By solving the linear equations we get the final values of x = 4 & y = 4.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order term are included.
We have,
2x + 7y = -20 ----------(i)
x - 3y = 16 ----------(ii)
By multiplying equation (ii) with 2 we get,
2x + 7y = -20 ---------(III)
2x - 6y = 32 -----------(IV)
taking subtraction of equations (III) and (IV), we get
y = 4
by putting value of y in equation (ii) we get,
x = 4
Hence by solving the linear equations we get the values of x = 4 & y = 4.
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4) What type of slope does the following line have?
Answer: zero slope
Step-by-step explanation:
When the slope of a line is zero it creates a horizontal line.
Please help me with this (ASAP) 15 POINTS
At 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
If he continues at this rate, at what time will he reach `10000` steps?
Answer:
9:55 a.m.
Step-by-step explanation:
Sothy starts at 8 a.m. and plans for 10,000 steps. At 8:23 a.m., she walked 2000. We are solving for when she reaches 10,000 steps.
This means that she walks 2,000 steps in 23 minutes
If she walks 2,000 steps in 23 minutes, then we can multiply by 5 to get 10,000 steps in 115 minutes.
Now, we need to add 115 minutes to 8 a.m.
we can round 115 minutes to 120 minutes.
If you add 120 minutes to 8 a.m., you get 10 a.m.
Now subtract the 5 minutes you added earlier to get 9:55 a.m.
a large company states in its promotional literature that 74% of its employees have college degrees. assume this claim is true. if 3 employees are selected at random from this company, what is the probability that at least 1 of the selected employees will not have a college degree?
The probability of having at least one employee not have a college degree is 0.595
Here it is given that the 74% of employees have a college degree.
Hence, the probability of one employee having a college degree is
74/100
= 0.74
The probability that an employee does not have a college degree is
1 - 0.74
= 0.26
Hence
The above problem is clearly a Binomial distribution. with n = 120 and p = 0.26
"success" is when one employee does not have a college degree.
Therefore the probability that at least 1 employee does not have a college degree is
P(X≥1)
= 1 - P(X = 0)
A binomial distribution with sample n and probability p has a PMF
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
where x is a random variable
Here
n = 3
p = 0.28
x = 0
Hence we get
³C₀ X 0.26⁰ X (0.74)³
0.405
Therefore,
P(X≥1)
= 1 - 0.405
= 0.595
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Given that x is a nonnegative number, a student conjectured that x+4
Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
(x equals negative one fourth)
B. x=−4
C. x = 1
D. x = 4
The value of x that is a counterexample to the student's conjecture is (a) x = -1/4
How to determine the value of x?From the question, we have the following statement that can be used in our computation:
x = Non-negative number
Student's conjecture:
x + 4 < x²
Using the options, we have:
(a) x = -1/4
x + 4 < x²
-1/4 + 4 < (-1/4)²
3.75 < 1/16 -- false
(b) x = -4
x + 4 < x²
-4 + 4 < (-4)²
0 < 16 -- true
(c) x = 1
x + 4 < x²
1 + 4 < (1)²
5 < 1 -- false
This cannot be used because x is non-negative
(c) x = 4
x + 4 < x²
4 + 4 < (4)²
8 < 16 -- true
The false statements are the counterexamples
Hence, the value of x is (a) x = -1/4
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Complete question
Given that x is a nonnegative number, a student conjectured that x + 4 < x². Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
B. x=−4
C. x = 1
D. x = 4
AB has endpoints at A(-4, 4) and B(5, -1).
Find the coordinates
(x, y) of the midpoint.
Answer:
(0.5, 1.5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is
M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (- 4, 4 ) and (x₂, y₂ ) = B (5, - 1 ) ,then
M = ( [tex]\frac{-4+5}{2}[/tex] , [tex]\frac{4-1}{2}[/tex] ) = ( [tex]\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = (0.5, 1.5 )
Answer:
The midpoint is at ( 1/2, 3/2)
Step-by-step explanation:
Midpoint
To find the x coordinate of the midpoint
Add the x coordinates of the endpoints and divide by 2
( -4+5)/2 = 1/2
To find the y coordinate of the midpoint
Add the y coordinates of the endpoints and divide by 2
( 4+-1)/2 = 3/2
The midpoint is at ( 1/2, 3/2)
Can you please help me in this question.
Answer:
k = - 6 , c = 8
Step-by-step explanation:
f(x) = x² + kx + c
given f(2) = 0 , substitute (2, 0 ) into f(x)
0 = 2² + 2k + c
0 = 4 + 2k + c ( subtract 4 from both sides )
- 4 = 2k + c → (1)
given f(- 3) = 35 , substitute (- 3, 35 ) into f(x)
35 = (- 3)² - 3k + c
35 = 9 - 3k + c ( subtract 9 from both sides )
26 = - 3k + c → (2)
subtract (2) from (1) term by term to eliminate c
- 4 - 26 = 2k - (- 3k) + (c - c)
- 30 = 2k + 3k
- 30 = 5k ( divide both sides by 5 )
- 6 = k
substitute k = - 6 into (1) and solve for c
- 4 = 2(- 6) + c
- 4 = - 12 + c ( add 12 to both sides )
8 = c
then
k = - 6 and c = 8
48+3u=9u
Solve for u
Answer:
u=8
Step-by-step explanation:
48+3u=9u
-3u both sides
48=6u
divide by 6 on both sides
8=u
whats the answer.......................
The statement that describes the x-intercept of the graph is: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.
What is the X-intercept of a Linear Relationship?The x-intercept of a linear relationship between variable x and y can be described as the value of x when the value of y is zero.
On a graph, the x-intercept is the point on the graph where the line intercepts the x-axis. The value of y at this point is 0.
in the graph that shows a linear relationship between the number of monthly payments made and the remaining balance left on a loan, the line intercepts the x-axis at 60.
Therefore, it means: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3* + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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Last year, James earned £2,100 per month.
This year, he's had a 6% increase in his monthly pay.
He worked 35 hours per week for 46 weeks in the year.
What is James' average pay per hour this year?
Give your answer to 2 dp.
James average pay per hour is $17.40
How to find James average pay per hour
information given in the problem are
Last year, James earned £2,100 per month
This year, he's had a 6% increase in his monthly pay
35 hours per week for 46 weeks in the year
The question is a percentage problem
6% increase a factor of 1.16
2100 * 1.16 = 2436
number of hours in a month
35 hours = 1 week
? hours = 4 weeks
? = 4 * 35
? = 140 hours in 4 weeks = 1 month
James average pay per hour is gotten form the calculation below
if 140 hours pays 2436 then1 hour will pay ?
140 = 2346
1 = ?
cross multiplying
? * 140 = 2436 * 1
? = 2436 / 140
? = $17.40
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the sales force for a publishing company is constantly on the road trying to sell books. as a result, each salesperson accumulates many travel-related expenses that he or she charges to a company-issued credit card. to prevent fraud, management hires an outside company to audit a sample of these expenses. for each salesperson, the auditor prints out the credit card statements for the entire year, randomly chooses one of the first 20 expenses to examine, and then examines every 20th expense from that point on. which type of sampling method is the auditor using for each salesperson?
Systematic random sampling is the sampling method is the auditor using for each salesperson.
Define sampling method.Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study. If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.
Given,
The sales force for a publishing company is constantly on the road trying to sell books. as a result, each salesperson accumulates many travel-related expenses that he or she charges to a company-issued credit card. to prevent fraud, management hires an outside company to audit a sample of these expenses. for each salesperson, the auditor prints out the credit card statements for the entire year, randomly chooses one of the first 20 expenses to examine, and then examines every 20th expense from that point on.
Systematic random sampling is the sampling method is the auditor using for each salesperson.
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What is the SLOPE?
Which is the slope of a line that is perpendicular to the line that passes through the points (-9,-4) and (3,4)? Type your response as an integer or fraction.
Answer:
y = -1.5
Step-by-step explanation:
use the method y2 - y1 / x2 - x1
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
-4, (-2 , 1)
0, (-1, 21)
The equation of straight line having
(a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7
(b) gradient 0 and coordinates (-1,21) is y = 21 .
In the question ,
the gradient and coordinates of the point on the line is given .
we have to find the equation of the straight line .
Part(a)
the gradient of the line [tex]=[/tex] -4 ,
the coordinates of a point on the line = (-2,1)
So , the equation of the line is
(y - 1) = (-4)*(x -(-2))
y - 1 = -4(x + 2)
y - 1 = -4x - 8
4x + y = -8 + 1
4x + y = -7
the equation is 4x + y = -7 .
Part(b)
the gradient of the line = 0 ,
the coordinates of a point on the line = (-1 , 21)
So , the equation of the line is
(y - 21) = 0(x-(-1))
y - 21 = 0
y = 21
the equation of the line is y = 21 .
Therefore , The equation of straight line having (a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7 and (b) gradient 0 and coordinates (-1,21) is y = 21 .
The given question is incomplete , the complete question is
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
(a) -4, (-2 , 1)
(b) 0, (-1, 21)
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(b) Work out the value of (2.3 × 10³) × (5.9 × 105)
Give your answer in standard form.
Answer: 1424850
Step-by-step explanation:
2.3 x 10³ = 2300
5.9 x 105 = 619.5
2300 x 619.5 = 1424850
Pls thank and rate <3 (and branliest if ok with u :)))
Determine the equation of the line.
(Write the answer in slope-intercept form.)
Answer:
y = 1x + -2
Step-by-step explanation:
Step 1: Calculating Slope (m).
m = y2 - y1 / x2 - x1
m = -4 - 0 / -2 - 2
m = -4 / -4
m = 1
Now put value of m in equation...
y = 1x + b
Step 2: Calculating Y-intercept (b).
Lets choose the first point, ( 2, 0) for calculating y-intercept:
y = m ( x ) + b
0 = 1 ( 2 ) + b
0 = 2 + b
-2 = b
b = -2
Now put value of b in equation for your final answer...
y = 1x + -2
Hope this helps!
Use the "Insert Line" Tool to construct the line
showing the given distance. If you need to extend
the line outside the shape, use a dotted line.
The distance from B to AC can be constructed as
The distance from G to EF can be constructed as
The distance from Q to SR can be constructed as
What is the distance of a line from a point?
A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.
For the first figure,
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The probability of tails of a weighted coin is 0. 65. The number of tails is noted each of the 15 times the coin is tossed. If this procedure is repeated 100 times, what type of distribution is simulated?
A. A sampling distribution of the sample proportion with n=15 and p=0. 65
B. A sampling distribution of the sample proportion with n=100 and p= 0. 65
C. A binomial distribution with n=15 and p= 0. 65
D. A binomial distribution with n=2 and p= 0. 65
E. There is not enough information to determine the type of distribution
A sampling distribution of the sample proportion with n=15 and p=0. 65 is stimulated here when The probability of tails of a weighted coin is 0. 65. The number of tails is noted each of the 15 times the coin is tossed.
What is probability?Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.
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Given f(x) = x2 + 5x − 6 and g(x) = 2x2 − 8, find each value.
f(−2) =
g(3) =
Step-by-step explanation:
those are the answers if I am wrong you can correct
Seventh grade > M.6 Percent of a number: tax, discount, and more SPN
A store pays $871 for a gold ring. The store marks up the price by 26%. What is the
amount of the mark-up?
