Answer:
Rainfall: Continuous
Soil type: Discrete
Voting districts:Discrete
Temperature:Continuous
Elevation: Continuous
Vegetation type:Discrete
Step-by-step explanation:
Discrete data is one that involves round, definite numbers that can be determined by just counting whereas continuous data is one that involves complex numbers that are usually measured across a specific time interval. In a nutshell, we can say that discrete data is one that is counted while continuous is one that is measured.
Rainfall: This will be considered as a continuous data because it can't be counted in a definite number but can only be measured over a long period of time.
Soil type: This is Discrete because it can be counted. We can count the number of soil types we have in different areas.
Voting districts: This is Discrete because we can count the number of districts we have at any given time.
Temperature: This is Continuous because temperature cannot be counted but measured by the use of a thermometer.
Elevation: This continuous because it can't be counted as a number but measured.
Vegetation type: This is Discrete as we can count the number of places that have a particular vegetation type.
Fathi has \$1.10$1.10dollar sign, 1, point, 10 in his printing account. Each sheet of paper he uses reduces his printing account balance by \$0.25$0.25dollar sign, 0, point, 25. Fathi wants to print out a PDF document that is 474747 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet. After Fathi prints, what will be the balance in his printing account?
Answer:
$-4.90.
Step-by-step explanation:
Fathi has $1.10. Each sheet costs him $0.25. He wants to print 47 pages.
If he prints double sided, then he will use 47 / 2 = 23.5 sheets of paper. But he can't print a half-sheet, so he will use 24 sheets of paper.
Each sheet costs $0.25. 0.25 * 24 = 6. The printing will cost him $6.
Since he only has $1.10, his remaining balance will be 1.1 - 6 = -4.9. The balance on his printing account will be $-4.90.
Hope this helps!
Answer:
-1.90
Step-by-step explanation:
Khan Academy
I got it right for sure
A random sample of 13 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 950 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student’s t.
1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 20. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
Answer:
1. The 99% confidence interval is from 941.527 to 958.473
2. The 99% confidence interval is from 933.054 to 966.946
3. The 99% confidence interval is from 916.108 to 983.892
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size,
s is the sample standard deviation,
[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level
The t-score corresponding to 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 13 - 1 = 12
From the t-table at α = 0.005 and DoF = 12
t-score = 3.055
1. 99% Confidence Interval when s = 10
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]
The 99% confidence interval is from 941.527 to 958.473
2. 99% Confidence Interval when s = 20
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]
The 99% confidence interval is from 933.054 to 966.946
3. 99% Confidence Interval when s = 40
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]
The 99% confidence interval is from 916.108 to 983.892
As the sample standard deviation increases, the range of confidence interval also increases.
Find the rate of change of the height from age 8 to 16 and from age 60 to 80. Express both answers in units of cm per year, to two significant figures. Separate your answers with a comma.
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
a
[tex]z = 6.25 \ cm/yr[/tex]
b
[tex]k = -0.25 \ cm /yr[/tex]
Step-by-step explanation:
From the first image the rate of rate of change of the height from age 8 to 16
is mathematically evaluated from the graph as
[tex]z = \frac{175 - 125}{16-8}[/tex]
[tex]z = 6.25 \ cm/yr[/tex]
From the first image the rate of rate of change of the height from age 60 to 80.
is mathematically evaluated from the graph as
[tex]k = \frac{175 - 170}{60-80}[/tex]
[tex]k = -0.25 \ cm /yr[/tex]
Which of the following systems of inequalities would produce the region indicated on the graph below?
Answer:
A. y > x+1; y≤10; x≥0
Step-by-step explanation:
Other things being equal, which they are, you're looking for an inequality that has "y >". You know this because shading is above (>) the dashed line (not ≥). Only choice A matches.
__
If the boundary line were solid, you would be looking for "y ≥", since y=(boundary line) is included in the solution set in that case.
Q‒1. [5×4 marks] a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? (150) b) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? c) How many odd numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? d) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? e) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once?
Answer:
a) 294
b) 180
c) 75
d) 174
e) 105
Step-by-step explanation:
I assume that for each problem, the first digit can't be 0.
a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.
6×7×7 = 294
b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.
6×6×5 = 180
c) Again, each digit can only be used once, but this time, the last digit must be odd.
