Answer:
the two integers are 11 and -8
Step-by-step explanation:
Let's call the two integers we're trying to find "x" and "y".
From the problem statement, we know two things:
x + y = 3 (the sum of the two integers is three)
x^2 + y^2 = 185 (the sum of the squares is 185)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:
y = 3 - x
Now we can substitute this expression for "y" into the second equation:
x^2 + (3 - x)^2 = 185
Expanding the square on the left-hand side, we get:
x^2 + 9 - 6x + x^2 = 185
Combining like terms, we get:
2x^2 - 6x - 176 = 0
We can simplify this equation by dividing both sides by 2:
x^2 - 3x - 88 = 0
Now we can solve for "x" using the quadratic formula:
x = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)
Simplifying, we get:
x = (3 ± sqrt(361)) / 2
We can ignore the negative root, since it would give us a negative value for "y". So, taking the positive root, we get:
x = (3 + 19) / 2 = 11
Now we can use the first equation to solve for "y":
y = 3 - x = 3 - 11 = -8
During an experiment, the temperature of a mixture changes from 121 1/4 °F to 15 3/5 °F. What is the percent of increase in the temperature of the mixture? Enter your answer in the box as a percent rounded to the nearest hundredth.
The percentage decrease in the temperature is 87.13 %.
What is a percentage?The percentage formula is dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The temperature of a mixture changes from 121(1/4)°F to 15(3/5)°F.
This means,
Initial temperature = 121(1/4) = 485/4
Final temperature = 15(3/5) = 78/5
The change in temperature.
= 78/5 - 485/4
= (312 - 2425)/20
= 2113/20
= - 105(13/20)
This means,
There is a decrease in temperature.
Now,
The percentage decreased.
= 105(13/20) / (485/4) x 100
= (2113/20) / (485/4) x 100
= 2113/20 x 4/485 x 100
= 2113/2425 x 100
= 87.13%
Thus,
The percentage decrease in the temperature is 87.13 %.
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let u and v be distinct vectors of a vector space v. show that if { u, u} is a basis for v and a and b are nonzero scalars, then both { u v, au} and {au, bu} are also bases for v.
A + B =0 => {u + v, au} is linearly independent set of two vectors
=> {u + v, au}is a basis for V.
Let u and v be distinct vectors of a vector space V and {u, v} is a basis for V and a and b are nonzero scalars.
We have to show: both {u + v, au} and {au, bv} are also bases for V.
[tex]u\neq v,a,b\neq 0[/tex]
{u, v} is a basis for V => {u + v , au} and {au, bu} are bases for V
From basis {u , v} we get dimension of V
{u , v} is a basis for V
=> V is a 2-dimensional vector space and (.) [tex]\alpha u+\beta v=0= > \alpha =\beta =0[/tex]
Show {u + v, au} is a basis for V:
{u + v, au} :
A(u + v) + B(au) = 0 <=> Au + Av + Bau = 0
<=> (A + Ba)u + (B)v = 0
By the step (in second step)
A + Ba = 0 , [tex]a\neq 0[/tex]
B = 0
=> A + B =0 => {u + v, au} is linearly independent set of two vectors
=> {u + v, au}is a basis for V.
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compute 90 and 95% cis for the parameter associated with age. using just these intervals what could we have deduced about the p-value for age in the regression summary?
We cannot deduce anything about the p-value for age in the regression summary from just the 90% and 95%. cis for the parameter associated with age.
The 90% and 95% cis for the parameter associated with age tell us the range of values that the parameter could take, given the data. This range does not tell us anything about how likely the parameter is to take any of these values.
To determine how likely it is to take any of these values, we need to look at the p-value for age in the regression summary. The p-value tells us the probability that the parameter associated with age is different from zero.
It is the level of significance and is used to determine if the parameter is statistically significant. It is the only way to determine the likelihood of the parameter taking any of the values in its 90% and 95% cis.
Therefore, we cannot deduce anything about the p-value for age in the regression summary from just the 90% and 95% cis for the parameter associated with age.
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A recent study showed that tea drinkers have lower stress levels than coffee drinkers. Tea drinkers are known to have a higher proportion of yoga practitioners than coffee drinkers, and they exercise on average two hours per week more than their coffee-drinking counterparts. What is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers?
The additional factors that might have an effect on the stress levels of tea drinkers are called confounding variables. Confounding variables are variables that are not the main focus of the study but may have an impact on the results.