Round your answer to the nearest dollar: $
Submit
Answer:
$1097.46
Step-by-step explanation:
Assume P is the finall price. The markup of 26% can be written in decimal form as 0.26. This is in additon to the full price paid for the gold ring, so we can add 1.00 to 0.26 to arrive at the factor 1.26. Multiply 1.26 times the store cost of $871 to find the amount after 26% markup:
($871)*(1.26) = $1097.46
A blue whale weighs about 200 tons. It eats only small sea creatures called krill. The blue whale
eats 2% of its body weight each day. How many tons of krill does the blue whale eat each day?
Explain your thinking.
Answer:
4 tons of its body weight
Step-by-step explanation:
In this situation you must find 2% of 200. This is simply 4.
Answer: 4 tons
Step-by-step explanation:
the whale eats 2% of itself everyday, so it would be x/200= 2/100 and the whale would eat x tons, which equals 4 so it eats 4 tons of krill a day
find an equation for the perpendicular bisector of the line segment whose endpoints are (9,-5) and (-5,-1)
The equation y = (13 / 4) · x - 19 / 2 represents the perpendicular bisector of the line segment.
How to find the equation for the perpendicular bisector of a line segmentIn this problem we need to determine the equation of the line perpendicular to a line segment whose endpoints are known. The equation of the line is represented by a first grade polynomial of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.And the relationship between the slopes of two perpendicular lines:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.And the slope of the original line can be found by the secant line formula:
m = Δy / Δx
And the midpoint of a line segment between two endpoints is defined below, necessary for the location of the bisector:
M(x, y) = 0.5 · A(x, y) + B(x, y)
Where:
M(x, y) - MidpointA(x, y), B(x, y) - EndpointsFirst, find the slope of the line segment by secant line formula:
m = [- 1 - (- 5)] / (- 5 - 9)
m = - 4 / 13
Second, find the slope of the perpendicular bisector by the slope relationship between two perpendicular lines:
m' = - 1 / m
m' = - 1 / (- 4 / 13)
m' = 13 / 4
Third, determine the midpoint of the line segment by the midpoint formula:
M(x, y) = 0.5 · (9, - 5) + 0.5 · (- 5, - 1)
M(x, y) = (4.5, - 2.5) + (- 2.5, - 0.5)
M(x, y) = (2, - 3)
Fourth, find the intercept of the perpendicular bisector by means of the equation of the line:
b = y - m' · x
b = - 3 - (13 / 4) · 2
b = - 3 - 26 / 4
b = - 3 - 13 / 2
b = - 19 / 2
The equation for the perpendicular bisector is y = (13 / 4) · x - 19 / 2.
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HELPPP MEEEEE PLEASEEEE
Answer: 2176 cm^2 i think
Step-by-step explanation:
Answer:
60 cm
Step-by-step explanation:
we can use the Pythagorean theorem:
a^2 = b^2 + c^2 where a is the hypothenuse
so 68^2 = 32^2 + c^2
rearrange: 68^2 - 32^2 = c^2
so 4624 - 1024 = c^2
= 3600
square root of 3600 = 60
missing side = 60 cm
3. Is this graph a function?
This is a function.
This is not a function.
This cannot be determined from this graph.
Answer:
that is a quadratic function so yes it is a function
Step-by-step explanation:
it is a function becausr you can write an equation with it. Hope I could help!
What number is 763 less than 850.08?
Answer:
87.08.
850.08 - 763 = 87.08.
Arianna is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. Let
C
C represent the total cost of using a computer for
t
t minutes at the internet cafe. The table below has select values showing the linear relationship between
t
t and
C
.
C. Determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.
Using the linear function, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.
In the given question,
Arianna is going to use a computer at an internet cafe.
The cafe charges an initial fee to use the computer and then an additional price per minute of usage.
Let C represent the total cost of using a computer for t minutes at the internet cafe.
We have to determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.
