1. Explain, without graphing, how you can determine whether the table below represents a
linear equation
X
y
-6-3
-2-1
0
1
1
2
4
6
Answers
Answer:
below
Step-by-step explanation:
you can find the distance between the y values for each x value and if it comes out to be an even increase/decrease you know it is linear
Answer:
It does not form a linear equation.
Step-by-step explanation:
For this question, you should check that they all have the same gradient.
To work out the gradient, use [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
Using the top 2 rows, this gives [tex]\frac{-1--3}{-2--6}[/tex], or [tex]\frac{2}{4}[/tex], simplified to [tex]\frac{1}{2}[/tex]. This means for every increase in x by 1, y increases by [tex]\frac{1}{2}[/tex].
Between the first 2 rows, x increases by 4 and y by 2 (half of 4), so it is true.
Between the second and third rows, x increases by 2 and y by 2 (which isn't half of 2). This is false, meaning this does not form a linear equation.
**This question involves solving linear equations using gradients, which you may want to revise. I'm always happy to help!
Related Questions
What are the solutions of the quadratic equation 2x2 - 4x = 3?
Answers
Answer:
a 1+- square root of 10
Step-by-step explanation:
subtract 3 set equation to zero then do quadratic formula break it down then you 2 square root of 10 over 2 divide to get square root of 10 by itself 2 divided by 2 is 1 therefore leaves 1 ^^.
The histogram below shows the grade ranges for Mrs. Granderson's class.
Student Scores on Test 4
10
8
6
Prequency
60-69
70 - 79
80 - 89
90 - 100
How many students earned an 80 or better on Test 4?
There were
students who earned an 80 or better on the test.
Answers
Answer:
The answer is 14.
Step-by-step explanation:
All you had to do was add all the amount of students that scored 80 to 100 and you would have got your answer.
A researcher is concerned about the impact of students working while they are enrolled in classes, and she likes to know if students work too much and therefore are spending less time on their classes than they should be. The researcher chooses a sample of 150 students and found that the sample mean is 7.10 hours and the sample standard deviation is 5. Construct a 90% confidence interval estimate of the mean hours a week students are working. a. What is the point estimate: _____________b. Find the critical value: ________________ Round to 3 decimal places. c. What is the margin or error: __________________ Round the answer to three decimal places d. Construct the confidence interval: Express the answer as (x,x), ______________ round to one decimal place. e. State the final Conclusion.
Answers
Answer:
(a) Point estimate = 7.10
(b) The critical value is 1.960
(c) Margin of error = 0.800
(d) Confidence Interval = (6.3, 7.9)
(e) We are 90% confident that the average number of hours worked by the students is between 6.3 and 7.9
Step-by-step explanation:
Given
[tex]\bar x = 7.10[/tex] -- sample mean
[tex]\sigma=5[/tex] --- sample standard deviation
[tex]n = 150[/tex] --- samples
Solving (a): The point estimate
The sample mean can be used as the point estimate.
Hence, the point estimate is 7.10
Solving (b): The critical value
We have:
[tex]CI = 90\%[/tex] --- the confidence interval
Calculate the [tex]\alpha[/tex] level
[tex]\alpha = 1 - CI[/tex]
[tex]\alpha = 1 - 90\%[/tex]
[tex]\alpha = 1 - 0.90[/tex]
[tex]\alpha = 0.10[/tex]
Divide by 2
[tex]\frac{\alpha}{2} = 0.10/2[/tex]
[tex]\frac{\alpha}{2} = 0.05[/tex]
Subtract from 1
[tex]1 - \frac{\alpha}{2} = 1 - 0.05[/tex]
[tex]1 - \frac{\alpha}{2} = 0.95[/tex]
From the z table. the critical value for [tex]1 - \frac{\alpha}{2} = 0.95[/tex] is:
[tex]z = 1.960[/tex]
Solving (c): Margin of error
This is calculated as:
[tex]E = z * \frac{\sigma}{\sqrt n}[/tex]
[tex]E = 1.960 * \frac{5}{\sqrt {150}}[/tex]
[tex]E = 1.960 * \frac{5}{12.25}[/tex]
[tex]E = \frac{1.960 *5}{12.25}[/tex]
[tex]E = \frac{9.80}{12.25}[/tex]
[tex]E = 0.800[/tex]
Solving (d): The confidence interval
This is calculated as:
[tex]CI = (\bar x - E, \bar x + E)[/tex]
[tex]CI = (7.10 - 0.800, 7.10 + 0.800)[/tex]
[tex]CI = (6.3, 7.9)[/tex]
Solving (d): The conclusion
We are 90% confident that the average number of hours worked by the students is between 6.3 and 7.9
the furniture store sells dining room tables and chairs. single chairs for particular table sell for 75.00 each. the cost for four chairs when the customer purchases the entire set is 200. what is the percent savings on the 4-chair set rounded to the nearest whole percent?
a.25%
b.33%
c.50%
d.66%
Answers
Answer:
B, 33%
Step-by-step explanation:
Let us find the original price of four chairs without the special deal, and compare it with the deal to find the percent savings.
Step 1:
A customer must buy 4 chairs costing $75 each to recieve the deal. Let us multiply 4 by 75 to find the total cost without the deal:
[tex]4*75=\\300[/tex]
Step 2:
We now know the original cost of the 4 chairs, and the price of 4 chairs with a deal. Let us subtract the difference of costs and convert it into a percentage to find percent savings:
[tex]300-200=100\\\frac{100}{300} =\frac{1}{3}[/tex]
[tex]\frac{1}{3}=33[/tex]%
Therefore, B, the percent savings is 33%.
I hope this helps! Let me know if you have any questions :)
Un deposito de agua tiene forma de prisma rectangular con los lados de la base de 25 y 20 metros. Calcula la altura que pueda contener 1000 metros cúbicos de agua
Answers
Answer:
La altura del depósito para que pueda contener 1000 metros cúbicos de agua es 2 m.
Step-by-step explanation:
Para calcular el volumen de un prisma rectangular, es necesario multiplicar sus 3 dimensiones: longitud*ancho*altura. El volumen se expresa en unidades cúbicas.
En este caso, se conoce la longitud y el ancho, cuyos valores son 25 y 20 metros. A su vez, se sabe que el depósito de agua debe contener 1000 m³. Entonces, siendo:
Volumen= longitud*ancho*altura
Y reemplazando los valores se obtiene:
1000 m³= 25 m* 20 m* altura
Resolviendo:
1000 m³= 500 m²* altura
[tex]altura=\frac{1000 m^{3} }{500 m^{2} }[/tex]
altura= 2 m
La altura del depósito para que pueda contener 1000 metros cúbicos de agua es 2 m.
What is the slope of the line that passes through the points (3,4) and (0,-2)
Answers
Answer:
slope of a line is 2/3
Step-by-step explanation:
the coordinate points are:
(3,4)=(x1 , y1)
(0,-2)=(x2 , y2)
slope=y2 - y1/x2 - x1
=-2-4/0-3
=-2/-3
=2/3
Which best describes the circumcenter of a triangle?
• A. The point where the three angle bisectors of the triangle inters
•
B. The point where the perpendicular bisectors of the three sides
the triangle intersect
• c. The point where the three altitudes of the triangle intersect
D. The point where the three medians of the triangle intersect
Answers
Answer:
B
Step-by-step explanation:
Not much to say but that i the definition. You sing the midpoint of each side, make a perpendicular line and see where the three perpendicular bisectors intersect.
A is the incenter, C sounds like the Orthocenter and D sounds like the centroid.
Aside from being able to tell from the parts of the words, you just kinda have to memorize these.
In circle H with mZGHJ = 92°, find the angle measure of minor arc GJ
Answers
Answer:
x = 92°
Step-by-step explanation:
The angle measure of the central angle is congruent to the measure of the intercepted arc.
If there was a total of 80 vehicles an a percentage of 70% of cars how much car was used
Answers
Answer:
56
Step-by-step explanation:
I don't quite understand your question but I assumed you meant what is 70% of 80
A line of best fit....?
a) must pass through the median of the data
b) must pass through the origin
c) represents the trend of the data
d) must have a positive slope
Answers
A 3-member committee has to be formed from 2 teachers and 2 parents. How many combinations are possible?
Answers
Step-by-step explanation:
the answer is in the above image
The number of combinations possible if a 3-member committee has to be formed from 2 teachers and 2 parents is 4 combinations
Combination and permutationCombinations have to do with selection compared to permutation that has to do with the arrangement.
If a 3-member committee has to be formed from 2 teachers and 2 parents, the total committee is given as:
Total committee members = 2 + 2
Total committee members = 4 committees
If 3-member committee has to be formed from them, the number of ways this can be done is given as:
4C3 = 4!/(4-3)!3!
4C3 = 41/3!
4C3 = 4 ways
Hence the number of combinations possible if a 3-member committee has to be formed from 2 teachers and 2 parents is 4 combinations
Learn more on combination here: https://brainly.com/question/11732255
Samantha is creating concrete spheres for a weight-lifting competition. One of the spheres needs to have a weight of 350 pounds. Samantha knows that concrete weighs 150 pounds per cubic foot, in feet, of the sphere that Samantha will create?