The term used to describe these additional factors that might have an effect on the stress levels of tea drinkers is "confounding variables." Confounding variables are extraneous factors that can affect the relationship between two variables of interest and can lead to incorrect conclusions about the relationship. In this case, the higher proportion of yoga practitioners and the increased exercise among tea drinkers could be considered confounding variables because they may be influencing the observed relationship between tea drinking and lower stress levels, rather than tea consumption alone.
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Jason and Caleb shared the profits from their lemonade stand in a ratio of 2:3. if they earned $40 all together how much money did Jason make?
Answer: Jason made $16
Step-by-step explanation:
Start by using the ratio of 2:3 to find the fraction of the total profit that Jason earned: Jason's share: 2/(2+3) = 2/5
Caleb's share: 3/(2+3) = 3/5
We can then use this fraction to calculate how much money Jason made:
Jason's share = (2/5) x $40 = $16
Therefore, Jason made $16 from the lemonade stand profits.
Let X and Y be continuous random variables with joint density f
X
,
Y
(
x
,
y
)
=
e
−
y
,
f
o
r
0
<
x
≤
y
<
[infinity]
and 0 otherwise.
Find rho
X
Y
.
The correlation coefficient of X and Y is 1, since their joint density is always positive for x ≤ y.
The correlation coefficient of two continuous random variables X and Y is a measure of how similar the two variables are in terms of their behavior. In this case, X and Y have a joint density of e−y, for 0 < x ≤ y < ∞ and 0 otherwise. This implies that the correlation coefficient of X and Y is 1, since their joint density is always positive for x ≤ y. This means that there is a perfect linear relationship between the two variables, meaning that as one variable increases, the other will also increase by the same amount.
To calculate the correlation coefficient, we need to calculate the covariance and variances of X and Y. The covariance is calculated by integrating the joint density of X and Y over the given range. The variance of X and Y is then calculated by taking the square root of the expected value of the squares of the differences between the expected value of X and Y and their respective observed values. Since the joint density of X and Y is always positive for x ≤ y, the correlation coefficient of X and Y will always be 1.
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Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2. This system of equations models the scenario: 4x + 2y ≤ 16 x + y ≥ 4 Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points) Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points) Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
Part A: the system of inequalities has a definite solution to it.
Part B: Yes the point is a part of Solution Area
What is Linear Inequality?
In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
Solution:
The inequalities 4x + 2y ≤ 16
And x + y ≥ 4 is attached below please refer to it.
Part A: The graph of both inequalities intersects each other therefore the system of inequalities has a definite solution to it.
Part B: Yes point (2, 3) is included in the solution area, the following is the mathematical proof.
Using substitution 4*2 + 2*3 ≤ 16
8+6 ≤ 16
14 ≤ 16
And 2+3 ≥ 4
5 ≥ 4
Hence, the point is included in the solution area.
Part C:
Let’s assume a point 1,1 in the solution set so it implies that only the inequality 4x + 2y ≤ 16 is satisfied. Thus, not giving a feasible solution.
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NO LINKS!! URGENT HELP PLEASE!!
Find the shaded area of each figure, round your answer to one decimal place if necessary.
Answer:
7) 216 ft²
8) 106 yd²
9) 200 m²
Step-by-step explanation:
To calculate the area of each given figure, subtract the area of the cut-out rectangle (marked in blue on the attached diagram) from the area of the larger rectangle.
[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]
Question 7Note: The height of the larger rectangle is not complete. I have assumed it is 12 ft.
[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&=21 \cdot 12- 6\cdot 6\\&=252-36\\&=216\; \sf ft^2\end{aligned}[/tex]
Question 8[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 17\cdot 10- (17-9)\cdot 8\\&= 17\cdot 10- 8\cdot 8\\&=170-64\\&=106\; \sf yd^2\end{aligned}[/tex]
Question 9[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 15\cdot 20- 10\cdot 10 \\&=300-100\\&=200\; \sf m^2\end{aligned}[/tex]
If y varies directly as x, and y=4 find y when x=6 find y when x=5
Hence, The value of y = 12 when x = -6.
Given that , Y varies directly with x .
If y=−4 when x=2,
Find y when x=−6.