The additional change per unit = Slope of the linear function
The linear function C(t) given as;
C(t)=mt+b...............(1)
where m=slope and b=vertical intercept
Then, Slope = change in C(t)/change in t
Slope = ∆C(t)/∆t
We taking he given two point to find the slope
C(t) = 9.90 for t=1
C(t) = 15.30 for t=7
∆C(t)=15.30-9.90
∆C(t)=5.40
∆t=7-1
∆t=6
So, The required slope=5.40/6
The required slope=0.9=m
Now finding the value of b.
As we know that,
C(t) = 9.90 for t=1
The equation using this should be
9.90=m×1+b
Now putting the value of m in this equation
9.90=0.9×1+b
9.90=0.9+b
Subtract 0.9 on both side, we get
b=9
Now finding the number of minutes Arianna can use a computer if she only has $15.75 available to pay.
Putting the value in equation (1)
15.75=0.9t+9
Subtract 9 on both side
15.75-9=0.9t+9-9
0.9t=6.75
Divide by 0.9 on both side
0.9/0.9 t=6.75/0.9
t=7.5
Hence, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.
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Which of these expressions can be used to calculate the monthly payment for
a 25-year loan for $150,000 at 13.8% interest, compounded monthly?
O A.
OB.
$150 000 0.0115 (1+0.0115) 300
(1+0.0115) 3⁰0 +1
OD.
$150 000 0.0115(1-0.0115) 300
(1-0.0115) 300 -1
O C. $150 000 .0.0115 (1+0.0115) 3⁰⁰0
(1+0.0115) 300-1
$150 000 0.0115(1-0.0115) 3⁰⁰
300
(1-0.0115) 3⁰⁰ +1
The monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1
What is compound interest?
When you earn interest on both the money you've saved and the interest you've earned, this is known as compound interest.
what is the monthly payment?
The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.
Here,
We know that the monthly payment is given as
MP = [Pr(1 + r)¹²ⁿ] / [(1 + r)¹²ⁿ - 1]
Where MP monthly payment, P is the initial amount, r is the rate of interest, and n is the number of years.
we have
r = 0.0115
P = $150,000
n = 25 * 12
n = 300
Then we have
MP = $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1
Hence, the monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1
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A 7-pound box of strawberries costs $12.32. What is the price per ounce?
Step-by-step explanation:
Answer: 9.090909090909091
Step-by-step explanation: Knowing this we can solve. We have 7 pounds, and there are 16oz in 1 pound so we multiply the number of pounds by the number of ounces in 1 pound. 7 x 16 = 112 ounces. So there are 112oz total, which costs $12.32. Now we divide $12.32 by 112oz to find the price per ounce which would be roughly 9.09
you have a deck and you take one card at random and guess what the card is. what is the probability you guess right?
There are 52 cards in the deck and so the probability of guessing the card right is 1/52.
What is probability?Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.
Here,
We can find this probability by seeing that
=1/4×1/13
=1/52
Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.
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Suppose that each semester at a particular community college Manuel has to pay $1478 in tuition and $121 in fees.
If Manuel has x semesters remaining, write an algebraic expression representing the total amount he will need for tuition.
If Manuel has x semesters remaining, write an algebraic expression representing the total amount he will need for the fees.
If Manuel has × semesters remaining, write an algebraic expression representing the total amount of money he will spend for tuition and
Answer:
Step-by-step explanation:
Let x be time, in semesters, remaining before Manuel graduates. We find that Manuel's expenses are:
$1478/semester in tuition, and
$121/semester in fees
1. x semesters remaining: fees
Remaining cost for fees, y, is the product of the fee times the number of semesters, x:
y =($121/semester)*x
y = ($121)*x
2. x semesters remaining: tuition
Remaining cost, y, is the product of the tuition (times the number of semesters, x.
y = ($1478/semester)*x + ($121/semester)*x
y = ($1599)*x
3. x semesters remaining: tuition and fees
Remaining cost, y, is the sum of the products of the tuition (times the number of semesters, and the fees (tix.
y = ($1478/semester)*x + ($121/semester)*x
y = ($1599)*x