The quadratic expression can be factorized to:
x*(x - 6)
How to factorize the expression?Here we have the expression:
x^2 - 6x
To factorize this, first, we need to find the roots, which are the solutions of:
x^2 - 6x = 0
Notice that one of the solutions is trivial, and it is x = 0.
If now we assume that x ≠ 0 and divide both sides by x, we get:
x - 6 = 0
x = 6
That is the other solution.
Now, for a square polynomial with the roots a and b, the factorized form is:
(x - a)*(x - b)
In this case, the roots are 0 and 6, then:
x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)
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what is the quotient of 84/0.729
Answer:
115.226337449
Step-by-step explanation:
84/0.729= 115.226337449
And thank you and your welcome
Answer: the quotient of 84/0.729 is 115.226337
Which of the following is the independent variable of F(G(x))?
O A. V
• B. x
• C. F(x)
• D. F(G(x))
Answer:
D
Step-by-step explanation:
can someone please solve (iii)
The point on a line that is at an equal distance from either end.
Hence, the equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].
What is midpoint ?
The point on a line that is at an equal distance from either end.
Here, the coordinates of [tex]A(1,-1),P(3,7),Q(\frac{-1}{2},\frac{7}{2})[/tex]
The general formula of the midpoint is
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+t_2}{2})[/tex]
The equation of [tex]AP[/tex] is
[tex]AP=(\frac{1+3}{2},\frac{7-1}{2})\\AP=(\frac{4}{2},\frac{6}{2})\\AP=(2,3)\\[/tex]
The equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is
where [tex]AP(2,3),Q(\frac{-1}{2},\frac{7}{2})[/tex].
[tex](AP,Q)=(\frac{2+\frac{-1}{2}}{2},\frac{3+\frac{7}{2}}{2})\\(AP,Q)=(\frac{\frac{4-1}{2}}{2},\frac{\frac{6+7}{2}}{2})\\(AP,Q)=(\frac{\frac{3}{2}}{2},\frac{\frac{13}{2}}{2})\\\\(AP,Q)=(\frac{3}{4},\frac{13}{4})\\[/tex]
Hence, the equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
From the graph:
vertex:
The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.
here vertex = (-2,2)
Axis of symmetry:
The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.
x = -2.
Parabola:
It is clearly visible that the parabola is facing downward so it is a downward parabola.
Therefore the vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
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Hey I would rlly appreciate if someone can help IVE been stuck on this and pls make sure to find measure BCD
Answer:
140
Step-by-step explanation:
2x+5x+40=180
7x+40=180
7x=140
x=20
5x+40=BCD
5(20)+40
100+40
140
suppose that 47% of americans are iphone users. (a) if a random sample of 100 americans are surveyed, what is the probability that the proportion of the sample who are iphone users is between 45% and 50%? (b) if a random sample of 50 americans are surveyed, what is the probability that more than 50% of americans are iphone users?
The probability that the proportion of the sample who are iphone users is between 45% and 50% be 22.87%.
The probability that more than 50% of americans are iphone users be 11.12%.
(a)We know, p = 0.47 and n = 100. First, we should check our conditions for the sampling distribution of the sample proportion.
np = (100)(0.47) = 47 and n(1 - p) = (100)(1 - 0.47) = 53
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(0.53)/100 ≈ 0.05
P(0.45<X<0.50) = P((0.45 - 0.47)/0.05 < Z < (0.50-0.47)/0.05)
P(0.45<X<0.50) ≈ 0.2287
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 100.
(b) Now, p = 0.47 and n = 50.
np = (50)(0.47) = 23.5 and n(1 - p) = (50)(1 - 0.47) = 26.5
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(26.5)/50 ≈ 0.25
P(X>0.50) = P(Z > (0.50-0.47)/0.25)
P(X>0.50) ≈ 0.1112
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 11.12% chance that we would see a sample proportion more than 50% when the sample size is 50.
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4. Which theorem would explain why TU > SV?
Answer:
B. Hınge theoremStep-by-step explanation:
We can observe:
ST = UV, marked as equal;VT = TV, common side;m∠TVU = 45° > m∠STV = 44°, as marked.According to Hınge theorem if two sides of different triangles are equal and the angles between the two sides are different, then the larger angles has greater side opposite to it.
As TU is opposite to the larger angle, and SV is opposite to smaller angle, then TU > SV.
Correct angle choice is B.
A solon prices bottles of conditioner by the ounce. An 8-ounce bottle of Brand C cost $14. tHe cost of Brand S is represented by the equations y = 1.5x, where y is the total cost for a bottle with x ounces
Store´s B bottle cost less per ounce.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Store A
Cost of a 8-ounce bottle of water: $14
Store B
Cost of bottle: y= 1.5x
Cost per ounce (A)
=$14/ 8
= $1.75per ounce
Cost per ounce (B); $1.5 per ounce
So, $1.75 > $1.5
Hence, Store´s B bottle cost less per ounce.
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Brandon invested $7,900 in an account paying an interest rate of 6\tfrac{1}{8}6 8 1 % compounded daily. Jacob invested $7,900 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 % compounded monthly. After 15 years, how much more money would Jacob have in his account than Brandon, to the nearest dollar?
Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.
Brandon invested $7,900 at the rate of 6 1/8% compounded daily.
Principal = $7900
Time = 15 years
Rate = 6 1/8% = 49/8 %
Amount earned after n years:
[tex]A=P (1+\frac{r}{n})^{nt}[/tex]
Now we will use these values to find the amount at the end of 15 years.
P = 7900
r = 0.06625
n = 365
t = 15
[tex]A=P (1+\frac{.06125}{365})^{15\times 365}[/tex]
or, A = 19797.104...
or, A ≈ 19797.1
Again, Jacob invested the same sum at compound interest monthly at
6 5/8% .
Amount earned after 15 years:
P = 7900
r = 6.125
n = 12
t = 15
[tex]A=P (1+\frac{.06625}{12})^{15\times 12}[/tex]
or, A = 21282.383..
or, A ≈ 21282.38
Amount earned by Jacob more than Brandon
= $21282.38 - $19797.1
= $148785.283..
≈ $1485
Hence Jacob will have $1485 more than Brandon in his account.
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Don't understand problem. Need help solving problem.
Answer:
x = -12
Step-by-step explanation:
x/-3 + 5 - 5 = 9 - 5
x/-3 = 4
x/-3 (-3) = 4(-3)
x = -12
suppose that 10 green balls and 14 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn? a) 0.1224 b) 0.6250 c) 0.8333 d) 0.4167 e) 0.5833 f) none of the above.
The probability that the second ball drawn is a purple ball is (e) 0.5833
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Green balls = 10
Purple balls = 14
This means that the total number of balls is
Total = 10 + 14
Evaluate the equation
So, we have
Total = 24
From the question, we understand that the ball is replaced
So, the probability that the second ball is purple ie
P(second purple) = purple/total
This gives
P(second purple) = 14/24
Evaluate
P(second purple) = 0.5833
Hence, the probability is (e) 0.5833
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Mr. Williams is planting a garden. It measures 30 meter along one side. He makes a mark every 1/5 meter. What is the total number of marks that Mr. Williams will make?
Answer:
150 marks
Step-by-step explanation:
Every meter has 5 marks.
30 meters × 5 marks = 150 marks
PLEASE HEIP MEE
What sequence equation would represent this graph?
The equation would represents the graph is y = 20000 + 1750x and the graph has been plotted
From the table
The investment in 1 year = $20000
The investment in 2 year = $21750
The investment in 3 year = $23500
The investment in 4 year = $25250
The investment in 5 year = $27000
Then the equation will be
y = 20000 + 1750x
Where y is the investment in dollars
x is the number of years
Draw the graph as number of years in x axis and the amount of investment in y axis
Hence, the equation would represents the graph is y = 20000 + 1750x and the graph has been plotted
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Jose has $580 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $284.52. He buys 4 bicycle reflectors for $15.65 each and a pair of bike gloves for $11.31. He plans to spend some or all of the money he has left to buy new biking outfits for $31.95 each. What is the greatest number of outfits Jose can buy with the money that's left over?
The greatest number of outfits Jose can buy is 6
How to determine the greatest number of outfits he can buy?The given parameters are:
Budget = $580New bicycle = $284.524 bicycle reflectors = $15.65 eachPair of a bike gloves = $11.31New biking outfits = $31.95 each.Let the number of new biking outfits be x
So, we have
New bicycle + 4 * price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget
This gives
284.52 + 4 * 15.65 + 11.31 + 31.95x ≤ 580
This gives
358.43 + 31.95x ≤ 580
Solve the inequality
31.95x ≤ 221.57
Divide
x ≤ 6.93
This gives
x ≤ 6
Hence, the greatest number of outfits is 6
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solve this equation using the most direct method:
3x(x+6)=-10
Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using (+-) symbol
The solution set for the given quadratic equation is (-0.62, -5.38).
The given equation is 3x(x+6)=-10.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 3x(x+6)=-10
⇒ 3x²+18x=-10
⇒ 3x²+18x+10=0
By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get
a=3, b=18 and c=10
Using quadratic formula x = [-b ± √(b² - 4ac)]/2a
= [-18 ± √(18² - 4×3×10)]/2×3
= [-18 ± √(324 - 120)]/6
= [-18 ± √(204)]/6
= [-18 ± √(204)]/6
= [-18 ± 14.28]/6
= [-18 + 14.28]/6 and [-18 - 14.28]/6
= -0.62 and -5.38
Hence, the solution set for the given quadratic equation is (-0.62, -5.38).
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Clay asks Donte to play the following number puzzle:
Pick a number
Add 4
Multiply by 2
Subtract 3
Add your original number
Donte’s final result is 32. Which number did he start with?
Group of answer choices below
A. 7
B. 9
C. 4
D. 23
E. 0
Find the length of the missing segment.
In accordance to Thales's theorem, the geometric system has a missing side length of 15 units.
How to determine missing lengths in geometric systems by ratiosIn this problem we find a geometric system formed by two proportional trapezoids. This similarity and proportionality is defined by Thales's theorem, which states that a triangle segmented by several lines parallel to each other and parallel to the base of the figure creates triangles and quadrilaterals proportional to each other.
Then, two figures of the given trapezoids are represented by side proportionality ratios. Then, the proportionality ratio is described and its variable x is cleared within by algebra properties:
First, define the proportionality ratio associated to the geometric system:
4 / (10 + 4) = (21 - x) / 21
Second, simplify the equation and clear the variable x:
4 / 14 = 1 - x / 21
2 / 7 = 1 - x / 21
42 / 7 = 21 - x
6 = 21 - x
x = 21 - 6
x = 15
The missing length is equal to 15 units.
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How to find correlation coefficient? I'm stuck pls help me
(0,1132), (1,1107), (2,1000), (3,1019)
The correlation coefficient of the data (0,1132), (1,1107), (2,1000), (3,1019) is -0.89
How to determine the correlation coefficient?Correlation coefficients are used to measure how strong a relationship is between two variables
Given: (0,1132), (1,1107), (2,1000), (3,1019)
x >>>> y >>>> x² >>>> y² >>>> xy
0 1132 0 1281424 0
1 1107 1 1225449 1107
2 1000 4 1000000 2000
3 1019 9 1038361 3057
................................................................................................
6 4258 14 4545234 6164
.................................................................................................
The formula for the correlation coefficient is:
r = ( n∑xy -(∑x)(∑y) ) / ( √(n∑x² - (∑x)²) .√(n∑y² - (∑y)²) )
From the table:
∑x = 6, ∑y = 4258, ∑x² = 14, ∑y² = 4545234 and ∑xy = 6164
n = 4 (number of data points)
Substituting the values into the formula will give:
r = ( 4×6164 -(6)(4258) ) / ( √(4×14 - (6)²) .√(4×4545234 - (4258²) )
r = 24656-25548 / √(20).√(50372)
r = -892/√(1007440)
r = -0.89
Therefore, the correlation coefficient is -0.89
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k
The given function is f(x)=7x^2.
The given vertex = (3,5)
The equation of the parabola with the vertex of (h,k) is
y=a(x-h)^2+k
On comparing we get; a=7, h=3, k=5
Now putting the value
f(x)=7(x-3)^2+5
Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
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2) What is the slope of the line from the following table? (Please show your work)
Answer:
pick any two points
im going to chose (1,3) and (3,7)
so the equation y2-y1/x2-x1
1 = x1
3=y1
3=x2
7=y2
so 7-3/3-1 is 4/2
which is 2
A rectangle plot of land has a width of 3x+5 feet, and a length of 2x-1 feet.
A- express the area of the plot as a function of x.
B- express the perimeter of the plot as a function of x
A- the area of the plot as a function of x. is 6 x^2 +10x-5
B- the perimeter of the plot as a function of x is 10x+8
A rectangle plot of land has a width of 3x+5 feet,
and a length of 2x-1 feet.
A) the area of the plot as a function of x is given by
A= length * width
= ( 2x-1) * ( 3x+5)
=6 x^2 +10x-5
B) the perimeter of the plot as a function of x
P = 2( l+ W)
= 2 (( 2x-1) +( 3x+5))
= 2( 5x +4)
= 10x +8
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How do I know where to shade on this graph?
y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Relationship between two expressions or values that are not equal to each other is called 'inequality.
y≤-3x+4 is the given inequality.
The sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
In the inequality we have lesser than or equal to symbol so we shade the below line.
Hence, y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
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an employee group requires 6 people be chosen for a committee from a group of 12 employees. determine the following probabilities of randomly drawn committee of 6 employees. write your answers as percents rounded to 4 decimal places. the employee group has 9 women and 3 men. what is the probability that 3 of the people chosen for the committee are women and 3 people chosen for the committee are men? % the committee requires that exactly 2 people from human resources serve on the committee. there are 4 people in human resources. what is the probability that exactly 2 of the people chosen for the committee are from human resources? %
The probability of choosing 3 men and 3 women to form the committee is 0.4329 and the probability to select exactly 2 people from the human resources is 0.4545.
It is given that there are 12 employees.
The number of male employees is 6
number of female employees is 6
A committee of 6 is to be formed. We need to find the probability that out of 6, 3 are male and 3 are female.
Let A be the event of having 3 men and 3 women on the committee
The total number of ways to choose 6 people is
¹²C₆
Probability = number of favorable outcomes / total number of outcomes
n(A) = ⁶C₃ X ⁶C₃
Therefore,
P(A) = (⁶C₃ X ⁶C₃) / ¹²C₆
= (20 X 20) / 924
= 400/924
= 0.4329
It is given that the number of employees in human resources from the group is 4
Let B be the event to choose exactly 2 employees from the human resource
n(B) = ⁴C₂ X ⁸C₄
P(B) = ⁴C₂ X ⁸C₄ / ¹²C₆
= 6 X 70 / 924
= 420 / 924
= 0.4545
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Find the length of each side of triangle XYZ, then classify the triangle by its side: X(7,6), Y(5,1), Z(9,1) show work, please!!!
Answer:
(9,1), Z(5,1)
Step-by-step explanation:
3/8 - 5/6 Please put a step by step
Answer:
(-11/24)
Step-by-step explanation:
3 5
------- - -------
8 6
3(3) 5(4)
------- - -------
8(3) 6(4)
9 20 - 11
------- - ------- = -------
24 24 24
I hope this helps!
What is the value sine?
5/12
5/13
12/13
13/5
Answer:
(C.) 5/13
Step-by-step explanation:
The sine proportion is opposite / hypotenuse
Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse
Thus, sine is 5/13
Can someone teach me how to do this?
sin^-1(-1/2) enter directly into a calculator and you'll find your answer
over the past month, george the tortoise has been flipped onto his back 146 times by angie the tortoise. george has been able to get back on his feet without help 3 times. what's the empirical probability that george will be able to get back on his feet without help the next time angie flips him over?
The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
Describe the term empirical probability?The likelihood of an event is closely related to an empirical probability, also described as an experimental probability. Empirical probability bases its evaluation of the likelihood that a specific result will recur on the number of instances of that outcome together within sample set.For the given question.
We include George the turtle, who Angie has successfully turned over 146 times the turtle.3 times George has used the assistance to get back up on his feet. The empirical probability is really what we seek.Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.
empirical probability = 3/146
Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
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Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
It will take 25 minutes for the two containers to have the same amount of water .
In the question ,
it is given that ,
water present in container A = 200L
water present in container B = 500L
rate at which the water is filling in container A= 6 liter/minute
rate at which the water is draining in container B = 6 liter/minute
let the time taken = m minutes ,
So , According to the question ,
the equation representing the situation is
200 + 6m = 500 - 6m
Simplifying further , we get
6m + 6m = 500 - 200
12m = 300
m = 300/12
m = 25
Therefore , It will take 25 minutes for the two containers to have the same amount of water .
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A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 8. 75 percent of her students received grades of a. What is the minimum score needed to receive a grade of a?.
The minimum score needed to receive a grade of A is 88.51
Let, X, be the scores of the student's
X follows Normal Distribution with mean = μ = 73 and standard deviation = σ = 11
The professor has informed us that 7.93 percent of her students received grades of A.
That is P( X > a ) = 7.93% = 0.0793 .
We have to find a.
P( X > a ) = 7.93% = 0.0793
So, P( X <= a ) = 1 - 0.0793 = 0.9207
Using function = NORMINV( probability , μ ,σ )
a = NORMINV( 0.9207, 73 , 11 ) = 88.51
The minimum score needed to receive a grade of A is 88.51
We have to find P( X <= 57.93 )
Using function = NORMDIST( x, μ , σ , 1 )
P( X <= 57.93 ) =NORMDIST( 57.93 , 73 , 11 , 1 ) = 0.0853 = 8.53%
8.53 percent of students failed the course
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