According to the question,
This is a direct variation , y = kx
If,
y = −4 when x=2,
y = kx
-4 = 2k
k = -2
To find ;
y when x = −6
y = kx
y = (-2) (-6)
y = 12
(x - 5)² +15=143
Find x
The solution is, the value of x = 5+ 8√2, 5- 8√2
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
(x - 5)² +15=143
we know, (a-b)^2 = a^2 -2ab + b^2
so, we get,
x^2 - 10x + 25+15 = 143
or, x^2 -10x -103 = 0
now, solving we get,
x = 5+ 8√2, 5- 8√2
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f ( x ) = { 2 x + 4 , x ≤ − 2 4 + 1 2 x , − 2 < x < 2 − x + 5 , 2 ≤ x Which of the following is the graph of the function shown above? A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at a closed circle (2, minus 3) and passes through (5, 0). The third line with 2 open circles at (2, 6) and (minus 2, 3) W. A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at a closed circle (2, minus 3) and passes through (5, 0). The third line with 2 open circles at (2, 3) and (minus 2, 5) X. A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at a closed circle (2, 3) and passes through (5, 0). The third line with 2 open circles at (minus 2, 3) and (2, 5) Y. A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at an open circle (2, 3) and passes through (5, 0). The third line with an open circle at (minus 2, 3) and a closed circle at (2, 5) Z. A. W B. X C. Y D. Z
Answer:
The correct graph of the given function is option C. Y.
Step-by-step explanation:
The correct graph is option B (X) because it satisfies all the conditions specified in the function definition.
The first segment of the graph starts at x=-2 and goes to the left, passing through the point (-4,-4) and representing the equation 2x+4. The second segment of the graph starts at x=-2 and goes to the right, passing through the point (2,3) and representing the equation 4+1/2x. The third segment of the graph starts at x=2 and goes to the right, passing through the point (5,0) and representing the equation -x+5.
Option A (W) has a line that passes through the point (2,6), which is not on the graph of the function, and option C (Y) has a line that passes through the point (2,5), which is also not on the graph of the function. Option D (Z) has an open circle at (-2,3), which should be a closed circle according to the function definition, and a closed circle at (2,5), which should be an open circle according to the function definition.
A student scores in a history class are listed 45 52 65 68 68 70 77 78 78 81 85 96 100 which of the following histogram correctly represent the data
Answer:
second
Step-by-step explanation:
Find the volume common to two spheres, each with radius r, if the distance between their centers is r/2.
(given information: A cap of a sphere with radius r = 5 and height h = 2.)
The common volume of the two spheres is 5πr³/6. Since the two spheres are identical, the volume of the common portion is twice the volume of the spherical cap.
Since the distance between the centers of the two spheres is r/2, a cross-section of the two spheres and the plane perpendicular to their centers of symmetry will form an isosceles triangle with height h=r/2 and base 2√(r²-(r/2)²). The intersection of the two spheres will be a spherical cap with height h and radius r. The volume of this spherical cap is
V_cap = (1/3)π[tex]h^2[/tex](3r-h).
Since the two spheres are identical, the volume of the common portion is twice the volume of the spherical cap, so
V_common = 2V_cap = (2/3)π[tex]h^2[/tex](3r-h) = (5/6)πr³.Substituting h=r/2, we get
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Sergio has
p
pp paintings in his art collection. He and other local painting collectors agreed to donate a total of
48
4848 paintings to the local museum. Each of the
12
1212 collectors will donate the same number of paintings.
How many paintings will Sergio have in his art collection after his donation?
Write your answer as an expression.
Answer: Let's assume that each of the 12 collectors donates n paintings. Then the total number of paintings donated will be 12 * n. We know that the total number of paintings donated by all collectors is 48, so we have the equation:
12 * n = 48
Dividing both sides by 12, we find that each collector donates n = 4 paintings. So, if Sergio has p paintings in his collection, after his donation he will have p - 4 paintings in his collection. The final answer is:
p - 4
Step-by-step explanation:
En una progresión aritmética sabemos que a2 =1 y a5 =7. Halla el término general y los términos a8 , a15 y a20
The general rule of the arithmetic sequence is given as follows:
[tex]a_n = -1 + 2(n - 1)[/tex]
The terms are given as follows:
[tex]a_8 = 13[/tex][tex]a_{15} = 27[/tex][tex]a_{20} = 37[/tex]What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
The difference between the 3 terms is of 6, hence the common difference is given as follows:
3d = 6
d = 2.
