The simplified for of the Algebraic expression which is the sum of two terms is 1 + 7x
What is an Algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms which can either be a variable or a constant .
11 + 5(3x - 2) -8x
multiply out the bracket we have,
11 + 15x - 10 -8x
collect like terms and simplify
11 - 10 + 15x - 8x
1 + 7x
In conclusion, the expression 11 + 5(3x - 2) as a sum of two terms is 1 + 7x
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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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(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
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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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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
What is 7) 952 divided?
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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PLS HURRY!!!Juan divided 12 jar of fish food into 7 equal parts. He feeds his fish one part each day.
What fraction of the jar of food will Juan will feed his fish each day?
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:1/14
Step-by-step explanation:He divides 1/2 of the jar into sevenths, but if he had the whole jar it would be fourteen parts because 2x7=14, or 14÷2=7
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
9x + 7y = 3
x - 7y=-8
Answer:
The point at which these lines intersect is (-0.50, 1.07). We can solve this in two ways: mathematically or graphically. Both are described.
Step-by-step explanation:
We have 2 equations, so we'll assume that the question is to find if they intersect, and if they do, where is the point of intersection.
Let's rewite the equations in slope-intercept format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
1) 9x + 7y = 3
7y = -9x + 3
y = -(9/7)x + (3/7) This line has a slope of -(9/7) and a y-intercept of +(3/7).
2) x - 7y=-8
-7y = -x - 8
y = (1/7)x + (8/7) This line has a slope of (1/7) and an intercept of (8/7)
The line have different slopes, so they will intersect. We can find the intersection point by either graphing or by substitution. We'll do both:
Substitution
We'll rearrange one equation in terms of x and then use that value of x in the second equation. Thuis has the effect of eliminating one of the variables (x or y) so that we can solve for the remaining value of x or y,
We've rearranged both equations so that they have y equal to an expression involving x. If the lines intersect, we know that y in both equations will be the same at that point, so set the equations equal to each other and solve for x:
y = -(9/7)x + (3/7)
y = (1/7)x + (8/7)
Therefore: -(9/7)x + (3/7) = (1/7)x + (8/7)
-(9/7)x -(1/7)x = + (8/7) - (3/7)
-(10/7)x = +(5/7)
x = (5/7)*(-7/10)
x = (-35/70)
x = -0.50
Now we can use this value of x to find y:
9x + 7y = 3
9(-0.50) + 7y = 3
-4.5 + 7y = 3
7y = 3+4.5
y = (7.5/7)
y = 1.07
The point at which these lines intersect is (-0.50, 1.07)
Graphing:
We can also graph the two equations and then look for the intersection. See the attached graph. The lines intersect at (-0.50, 1.07)
The mathematical approach has more certainty, since it does not require interpreting the intersection point on a graph. Use the graphing approach to check the conclusion from the substitution approach.
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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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!
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.
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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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!
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
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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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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Please help me with this (ASAP) 15 POINTS
jeremiah is testing the impact of different fertilizers on crop yields. six different fertilizers have been applied to one field. suppose he uses an anova to test whether or not there are differences in yields. how many treatments are in this test?
The impact of different fertilizers on crop which yields six different fertilizers have been applied to one field. here, the number of treatments in the test are 6.
Treatments are the numerous values of the factor.
The factor here is the effect of various fertilizers on crop yields.
Six different fertilizers were used.
As a result, the number of treatments equals the number of different fertilizers used = 6.
Fertilizers supply essential nutrients such as nitrogen to crops, allowing them to grow larger, faster, and produce more food. However, overfertilization can be a problem because it causes greenhouse gas emissions and eutrophication.
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A) A box of mass 9 kg contains x articles each of mass 1.2 kg. Write down an expression for the total mass of the box and its contents.
B) How many articles are there in the box if the total mass of the box and articles is 21 kg?
Step-by-step explanation:
A. total mass = 9 + (x × 1.2)
B. 21 - 9 = 12kg
12 ÷ 1.2 = 10 articles.
hope it helps. :)
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)
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.
What number is 763 less than 850.08?
Answer:
87.08.
850.08 - 763 = 87.08.
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
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
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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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
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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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
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