If only the last digit is odd, there are 3×3×3 = 27 possible numbers.
If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.
If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.
If all three digits are odd, there are 3×2×1 = 6 possible numbers.
The total is 27 + 24 + 18 + 6 = 75.
d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.
If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.
If the first digit is greater than 3, there are 3×7×7 = 147 numbers.
The total is 6 + 21 + 147 = 174.
e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.
If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.
The total is 15 + 90 = 105.
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: a) 8.779 years
b) 8.664 years
Step-by-step explanation:
a)
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
A: accumulated amount (balance)P: principal amount (original/initial investment)r: interest rate (convert to a decimal)n: number of times compounded per yeart: number of yearsGiven: A = 1800, P = 900, r = 8% = 0.08, n = 3, t = unknown
[tex]1800=900\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\2=\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=ln \bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=3t\ ln\bigg(1+\dfrac{0.08}{3}\bigg)\\\\\\\dfrac{ln\ 2}{3\ ln\bigg(1+\dfrac{0.08}{3}\bigg)}=t\\\\\\\large\boxed{8.779=t}[/tex]
b)
[tex]A=Pe^{rt}[/tex]
[tex]1800=900e^{0.08t}\\\\\\2=e^{0.08t}\\\\\\ln\ 2=0.08t\\\\\\\dfrac{ln\ 2}{0.08}=t\\\\\\\large\boxed{8.664=t}[/tex]
X = ??????geometryyyy
Answer:
3.75Step-by-step explanation:
Using Secant-Secant theorem we can find the value of x.
The product of one segment and its external segment is equal to the product of the other segment and its external segment.
5 × 3 = x × 4
15 = 4x
15/4 = x
3.75 = x
Joan is selling handmade bead necklaces
at a local art fair. She paid $180 to
reserve her booth. The cost of supplies
for each necklace averages $2. So, her
cost, y, for x necklaces is represented by
y = $180 + 2x. If she sells her necklaces
for $12, her revenue, y, is represented
by y = 12x.
The solution of this system is the break-
even point, the point beyond which she
starts making a profit.
HELP PLS QUICK
Answer:. x = 18
Step-by-step explanation:
Solve by substitution. Given: y= 12x. Rewrite the original equation y= 180 + 2x to 12x = 180 +2x. Subtract 2x from both sides. 10x = 180. Then divide both sides by 10.
x=18
So once she has sold 18 necklaces, she has covered her costs (180 + 36) and she begins to make a profit.
What is the volume of the cylinder below? A cylinder with a height of 12 millimeters and diameter of 18 millimeters. 108 pi mm3 216 pi mm3 648 pi mm3 972 pi mm3
Answer:
V =972 pi mm ^3
Step-by-step explanation:
The diameter is 18 so the radius is 1/2 of the diameter
18/2 = 9
r=9
The volume of a cylinder is
V = pi r^2 h
V = pi (9)^2 12
V =972 pi mm ^3
Answer:
972pi mm^3
Step-by-step explanation:
What is the volume of the cylinder below? A cylinder with a height of 12 millimeters and diameter of 18 millimeters. 108 pi mm3 216 pi mm3 648 pi mm3 972 pi mm3
V = (pi)r^2h
r = d/2 = 18 mm/2 = 9 mm
V = (pi)(9 mm)^2(12 mm)
V = 972pi mm^3
Please help I don’t understand And I need an explanation
Hey there! :)
Answer:
56 m².
Step-by-step explanation:
To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:
Solve for the rectangle: (A = l × w)
A = 8 × 5
A = 40 m²
Solve for the triangle: (A = 1/2 (bh))
A = 1/2(4 · 8)
A = 1/2(32)
A = 16 m².
Add up the two areas:
40 + 16 = 56 m².
Answer:
Area of triangle+ the area of rectangle
Step-by-step explanation:
Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²
Area of rectangle is length × breadth= 5×8: 40 m²
Area of the shape is 40m²+16m²= 56m²
A random sample of n = 8 E-glass fiber test specimens of a certain type yielded a sample mean interfacial shear yield stress of 32.9 and a sample standard deviation of 4.9. Assuming that interfacial shear yield stress is normally distributed, compute a 95% CI for true average stress. (Give answer accurate to 2 decimal places.)