As the 2nd term is of 1, the first term is of:
[tex]a_1 = 1 - 2 = -1[/tex]
Hence the rule is given as follows:
[tex]a_n = -1 + 2(n - 1)[/tex]
The terms are given as follows:
[tex]a_8 = -1 + 2 \times 7 = 13[/tex][tex]a_{15} = -1 + 2 \times 14 = 27[/tex][tex]a_{20} = -1 + 2 \times 19 = 37[/tex]More can be learned about arithmetic sequences at https://brainly.com/question/30544915
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a sample of 40 country cd recordings of willie nelson has been examined. the average playing time of these recordings is 51.3 minutes, and the standard deviation is s
We can be 95% confident that the true mean playing time of all Willie Nelson recordings is between 48.89 and 53.71 minutes.
Using a t-multiplier for a 95% confidence interval with 39 degrees of freedom (n-1), we get t* = 2.022.
The margin of error is t* times the standard error of the mean, which is s / sqrt(n), where n is the sample size.
Thus, the margin of error is 2.022 * (5.8 / sqrt(40)) = 2.41 minutes.
To construct the confidence interval, we add and subtract the margin of error to the sample mean:
Lower limit = 51.3 - 2.41 = 48.89
Upper limit = 51.3 + 2.41 = 53.71
Therefore, we can be 95% confident that the true mean playing time of all Willie Nelson recordings is between 48.89 and 53.71 minutes.
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Watson, Raimey
8 x 40
A gallon can of stain covers approximately 70 square feet of wooden deck. Joaquin has purchased 8 gallons of stain.
Select all deck sizes that Joaquin could fully cover if he must apply 2 coats to the deck.
10 x 18
13 x 22
14 x 20
17 x 17
Answer: A gallon of stain covers 70 square feet, so 8 gallons would cover 8 x 70 = 560 square feet. If Joaquin must apply 2 coats to the deck, he needs enough stain to cover the deck twice, so he needs 560 square feet x 2 = 1120 square feet.
Of the deck sizes listed, the largest one that Joaquin can fully cover with 2 coats of stain is 14 x 20 = 280 square feet, which is less than 1120 square feet. This means that Joaquin can fully cover all of the listed deck sizes if he must apply 2 coats of stain.
Step-by-step explanation:
eighty-two percent of all women who submit to pregnancy tests are pregnant. a new pregnancy test gives a false positive result with probability 0.02 and a correct positive result with probability 0.95. define the events: p: {a woman is pregnant} and : {the pregnancy test is positive}. a)
The probability that a woman is actually pregnant given that the test is positive is 0.974 (or 97.4%).
a) To find the probability that a woman is actually pregnant given that the test is positive, we can use Bayes' theorem:
P(p|+) = P(+|p) P(p) / P (+)
where P(p) is the prior probability of a woman being pregnant (which is 0.82), P (+) is the probability of a positive test result, and P(+|p) is the conditional probability of a positive test result given that the woman is pregnant.
We are given that the test has a false positive rate of 0.02, which means that P(+|~p) = 0.02 (where ~p denotes "not pregnant"). We are also given that the test has a correct positive rate of 0.95, which means that P (+|p) = 0.95. Therefore, we can calculate:
P (+) = P(+|p) P(p) + P(+|~p) P(~p)
= 0.95 * 0.82 + 0.02 * (1 - 0.82)
= 0.802
Substituting into Bayes' theorem, we get:
P(p|+) = 0.95 * 0.82 / 0.802
= 0.974
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A plane left New York at 3:30pm EST and arrived in Los Angeles at 4:15pm PST. How long did the flight take?
The flight takes a total of 3 hours 45 minutes
How to determine how long did the flight take?From the question, we have the following parameters that can be used in our computation:
Inital time = 3:30 pm EST
Final time = 4:15 pm PST
When converted, we have
Inital time = 12:30 pm PST
Final time = 4:15 pm PST
So, we have
Difference = 4:15 pm PST - 12:30 pm PST
Evaluate the difference
Difference = 3 hours 45 minutes
Hence, the diration is 3 hours 45 minutes
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27
Select the correct answer.
Number of Players on the Team Time Taken to Complete Game (in minutes)
Teams with varying numbers of players are playing a group card game. The time taken by each team to complete one game is given in the table.
What is the relationship between the two variables?
2
3
4
5
O A. positive linear association
O B. exponential relationship
O C.
negative linear association
32
26
20
14
The relationship between the two variables negative linear association.
What is Linear Association?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
Given:
The data table is organized as follows:
1 2 3 4 5
32 26 20 14 8
We see that more the number of members in the team increase, the more the times decrease.
The correlation is a negative linear association, we conclude.
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square root of 64 minus 10 plus 13
Answer:
11
Step-by-step explanation:
[tex]\sqrt{64}[/tex] -10 + 13
8 - 10 + 13
-2 + 13
11
If sin(θ)>0 and sec(θ)<0, in which quadrant does θ lie?
