By substitution, the solution of the system of equations, 3c + 2d = 2 and d = 4, is (c , d) = (-2 , 4).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in variables c and d,
3c + 2d = 2 (equation 1)
d = 4 (equation 2)
Since the second equation is already expressed in d in terms of a constant, substitute the second equation to the first equation.
3c + 2d = 2 (equation 1)
3c + 2(4) = 2
3c + 8 = 2
Combining all terms containing the variable c on one side and the constants on the other side of the equality, and solving for c.
3c + 8 = 2
3c = 2 - 8
3c = -6
c = -6/3
c = -2
Hence, the solution of the given system of equations is (c , d) = (-2 , 4).
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An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment values shown in the table:
Enrollment Month
January February March April May June
Actual 500 400 550 550 750 400
Predicted 410 450 650 650 600 450
Residual 90 −50 −100 −100 150 −50
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit. (1 point)
No, the equation is not a good fit because the sum of the residuals is a large number.
No, the equation is not a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the residuals are not all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.
The correct option regarding the linear regression equation is:
No, the equation is not a good fit because the sum of the residuals is a large number.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In possession of the equation, the residuals are given by the difference of the predicted values(with the equation) and the actual values.
The model represents a good fit if the sum of the residuals is close to 0.
For this problem, the sum of the residuals is given by:
90 - 50 - 100 - 100 + 150 - 50 = -60.
The sum is a large number, hence the model is not a good fit.
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Prove the vector property. Let →a = and →b = .
scalar multiplication: k(→a + →b) =k→a + k→b , where k is a scalar
The scalar multiplication [tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]has been proved.
Scalar Multiplication Property:
Basically a scalar means the real number.
The scalar multiplication property states that the product of a sum or difference of a number is equal to the sum or difference of the products.
The general form of scalar multiplication as follows:
k (A + B) = kA + k B
where
k is the scalar.
Given,
Let
[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]
and
[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]
Then we have to prove the following scalar multiplication property,
[tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]
We know that,
"The vector is an object that has both a magnitude and a direction. And vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction."
Here we have two vectors like [tex]\overrightarrow{a},\overrightarrow{b}[/tex].
Now we need to use the definition of the scalar multiplication property,
Then, the LHS of the expression is written as,
[tex]\implies k(\overrightarrow{a}+\overrightarrow{b})[/tex]
Apply the values of the vectors then we get,
=> k(<x₁, y₁> + <x₂, y₂>)
When we expand the terms then we get,
=> k<x₁, y₁> + k<x₂, y₂>
And it can be written as,
[tex]\implies k\overrightarrow{a}+k\overrightarrow{b}[/tex]
Therefore, the scalar multiplication property has been proved.
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Determine whether the event is mutually exclusive or not mutually exclusive. Explain your reasoning.
Rolling a pair of dice and getting a sum of 7 and 6 on the face of one die
We can see that there is no element which is common Hence, they are mutually exclusive events.
Let A be the event of getting a sum of 7 on dice.
Let B be the events of getting a sum of 6 on dice.
A={ (1,6), (2,5), (3,4), (4,3), (5,2) }
B = { (1,5) , (2,4), (3,3), (4,2), (5,1), }
What are Mutaullty exclusive events?Mutaullty exclusive events are those when there is no common event between two events.
Where there is empty set of intersection.
But we can see that there is no element which is common
So, n(A∩B) = ∅
Hence, they are mutually exclusive events.
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Find the measures of two supplementary angles if the difference between the measures of the two angle is 62 degrees
Answer:
121° and 59°
Step-by-step explanation:
We'll assign the two angles 'a' and 'b'. Since they are supplementary, this means they add to 180°. We can model this peoblem with the expressions:
a + b = 180° and a - b = 62°
Let's use the second equation to find a substitution for a:
a - b = 62°
a = 62° + b
Now substitute this in the first equation and solve:
(62° + b) + b = 180°
62° + 2b = 180°
2b = 118°
b = 59°
59° + 62° = 121° this is angle a
Which is the inverse of g (h) = 10√h-6?
The inverse function as g⁻¹ (h) = [(h+6)/10]² which is the correct answer would be an option (E).
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
To determine the inverse of a function, all you have to do is switch where h and g are and resolve for g.
So after switching h and g,
g = g(h) = 10√h - 6
becomes
h = 10√g - 6
Now, we solve for h regularly.
h + 6 = 10√g
(h + 6)/10 = √g
[(h+6)/10]² ⇒ g = [(h+6)/10]² = g(x)
Therefore the inverse of g(x) is g⁻¹ (h) = [(h+6)/10]²
Hence, the inverse function as g⁻¹ (h) = [(h+6)/10]²
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A triangle abc has angle measures of 45,45 and 90 and two congruent (equal sides). How would this triangle be classified?
Answer:
A right triangle
Step-by-step explanation:
The angle of 90 degrees is a right angle
The plot below shows the volume of 11 river water samples collected by an ecologist.How many times as great is the volume of the largest sample than the volume of the smallest sample
volume of the largest sample is 7 times the volume of the smallest sample.
What is box plot?A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
given:
The volume of the largest sample is 7/8 gallon.
The volume of smallest sample is is 1/8 gallon.
So,
volume of the largest sample/volume of the smallest sample
=7/8 / 1/8
=7/8 * 8/1
=7
Hence, volume of the largest sample is 7 times the volume of the smallest sample.
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Simplify 2x multiplied by x^(-1/2)
(the above is x to the power of minus a half)
Answer:
[tex]2\sqrt{x}[/tex]
Step-by-step explanation:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]
[tex]2x \cdot x^{-\frac{1}{2}} = 2x^{1-\frac{1}{2}} = 2x^{\frac{1}{2}} = 2\sqrt{x}[/tex]
Another way of doing this is to see that
[tex]x^{-\frac{1}{2}} = \frac{1}{\sqrt{x} }[/tex]
So [tex]2x \cdot x^{-\frac{1}{2}} = \frac{2x}{\sqrt{x} } =2\sqrt{x}[/tex]
Percent Obese by State
Computer output giving descriptive statistics for the percent of the population that is obese for each of the 50 US states, from the
USStates dataset, is given in the table shown below. Since all 50 US states are included, this is a population, not a sample.
Variable N Mean StDev Minimum
Q1 Median Q3
Maximum
Obese 50 31.43 3.82
28.6 30.9 34.4
Need help with b) and c)
Using the normal distribution, it is found that:
b)
The maximum 39.5% obese has a z-score of 2.11, hence it is 2.11 standard deviations above the mean.
The minimum 23% obese has a z-score of -2.21, hence it is 2.21 standard deviations below the mean.
c) The interval is 23.79% to 39.07%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the parameters are given as follows:
[tex]\mu = 31.43, \sigma = 3.82[/tex]
The maximum weight is of 39.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (39.5 - 31.43)/3.82
Z = 2.11.
The maximum 39.5% obese has a z-score of 2.11, hence it is 2.11 standard deviations above the mean.
The maximum weight is of 23, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (23 - 31.43)/3.82
Z = -2.21
The minimum 23% obese has a z-score of -2.21, hence it is 2.21 standard deviations below the mean.
For item c, we consider the Empirical Rule, which states that 95% of the measures are within 2 standard deviations of the mean.
Then:
31.43 - 2 x 3.82 = 23.79.31.43 + 2 x 3.82 = 39.07.The interval is 23.79% to 39.07%.
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the tuition for a private college is currently 18000 for each semester. The college will raise tuition by 500 dollars per semester per year How much is tuition per year. By how much will tuition increase each year.
Based on the calculations below, the amount of tuition per year is $36,000 while the amount of the increase in tuition each year is $1,000.
How are tuition and an increase in tuition calculated?Note: There are two questions in this question as follows:
1. How much is tuition per year?
2. By how much will tuition increase each year?
We can calculate the tuition per year and the increase in the tuition each year as below:
Number of semesters in a year = 2
Tuition in each semester = $18,000
Increase in the tuition per semester = $500
Using the above information, we can proceed as follows:
Tuition per year = Tuition in each semester * Number of semesters in a year = $18,000 = $36,000
Increase in the tuition each year = Increase in the tuition per semester * Number of semesters in a year = $500 * 2 = $1,000
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4 7/12+ 2 3/4+ 7 5/12
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
Calm down, I gotcha!
Step-by-step explanation:
4 7/12+ 2 3/4+ 7 5/12=14.75
avas sister is 9 years less than twice avas age b
Ava's age = b
Ava's sister's age = 2b -9
Simplify by combining like terms. y² / 2 + y/3 + y²/3 - y/5
On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5 the simplified value is 5y²/6 +2y/15.
In an algebraic expression Like terms are defined as those terms that have same variable and that variable has the same power .
For Example : 5a,9a are like terms .
In the given question
=y²/2 +y/3 +y²/3 -y/5
On combining the like terms , one with y² and other with y.
We get;
=y²/2 +y²/3 +y/3 -y/5
Taking LCM of like terms with y² as "6"
and LCM of like terms with y as "15".
We get ;
=(3y²+2y²)/6 +(5y-3y)/15
=5y²/6 +2y/15
Therefore , On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5, the simplified value is 5y²/6 +2y/15.
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Determine whether the events are independent or dependent. Then find the probability.
You roll a die and get a 2. You roll another die and get a 3.
1/3 is the probability when You roll a die and get a 2. You roll another die and get a 3.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.when a dice is thrown we get the following out comes
S = { 1,2,3,4,5,6}
n(S) = 6
probability of getting 3 is 1/6 [as there is only one 3]
probability of getting 4 is 1/6 [ there is only one 4]
Using addition theorem of of probability ,
probability of getting 3 or 4 is 1/6 + 1/6 = 2/6 = 1/3
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Which of the following systems of equations has the solution (1, 4)?
y = –3x – 1
y = –x + 5
y = 3x + 1
y = –x + 5
y = 3x + 1
y = x – 5
y = 3x + 1
y = –x – 5
Answer:
y = 3x + 1
y = -x + 5
Step-by-step explanation:
Take the system of equations and substitute (1 ,4) in any one of the equations. If both the sides are justified, then (4,1) is the solution to that pair of equations.
1) y = -3x - 1 ---------(I)
y = -x + 5
Substitute (1,4) in equation (I)
4 = -3*1 - 1
4 = -3-1
4 ≠ -4
So, (1, 4) is not a solution.
2) y = 3x + 1 ---------------(II)
y = - x + 5
Substitute (1 ,4) in equation (II)
4 = 3*1 + 1
4 = 3 + 1
4 = 4
(1 ,4) is the solution for this system of equation.
3. greg took a random sample of size 100 from the population of current season ticket holders to the state
college men's basketball games. then he took a random sample of size 100 from the population of ccurrent
season ticket holders to the state college women's basketball games
what sampling technique did greg use to sample from the population of current ticket holders?
The sampling technique Greg used is stratified sampling.
Stratified sampling is used when the population is more heterogeneous. Then we divide the population into subgroups or strata which will be more homogeneous and take samples from each strata. This will ensure the equal representation from each group in population. Stratified sampling helps to reduce the variability of the estimates also.
Here the population of current season ticket holders consist both for men's basketball games and women's basketball games. So Greg considered both as separate subgroups of the population and collected random samples of size 100 from each group. This technique for sampling is known as stratified sampling.
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On his first 2 tests Nate's average score was 80 percent.
On his next 3 tests Nate's average score was 90 percent.
What was his average score for all 5 tests? (Hint: Find the
total number of points scored on all tests, then divide by 5.)
Answer:
i think the answer may be possibly 86%
whats the recipocal o 3 1/4
Answer:
4/31
Step-by-step explanation:
reciprocal=same thing upside- down,
Determine whether each list is a sequence or a series and finite or infinite. 2.3+4.6+9.2+18.4
From the list of numbers presented we can determine that this is a finite sequence.
What are sequences?A sequence is defined by an order of values and/or elements that have a relationship of variation as a ratio or proportion that makes them predictable.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
2.3 + 4.6 + 9.2 +18.4
We can clearly notice that we have a larger limit number and it is 18.4, as we know the beginning of the sequence and the exact end we can know that we are in the presence of a finite sequence.
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You’ve paid $120 for membership to a racquetball club. Court time is $5 per hour. Let x = the number of hours you play.
Part a: Write an equation that represents the total cost C.
Part b: Write an equation that represents the average cost A per hour.
Part c: Use the graph of the model shown below to estimate the number of hours you must play before the average cost per hour drops to $10 per hour.
Part a - C = 120 + 5x
Part b - A = [120 + (5 x (x)] / x
Part c - The number of hours you must play before the average cost per hour drops to $10 per hour is 15 hours.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Membership fees = $120
Cost per hour = $5
x = number of hours
The equation that represents the total cost:
C = 120 + 5x
The equation that represents the average cost per hour:
A = [120 + (5 x (x)] / x
From the graph, we can assume that the y-axis indicates the average cost per hour and the x-axis indicates the number of hours.
We see that in 16 hours the average cost per hour is $10 so the number of hours to play before the average cost per hour drops to $10 per hour is 15 hours.
Thus,
Part a - C = 120 + 5x
Part b - A = [120 + (5 x (x)] / x
Part c - The number of hours you must play before the average cost per hour drops to $10 per hour is 15 hours.
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There is a cell phone tower in the field across from Jen's house. If Jen walks 50 feet from the tower, and finds the angle of elevation from her position to the top of the tower to be 60°C, how tall is the tower?
A cell phone tower is 173.21 feet high.
Consider the following diagram
Let AB be the height of tower, C be the position of Jen.
Jen walks 50 feet from the tower, and finds the angle of elevation from her position to the top of the tower to be 60°
An angle ACB be an angle of elevation.
⇒ ∠ACB = 60°
And AC = 50 ft
We need to find the distance AB.
Consider tangent of angle ACB.
⇒ tan(60) = AB / BC
⇒ 1.7321 = AB / 100
⇒ AB = 1.7321 × 100
⇒ AB = 173.2 feet
Therefore, a cell phone tower is 173.21 feet high.
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Solve the equation. x³-6 x²+6 x=0 .
answer:
x=0 or x=4.732050807568877 or x=1.2679491924311228
Chetis camping with 75 people from this after school club. A tent can
hold up to 8 people. How many tents are needed? Explain your thinking
Answer:
10 tents
Step-by-step explanation:
I don't know if Chetis a person name or not but if it a person name then 76÷8=9.5 because 75+1=76 (including him)
if Chetis is not a person name then 75÷8=9.375
The answer would still be the same which is 10 tents needed.
SOMEBODY PLEASE: Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks. He must arrive at his friend’s house by 7:00 p.m. What is the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?
Answer:
8:30 a.m.
Step-by-step explanation:
The total time it takes for Lyle to reach his friend's house is 720/80 + 1 + 0.25 * 2, which is 9 + 1.5 = 10.5 hours
The latest possible time that Lyle would be able to leave his house to reach on time is 8:30 a.m.
PLEASE HELP ME
also do the check ur work so do the work then show me how u checked it
Answer:
first remove the brackets
then find the like terms
and work out
Adriano runs a website that helps writers write better stories. Every month, Adriano receives a subscription fee of \$5 dollar sign, 5 from each of the subscribers to his website. The website had 200subscribers last month. This month 40 new members joined the website and 10 members cancelled their subscription.
How much money will Adriano’s online business earn this month?
Considering the definition of an equation and the way to solve it, the money earned by Adriano's online business this month is $1,150.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
This caseIn this case, you know that every month, Adriano receives a subscription fee of $5 from each of the subscribers to his website. Then, the amount of money earned by Adriano's online business each month will be represented by the following equation:
Money earned by Adriano's online business each month= $5x
where x is the number of subscribers on the website.
On the other hand, you know:
Number of subscribers last month = 200Number of new subscribers this month = 40Number of cancellations = 10Then, the number of subscribers this month can be calculated as:
Number of subscribers this month = 200 + 40 - 10
Number of subscribers this month = 230
So, the amount of money earned by Adriano's online business this month is calculated by substituting this value in the equation above:
Money earned by Adriano's online business this month= $5×230 subscribers
Money earned by Adriano's online business this month=$1,150
Finally, the money earned by Adriano's online business this month is $1,150.
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Rewrite the number 8,000,000,000,000,000,000,000,000,000,000,000,000,000,000 using scientific notation.
Answer:
8,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Step-by-step explanation:
8(10^42)
Parenthesis is the multipication sign btw
I really don't understand this. Can someone answer and explain?
ABCD ∽ EFGH, meaning both quadrilaterals are similar, therefore the proportionos of their corresponding sides are equal, thus
[tex]\cfrac{AB}{EF}~~ = ~~\cfrac{CD}{HG}\implies \cfrac{\stackrel{AB}{3}}{\underset{EF}{2}}~~ = ~~\cfrac{\stackrel{CD}{4.5}}{\underset{HG}{y}}\implies 3y=9\implies y=\cfrac{9}{3}\implies y=3[/tex]
Sam has a car that is worth $8,500. However,
he still owes $4,750 on the car. He also has
$1,500 in his savings account, a comic book
collection worth $900 and owes $475 on his
credit card. What is the total of Sam's
liabilities?
The total of Sam's liabilities are $5225.
What is a liability?A liability is an obligation of an individual towards his creditors arising out of some transactions. Bank loans, credit card bills, accounts payable , accrued expenses are examples of liabilities.
Given that Sam has a car that is worth $8,500. However, he still owes $4,750 on the car. He also has $1,500 in his savings account, a comic book collection worth $900 and owes $475 on his credit card.
Irrespective of his assets and savings Sam still owes $4750 on the car and $475 in his card card , therefore these are his liabilities.
Total liabilities of Sam = $4750+$475 = $5225
Therefore, total of Sam's liabilities are $5225
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Write the equation of the line in slope-intercept form.
12. A line that passes through (-1, -5) and (4, -2)
The equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .
What is the slope intercept form of a line ?
The equation of a straight line in the form y = mx + c is known as the slope intercept form, where m denotes the slope and c denotes the y-intercept of a line.
It is given that line is passing through (x1 , y1) and (x2 , y2) that is , (-1, -5) and (4, -2).
Let's find out the value of slope first.
We know that , slope (m) = (y2-y1) / (x2-x1)
⇒ m = [(-2-(-5)] / [4 - (-1)]
⇒ m = 3 / 5
Now we will use the slope to find the y-intercept.
∵ y = mx + c
where , c is the y-intercept.
(-2 -(-5)) = (3/5) × (4-(-1)) + c
3 = [ (3/5) × 5 ] + c
3 = 3 + c
c = 0
Now ; we will write the equation in slope intercept form that is ;
y = mx + c
or
y = [tex]\frac{3}{5}[/tex] × x + 0
or
y = [tex]\frac{3}{5}[/tex] x
Therefore , the equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .
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