Answer:
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=32.9[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=4.9 represent the sample standard deviation
n=8 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
the degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this cae would be [tex]t_{\alpha/2}=2.365[/tex]
Now we have everything in order to replace into formula (1):
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
Julie has three boxes of pens. The diagram shows expressions for the number of pens in each box. Look at these equations.
Equals B +12
B equals C +4
Write an equation to show the relationship between a + c
Answer:
a=c+16here,
a=b+12
b=a-12----> equation (i)
b= c+4
putting the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
hope this helps...
Good luck on your assignment...
The value of a + c is 16.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
a=b+12
So, b=a-12 ---- equation (i)
and, b= c+4
Substitute the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
Hence, the value of a+ c is 16.
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There are 4 Board of Directors positions open. 2 will be for men, 2 will be for women.
Out of 20 candidates, 11 are men, 9 are women. How many total outcomes are
possible?
Answer:
4290
Step-by-step explanation:
Lets find the total number of men and women .
9 women are out and 2 became the member of the Board=> total 11 women
11 men are out and 2 became the member of the Board=> total 13 men
11 women-candidates for 2 positions can make C11 2 outcomes =11!/(11-2)!/2
13 men-candidates for 2 positions can make C13 2 outcomes= 13!/(13-2)!/2
The total number of outcomes is C11 2 *C13 2 = 13!*11!/9!/11!/2/2=
10*11*12*13/2/2=11*13*5*6=4290 outcomes
Which statements about the dilation are true? Check all that apply. Triangle X prime Y prime Z prime. Point X prime is 2 units from the center of dilation C and point Z prime is 3 units from the center of dilation. Triangle X Y Z. Point X is 5 units from point C and point Z is 7.5 units from point C.
Answer:
A,B,E
Step-by-step explanation:
Just took the quiz
Answer:
A,B,E
Step-by-step explanation:
Give me brainliest.
Diane's bank is offering 5% interest, compounded monthly. If Diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? Round to the nearest tenth of a year.
Answer:
The time period is 13 years.
Step-by-step explanation:
Interest rate (r )= 5% or 5%/12 = 0.42% per months
The investment amount (Present value) = $10500
Final expected amount (future value) = $20000
Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.
Use the below formula to find the time period.
Future value = present value (1 + r )^n
20000 = 10500(1+0.0042)^n
1.9047619 = (1+0.0042)^n
1.9047619 = 1.0042^n
n = 153.74 months.
Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)
Choose the correct number to finish the sentence. For the function f(x)=√x+4, the average rate of change to the nearest hundredth over the interval 2 ≤ x ≤ 6 is? A. 0.2 B. 0.17 C. 0.16 D. 0.18
Answer:
See below under "explanation".
General Formulas and Concepts:
Algebra I
Functions
Function NotationAverage Rate of Change Formula:
[tex]\displaystyle \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}[/tex]
Step-by-step explanation:
*Note:
The function is unclear, so I will provide 2 possible answers.
Step 1: Define
Identify given.
[tex]\displaystyle \begin{aligned}1. \ f(x) & = \sqrt{x} + 4 \\2. \ f(x) & = \sqrt{x + 4} \\\end{aligned}[/tex]
[tex]\displaystyle \text{Interval: } 2 \leq x \leq 6[/tex]
Step 2: Find Average Rate of Change
For the 1st function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\big( \sqrt{b} + 4 \big) - \big( \sqrt{a} + 4 \big)}{b - a} \\& = \frac{\big( \sqrt{6} + 4 \big) - \big( \sqrt{2} + 4 \big)}{6 - 2} \\& = \frac{\sqrt{6} - \sqrt{2}}{4} \\& = 0.258819 \\& \approx \boxed{0.26} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 1st defined function, will be approximately 0.26.
For the 2nd function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\sqrt{b + 4} - \sqrt{a + 4} }{b - a} \\& = \frac{\sqrt{6 + 4} - \sqrt{2 + 4}}{6 - 2} \\& = \frac{\sqrt{10} - \sqrt{6}}{4} \\& = 0.178197 \\& \approx \boxed{0.18} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 2nd defined function, will be approximately 0.18.