Answer:
Quadrant II
Step-by-step explanation:
sin (∅) > 0 means sin (∅)is positive
sec (∅) < 0 means sec (∅) is negative
thus,
∅ lies in quadrant II
Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this ques- tion (CBS News website, December, 2014). Consider the responses by age groups shown below Response Age 18-29 30+Yes 134 131No 293 432Unsure a. What is the probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime?b. What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime? c. For a randomly selected respondent, what is the probability that a respondent answers yes? d. Based on the survey results, does there appear to be a difference between ages 18-29 and 30+ regarding concern over global warming?
From the given data the probability that a respondent 18-29 years and 30+ years are 0.536 and 0.654 espectively. The probability that they answer yes (i.e. global warming will have an impact on them during their lifetime) is 0.265. There also appears to be a difference between ages 18-29 and 30+ regarding concern over global warming.
The probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime is:
P(18-29 and No) = 293/(134 + 293 + 117) = 0.536
The probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime is:
P(30+ and No) = 432/(131 + 432 + 178) = 0.654
For a randomly selected respondent, the probability that they answer yes (i.e. global warming will have an impact on them during their lifetime) is:
P(Yes) = (134 + 131)/(134 + 131 + 293 + 432 + 117 + 178) = 0.265
Yes, there appears to be a difference between ages 18-29 and 30+ regarding concern over global warming. The probability of a respondent 30+ years of age thinking that global warming will not pose a serious threat during their lifetime (0.654) is higher than the corresponding probability for respondents 18-29 years of age (0.536). This suggests that older respondents are less concerned about global warming than younger respondents. However, a formal statistical test would be needed to confirm this difference.
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5. Identify the mean and standard deviation of the graph.
O
8.2 13.4 18.6 23.8 29 34.2 39.4
mean = 18.6; standard deviation = 5.2
mean = 23.8; standard deviation 2.7
mean = 23.8; standard deviation = 5.2
mean = 18.6; standard deviation = 2.7
The mean and the standard deviation for the data-set are given as follows:
mean = 23.8; standard deviation = 5.2.
How to obtain the mean and the standard deviation?The mean of a data-set is given by the sum of all the observations in the data-set divided by the number of observations, hence:
Mean = (8.2 + 13.4 + 18.6 + 23.8 + 29 + 34.92 + 39.4)/7
Mean = 23.8.
The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of observations, hence:
s = sqrt([(8.2-23.8)² + (13.4-23.8)² + (18.6-23.8)² + (23.8-23.8)² + (29-23.8)² + (34.92-23.8)² + (39.4-23.8)²]/7)
s = 5.2.
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Use the diagram below to find x and y.
A-
4x - 1
B
6x-5
33
'С
4y+1
t
In the linear equation, The value of the x and y are 11/6, -5 and 18/4.
What is linear equation?The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
here, we have,
We have to find that the value of the x and the y.
From the given information:
The equations are :
(4y - 18)
(6x - 11)
(x + 5)
Now take all equation equal to zero.
Then
4y - 18 = 0
y = 18/4
And then
6x - 11 = 0
x = 11/6
And then
x + 5 = 0
x = -5.
So, In the linear equation, The value of the x and y are 11/6, -5 and 18/4.
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Which of the following is true of the location of the terminal side of an angle 0 who's sine value is 1/2?- has a reference angle of 30° and is in quadrant one or two- as a reference angle 30° and is in quadrant one or four- has a reference angle of 60° and is in quadrant one or two- as a reference angle of 60° in is in quadrant one or four
Out of the following the statement has a reference angle of 30° and is in quadrant one or two- is true of the location of the terminal side of an angle 0 whose sine value is 1/2.
Since the reason behind this is that the sine value of 1/2 can be written as sin(30°), this means that the terminal side of the angle is located at 30°, which is either quadrant one or two. Quadrant one is the upper right quadrant of the coordinate plane, and quadrant two is the upper left quadrant.
The reference angle of an angle is the angle between the terminal side of the angle and the positive x-axis. In this case, the reference angle would be 30°. The reference angle of an angle is important because it is used to determine the quadrant in which the terminal side of the angle is used to determine the quadrant in which the terminal side of the angle is located. The reference angle must be less than 90° in order for the terminal side to be located in the first and second quadrants.
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susan wants to go to the bank to deposit her paycheck, then go to the outlet mall, then return home. on the map below, point b represents susans home, point a respresents the bank, and point c represents the outlet mall. what is the total distance around the triangle in miles
James baked some cupcakes. If he gave 3 cupcakes to each cousin, he would have 25 cupcakes left. If he gave 15 cupcakes to each cousin, he would need to bake 71 more cupcakes. (a) How many cousins did he have? (b) How many cupcakes did he bake?
Answer:
8 cousins49 cupcakesStep-by-step explanation:
If James gave each cousin 3 cupcakes, there would be 25 left. James is 71 cupcakes short of being able to give each cousin 15 cupcakes. You want to know the number of cousins and the number of cupcakes.
SetupThe given relations between the number of cupcakes (n) and the number of cousins (c) are ...
n -3c = 25 . . . . . 3 each ⇒ 25 left
n -15c = -71 . . . . . 15 each ⇒ 71 short
SolutionSubtracting the second equation from the first, we have ...
(n -3c) -(n -15c) = (25) -(-71)
12c = 96
c = 8 . . . . . . divide by 12
n = 3c +25 = 24 +25 = 49
(a) James has 8 cousins.
(b) James baked 49 cupcakes.
For each of the following, determine the constant c so that f(x) satisfies the conditions of being a pmf for a random variable X, and then depict each pmf as a line graph: (a) f(x) =x/c, x=1.2.3.4. (b) f(x)-cx, x = 1, 2, 3, . . . , 10. (d) f(x) = c(x + 1)2, x=0.1,2.3. (e) f(x) = x/c, x = 1,2,3, . . . ,n. (f) f(x) = x=0.1.2.3, . . . . (x+1)(x+2), HINT: In part (f), write f(x) 1/(x +1)-1/(x+2).
The problem involves finding a constant c that makes each given function a valid probability mass function given are f(x) = x/c, x=1,2,3,4; f(x) = cx, x=1,2,3,...,10; f(x) = c(x+1)², x=0,1,2,3; f(x) = x/c, x=1,2,3,...,n; f(x) = (x+1)(x+2)/[x(x+3)], x=0,1,2,3,...
(a) We know that the sum of all the probabilities in a pmf must be equal to 1.
Therefore, we have:
1/c + 2/c + 3/c + 4/c = 1
Solving for c, we get:
c = 10
The pmf can be depicted as:
x f(x)
1 0.1
2 0.2
3 0.3
4 0.4
(b) Again, we know that the sum of all the probabilities in a pmf must be equal to 1. Therefore, we have:
c(1 + 2 + 3 + ... + 10) = 1
Solving for c, we get:
c = 1/55
The pmf can be depicted as:
x f(x)
1 1/55
2 2/55
3 3/55
... ...
10 10/55
(d) We can use the same approach as in part (a) to find c:
c(1 + 4 + 9) = 1
Solving for c, we get:
c = 1/14
The pmf can be depicted as:
x f(x)
0 1/14
1 1/6
2 1/3
3 4/14
(e) Similar to part (a), we have:
1/c + 2/c + 3/c + ... + n/c = 1
Solving for c, we get:
c = (n+1)n/2
The pmf can be depicted as:
x f(x)
1 1/(n+1)
2 2/(n+1)
3 3/(n+1)
n n/(n+1)
(f) We can use the hint given in the problem:
f(x) = 1/(x + 1) - 1/(x + 2)
We can see that this is a telescoping series, where all terms cancel out except for the first and the last term. Therefore, we have:
f(0) = 1/1 - 1/2 = 1/2
f(1) = 1/2 - 1/3 = 1/6
f(2) = 1/3 - 1/4 = 1/12
f(3) = 1/4 - 1/5 = 1/20
The pmf can be depicted as:
x f(x)
0 1/2
1 1/6
2 1/12
3 1/20
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2. For the expression not chosen, describe a situation that the expression might represent. x-8
The expression that represents the number of inches the plant grew is 8 - x.
What is Expression?An expression is combination of variables, numbers and operators.
A plant measured x inches tall last week and 8 inches tall this week.
We have to find the expression which represent the plant grew this week.
The number of inches the plant grew can be represented by the difference between its height this week and its height last week.
Eight minus x is the required expression.
8 - x
Hence, the expression that represents the number of inches the plant grew is 8 - x.
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Complete question
A plant measured x inches tall last week and 8 inches tall this week. Represent the number of inches the plant grew
A. X - 8
B. 8 - X
For the expression not chosen, describe a situation that the expression might represent.