to get the equation of any straight line, we simply need two points off of it, let's use those two in the table
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{Year}{x}&\stackrel{students}{y}\\ \cline{1-2} 1&8295\\ 2&8072\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{8295})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8072}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8072}-\stackrel{y1}{8295}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ -223 }{ 1 } \implies - 223[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8295}=\stackrel{m}{- 223}(x-\stackrel{x_1}{1}) \\\\\\ y-8295=-223x+223\implies {\Large \begin{array}{llll} y=-223x+8518 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{for year 4, x = 4}}{y=-223(4)+8518} \implies y=7626~students[/tex]
how do i find the equation of the line
Answer: look at explanation <3
Step-by-step explanation:
Steps to find the equation of a line from two points:
Find the slope using the slope formula
Use the slope and one of the points to solve for the y-intercept (b).
One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
Your task is to create a unique word problem that needs to be solved using a quadratic equation.
solve the equation by factoring x^2-4x=12
Answer:
x = - 2 , x = 6
Step-by-step explanation:
x² - 4x = 12 ( subtract 12 from both sides )
x² - 4x - 12 = 0 ← in standard form
to factor, consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 4)
the factors are - 6 and + 2 , since
- 6 × 2 = - 12 and - 6 + 2 = - 4 , then
(x + 2)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 6 = 0 ⇒ x = 6
ABC and DEF are similar. Find the missing side length.
Answer:
DF = 24
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion.
[tex]\frac{DF}{AC}[/tex] = [tex]\frac{EF}{BC}[/tex] ( substitute values )
[tex]\frac{DF}{4}[/tex] = [tex]\frac{36}{6}[/tex] = 6 ( multiply both sides by 4 )
DF = 4 × 6 = 24
Please Help!
In the diagram, ΔMTD ≅ ΔSLD. Which statement is true?
Answer:
First one
Step-by-step explanation:
first one because of the 2 letters which occur the same number an causing a little change
Determine if x and y are inversely proportional. If applicable, find the constant of variation.
Answer:
x and y are inversely proportional , constant of proportion k = 30
Step-by-step explanation:
If x and y are inversely proportional then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion
multiply both sides by y , then
k = xy
to check that k is constant use the ordered pairs from the table
(0.1, 300 )
k = 0.1 × 300 = 30
(0.5, 60 )
k = 0.5 × 60 = 30
(75, 0.4 )
k = 75 × 0.4 = 30
(100, 0.3 )
k = 100 × 0.3 = 30
thus x and y are inversely proportional with constant of proportion k = 30
anufacturing machine has a 5% defect rate. if 4 items are chosen at random, what is the probability that at least one will have a defect?
The probability that at least one will have defect is 0.1855 if a manufacturing machine has a 5 % defect rate.
If manufacturing machine has 5% defect rate. The probability is ration of the number of favorable outcomes. Probability is the branch of math in which we calculate he number of observation and favorable outcomes of a certain event to be occur. if the manufacturing company has 5% defect rate then there is also to find the number probability of non defect rate. so,
Probability of defect (p) = 0.05
Probability of non defect (q) = 1- 0.05 = 0.95
4 items are chosen at random .
We have to calculate the probability that at least one will have a defect.
Now ,
P ( at least one will have defect ) = 1 - P ( None will have defect )
P ( none will have defect) = 1 × 1 × 0.81450625
P (none will have defect) = 0.81450625
putting the value we get,
P ( at least one will have defect) = 1 - 0.81450625
P ( at least one will have defect) = 0.18549375
P ( at least one will have defect) = 0.1855
To learn more about Probability please visit:
https://brainly.com/question/13604758
#SPJ4
Identify as an increase or decrease. Then find the percent of increase or decrease. If necessary,
round to the nearest percent.
Original: 180
New: 150
96 Select an answer
The percentage decrease when original is 180 and the new is 150 is 16.7%
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
In this case, the original is 180 and the new is 150. The percentage decrease will be:
= (180 - 150) / 180 × 100
= 30/180 × 100
= 1/6 × 100
= 16.7%
The percentage is 16.7%
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Help me please..30points!!!!
Answer:
Step-by-step explanation:
a) 10/18 · 9/17
5/9 · 9/17
5/17
b) 8/18 · 7/17
4/9 · 7/17
28/153
c) 10/18 · 8/17
5/9 · 8/17
40/153
Answer:
[tex]\textsf{a)} \quad \dfrac{5}{17}=29.4\%[/tex]
[tex]\textsf{b)} \quad \dfrac{28}{153}=18.3\%[/tex]
[tex]\textsf{c)} \quad \dfrac{40}{153}=26.1\%[/tex]
Step-by-step explanation:
Bag of 18 fruit drop sweets:
10 apple flavoured8 blackberry flavoured[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Part (a)The probability of the first sweet chosen being apple flavoured is:
[tex]\implies \sf P(apple)=\dfrac{10}{18}[/tex]
Now there are 9 apple flavoured sweets and a total of 17 sweets remaining, so the probability of choosing a second apple flavoured sweet is:
[tex]\implies \sf P(apple)=\dfrac{9}{17}[/tex]
Therefore, the probability of both sweets being apple flavoured is:
[tex]\implies \sf P(apple)\;and\;P(apple)= \dfrac{10}{18} \times \dfrac{9}{17}=\dfrac{5}{17}[/tex]
Part (b)The probability of the first sweet chosen being blackberry flavoured is:
[tex]\implies \sf P(blackberry )=\dfrac{8}{18}[/tex]
Now there are 7 blackberry flavoured sweets and a total of 17 sweets remaining, so the probability of choosing a second blackberry flavoured sweet is:
[tex]\implies \sf P(blackberry )=\dfrac{7}{17}[/tex]
Therefore, the probability of both sweets being blackberry flavoured is:
[tex]\implies \sf P(blackberry )\;and\;P(blackberry )= \dfrac{8}{18} \times \dfrac{7}{17}=\dfrac{28}{153}[/tex]
Part (c)The probability of the first sweet chosen being apple flavoured is:
[tex]\implies \sf P(apple)=\dfrac{10}{18}[/tex]
Now there are 9 apple flavoured sweets, 8 blackberry sweets, and a total of 17 sweets remaining, so the probability of choosing a blackberry flavoured sweet is:
[tex]\implies \sf P(blackberry)=\dfrac{8}{17}[/tex]
Therefore, the probability of the first sweet being apple flavoured and the second sweet being blackberry flavoured is:
[tex]\implies \sf P(apple)\;and\;P(blackberry)= \dfrac{10}{18} \times \dfrac{8}{17}=\dfrac{40}{153}[/tex]
a local ice cream shop has a parking lot with enough space for 18 cars. there are 7 cars in the parking lot right now.let x represent how many more cars can park in the lot. which inequality describes the problem?
The inequality describes the problem of a local ice cream shop has a parking lot with enough space for 18 cars is x + 7 ≤ 18
What is an Inequality?In mathematics, an inequality describes a relationship between two values of an algebraic expression that are not equal. “If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then, this relationship is called an inequality." For example, x>8 (x should be greater than 8).
We have, a local ice-cream shop has a parking lot with enough space.
The maximum number of cars will be parked in parking lot = 18.
At right now, the number of cars in parking lot= 7. Let assume that x be number of more cars can park in the lot. We have to express this in form of an Inequality. Total cars in parking lot = 7 + x but this number of cars cannot exceed the 18 , so x + 7 ≤ 18
Hence, required Inequality is x + 7 ≤ 18.
To learn more about Inequality, refer:
https://brainly.com/question/25944814
#SPJ4
Lonna watched 1/2 of a movie in the morning, and he watched ome more at night. By the end of the day, he till had 2/5 of the movie left to watch. How much of the movie did Lonna watch at night?
[tex]\frac{1}{10}[/tex] part of movie the Lonna will watch at night.
As per the given data in question:
Watched movie in morning = [tex]\frac{1}{2}[/tex]
Movie Left to watch = [tex]\frac{2}{5}[/tex]
Subtraction of fractions: Subtracting fractions include the subtraction of two or more fractions with the same or different denominators.
Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.
Movie she watch at night = 1 - Watched movie in morning - Movie Left to watch
Movie she watch at night = 1 - [tex]\frac{1}{2}[/tex] - [tex]\frac{2}{5}[/tex]
LCM denotes the least common factor or multiple of any two or more given integers.
By taking L.C.M
Movie she watch at night = [tex]\frac{(10-5-4) }{10}[/tex]
[tex]=\frac{10-9}{10}[/tex]
Movie she watch at night = [tex]\frac{1}{10}[/tex] Part
For more questions on Subtraction of fractions
https://brainly.com/question/29432379
#SPJ4
The test scores for
the 10 boys in a class
are
78
5879
45 39
The mean score for
the 5 girls in the class
is 8
Calculate the mean
for this class.
Answer: The mean score for this class is 17.13.
Step-by-step explanation:
Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249
Add the mean score for the girls: 249 + 8 = 257
Add up the number of students in the class: 10 + 5 = 15
Divide the total score by the number of students to find the mean: 257 / 15 = 17.13
What do you understand by mean and how many methods are there to find it ?
Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:
Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.
Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.
There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.
To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys. We have: 78+58+79+45+39 = 249
Next, let's add the mean score for the girls, which is 8.
So the total is now: 249 + 8 = 257.
Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.
Therefore, the mean score for this class is :
257/15 = 17.13.
To learn more about mean from the given link https://brainly.com/question/1136789
#SPJ1
The mean score for this class is 17.13.
Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249
Add the mean score for the girls: 249 + 8 = 257
Add up the number of students in the class: 10 + 5 = 15
Divide the total score by the number of students to find the mean: 257 / 15 = 17.13
What do you understand by mean and how many methods are there to find it?
Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:
Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.
Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.
There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.
To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys.
We have: 78+58+79+45+39 = 249
Next, let's add the mean score for the girls, which is 8.
So the total is now: 249 + 8 = 257.
Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.
Therefore, the mean score for this class is :
257/15 = 17.13.
To learn more about mean from the given link
brainly.com/question/1136789
#SPJ1
A basketball team scored 50 points in a game last week. This week, they scored 55 points. What was the percent increase in points scored from last week to this week?
imagine that two friends (heather and suzanne) are playing a video game where the player goes on quests to earn coins. the average number of coins earned on a quest is 2000. heather plays quite a bit, and goes on an average of 20 quests a day. suzanne doesn't play quite as much, and only goes on 5 quests a day. on a particular day, which person is less likely to record an average earning below 1500 coins?
When two friends are playing a video game where the player goes on quests to earn coins with an average number of 2000 coins earned in a quest, if one plays an average of 20 quests a day and other play 5 quests a day, none of them are likely to record an average earning below 1500 coins in a day.
Therefore the answer is both Heather and Suzanne are less likely to record an average earning below 1500 coins.
Here the average number of coins earned in a quest is not dependent on the number of quests played in a day. So for both Heather and Suzanne the average earning is to be 2000, so they are less likely to earn below 1500 coins.
To know more on dependency of event
https://brainly.com/question/12138721
#SPJ4
What is 3x+2y(5) equal?
Answer:
3x+10y
Step-by-step explanation:
3x+2y(5) =
3x+2(5)y =
3x+2*5y = 3x+10y
Which points have a distance of 3 units between them?
Select all that apply.
N=(1,4) and P=(1,1)
M=(−2,4) and N=(1,4)
R=(1,−2) and S=(−3,−2)
P=(1,1) and R=(1,−2)
P=(1,1) and Q=(3,1)
Answer:
Step-by-step explanation: The points that have a distance of 3 units between them are:
N=(1,4) and P=(1,1)
P=(1,1) and R=(1,-2)
P=(1,1) and Q=(3,1)
My question is in the picture can someone answer this I’ll give you brainliest and no fraud answers I really need this answer.
Answer:
Parralel lines are congruent
Step-by-step explanation:
Tbh i would say that RU is congruent to TS because they are both parralel lines to eachother, and parralel lines are always congruent to eachother.
I hope this helps
:))
Compare the cubed root of 92 and 450% using <,>, =
Answer:
450%<cube root of 92
Step-by-step explanation:
for which of the three f-tests in a two-way anova do you collapse across the levels of the other factor(s) in computing the means?
The three f-tests in a two-way ANOVA do you collapse across the levels of the other factor(s) in computing the means both the A main effect and the B main effect.
What is meant by f-test?
In math, f-test refers to carry out the test for the equality of the two population variances.
Here we need to find in which of the three f-tests in a two-way ANOVA do you collapse across the levels of the other factor(s) in computing the means.
As per the definition of f-test, here we know that a two-way ANOVA do you collapse across the levels of the other factor has only two options that is main effect and interaction effect.
As we know that ANOVA separates the within group variance from the between group variance and the F-test is the ratio of the mean squared error between these two groups.
Therefore, in this one, both A and be has the main effect on each other.
To know more about f-test here.
https://brainly.com/question/28957899
#SPJ4
completed the questions below
The slope of the line y = 10x + 3 is 10
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values
Hence in the equation of the form y = 10x + c when compared with the equation of line in slope intercept form y = 10x + c
We can see that m which is the slope is 10
Learn more about slope of linear functions at:
https://brainly.com/question/20277632
#SPJ1
Paying $40 for 6 pounds of chocolate.
Answer:
240$
Step-by-step explanation:
we multiply 40 with 6
(40×6)
Mr. Tran mowed
1
4
of her lawn. Her on mowed
3
7
of it. Who mowed mot of the lawn? How much of the lawn till need to be mowed?
Mrs. Tran's son mowed more land than she and 9/28 of the land still need to be mowed.
let us convert all the fractions into equivalent fractions to make our calculations easy.
The land mowed by Mrs Tran = 1/4 x 7/7 = 7/28
The land mowed by her son = 3/7 x 4/4 = 12/28
Hence, we can clearly see that Mrs. Tran's son mowed more land than she.
The total land mowed by both of them = 7/28 + 12/28
= 19/28
The total land to be mowed = 1 - 19/28
= (28 - 19)/28
= 9/28
Hence, the land still to be mowed is 9/28.
Read more about Fractions:
brainly.com/question/78672
#SPJ4
The complete question is -
Mrs. Tran mowed 1/4 of the lawn. Her son mowed 3/7 of it. Who mowed more? How much of the lawn still needs to be mowed?
Choose by clicking the graph. Find Ltheta if sec theta = -13/5 and tan theta negative
The results of the two equations show that the tangent of a negative angle is always equal to its tan.
What if tan angle is negative?In trigonometric mathematics, this expression is known as the tangent of negative angle identity.Tan of negative angle identity is a mathematical relationship between the tangents of a negative and positive angle.Formulatan(-∅) = - tan∅
Proof : By using a geometrical approach in trigonometry, the mathematical relationship between the tangent of a negative angle and the tan of a positive angle is obtained.Construction of triangle with negative angle : Create the same triangle with a negative angle. As a result, QOR has a negative theta angle, represented by -∅.Write the tan of the negative angle in terms of the ratio of the lengths of the respective sides based on this information.tan (- ∅) = QR / OQ
The length of the opposite side will be yet the length of the adjacent side will be due to the building of the triangle with negative angle.=> tan (- ∅) = -y /x.
To Learn more About negative angle refer to:
https://brainly.com/question/28452669
#SPJ1
What is the equation of a line with slope is -1/2 and passing through the p (-2, -1)
Answer:
y = -1/2x + 2
What is the slope of this line? Responses 1/3 1 third 2/3 2 over 3 −2/3 negative 2 over 3 −1/3
Answer:
2/3
Step-by-step explanation:
slope = rise/run
Start at point (0, -3).
Go up 2. That is a rise of 2.
Go right 3. That is a run of 3.
slope = rise/run = 2/3
you have sum([minutes of delay]) in your view. if aggregate measures is unchecked, what will the view show instead of sum([minutes of delay])?
It will show the individual values for each row in the view, rather than a sum of the values By time
When the aggregate measures option is unchecked, Tableau will display the individual values for each row in the view instead of totaling them up. This means that instead of showing the sum of the minutes of delay, the view will show the individual delay minutes for each row.
For example, if the view contains three rows with a delay of 10 minutes, 15 minutes and 20 minutes of time, the view will display 10, 15 and 20 instead of 45.
Learn more about time here
https://brainly.com/question/28050940
#SPJ4
Please help me answer this question with a simple answer
Answer:
Subtract 2.5d from both sides.
Step-by-step explanation:
Subtract 2.5d from both sides.
7.5d = 2.5d
5d = 0
d = 0
The ratio of a to b is 3:5. The difference between angle a and b is 36°. What is the size of angle C
No links please it’s been bugging me for 30 minutes
Answer:
The ratio of a to b is 3:5, which means that the value of a is 3/8 of the value of b. This means that if the difference between the angles a and b is 36°, then the size of angle a is 3/8 * 36° = 9°.
To find the size of angle C, we need to add the size of angle a to the size of angle b. Since the size of angle a is 9° and the difference between the sizes of angles a and b is 36°, the size of angle b is 36° + 9° = 45°.
The size of angle C is the sum of the sizes of angles a and b, so the size of angle C is 9° + 45° = 54°. Therefore, the size of angle C is 54°.
boxplot statistics question - see image below
Kristiana collected data on the amount of time in minutes each person in a large sample of customers spent in a local sporting store. The data also included recording the gender for each customer. These data were used to generate the boxplots shown to the right.
a. the range in the amount of time in minutes males in the sample of customers spent in the store is approximately 40 minutes.
b. the mean amount of time in minutes in the sample of customers spent in the store is approximately 20 minutes.
c. the third quartile of the amount of time in minutes males in the sample of customers spent in the store is approximately 45 minutes.
d. the interquartile range of the amount of time in minutes females in the sample customers spent in the store is 15 minutes.
e. approximately half of the males in the sample of customers spent at least as much time in the store as any females in the sample of customers.
The option that correctly describes the given box plot is; e. approximately half of the males in the sample of customers spent at least as much time in the store as any females in the sample of customers.
How to interpret boxplot in statistics?A box plot is defined as a method for graphically showing the locality, spread and skewness groups of numerical data through their quartile.
Some of the terms in box plot is as follows;
Minimum Score; This is the lowest score, that excludes the outliers (located at the end of the left whisker).
Lower Quartile; This is twenty-five percent of scores that fall below the lower quartile value (the first quartile).
Median; This is the mid-point of the data and is shown by the line that divides the box into two parts.
Now, looking at the box plot in the given attachment, we see that the middle line on a boxplot graph is the same as the median of the data, which for the males was equivalent to the highest value for females. This tells us that approximately half of the males spent more time in the store than any females.
Read more about Box Plot at; https://brainly.com/question/14277132
#SPJ1
The sequence 1, 3, 5, 7, 9, ..., is monotone
a) Decreasing
b) increasing
c) constant
d) oscillating
Answer: b) increasing
Step-by-step explanation: It seems evident that the sequence is made up of all the odd numbers.
[tex]\begin{gathered} \bold{a_1=1}\\ \bold{a_2=3=a_1+2}\\ \bold{a_3=5=a_2+2}\\ \bold{a_4=7=a_3+2} \\ \bold{a_n=a_{n- 1}+2}\end{gathered}[/tex]
As we can see, in the nth position (any position), we take the value of the previous position and add 2 to it. This leads us to conclude that the sequence is monotonic increasing since as we add 2 to the values, these grow up.