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---
Topic: Algebra I
Calculate
(14x5x4) / (28 x 2)
Answer:
5
Step-by-step explanation:
(14 × 5 × 4) ÷ (28 × 2)
Solve brackets.
280 ÷ 56
Divide.
= 5
I NEED HELP PLEASE, THANKS! :)
Answer:
Option B
Step-by-step explanation:
Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -
[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]
Convert this to slope - intercept form -
[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]
Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -
( 0, 10 ),
( 15, 9 ),
( 17, 0 )
When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -
Option B
When should the IQR should be used to measure variance?
Select one:
When an outlier exists.
When data is gathered from a sample of the population.
When a data set does not have an outlier.
When the data set includes decimal values.
Answer:
When an outline exists.
Step-by-step explanation:
As compared to the range, the interquatile range is somewhat resistant to the outliers. This is because the interquartile range itself is not always affected by the outliers if they lie at both ends of the data sets.
The IQR only describes the range of the middle 50% of the values in a data set, which is calculated as the difference between the 75th and 25th percentile values.
It also helps in the identification of these outliers using mild outliers being those values lower than the 25th quartile minus 1.5×IQR, or those values greater than the 75th quartile plus 1.5×IQR.
SOS Help me please
Q‒2. [5×4 marks] Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that
a) the bit string has exactly two 1s;
b) the bit string begins and ends with 0;
c) the bit string has the sum of its digits equal to seven;
d) the bit string has more 0s than 1s;
e) the bit string has exactly two 1s, given that the string begins with a 1.
Answer:
a. 45/1024
b. 1/4
c. 15/128
d. 193/512
e. 9/256
Step-by-step explanation:
Here, each position can be either a 0 or a 1.
So, total number of strings possible = 2^10 = 1024
a) For strings that have exactly two 1's, it means there must also be exactly eight 0's.
Thus, total number of such strings possible
10!/2!8!=45
Thus, probability
45/1024
b) Here, we have fixed the 1st and the last positions, and eight positions are available.
Each of these 8 positions can take either a 0 or a 1.
Thus, total number of such strings possible
=2^8=256
Thus, probability
256/1024 = 1/4
c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string. Also, it means there must also be exactly three 0's
Thus, total number of such strings possible
10!/7!3!=120
Thus, probability
120/1024 = 15/128
d) Following are the possibilities :
There are six 0's, four 1's :
So, number of strings
10!/6!4!=210
There are seven 0's, three 1's :
So, number of strings
10!/7!3!=120
There are eight 0's, two 1's :
So, number of strings
10!/8!2!=45
There are nine 0's, one 1's :
So, number of strings
10!/9!1!=10
There are ten 0's, zero 1's :
So, number of strings
10!/10!0!=1
Thus, total number of string possible
= 210 + 120 + 45 + 10 + 1
= 386
Thus, probability
386/1024 = 193/512
e) Here, we have fixed the starting position, so 9 positions remain.
In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.
Thus, total number of such strings possible
9!/2!7!=36
Thus, probability
36/1024 = 9/256
Find the area of the figure below
Answer:
a
Step-by-step explanation:
Mahesh has Rs 150 and he buys a pen costing Rs 75 now he has to buy a copies costing Rs 10 each what is the maximum number of copies did he buy?
Answer:
7
Step-by-step explanation:
Rs 150- Rs 75=Rs 75 remaining
Rs 75/10= 7 as whole
Step-by-step explanation:
given,
total amnt =rs.150
cost of pen= rs.75
now,
left money =150_75
=rs.75
now,cost of 1 copy=10
then , no. of copies=75/10
=7.5
so he can buy 7 copies.
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answer:
1140 ways.
Step-by-step explanation:
The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).
The 17 identical candies, can be distributed among the 4 children in :
=(17 + 4 - 1)C(4–1) = 20C3 ways.
= 20!/((20–3)!*3!) ways.
= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways
= 20*19*3 ways.
=1140 ways.
What are the vertex and X intercepts of the graph of the function below Y =(x+4)(x-2)
Answer:
Vertex: ( -1 , − 9 )
X intercepts (0,-4)(0,2)
Step-by-step explanation:
Answer:
( -1, -9)
And
x-intercepts: (-4, 0), (2,0)
Step-by-step explanation:
Sacrificed my grade
Adding polynomials help please
Answer:
A
Step-by-step explanation:
Answer:
D. None of these choices are correct
Step-by-step explanation:
* indicates the square sign.
w=6xy
l=xysq
P=2(l+w)
=2(xy*+6xy)
=2xy*+12xy
What is the equation of the line, in general form, that passes through the point (1, 1) and has a y-intercept of 2. A. x - y - 2 = 0 B. x - y + 2 = 0 C. x + y - 2 = 0
Answer:
The answer is option C
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the line first find the slope
The line has a y intercept of 2 which is
(0 , 2)
Slope of the line using points
( 1 ,1) and (0,2) is
[tex]m = \frac{2 - 1}{0 - 1} = \frac{1}{ - 1} = - 1[/tex]
So the equation of the line using point (1,1) is
y - 1 = - 1(x - 1)
y - 1 = - x + 1
x + y - 1 - 1 = 0
We have the final answer as
x + y - 2 = 0Hope this helps you
Please Help. Which system of linear equations is represented in the graph?
Answer:
y = x - 3
y = -5x +2
Step-by-step explanation: for The "missing" coefficient of x (m in the y=mx+b format) is an implied +1. So the slope is "up-one & over one." y-intercept is -3
y = -5x +2 The slope is -5 so "down 5 & over 1" on the graph, The y-intercept is +2
Solve the system of linear equations.
Answer:
dependent systemx = 2 -ay = 1 +az = aStep-by-step explanation:
Let's solve this by eliminating z, then we'll go from there.
Add 6 times the second equation to the first.
(3x -3y +6z) +6(x +2y -z) = (3) +6(4)
9x +9y = 27 . . . simplify
x + y = 3 . . . . . . divide by 9 [eq4]
Add 13 times the second equation to the third.
(5x -8y +13z) +13(x +2y -z) = (2) +13(4)
18x +18y = 54
x + y = 3 . . . . . . divide by 18 [eq5]
Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:
y = 3 -x . . . . solve eq5 for y
x +2(3 -x) -z = 4 . . . . substitute into the second equation
-x +6 -z = 4
x = 2 - z . . . . . . add x-4
y = 3 -(2 -z)
y = z +1
So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...
x = 2 -a
y = 1 +a
z = a
_____
Check
First equation:
3(2-a) -3(a+1) +6a = 3
6 -3a -3a -3 +6a = 3 . . . true
Second equation:
(2-a) +2(a+1) -a = 4
2 -a +2a +2 -a = 4 . . . true
Third equation:
5(2-a) -8(a+1) +13a = 2
10 -5a -8a -8 +13a = 2 . . . true
Our solution checks algebraically.
25% of the University's freshman class for majoring in engineering. 500 students in the Freshman Class are engineering Majors, how many students are in the Freshman Class
Answer:
2000
Step-by-step explanation:
percentage o students for majoring in engineering=25%
no pf students for majoring in engineering=500
therfore, 25% of x =500
25/100*x=500
x= 500*100/25
=500*4 =2000
In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes.
Part A
Find the constant of proportionality in terms of minutes per bracelet.
Part B
What does the proportionality constant represent in this situation?
Part C
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part A. Be sure to assign a variable for each quantity.
Part D
Now find the constant of proportionality in terms of number of bracelets per minute.
Part E
What does the proportionality constant represent in this situation?
Part F
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part D. Be sure to assign a variable for each quantity.
Part G
How are the constants of proportionality you found in parts A and D related?
Part H
Are the two equations you developed in parts C and F equivalent? Explain.
Answer:
Step-by-step explanation:
A) The constant of proportionality in terms of minutes per bracelet is
15/3 = 5 minutes per bracelet
B) The constant of proportionality represents man hour rate
C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
t = kb
D) the constant of proportionality in terms of number of bracelets per minute is
3/15 = 1/5
E) The constant of proportionality represents production rate
F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
b = kt
G) The constants of proportionality are reciprocals
H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.
Answer:the sample answers, change them up so you dont get in trouble
A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality=15 MINUTES/3 BRACELETS=5 minutes per bracelet.
B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.
C Here’s one way to set up the equation:
time = constant of proportionality × number of bracelets
Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.
thats all ik srry
Step-by-step explanation: