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Answer:
(x, y) = (0, -2)
Step-by-step explanation:
When solving by substitution, you usually want to find an expression for one of the variables in terms of the other. So, the first thing you look for is an equation that has a coefficient of 1 or -1 on one of the variables. Recognizing that the second equation's terms all have a common factor of 3, you basically have two choices.
Substitute for yUsing equation 1, you can write an expression for y:
y = 5x -2 . . . . . . add 5x to both sides
Then substituting this into the original equation 2, you have ...
-3x +6(5x -2) = -12
27x -12 = -12 . . . . . . . simplify
27x = 0 . . . . . . . . . add 12
x = 0 . . . . . . . . . divide by 27
y = 5(0) -2 = -2 . . . . find y using the expression for substitution
The solution is (x, y) = (0, -2).
__
Substitute for xIf you decide you'd rather substitute for x, you can solve the second equation easily for x.
-3x +6y = -12
x -2y = 4 . . . . . . divide by -3
x = 2y +4 . . . . . . add 2y
Substituting for x in the first equation gives ...
-5(2y +4) +y = -2 . . . . substitute for x
-9y -20 = -2 . . . . . . . simplify
-9y = 18 . . . . . . . . . add 20
y = -2 . . . . . . . . . . . divide by -9
x = 2(-2) +4 = 0 . . . . find x using the expression for substitution
The solution is (x, y) = (0, -2).
_____
Additional comment
In some cases, there are no variables that have a coefficient of ±1, so you just need to "bite the bullet" and deal with the resulting fractions.
Example:
solve for y: -5x +2y = -2
2y = 5x -2
y = 5/2x -1 . . . . expression used to substitute for y
Of course, you can multiply the equation after substitution by 2 to eliminate fractions, or just work the problem as is. The point of looking for coefficients of ±1 is to avoid having to do arithmetic with fractions. It can help avoid errors to work with integers, but ultimately the method is the same regardless of the form of the numbers.
__
You don't always have to substitute for the "bare" variable. Sometimes it can save steps to substitute for expressions instead of variables. If our system of equations were ...
-5x +2y = -2-3x +6y = -12You can substitute into the second equation for (2y). In that case, the second equation becomes ...
-3x +3(2y) = -12
-3x +3(5x-2) = -12 . . . . . . where 2y = 5x -2
The correlation between a student’s shoe size and their score on a final exam is −0.79.What conclusions can be drawn based on the correlation coefficient? Select all that apply.
There is a relationship between a student’s shoe size and their final exam score.Big shoe sizes correlate to low exam scores.Large shoe sizes cause students to do poorly on the final exam.As the shoe size decreases, the final exam score increases.Small shoe sizes cause students to do well on the final exam.
(1,2,4) (A,B,D)
Answer:
The first one, the second, and fourth one are correct.
Select A,B, and D.
ED2021
Answer:
A, B, and C
Step-by-step explanation:
I got it right ;)
Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a 5 2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?
In this question, the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Parameter of 5.2 per square yard:
This means that [tex]\mu = 5.2r[/tex], in which r is the radius.
How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?
We want:
[tex]P(X \geq 1) = 1 - P(X = 0) = 0.99[/tex]
Thus:
[tex]P(X = 0) = 1 - 0.99 = 0.01[/tex]
We have that:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.2r}*(5.2r)^{0}}{(0)!} = e^{-5.2r}[/tex]
Then
[tex]e^{-5.2r} = 0.01[/tex]
[tex]\ln{e^{-5.2r}} = \ln{0.01}[/tex]
[tex]-5.2r = \ln{0.01}[/tex]
[tex]r = -\frac{\ln{0.01}}{5.2}[/tex]
[tex]r = 0.89[/tex]
Thus, the radius should be of at least 0.89.
Another example of a Poisson distribution is found at https://brainly.com/question/24098004
After analyzing a data set using the one-way ANOVA model, the same data are analyzed using the randomized block design ANOVA model. SS (Treatment) in the one-way ANOVA model is ________ the SS (Treatment) in the randomized block design ANOVA model.
a. Always equal to.
b. Always greater than.
c. Always less than.
d. Sometimes greater than.
Answer: Always equal to
Step-by-step explanation:
A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means.
Based on the options given, it should be noted that SS (Treatment) in the one-way ANOVA model is always equal to the SS (Treatment) in the randomized block design ANOVA model.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = 6/5x-1
Step-by-step explanation:
We have two points so we can find the slope
(-5,-7) and (5,5)
The slope is
m = ( y2-y1)/(x2-x1)
= ( 5- -7)/( 5 - -5)
= (5+7)/(5+5)
= 12/10
= 6/5
The slope intercept form of a line is
y = mx+b
y = 6/5x+b
Using the point (5,5)
5 = 6/5(5)+b
5=6+b
b=-1
y = 6/5x-1
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the first marble is white and the second marble is blue.
Answer:
3/56
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.
The total number of marbles in the box
= 1 + 3 + 2 + 2
= 8 marbles
The probability that the first marble is white and the second marble is blue
= 3/8 * 1/7
= 3/56
Worth a lot of points.
Answer:
It's the last one.
Step-by-step explanation:
For example, if you have 0, the absolute valeu of 0 is 0. A postive number like 2, has an absolute value of 2. 0 is not greater than 0 and 2 is not greater than 2. Hope this helps!
Answer: Kayla is incorrect. The absolute value of 0 or a positive number is equal to the number.
Absolute numbers cannot be negative numbers. Therefore, an absolute number of a positive number will always be the positive number.Please answer in detail
Answer:
y=5x-1 I think because the snd option doesn't make sense but you should try y =5x-1
Find h(-5) when: h(x) = x2 + 2x + 2
Answer:
17
Step-by-step explanation:
h(x) = x^2 + 2x + 2
Let x = -5
h(-5) = (-5)^2 + 2(-5) + 2
= 25 -10 +2
= 17
Find the shortest distance from A to D in the diagram
Answer:
I will choose (a) I did a problem like this last week
Để tuyển nhân viên, một công ty tổ chức kiểm tra 3 vòng độc lập. Một người tham gia thi tuyển với xác suất qua các vòng lần lượt là 0,8 và 0,6 và 0,25.
a) Tìm xác suất để người đó không được nhận vào công ty?
b) Tìm xác suất để người đó thi đỗ ít nhất 1 vòng.
c) Tìm xác suất để người đó thi không đỗ ở vòng 2.
Students apply for admission to different academic programs within a college. Because of space, each program can only accept a limited number of students. The table below shows the acceptance data for a selection of majors in the college.
Acceptance Status
Accepted Rejected Total
College Major Chemistry 72 18 90
Business 65 35 100
Spanish 45 15 60
Total 182 68 250
What is the probability that a student was accepted, given that the student applied to the business program?
26.0%
35.0%
35.7%
65.0%
I think the answer is (A). 26%. Can someone check?
Answer:
Your wrong, it's 65%.
Step-by-step explanation:
The reason why: You can calculate the percentage by dividing the number of accepted students by the total of business students, 65/100 which equals 65%.
yw :)
The probability that a student was accepted is 5.0% since option b be the correct answer.
ProbabilityProbability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,
How to find probability?We have to find out the probability of the selection of a student applied for the business program.
We know that, Probability= Total number of events occurred÷ Total number of possible outcomes/events
So, Probability that a student applying to the business program got selected= No of accepted students for business program÷Total number of students applied for business program=65÷100=0.65For converting a number into percentage we multiply the number by 100 that is 0.65*100=65%So, probability that a student applying for business program gets selected is 65%.
Learn more about probability here- https://brainly.com/question/11234923
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The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
Answer:
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
ulwazi's Father offered to pay for Ani's wedding ring, which cost R1349 excluding 14%VAT calculate the selling price
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Answer:
₹1537.86
Step-by-step explanation:
With the 14% tax added, the final cost is ...
₹1349 × (1 +14%) = ₹1349×1.14 = ₹1537.86
PLEASE HELP!! URGENT
Answer:
y=105
Step-by-step explanation:
82+75+x=180
157+x=180
x=23
82+23=y
105=y
The length of a rectangle is five times its width. If the perimeter of the rectangle is 108 in, find its area.
Answer:
Step-by-step explanation:multiple 5 times 108 and that gives you your answer..
75,000 live bacteria are present in a culture in a flask. When an antibiotic is
added to the culture, the number of live bacteria is reduced as shown by the
equation. Approximately how many hours have passed when there are 4500
bacteria left alive?
4500 = 75,000 e-0.1733t
Answer:
16.23 hours
Step-by-step explanation:
To obtain the number of hours that have passed ; we have to solve for t on the equation ;
4500 = 75,000 e^-0.1733t
Divide both sides by 75000
4500/75000 = e^-0.1733t
0.06 = e^-0.1733t
Take the In of both sides ;
In(0.06) = - 0.1733t
-2.813410 = - 0.1733t
Divide both sides by - 0.1733
t = 16.23 hours
What is the classification for this polynomial?
-9m^2n^3
Answer:
(a) Monomial
(b) Cubic
Step-by-step explanation:
Given
[tex]-9m^2n^3[/tex]
Required
Classify
By number of terms
The above polynomial is single term.
Single term polynomials are referred to as monomial
By degrees
To determine the degree, we consider the variable farthest from the constant.
In this case, n is farther from 9 than m.
And the power or degree of n is 3.
Polynomials with degree 3 are referred to as cubic polynomial
I need help answering this ASAP
can you zoom in on my pic more or no does it say 1/z
Answer:
Option A. Reciprocal
Answered by GAUTHMATH
If x/4-y/6=1/6 and y/z=1/2, then what is the value of 3x-z?
A. 4
B.6
C. 3
D. 2
E. None
Alan's aunt gave him $95 to spend on clothes at the mall. He bought 5 shirts that cost $6 each and a pair of pants that cost $17. How much money does Alan have left to buy more clothes? (one more)
Answer:
he has 48 dollars left to spend on clothes
(d) 320 If the measurement of two angles of a triangle are 72º and 70%, find third ange in degrees. If the measurement of two angles of a triangle are 630 and 100
vvorth 1 points
(01.02 MC)
Which of the following describes the correct process for solving the equation 2x - 4 = 20 and arrives at the correct solution?
O Add 4 to both sides, and then divide by 2. The solution is x = 12.
O Divide both sides by -4, and then subtract 2. The solution is x = -7.
O Subtract 4 from both sides, and then divide by 2. The solution is x = -12.
O Multiply both sides by -4, and then divide by 2. The solution is x = -40.
Hi there!
»»————- ★ ————-««
I believe your answer is:
"Add 4 to both sides, and then divide by 2. The solution is x = 12."
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
To solve for 'x', we would have to use inverse operations. We would first have to add four to both sides to undo the negative four. Addition is the opposite of subtraction. We would then divide by 2 to isolate 'x'. Division is the opposite of multiplication.⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\2x - 4 = 20\\------------\\\rightarrow 2x - 4 + 4 = 20 + 4\\\\\rightarrow 2x = 24\\\\\rightarrow \frac{2x=24}{2}\\\\\rightarrow \boxed{x = 12}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Anyone?? Help????
Please!!!
Answer:
625 (answer A)
Step-by-step explanation:
Sorry for no explanation I can't explain stuff I just do it.
Which of the following can be used as "reasons" in a two-column proof?
Answer:
A definition and a theorem can be used as a reason in a two-column proof. A two column proof is assembled into statement and reason columns, where each statement should have verified reason.
Step-by-step explanation:
Answer:
Definitions and algebraic properties
Step-by-step explanation:
1. Đường kính của một loại trục máy là một đại lượng ngẫu nhiên có phân phối chuẩn N (μ = 250mm, σ2 = 25mm2). Trục máy được gọi là hợp quy cách nếu đường kính từ 245mm đến 255mm. Cho máy sản xuất 100 trục. Tính xác suất để:
a. Có 50 trục hợp quy cách.
b. Có không quá 80 trục hợp quy cách
Answer:
please ask in English
Step-by-step explanation:
then I can help
11
find the number of ways of forming
an executive Committee of four in a
social club consisting of 15 members,
If a particular man must be in
the comittee
There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members
Understanding Permutation and CombinationIf a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:
14Cr3 = [tex]\frac{14!}{3! 11!}[/tex] = [tex]\frac{14x13x12}{3x2x1}[/tex] = 364
Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.
Learn more about combination here:
https://brainly.com/question/28065038
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Question 7 of 10
What is the slope of the line described by the equation below?
y-9 = -2(x-8)
Answer:
The slope is -2 and a point on the line is (8,9)
Step-by-step explanation:
The equation is in point slope form
y -y1 = m(x-x1) where (x1,y1) is a point on the line and m is the slope
y-9 = -2(x-8)
The slope is -2 and a point on the line is (8,9)
A son is 8 years old. his father is 5 times as old. How old will the father be when he is twice as old as his son?
Enter the equation of the line in slope-intercept form. Slope is 4, and (6,4) is on the line. The equation of the line is y=
P = 14.7e-0.21x, where x is the number of miles above sea level. To the nearest foot, how high
is the peak of a mountain with an atmospheric pressure of 8.743 pounds per square inch?
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Answer:
13064 feet
Step-by-step explanation:
We can rewrite the formula so that x is in feet. Equating the new formula to 8.743 PSI, we have ...
8.743 = 14.7e^(-0.21x/5280)
Dividing by 14.7 and taking natural logs, we have ...
ln(8.743/14.7) = -0.21x/5280
Multiplying by the inverse of the coefficient of x gives ...
x = 5280·ln(8.743/14.7)/-0.21 ≈ 13064.0806
The peak of the mountain is about 13,064 feet high.
