbrellas. He actually sold 72 umbrellas.What are the values of a and b in the table below. Round to the nearest tenth if necessary
Answer:
The answer is A
Step-by-step explanation: