a) n = 4148
b) n = 2449
How to solveThe sample size for proportion:
Given that,
E = 2% = 0.02
c = 99% = 0.99
Using the z table,
= 2.576 for 99% confidene level.
Using the z-table, search for 0.9950 probability and see where is 0.9950 cumulative probability nearly and then see the corresponding z value.
Step 2/2
a)
Here p is unknown.
In this case, take p = 0.5
n = 4147.36
= 4148
b Here, p = 18% = 0.18
Now,
n = 2448.601344
= 2449
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What values of y and z make
The values of y and z that make the triangles to be congruent are 13 each
Calculating the values of y and zFrom the question, we have the following parameters that can be used in our computation:
The triangles
For the two triangles to be congruent, the following equations must be true
2y = y + 13
y + 5z - 20 = 2y + z + 19
When the above equations are evaluated, we have
y = 13
Next, we have
4z = y + 39
So, we have
4z = 13 + 39
Add and divide by 4
z = 13
Hence, the values of y and z are 13
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Break-Even Sales
BeerBev, Inc., reported the following operating information for a recent year (in millions):
Sales $6,512
Cost of goods sold $1,628
Gross profit $4,884
Marketing, general, and admin. expenses 592
Income from operations $ 4,292
Assume that BeerBev sold 37 million barrels of beer during the year, that variable costs were 75% of the cost of goods sold and 50% of marketing, general and administration expenses, and that the remaining costs are fixed. For the following year, assume that BeerBev expects pricing, variable costs per barrel, and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $21.09 million.
a. Compute the break-even sales (in barrels) for the current year. Round your answer to two decimal places. Enter your answers in millions.
The break even sales for the current year using the contribution per unit is 5.27.
The formula to find the break even sales is,
Break even sales = Fixed costs / Contribution per unit
Now,
Contribution per unit = Sales price per unit - Variable cost per unit.
Sales price = $6,512
Variable cost = (75% × cost of goods sold) + (50% × marketing, general and administration expenses)
= (75% × $1,628) + (50% × $592)
= $1517
Contribution margin = $6,512 - $1517 = $4995
Contribution per unit = $4995 / 37 = $135 per million
Fixed costs = (25% × cost of goods sold) + (50% × marketing, general and administration expenses)
= $703
Break even sales = 703 / 135 = 5.21
Hence the break even sales is 5.27.
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The two buses drove towards each other at constant speeds. The first left NY at 11AM and arrived in Boston at 4 PM, and the second left Boston at 12 PM and arrived in NY at 5 PM. What time did they meet?
The two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.
Since the two buses are traveling towards each other at constant speeds, we can use the formula for finding the time two objects meet when traveling at constant speeds in opposite directions:
t = (d2 - d1)/(v1 + v2)
Where t is the time they meet, d1 is the distance the first bus travels, d2 is the distance the second bus travels, v1 is the speed of the first bus, and v2 is the speed of the second bus.
In this case, d1 is the distance between NY and Boston (approx. 200 miles), d2 is the distance between Boston and NY (also approx. 200 miles), v1 is the speed of the first bus (200 miles in 5 hours, or 40 miles/hour), and v2 is the speed of the second bus (200 miles in 5 hours, or 40 miles/hour).
Plugging these values into the formula, we get:
t = (200 - 200)/(40 + 40)
t = 0/80
t = 0
Hence, the two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.
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please help me i will give brainiest to whoever answers the questions thank you
PLEASE HELP please help thank you please hurry fast i will give brainiest
Answer:
3) The graph that has three x-intercepts
9) Plot the points on the graphing calculator, and then generate a linear regression equation. That equation is:
y = 2.857x - 1.4286
The closest equation is y = 3x - 2. That equation best represents the regression line for this data.
tion 9, 2.2.5 The histogram to the right represents the weights (in pounds) of members of a certain high-school math team. How many team members are included in the histogram? he histogram represents 20 math team members. www 4- 2- 0- Points: 0 of 1 110 120 130 140 150 160 170
Based on the information provided in the question, we can conclude that the histogram represents 20 math team members.
[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]
♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]
Me podrían ayudar a resolver esto? Tengo la respuesta lo que necesito es el procedimiento. Muchas gracias
2√8p²q³r
The algebraic expression can be simplified to 4p√2q³r
How to simplify an algebraic expression?An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
The expression can be simplified as follow:
2√(8p²q³r) = 2 * √8 * √p² √(q³r)
= 2 * √(4 * 2) * p √(q³r)
= 2 * √4 * √2 * p √(q³r)
= 2 * 2 * √2 * p √(q³r)
= 4p√2q³r
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Question in English
Could you help me solve this? I have the answer what I need is the procedure. Thank you so much
2√8p²q³r
Point P is shown on the number line below. The distance between Point Q and Point P is 6 1/2 uhits. Which number
could represent Point Q?
The number that could represent point Q is to be considered as the option c. 2 1/2.
How to solveCalculation of the number:
Since
p = -4
q could be 6.5 units to the right or to the left of point p.
So, to the right, it should be like
=p + q
= -4 + 6.5
= 2.5
Hence, The number that could represent point Q is to be considered as option c. 2 1/2.
In mathematics, a tool known as a number line offers a graphical representation of numerical values arranged in sequential order from left to right with zero located in the center. This instrument is frequently applied throughout mathematical fields when interpreting negative and positive numbers along with fractions and decimals.
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y<-4x-2 choose the graph that best models the inequality
Answer:the upper right one( the dash line that hit -2
Step-by-step explanation:
Find the area of the circle. Round your answer to the nearest tenth. Use 3.14 or 22
area: about
mm²
9 mm
for π.
Answer:
254.34
Step-by-step explanation:
πr^2
3.14*81
254.34
Reyesburg Corporation is contemplating using a new, more expensive glue in the construction of its laminated veneer lumber. Of importance to the company is
the carrying load of the lumber. The company has tested 34 beams using the new glue, recording for each beam the pressure (in pounds per square foot) at
which the beam breaks. The data collected are presented in the following frequency distribution.
Carrying load
(in pounds per square foot)
860 to 879
880 to 899
900 to 919
920 to 939
940 to 959
Frequency
5
9
12
6
2
Based on the frequency distribution, using the midpoint of each data class, estimate the mean carrying load of the beams tested. For your intermediate
computations, use four or more decimal places, and round your answer to one decimal place.
Based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.
Estimate the mean carrying load of the beams tested.To estimate the mean carrying load of the beams tested, we need to find the weighted average of the midpoints of each data class.
First, we need to find the midpoint of each class interval. We can do this by taking the average of the lower and upper limits of each interval:
Midpoint of 860 to 879 = (860 + 879) / 2 = 869.5
Midpoint of 880 to 899 = (880 + 899) / 2 = 889.5
Midpoint of 900 to 919 = (900 + 919) / 2 = 909.5
Midpoint of 920 to 939 = (920 + 939) / 2 = 929.5
Midpoint of 940 to 959 = (940 + 959) / 2 = 949.5
Next, we can find the weighted average of these midpoints, using the frequencies as weights. We can set up a table to organize our calculations:
Data class Midpoint Frequency Midpoint x Frequency
860-879 869.5 5 4,347.5
880-899 889.5 9 8,005.5
900-919 909.5 12 10,914
920-939 929.5 6 5,577
940-959 949.5 2 1,899
Total 34 30,743.5
To find the weighted average, we divide the sum of the products in the last column by the total frequency:
Weighted average = Sum of (Midpoint x Frequency) / Total frequency
Weighted average = 30,743.5 / 34
Weighted average ≈ 904.2
Therefore, based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.
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f(x)=2(x−7)(x−3) y intercept
The y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).
What is y-intercept?The y-intercept is the point where a function or a curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
According to question:The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of the function F(x) = 2(x - 7)(x - 3), we need to substitute 0 for x in the equation:
F(x) = 2(x - 7)(x - 3)
So, we have:
F(0) = 2(0 - 7)(0 - 3)
Simplifying this expression, we get:
F(0) = 2(-7)(-3)
F(0) = 42
Therefore, the y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).
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3.25x×400=2.50x+600 solve to determine when costs are equal
Okay, let's solve this step-by-step:
3.25x×400=2.50x+600
1300x = 1500
x = 500
So when x = 500, the costs are equal.
The city of Raleigh has 9200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 109 said they'd vote for Brown, 235 said they'd vote for Feliz, and 6 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent.
That this is just an estimate of the true proportion of all voters who would vote for Brown, based on the sample of 350 voters surveyed. The true proportion could be different, due to sampling variability.
What is Statistic?
A statistic is a numerical measure that summarizes some aspect of a dataset. It is a way to describe a sample of data in a concise and meaningful way. Common examples of statistics include measures of central tendency such as the mean, median, and mode, as well as measures of variability such as the range, standard deviation, and variance.
The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is the sample proportion, which is the number of voters who said they'd vote for Brown divided by the total number of voters surveyed:
Number of votes who said they'd vote for brown
total number of surveyed
= 109/350
=0.31
Therefore, based on the sample of 350 voters surveyed.
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find the average rate of change of f(x)=2x^2-2 from 2 to 4
Answer:
average rate of change = 12
Step-by-step explanation:
the average rate of change of f(x) in the interval a ≤ x ≤ b is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here the interval is 2 ≤ x ≤ 4 , then
f(b) = f(4) = 2(4)² - 2 = 2(16) - 2 = 32 - 2 = 30
f(a) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6
then
average rate of change = [tex]\frac{30-6}{4-2}[/tex] = [tex]\frac{24}{2}[/tex] = 12
The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.
Number of Crimes by Area: A, B, C, D, E, F, G, H
Before: 14, 7, 4, 5, 17, 12, 8, 9
After: 2, 7, 3, 6, 8, 13, 3, 5
Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level.
a. What is the p-value?
The p-value method yields P (T > 2.119) = 0.0359. It may be said that, at a 1% level of significance, there has been no decline in crime since the program's inception.
Explain about the Paired T-Test:The observations for the paired t-test are drawn from a single random pair sample. There are the same number of observations in both samples. Each respondent has two observations for the experimental variable recorded.
The alternative is:
[tex]H_{0} =[/tex]: Since the program's launch, there has been no drop in the number of crimes.
The alternate theory is that:
[tex]H_{a} =[/tex] Since the start of the programme, fewer crimes have been committed.
Mathematically,
[tex]H_{0} =[/tex] μo = 0
[tex]H_{a} =[/tex] μd > 0
Given table:
Number of Crimes Before After d = (before - after) d²
A 14 2 14-2 = 12 14² = 144
B 7 7 17 - 7 = 0 0² = 0
C 4 3 4 - 3 = 1 1² = 1
D 5 6 5 - 6 = -1 -1² = 1
E 17 8 17-8 = 9 9² = 81
F 12 13 12 - 13 = -1 -1² = 1
G 8 3 8 - 3= 5 5² = 25
H 9 5 9 -5 = 4 4² = 16
Total 8 29 269
The formula for the t statistic is:
t = ∑d / √[n(∑d²) - (∑d)²] / (n - 1)
t = 29 / √[8*269 - 29²] / (8 - 1)
t = 2.119
As a result, the test statistic's value is 2.119.
8 – 1 Equals 7 degrees of freedom.The p-value method yields P (T > 2.119) = 0.0359.The p-value is inconsequential since it exceeds the specified significance level of 0.01 in this case.
This indicates that at a 1% level of significance, the null hypothesis cannot be ruled out.
As a result, it may be said that, at a 1% level of significance, there has been no crime decline in since the program's inception.
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160/30000 simplified
Answer:160/30000 simplified would be 2/375
Step-by-step explanation:
Exact Form:
[tex]\frac{2}{375}[/tex]
Decimal Form:
0.0053
A STUDY OF INTERIOR DESIGNERS OPIONIONS WITH RESPECT TO THE MOST DESIRABEL PRIMARY COLOR FOR EXECUTIVE OFFICES SHOWED THE FOLLOWING
The probability that a designer does not prefer red is 0.77. The Option 2 is correct.
What is probability?Probability is a measure of how likely an event is to happen. Probability is represented as a fraction and always lies between 0 and 1.
The total number of opinions is:
= 92 + 86 + 46 + 91 + 37 + 46 + 2
= 400
The number of designers who do not prefer red is the sum of the opinions for all colors except red:
= 86 + 46 + 91 + 37 + 46 + 2
= 308
Therefore, the probability that a designer does not prefer red is:
= 308/400
= 0.77.
Full question "A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that:
Primary Color Number of Opinions
Red 92
Orange 86
Yellow 46
Green 91
Blue 37
Indigo 46
Violet 2
What is the probability that a designer does not prefer red? 1.00 0.77 0.73 0.23".
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Suppose that the polynomial function f is defined as follows.
The zeros of f according to their multiplicity are:
Zero of multiplicity 1: x = -8, x = -3, x = 0, x = 9
Zero of multiplicity 2: None
Zero of multiplicity 3: None
Here,
We have,
The zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times it appears as a factor in the polynomial.
In the given function f(x), the zeros are the values of x that make the function equal to zero.
We can find these values by setting the function equal to zero and solving for x.
f(x) = 7x(x-9)(x+8)^2(x+3) = 0
Therefore, the zeros of f(x) are x = -8, x = -3, x = 0, and x = 9.
To determine the multiplicity of each zero, we can look at the degree to which the corresponding factor appears in the polynomial.
For example, x = -8 is a zero of multiplicity 2 because it appears as a factor twice in the function, as (x+8)^2.
Similarly, x = -3, x = 0, and x = 9 are zeros of multiplicity 1 because they each appear as a factor once in the function.
There are no zeros of multiplicity 3 or higher in this function, so we can list "None" for those categories.
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EASY POINTS!
On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles? Show your work!
Answer:
1.75 inches (pls give brainliest lol!)
Step-by-step explanation:
Let's use a proportion to solve the problem:
On the first map, 2.8 inches represents 25 miles:
2.8 / 1 = 25 / x
Simplifying the equation, we get:
x = 25(2.8)/1 = 70
Therefore, the distance between the two cities in the first map is 70 miles.
Now, let's find the distance between the same two cities on the second map, which has a scale of 1 inch to 40 miles:
We want to find how many inches on the second map represent 70 miles. Let's call this value y.
1 / 40 = y / 70
Solving for y, we get:
y = 70/40 = 1.75
Therefore, the two cities would be 1.75 inches apart on the second map with the 1 inch to 40 miles scale.
George plans to order flowers for his daughter's graduation. A bouquet of 12 roses will cost $61, while a bouquet of 18 roses will cost $79. What is the equation that represents the linear relationship between price and number of roses? Let P represent the price, and r the number of roses.
Answer:
Step-by-step explanation:
Start by finding the slope of the line that passes through both the 12 roses bouquet and the 18 roses bouquet.
point 1: (12,61)
point 2: (18,79)
m=y^2-y^1/x^2-x^1
m=79-61/18-12
m=18/6
m=3
then, using one of the points find the fixed costs
P=m*r+b
using 12,61
61=3*12+b
61-36=b
b=25
Answer:
The general equation that represents the linear relationship is:
P=25+3r
Ken volunteers 1hr25min each day. How many hours of volunteering is completed in 4 weeks? Enter a mixed number.
He completed volunteering in 39 hours 40 minutes in 4 weeks
How to determine this
If Ken volunteers 1 hr 25 mins each day
i.e 1 hr 25 mins = 1 days
By converting 1 hr 25 mins to mins
When 60 mins = 1 hr
1 hr 25 mins = 60 + 25 = 85 mins
How many hours of volunteering is completed in 4 weeks
Let x represent the numbers of hours
i.e x = 4 weeks
By converting 4 weeks to days
When 7 days = 1 week
4 weeks = 4 * 7 days
= 28 days
So, when 85 mins = 1 day
x mins = 28 days
x = 28 days * 85 mins/1 day
x = 2380 mins
By converting it back to hour
When 60 mins = 1 hour
2380 mins = x
x = 2380/60 hour
x = 39 hours 40 mins
Therefore, the hours that can be completed in 4 weeks is 39 hours 40 minutes
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Find the value of x. Write your answer in simplest form.
Answer:
[tex]x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} [/tex]
Find the missing angle measure. Show work.
17.
7
20
24
Solve the remaining parts of the triangle.
19.
B
38
12.5 C
7
13
17.
18.
19, AC=
AB-
mzB
Need help with all these please. Asap urgent help need this done before Monday
To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.
By subtracting these two angles from 180 degrees, we get:
180 - 38 - 12.5 = 129.5
Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.
The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.
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The accompany data represent the percentages of teenagers in various countries that have used certain drugs. Complete parts (a) through (c) below.
Country - A B C D E F G H I J K
Drug 1, x - 23 17 41 5 38 18 23 5 8 54 35
Other Drug - 3 2 21 2 15 9 15 2 2 32 25
The coefficient of determination is: 88%
How to solveThe following table shows the calculations:
X Y X^2 Y^2 XY
22 3 484 9 66
17 4 289 16 68
41 21 1681 441 861
5 1 25 1 5
36 16 1296 256 576
19 7 361 49 133
24 14 576 196 336
6 4 36 16 24
8 2 64 4 16
52 32 2704 1024 1664
35 23 1225 529 805
Total 265 127 8741 2541 4554
Sample size: n=11
Now,
Syy=1074.72727Sxx= 2356.90909Sxy = 1494.454545(a)
The coefficient of correlation is :
r=[tex]\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.94[/tex]
(b)
The slope of the regression equation is 0.63
S.
and intercept of the equation will be
[tex]b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=-3.729965\approx -3.73[/tex]
So the regression equation will be
y'=-3.73+0.63*x
(c)
The coefficient of determination is: 88%
Regression is a statistical analytical method that investigates correlations between two or more variables. Its widespread usage stems from its ability to forecast or assess the value of one contingent variable using one or many independently varying variables.
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z = 3x + y solve for x
Answer:
x = (y-z)/3
Step-by-step explanation:
z = 3x + y
3x = z - y
x = (z - y)/3
Find the angle of depression from the top of a lighthouse 400 feet above water level to the water line of a ship 18,410 ft offshore? Round your answer to the nearest hundredth of a degree.
To find the angle of depression, we can use the tangent function in trigonometry. In this situation, we have a right triangle where the height (opposite side) is 400 feet, and the distance (adjacent side) is 18,410 feet.
tan(angle) = opposite / adjacent
tan(angle) = 400 / 18,410
Now, we'll use the arctangent (inverse tangent) function to find the angle:
angle = arctan(400 / 18,410)
angle ≈ 1.25 degrees
The angle of depression from the top of the lighthouse to the waterline of the ship is approximately 1.25 degrees, rounded to the nearest hundredth of a degree.
Find the slope of the line shown below
The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.
How to Find the Slope of a Line?In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:
Slope (m) = change in y / change in x = y2 - y1 / x2 - x1
We have:
(-2, 1) = (x1, y1)
(0, -3) = (x2, y2)
Plug in the values:
Slope (m) = (-3 - 1) / (0 - (-2))
m = -4 / 2
Slope of the line (m) = -2
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The slope of the line represented by the graph is equal to -2.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (-3 - 3)/(0 + 3)
Slope (m) = (-6)/(3)
Slope (m) = -2.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.
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The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.
How to Find the Slope of a Line?In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:
Slope (m) = change in y / change in x = y2 - y1 / x2 - x1
We have:
(-2, 1) = (x1, y1)
(0, -3) = (x2, y2)
Plug in the values:
Slope (m) = (-3 - 1) / (0 - (-2))
m = -4 / 2
Slope of the line (m) = -2
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The slope of the line represented by the graph is equal to -2.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (-3 - 3)/(0 + 3)
Slope (m) = (-6)/(3)
Slope (m) = -2.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.
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i need the answer to 1 over 3
Answer:
1 over 3 would juts be 1/3
Please solve As soon as possible.
Answer:
-|x|+1
Step-by-step explanation:
What is the measure of <7 in degrees
A. Cannot be determined
B. 74
C. 16
D. 32
The measurement of angle Y which is a twin angle will be equal to 116 degrees which is option A.
What is an Isosceles Triangle?
The triangle which has any two sides equal in length is called as Isosceles Triangles. Also the two angles which is opposite to the equal sides are equal and third angle is unequal. The unequal side which is present is called the base of the triangle. Measurement of the altitude can be done from base to the vertex (which is topmost) of the triangle.
Here, the value of angle X is given 32 degree.
Therefore the value of angle Z will also be 32 degree (due to the property of isosceles triangle)
By angle sum property:
X+Y+Z=180
32+Y+32=180
Therefore, Y = 116 degree
To know more about triangles visit:
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