Answers
The volume occupied by a 350 pound sphere is 2.33 ft³.
EquationEquation is an expression used to show the relationship between one or more numbers and variables.
Let y represent the weight of the sphere in pounds and x represent the volume in feet³, hence:
y = 150x
For a 350 pounds sphere:
350 = 150x
x = 2.33 ft³
The volume occupied by a 350 pound sphere is 2.33 ft³.
Find out more on equation at: https://brainly.com/question/13763238
Find each difference. (10 Points!)
Answers
Answer:
1. -6y^4 +4y^2 -12
2. x - 19
Step-by-step explanation:
1.
(6y^4+3y^2-7) - (12y^4-y^2+5)
= -6y^4+ 4y^2- 12
2. 3(x-5) - (3x+4)
= (3x-15) - (3x+4)
= x-19
4x-8y less than or equal to -16
Answers
Answer:
x=0, y=2
Step-by-step explanation:
if you substutute the answers you will get the correct answer
Calculate the number of kilowatt-hour a 7kW industrial pump used in 15 hours?
Answers
Answer:
The answer is "105 kilowatt-hour".
Step-by-step explanation:
Number of kilowatts[tex]= 7\ KW[/tex]
Total hours[tex]= 15 \ hours[/tex]
The total number of kilowatt-hour:
[tex]=7 \times 15\\\\= 105 \ kilowatt-hour[/tex]
What are the missing variables? Plzzzz
Answers
Answer:
D. x ≈ 3.3, y = 15.7
Step-by-step explanation:
x = Opposite
y = Adjacent
16 = Hypotenuse
θ = 12°
To find x, we solve using the Trigonometric function of Sine
sin θ = Opposite/ Hypotenuse
x = Opposite
sin 12 = x/16
Cross Multiply
x = sin 12 × 16
x = 3.3265870531
Approximately, x ≈ 3.3
To find y, we solve using the Trigonometric function of cosine
cos θ = Adjacent/ Hypotenuse
y = Adjacent
cos 12 = y/16
Cross Multiply
y = cos 12 × 16
y = 15.650361612
Approximately, y ≈ 15.7
Therefore, x ≈ 3.3, y = 15.7
Option D is correct
what is the solution to the equation below sqrt x-2 = x-22
Answers
Answer:
√27-2 =27-22
√25. =5
the answer is option B
x=27
Answer:
option B : x = 27
Step-by-step explanation:
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
It is 300.88.
Step-by-step explanation: In order for the perimeter of the base to be 18.2, the length and width would have to be 9.1, knowing this, you can plug it into the formula for a pyramid like usual with the height provided.
consider the equation of the line y=-2x+4 what is the value of y when x=2
Answers
Answer: The value of y is 8
Step-by-step explanation:
Since we know x=2 we can sub in 2 for x in the equation
y=2(2)+4
y=4+4
y=8
Jaclyn estimates that the square root of 50 in the following way:
[tex]\sqrt{50[/tex] = [tex]2 \sqrt{25[/tex] = 2 * 5 = 10
Explain why her reasoning is incorrect. Please use complete sentences.
Answers
[tex]\sf\purple{The\: square\: root \:of \:50\: is\: 5√2.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}[/tex]
Error made by Jaclyn ⤵
[tex] \sqrt{50} [/tex]
[tex]\sf\red{=\:2√25}[/tex] ❌
Correct way to solve it ⤵
[tex] \sqrt{50} \\ \\ = \sqrt{5 \times 5 \times 2} \\ \\ = \sqrt{ {5}^{2} \times 2} \\ \\ = \sqrt{ {5}^{2} } \times \sqrt{2} \\ \\ = 5 \sqrt{2} \\ \\ (∵ \sqrt{ {a}^{2} } = a)[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Find the value of x.
Answers
Answer:
B. x=4
Step-by-step explanation:
It should be the short front length times the total length of the tangent.
6(16)=8(8+x)
96=64+8x
32=8x
4=x
The value of the variable x is 7.5. Option D
How to determine the valueA line that touches the circle at a single point is known as a tangent to a circle.
The point where tangent meets the circle is called point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects.
From the information given, we have that;
10(6) = 8(x)
expand the bracket, we get;
60 = 8x
Now, divide both sides by the coefficient of x, we get;
x = 60/8
Divide the values
x = 7.5
Learn about tangents at: https://brainly.com/question/30162650
#SPJ6
Solve the system of equations by graphing on your own paper. What is the y
coordinate of the solution?
= 2x-1
= -2x+5
Answers
Answer: The coordinate of the solution is (0.25,-0.5)
Step-by-step explanation:
the solution is (0.25,-0.5) because when you graph them on a graph, they both intercept at that point.
What is the answer and how did you get it
Answers
answer is 200 lol pretty easy
Answer:
He sold 200 loaves
Step-by-step explanation:
if he sells twice as many the next week the equation would be
100 times 2 = x
therefore, the answer is 200
The Sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.
Answers
Answer:
8 and 17
Step-by-step explanation:
Let the number x and y
Sum of numbers, x + y = 25 -----------( 1 )
One number exceeds other by 9,
that is difference between the numbers is 9, x - y = 9
=> x = 9 + y --------- ( 2 )
Substitute ( 2 ) in ( 1 )
( 9 + y ) + y = 25
2y = 25 - 9
2y = 16
y = 8
Substitute y = 8 in ( 2 ) : x = 9 + y
= 9 + 8 = 17
Therefore the 2 numbers are 8 and 17
Answer:
The answer would be that one number is 8 and the second is 17.
The sum of these two numbers is 25, ad 17 and 8 have a difference of 9
Step-by-step explanation:
Can someone solve this and show it step by step
3(x + 1) − 5(y + 2) = 12
5(−3 + 2x) − 3(4 − y) = −3
Answers
Answer:
x = 3, y = - 2
Step-by-step explanation:
Simplify the 2 given equations
3(x + 1) - 5(y + 2) = 12 ← distribute left side
3x + 3 - 5y - 10 = 12
3x - 5y - 7 = 12 ( add 7 to both sides )
3x - 5y = 19 → (1)
----------------------------------
5(- 3 + 2x) - 3(4 - y) = - 3 ← distribute left side
- 15 + 10x - 12 + 3y = - 3
10x + 3y - 27 = - 3 ( add 27 to both sides )
10x + 3y = 24 → (2)
-------------------------------------------
Solve the 2 equations simultaneously
3x - 5y = 19 → (1)
10x + 3y = 24 → (2)
Multiplying (1) by 3 and (2) by 5 and adding the result will eliminate y
9x - 15y = 57 → (3)
50x + 15y = 120 → (4)
Add (3) and (4) term by term to eliminate y
59x = 177 ( divide both sides by 59 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
3(3) - 5y = 19
9 - 5y = 19 ( subtract 9 from both sides )
- 5y = 10 ( divide both sides by - 5 )
y = - 2
Solution is x = 3, y = - 2
The nation of Finlandia has 120,000 people. Of these, 20,000 are children under 16, 72,000 have jobs, 8,000 don't have jobs but are looking for work, and 20,000 are retired. With this info, calculate the labor force participation rate and the unemployment rate.
Answers
Answer: labor force participation rate =60%
unemployment rate = 6.67%
Step-by-step explanation:
The labor force participation rate is computed as
[tex]\text{labor force participation rate}=\dfrac{\text{Total employed persons}}{\text{Total population}}[/tex]
i.e. [tex]\text{labor force participation rate}= \dfrac{72000}{120000}[/tex]
[tex]= 0.6\ or\ 60 \%[/tex]
The unemployment rate is computed as:
[tex]\text{unemployment rate}=\dfrac{\text{Number of personsdon't have jobs }}{\text{Total population}}\\\\\text{unemployment rate}=\dfrac{8000}{120000}\\\\\text{unemployment rate}=0.0667\ or\ 6.67\%[/tex]
Hence, labor force participation rate =60%
unemployment rate = 6.67%
Is pi over 2 rational or irrational
Answers
Answer:
rational
Step-by-step explanation:
Answer:
Step-by-step explanation:
Explanation: It is an irrational number. A number is rational if it can be expressed as a quotient of 2 integer numbers. Number π2 cannot be expressed as a quotient of integers, so it is an irrational number.
Angle Measurements 1”” degree help find out what’s the other side
Answers
Answer:
80 degree
Step-by-step explanation:
missing angle + 100 degree = 180 degree (being co interior angles )
missing angle = 180 - 100
missing angle 80 degree
Write an equivalent expression in expanded form. -1/4(-8x+12)
Answers
Answer:
2x - 3
Step-by-step explanation:
The Distributive Property of Multiplication applies here. Multiply each of the two terms inside parentheses by-1/4: 2x - 3
A:6 and 30
B:8 and 28
C:4 and 16
Answers
Answer:
C?
Step-by-step explanation:
