Answers
so, what does that mean? well, the median GP, gets cut by the point O, at a ratio of 2:1, the same is true for the other medians btw, EN and FM.
that means GO is twice as large as OP.
since we know that OP is 20 -x , let's use that then.
[tex]\bf GO:OP\qquad \cfrac{GO}{OP}\qquad 2:1\qquad \cfrac{2}{1}=\cfrac{GO}{OP}\implies \cfrac{2}{1}=\cfrac{4x-8}{20-x} \\\\\\ 40-2x=4x-8\implies 48=6x\implies \cfrac{48}{6}=x\implies \boxed{8=x}\\\\ -------------------------------\\\\ OP=20-(8)[/tex]
Related Questions
True or false: given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.
Answers
A 90% confidence interval will have a width of 2.36 which is false.
What is a confidence interval?Let μ be the mean, σ be the standard deviation, n be the ample size, and z be the z-score. Then we have
Confidence interval = μ ± z (σ / √n)
A sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points.
We know that the z-score for 90% of the confidence interval is 1.645. Then we have
Confidence interval = μ ± z (σ / √n)
Confidence interval = 2.1 ± 1.645 (0.7 / √10)
Confidence interval = 2.1 ± 0.364
For positive sign, then the width will be
⇒ 2.1 + 0.364
⇒ 2.46
A 90% confidence interval will have a width of 2.36 which is false.
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write a percent between 25percent and 50 percent then write it as a decimal and as a fraction in simplest form
Answers
35% as a decimal is 0.35
35% as a fraction = 35/100
35/100 simplest form = 7/20
hope this helps
Write an expression for 4 snacks at n pence each
Answers
Randy and Susie Moser are newlyweds. Randy drives their car to his job, twenty-seven miles away from home, each day. If Randy and Susie are both twenty, what premiums would they pay for bodily injury and property damage insurance in the amount of 50/100/10?
Answers
834.10
I am not 100% positive tho...
Mariana averaged 7474 on her first three history exams. the first score was 7777. the second score was 77 less than the third score. what did she score on the second and third exams
Answers
The second score was 77 less than the third score.
So here we first want to find the total score, by multiplying 7474 by 3.
7474*3 = 22422
So the total test score was 22422.
So first subtract 7777 from 22422 to find the total score of the second and third exams.
22422 - 7777 = 14645
So the total test score of the two is 14645.
Now, since the second score was 77 less, there's a few ways to do it.
I'ma just do a random method.
Say the second score = x, and the third score = x+77.
x + x + 77 = 14645
2x = 14645 - 77
2x = 14568
/2 /2
x = 7284
So the second score was 7284.
The third is 77 more then that.
7284 + 77 = 7361
So her third exam score was 7361.
Write a reciprocal function with asymptotes x=4 and y=-9.
Answers
Final answer:
To write a reciprocal function with asymptotes x=4 and y=-9, the function is f(x) = -9/(x-4).
Explanation:
To write a reciprocal function with asymptotes x=4 and y=-9, we need to find the equations of the vertical and horizontal asymptotes.
For the vertical asymptote, the equation is x=4. This means that the function approaches infinity as x approaches 4 from the left or right.
For the horizontal asymptote, the equation is y=-9. This means that the function approaches -9 as x approaches infinity or negative infinity.
Therefore, the reciprocal function with these asymptotes is:
f(x) = -9/(x-4)
Final answer:
To create a reciprocal function with asymptotes x=4 and y=-9, the function can be expressed as y = 1/(x-4) - 9. This form ensures a vertical asymptote at x=4 and a horizontal asymptote at y=-9.
Explanation:
To write a reciprocal function with asymptotes x=4 and y=-9, you need to include factors that will create these asymptotes in the function's equation. A reciprocal function generally has the form y = a/(x-h) + k, where (h, k) represents the horizontal and vertical shifts to create the asymptotes x=h and y=k. In this case, we have:
y = 1/(x-4) - 9
This function has a vertical asymptote at x=4 because as x approaches 4, the denominator approaches 0 causing the function to approach infinity. The horizontal asymptote at y=-9 occurs because as x goes to infinity, the value of 1/(x-4) approaches 0, and the entire function approaches -9.
dj14ven
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
12.7 units
16.9 units
24.0 units
33.9 units
Answers
The answer came from Rgwoot Ambitious
from another post in case anyone else needs it
What we know:
shape is rectangle which means the 2 long sides have equal distance and the 2 short sides have equal distance
we just need to find the distance of one long side and one short side for the perimeter which is the outline of the rectangle. Imagine the perimeter is the fence around the rectangle that you would probably have to paint every 3 years and the area would be where the grass would grow in the rectangle which you would probably have to cut every weekend.
perimeter=2l+2w
What we need to find: PERIMETER
Using pythagorean method a² +b²=h² to find length:
From point (-6,1) to point (3,8) is a rise of 9 and a run of 9 right to get from one point to another, those are my a and b in the pythagorean formula.
a² +b²=h²
(9)²+(9)²=h² substitution
81+81=h² simplified
162=h²
√162=√h2 used radical properties
√162=h length =√162
Using pythagorean method a² +b²=h² to find width:
From points (-6,-1) to point (-3,-4) is a down 3 units and left 3 units to reach from one point to another, these are my a and b for the pythagorean formula.
a² +b²=h²
(3)²+(3)²=h²
9+9=h²
18=h²
√18=√h²
√18=h this is the width=√18
Now we find perimeter:
p=2l+2w
p=2(√162)+2(√18)
p≈33.9
D. 33.9 units
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PRE CAL
f(x)=x^3+x^2+4x+4
Solve with Synthetic division and find all zeros of the function
Answers
Use the Remainder Theorem to identify the first zero.
From the Rational Zeros Theorem, possible zeros are +/- 1, +/- 2, +/- 4.
f(1) = 1 + 1 + 4 + 4 = 10 (not a zero).
f(-1) = -1 + 1 - 4 + 4 = 0 (This is a zero)
Therefore (x+1) is a factor of f(x).
Use Synthetic Division.
-1 | 1 1 4 4
-1 0 -4
----------------
1 0 4 0
There is no remainder, therefore
f(x) = (x+1)(x²+4)
Because x² = -4 yields x = 2i, -2i, there are a pair of conjugate complex zeros.
Answer:
All the zeros are -1, 2i, -2i.
A group of n students is assigned seats for each of two classes in the same classroom. how many ways can these seats be assigned if no student is assigned the same seat for both classes?
Answers
Now, consider the second class. Let's start by arranging three people first and then generalising n people to better understand what is going on.
Where we have 3 people:
First class: A B C = 3!
Second class _ _ _
Now, consider where each of these people can't actually sit.
For A, it's the first seat, for B, it's the second seat, and for C, it's the last seat.
This means that we have a restriction on EACH of the candidates.
So, to tackle this, let's consider A only; B and C will follow the same way.
A can sit in 2 different spots, namely the second and last seat: thereby, having 3C2 ways in sitting. _ A _
Now, when we fix one person, C can only go in one place: first seat. This means that for one single arrangement of the first class, we've made: 3C2 arrangements for the second class, for ONE particular person. Extend that to another person, and we get: 2C1 ways
This extends to what we call: a derangement where the number of permutations made contains no fixed element. We can regard things like picking up three/two/one pen as derangements, because really we're arranging AND not arranging them simultaneously.
Thus, we use the inclusion-exclusion method:
Total no. of perms:
[tex]n! \cdot n!\left(1 - 1 + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - ... + (-1)^{n} \cdot \frac{1}{n!}\right)[/tex]
The number of ways the seats can be assigned is equal to n factorial (n!).
Explanation:The number of ways the seats can be assigned is given by the permutation formula. Since there are n students and 2 classes, each student can be assigned a seat in the first class in n ways. After that, there are (n-1) seats left and (n-1) students remaining to be assigned seats in the second class. Therefore, the total number of ways to assign seats is n * (n-1) * (n-2) * ... * 1, which is equal to n factorial (n!).
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If the cost of a pound of nails increased from $2.29 to $2.48. what is the percent of the increase to the whole number percent?
Answers
hope it helps
The answer is provided in the image attached.
Have a great day!
Two consecutive even integers have a sum of 42 . find the integers.
Answers
so let x equal our first number
and to get the number next to it, we simply add 1
so.. x + (x+1) = 42
combine terms and subtract 1 from each side
2x = 41
divide each side by 2
x = 20.5
If two consecutive even integers have a sum of 42. The integers are 20 and 22.
What is an integer?it is defined as a whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0, etc.
It is given that, two consecutive even integers have a sum of 42.
The difference between two even numbers is 2.
Suppose two consecutive even integers are x , (x+2)
x + (x+2) = 42
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
2x +2 = 42
2x =42-2
2x = 40
x = 20
The two consecutive even integers are,
x =20
x+2 = 20 +2 =22
Thus, if two consecutive even integers have a sum of 42. The integers are 20 and 22.
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Jeremy ate p pieces of pizza. Brandon ate 5 less pieces than Jeremy. Write an expression to represent the total amount of pizza eaten by both boys.
Answers
An expression to represent the total number of slices eaten by the boys:
[tex]p+p-5[/tex]
Hope this helps.
-Benjamin
To start the school year, a teacher spends $54.35 in school supplies for her classroom. During the course of the year, she will restock her supplies and will spend $22 each time she restocks the supplies. The expression below describes this situation.
22x + 54.35
In this expression, what is the coefficient and what does it describe?
A.) x, which describes the number of times she restocks her supplies
B.) 22, which describes the amount she spends each time restocking her supplies
C.) 22x, which describes the total amount she spends each time she goes to the store
D.) 54.35, which describes the amount she originally spends on supplies
Answers
Erica is buying a $205,000 home. She has decided to purchase 2 points in order to lower her interest rate. The appraisal fee is $450, the processing fee is $575, and the title fee is $600. What is her total in closing costs?
Answers
205000×0.02=4,100 cost of 2 points
Closing costs is
4,100+450+575+600
=5,725....answer
Hope it helps!
Answer: $5,725
Step-by-step explanation:
Given: The cost of home = $205,000
If there is no down payment, then the mortgage amount = $205,000
We know that one point costs 1 % of mortgage amount .
2 points = 2 % of the mortgage amount =[tex]0.02\times205,000=\$4,100[/tex]
[tex]\text{Closing costs=}\text{cost of points + appraisal fee+processing fee+ title fee}[/tex]
[tex]=\$4,100+\$450+\$575+\$600=\$5,725[/tex]
Hence, her total in closing costs = $5,725.
What is the cosine of angle a?
a. 8/17
b. 15/8
c. 15/17
d. 8/15
Answers
how do you solve 5x^2+30x=10
Answers
25x+30x=10
55x=10
divide both sides by 55.
x =0.1818181818 etc. ( 18 repeating)
If a car with an average speed of 50 miles per hour travels for 30 minutes, how far will it have gone?
Answers
Monica ramirez works at the hospital as a nursing assistant. she works 15 hours per week and earns $8.50 per hour. what is monica's straight-time pay for each week?
Answers
Answer:
$127.50
Step-by-step explanation:
Given: Monica ramirez works at the hospital as a nursing assistant. She works 15 hours per week and earns $8.50 per hour.
To find: Monica's straight-time pay for each week.
Solution:
Monica earns $8.50 per hour.
Monica works for 15 hours per week.
To find the straight-time pay for each week, we need to multiply the per hour cost with the total number of hours she had worked in a week.
So, the straight-time pay for each week can be calculated as:
[tex]=15\times8.50=127.50[/tex].
Therefore, the straight-time pay for each week is $127.50
what is the volume of a cube with 1/2 inch sides
Answers
1/2 x 1/2 x1/2= 1/8
Answer:
the answer is 1/8
Step-by-step explanation:
Evaluate y= 50 X (0.3)^x for x= 2
A: 4.5
B: 750
C: 45
D: 225
Answers
y= 50×(0.3)² = 50×0.09 = 4.5
y= 4.5
A is your answer
What is the equation of a line perpendicular to the line y=(4/9)x-2 that passes through the point (4,3)?
a. y= -(4/9)x-2
b. y= (9/4)x+6
c. y= -(9/4)x+12
d. y= -(9/4)x-12
(pls explain solution!!)
Answers
This is in slope intercept form (y=mx+b), where m is the slope.
A perpendicular line will have the opposite reciprocal of the slope.
So if the slope here is 4/9, then the perpendicular line's slope will be -9/4.
Now that you have the slope (-9/4) and a point (4, 3), you can use the point-slope formula to find the equation.
y - y₁ = m(x - x₁)
y - 3 = (-9/4)(x - 4)
y - 3 = (-9/4)x + 9
y = (-9/4)x + 12
So the answer will be:
C. y= -(9/4)x+12
To find the equation of a line perpendicular to y=(4/9)x-2 that passes through the point (4,3), we need to determine the slope of the original line and then find the negative reciprocal of that slope. The equation of the perpendicular line is y = -(9/4)x + 12.
To find the equation of a line perpendicular to y=(4/9)x-2 that passes through the point (4,3), we need to determine the slope of the original line and then find the negative reciprocal of that slope. The original line has a slope of 4/9, so the perpendicular line will have a slope of -9/4. Using the point-slope form of a line, we can plug in the slope and the given point to find the equation of the perpendicular line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Plugging in the values, we get:
y - 3 = -(9/4)(x - 4)
Simplifying the equation, we get:
y = -(9/4)x + 12
Therefore, the equation of the line perpendicular to y=(4/9)x-2 that passes through the point (4,3) is y = -(9/4)x + 12.
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Icket sales tickets for a high school play are $3.00 each for students and $4.00 each for all others. find the total money collected from ticket sales if 315 student tickets are sold out of a total of 518 tickets
Answers
315 x 3 = 945
518 - 315 = 203
203 x 4 = 812
945 + 812 =1757
So the answer is $1,757 total
The total money collected from ticket sales for the high school play, with 315 student tickets sold at $3.00 each and 203 other tickets sold at $4.00 each, is $1,757.00.
To find the total money collected from ticket sales, we need to calculate the revenue from both student tickets and tickets sold to others. We know that 315 student tickets were sold at a price of $3.00 each, and the remaining tickets sold to others were at a price of $4.00 each. Since a total of 518 tickets were sold, the tickets sold to others amount to 518 - 315 = 203 tickets.
Revenue from student tickets = 315 tickets imes $3.00 per ticket = $945.00
Revenue from other tickets = 203 tickets imes $4.00 per ticket = $812.00
Total revenue from ticket sales = Revenue from student tickets + Revenue from other tickets = $945.00 + $812.00 = $1,757.00
Therefore, the total money collected from ticket sales is $1,757.00.
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation. What is the scale factor of the dilation?
Answers
Answer: Its option C. (4)
Step-by-step explanation: You're welcome you dirty cheaters.
The weight of 10 identical samples of a substance is 0.1 pound, what is the weight of 100 samples
Answers
Which is larger 1 meter or 105 centimeters?
Answers
That helps me remember that
1 meter = 100 centimeters
The original "1 meter or 105 centimeters" turns into "100 centimeters or 105 centimeters"
At this point, it is clear that 105 is larger than 100. So 105 cm is larger than 1 meter.
105 centimeters is bigger then 1 meter.
The equation below represents the fact that your driving rate (the distance divided by the time in hours) must be less than or equal to 65 mph by law. if you drive for 2.5 hours, what is the maximum distance you can drive and still be within the law
Answers
distance = 65 * 2.5
distance = 162.5 miles at most <==
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ? Enter your answer in the box.
Answers
y = mx + b
slope(m) = -3
(4,2)...x = 4 and y = 2
now we sub into the formula and find b, the y int
2 = -3(4) + b
2 = -12 + b
2 + 12 = b
14 = b
so ur perpendicular equation is : y = -3x + 14
Lines can be parallel, perpendicular or have no relationship at all.
The equation of the line is: [tex]\mathbf{y = -3x + 14}[/tex]
First, we calculate the slope of: [tex]\mathbf{y = \frac x3 - 1}[/tex]
A linear equation is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where:
m represents the slope
So, by comparison:
[tex]\mathbf{m = \frac 13}[/tex]
From the question, we understand that the required line is perpendicular to [tex]\mathbf{y = \frac x3 - 1}[/tex]
This means that, the slope (m2) of the required line is:
[tex]\mathbf{m_2 = -\frac 1m}[/tex]
So, we have:
[tex]\mathbf{m_2 = -\frac 1{1/3}}[/tex]
[tex]\mathbf{m_2 = -3}[/tex]
The equation of the line is:
[tex]\mathbf{y = m_2(x - x_1) + y_1)}[/tex]
Where:
[tex]\mathbf{(x_1,y_1) = (4,2)}[/tex]
So, we have:
[tex]\mathbf{y = -3(x - 4) + 2}[/tex]
Open bracket
[tex]\mathbf{y = -3x + 12 + 2}[/tex]
[tex]\mathbf{y = -3x + 14}[/tex]
Hence, the equation of the line is: [tex]\mathbf{y = -3x + 14}[/tex]
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what would be the maximum value for f(x) = −5x2 + 9
Answers
because it opens downwards, it looks like an arc, comes from the bottom up up up gets to a "maximum" or U-turn (vertex), then goes back down down down. So, where's the vertex anyway?
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} f(x) = &{{ -5}}x^2&{{ +0}}x&{{ +9}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{0}{2(-5)}~~,~~9-\cfrac{0}{4(-5)} \right)\implies (0~~,~~9)[/tex]
so, that's where the vertex is, and the maximum value for f(x), is the y-coordinate of course, or 9.
At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
Answers
Answer:
21
Step-by-step explanation:
Which graph represents the system of inequalities?
y+32x>−3
y−5≤−6x
Answers
Rewrite the systems of inequalities in slope-intercept form, and then graph the lines using the respective inequalities. The shaded area that overlaps will represent the solution to these systems of inequalities.
Explanation:In order to determine a graph that represents the system of inequalities, y+32x > -3 and y-5 ≤ -6x, you will need to write the systems of inequalities in mathematical terms, known as slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Firstly, let's rewrite the first inequality as y > -32x - 3. This inequality suggests that y is greater than -32x - 3, therefore the area above the line will be shaded.
Next, the second inequality is rewritten as y ≤ 6x + 5. This suggests y is less than or equal to 6x + 5, thus the area below the line will be shaded.
Remember, when creating the graph, a solid line should be used for ≤ symbol and a dashed line for the > symbol. The overlapping region of the two inequalities on the graph is the solution to the system of inequalities.
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