Answer:
a) 0.36
b) 0.3
c) Yes
Step-by-step explanation:
Given:
Probability of no traffic delay in one period, given no traffic delay in the preceding period = P(No_Delay) = 0.9
Probability of finding a traffic delay in one period, given a delay in the preceding period = P(Delay) = 0.6
Period considered = 30 minutes
a)
Let A be the probability that for the next 60 minutes (two time periods) the system will be in the delay state:
As the Probability of finding a traffic delay in one period, given a delay in the preceding period is 0.6 and one period is considered as 30 minutes.
So probability that for the next two time periods i.e. 30*2 = 60 minutes, the system in Delay is
P(A) = P(Delay) * P(Delay) = 0.6 * 0.6 = 0.36
b)
Let B be the probability that in the long run the traffic will not be in the delay state.
This statement means that the traffic will not be in Delay state but be in No_Delay state in long run.
Let C be the probability of one period in Delay state given that preceding period in No-delay state :
P(C) = 1 - P(No_Delay)
= 1 - 0.9
P(C) = 0.1
Now using P(C) and P(Delay) we can compute P(B) as:
P(B) = 1 - (P(Delay) + P(C))
= 1 - ( 0.6 + 0.10 )
= 1 - 0.7
P(B) = 0.3
c)
Yes this assumption should be questioned for this traffic problem because it implies that traffic will be in Delay state for the 30 minutes and just after 30 minutes, it will be in No_Delay state. However, traffic does not work like this in general and it makes this scenario unrealistic. Markov process model can be improved if probabilities are modeled as a function of time instead of being presented as constant (for 30 mins).
During the school year, there were 315 total points scored between basketball, soccer, baseball, and football. The baseball team scored 55 points. The soccer team scored twice as much as the baseball team. The football team scored 0.5 more than 1.5 times as much as the baseball team. How many points did the basketball team score?
Answer:
67.5p.
Step-by-step explanation:
315p in total.
- Baseball has 55p.
- Soccer teams points = 55x2 = 110p.
- Football team points = 110 x 0.5 = 55 x 1.5 = 82.5p.
So then you just do 315p - 82.5p - 55p - 110p = 67.5p
For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.
Answer:
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Step-by-step explanation:
For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,
( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.
( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120
Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )
_________________________________
So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
In accounting, a company's gross profit rate measures how well the company controls cost of goods sold to maximize gross profit. The gross profit rate, PPP, is calculated using the formula P = \dfrac{S - C}{S}P= S S−C P, equals, start fraction, S, minus, C, divided by, S, end fraction, where SSS is the net sales and CCC is the cost of goods sold. Rearrange the formula to solve for the cost of goods sold (C)(C)left parenthesis, C, right parenthesis. C=C=C, equals What is the cost of goods sold if the net sales is \$1{,}200{,}000$1,200,000dollar sign, 1, comma, 200, comma, 000 and the gross profit ratio is 0.20.20, point, 2? Round your answer, if necessary, to the nearest dollar. C=C=C, equals dollars
Answer:
$960,000Step-by-step explanation:
The gross profit rate of the company is expressed as [tex]P = \dfrac{S - C}{S}[/tex] where C is the cost of goods sold and S is the net sales. If the net sales S = $1,200,000, and gross profit ratio is 0.20, the cost of goods sold will be expressed as shown;
Making C the subject of the formula from the expression given.
[tex]P = \dfrac{S - C}{S}\\\\cross \ multiply\\\\SP = S-C\\\-C = SP-S\\\\C = S -SP\\[/tex]
Substituting P = 0.20 and S = $1,200,000 into the resulting equation, we will have;
[tex]C = $1,2000,000 - 0.2($1,2000,000)\\C = $1,2000,000- 240,000\\ C = 960,000[/tex]
Hence the cost of goods sold is $960,000
The solution system to 3y-2x=-9 and y=-2x+5
Answer:
[tex]\boxed{(3,-1)}[/tex]
Step-by-step explanation:
Hey there!
Well to find the solution the the given system,
3y - 2x = -9
y = -2x + 5
So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.
3(-2x + 5) - 2x = -9
Distribute
-6x + 15 - 2x = -9
-8x + 15 = -9
-15 to both sides
-8x = -24
Divide -8 to both sides
x = 3
Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.
y = -2(3) + 5
y = -6 + 5
y = -1
So the solution is (3,-1).
Hope this helps :)
is -2.75 an integer?
Answer:
yes
Step-by-step explanation:
every negative any positive number is an integer
Answer:
Step-by-step explanation:
No. Integers do not have fractions in them.
-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer
What is the approximate value of x in –2 ln (x + 1) − 3 = 7?
Answer:
x = 1/e^-5 - 1
Step-by-step explanation:
–2 ln (x + 1) − 3 = 7
–2 ln (x + 1) = 10
ln (x + 1) = –5
x + 1 = e^-5
x = e^-5 - 1
x = 1/e^-5 - 1
the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:
1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.
2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.
3. Simplify: -2 ln(x + 1) = 10.
4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.
5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.
6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.
7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.
8. Simplify: x ≈ -0.9933.
Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
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Suppose 65% of people in Georgia support a special transportation tax. Alejandro is not confident that this claim is correct. To investigate the claim, he surveys 150 people in his community and discovers that 78 people support a special transportation tax.
A. calculate sample proportion.
B. calculate standard error of the sample proportion, (SE). Give answer to three decimal places
C. Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
Answer:
C
Step-by-step explanation:
Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
A. The sample proportion is 0.52.
B. The standard error of the sample proportion is approximately 0.041.
C. The standard error of the sample proportion estimate is approximately 0.041.
A. To calculate the sample proportion, we divide the number of people who support the special transportation tax (78) by the total number of people surveyed (150):
Sample proportion = 78 / 150 = 0.52
B. To calculate the standard error of the sample proportion (SE), we use the formula:
[tex]SE = \sqrt{(p * (1 - p)) / n}[/tex]
where p is the sample proportion and n is the sample size. Substituting the values into the formula:
[tex]SE = \sqrt{(0.52 * (1 - 0.52)) / 150}\\\\SE = \sqrt{0.2496 / 150}\\\\SE = \sqrt{0.001664}\\\\SE = 0.0407[/tex]
Therefore, the standard error of the sample proportion is approximately 0.041 (rounded to three decimal places).
C. The standard error of the sample proportion estimate (SEest) is the same as the standard error of the sample proportion (SE) calculated in part B. Hence, the standard error of the sample proportion estimate is also approximately 0.041 (rounded to three decimal places).
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The lines below are parallel. If the slope of the green line is -4, what is the slope of the red line?
Answer:
-4
Step-by-step explanation:
Hey there!
Well the slopes of 2 parallel lines have the same slope,
meaning if the green line has a slope of -4 then the slope of the red line has a slope of -4.
Hope this helps :)
Write a differential equation that fits the physical description. The at time t is proportional to the power of its .
Complete Question
The complete question is shown on the first uploaded image
Answer:
The differential equation that fits the physical description is [tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
Step-by-step explanation:
From the question we are told that
The acceleration due to air resistance of a particle moving along a straight line at time t is proportional to the second power of its velocity v, this can be mathematically represented as
[tex]a(t) \ \ \alpha \ \ \ [v(t)]^2[/tex]
Where [tex]a(t)[/tex] is the acceleration at time t
and [tex]v(t)[/tex] is the velocity at time t
So
=> [tex]a(t)= z [v(t)]^2[/tex]
Where z is a constant
Generally acceleration is mathematically represented as
[tex]a(t) = \frac{d (v(t))}{dt}[/tex]
So
[tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
The top speed of this coaster is
128 mph. What is the tallest peak
of this coaster?
** Hint... convert mph into m/s.*
To convert miles per hour to meters per second divide by 2.237
128 miles per hour / 2.237 = 57.22 meters per second.
Using the first equation:
57.22 = sqrt(2 x 9.81 x h)
Remove the sqrt by raising both sides to the second power:
57.22^2 = (2 x 9.81 x h)
Simplify Both sides:
3274.1284 = 19.62h
Divide both sides by 19.62:
H = 3274.1284/ 19.62
H = 166.88 meters
I will rate you brainliest!
Answer:
B
Step-by-step explanation:
X must not be equal to -6, -1, 1 or 3
PLEASE HELP ME ASAP On a test, the average score of 25 boys and 15 girls is 68 points. The average test score of the boys is 62 points. What is the average score of the girls? SHOW YOUR WORK
Answer:
74
Step-by-step explanation:
The average score of boys and girls is 68 and boys is 62
Think of it as an equation (62 + x)/2 = 68, where x is the average score of girls
First multiply each side by 2 making the equation 62 + x = 136
Now subtract each side by 62, which will make the average score for girls 74
(x = 74)
We have to accept or reject a large shipment of items. For quality control purposes, we collect a sample of 200 items and find 24 defective items. Construct a 95% percent confidence interval for the proportion of defective items in the whole shipment.
Answer:
A 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .
Step-by-step explanation:
We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of defective items = [tex]\frac{24}{200}[/tex] = 0.12
n = sample of items = 200
p = population proportion of defective items
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics for proportions.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.12-1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] , [tex]0.12+1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] ]
= [0.075, 0.165]
Therefore, a 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .
If Tristan wants to stretch the spring by 9 inches, how many kilograms of weight must he apply to it? I need help with it please.
Answer:
9/3 = 3x/3
3 = x
The spring stretches 9 inches with 3 kilograms of weight attached to it
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3
Answer:The spring stretches 9 inches with 3 kilograms of weight attached to it.
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3:
The spring stretches 9 inches with 3 kilograms of weight attached to it.
1 liter of ink can print 5000 pages of text. If you had 100 gallons of ink then how many pages
could you print?
A recipe calls for 2 tablespoons of sugar for every 7 tablespoons of flour. If you plan on tripling the recipe what is the ratio of
sugar to flour?
-0)
A)
2 to 7
B)
2 to 21
5 to 10
DY
5 to 7
Answer:
It is still 2 to 7
Step-by-step explanation:
It is still 2 to 7 because if you triple the recipe, it will become 6 to 21 which still simplifies to 2 to 7.
The sum of two polynomials is 10a^2b^2-8a^2b+6ab^2-4ab+2 if one addend is -5a^2b^2+12a^2b-5 what is the other addend
Answer:
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Step-by-step explanation:
The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]
[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Answer:
A
Step-by-step explanation:
Will mark the brainliest i havent chosen an answer but I pressed accidentally
Answer:
The full answer is 4.40625 but rounded it would be 4.41
Urgent, please answer and show your work. In how many ways can two bishops be placed on a chessboard so that they do not attack each other? Note: a bishop can move any number of squares diagonally. A bishop on a white square, therefore, moves along white squares only. A bishop on a black square moves diagonally along black squares only.
Answer:
use the formula of permutation and combination
Step-by-step explanation:
In the game plan for model building on your multiple regression project, which of the following is true about the test that determines whether the interaction term(s) is/are significant in predicting y?
A. It will definitely be a t-test
B. It will either be a t-test or a best subset for partial) F-test depending on whether we kept or dropped the quadratic terms
C. It will definitely be a partial F-test
D. It will definitely be a global
Answer:
A. It will definitely be a t-test
Step-by-step explanation:
T-test is a type of inferential statistic test which used to determine whether there is a significant difference between mean of two group sets or variables.The t-test technique is widely used in hypothesis testing in statistics. When the model building for game play is determine through regression analysis, it will require t-test to be conducted to reach a conclusion.
If a person earns $8.74 per hour, estimate how much the person would earn per year. Assume a person works 40 hours per week and 50 weeks per year.
Answer:
$17,480 per year.
Step-by-step explanation:
Amount earned per hour = $8.74
If a person works for 40 hours every week for 50 weeks in a year, number of hours worked in a year = [tex] 40hrs*50weeks = 2000 hrs [/tex]
Estimated amount earned per year by the person = [tex] 2000hrs * 8.74 dollars [/tex]
= $17,480 per year.
A slope triangle for line l is shown on the graph below. If the
slope of the line is 4/3 what is the value of w?
Answer:
9
Step-by-step explanation:
What we have to note is that the slope of a line is rise/run. This means that the amount of y change in that line is 4, and the amount of x change is 3.
We can now use a proportion to find the value of w.
[tex]\frac{4}{3} = \frac{12}{x}[/tex]
Cross multiply:
[tex]12\cdot36 = 36\\\\36\div4=9[/tex]
Hope this helped!
Answer: 9
Step-by-step explanation:
8) The perimeter of a rectangle is 20x2 + xy - 7y2 and one of it's sides is
7x2 - xy. Find the other side.
Answer:
3x^2 + 3xy/2 - 7xy^2/2
Step-by-step explanation:
So we know the perimeter is 20x^2 + xy - 7y^2,
To find any perimeter you need 2l + 2w = P so,
One of the sides is 7x^2 - xy
First plug in the values,
2(7x^2-xy) + 2w = 20x^2 + xy - 7y^2
Multiply,
14x^2-2xy + 2w = 20x^2 + xy - 7y^2
Subtract,
14x^2 - 2xy - 14x^2 + 2xy + 2w = 20x^2 + xy - 7y^2 - 14x^2 + 2xy
2w = 6x^2 + 3xy - 7y^2
w = 3x^2 + 3xy/2 - 7xy^2/2
a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit
Answer:
$900
Step-by-step explanation:
To begin with let us estimate the total cash value of the prices
$1000 x 1= 1000
$500 x 1= 500
$50 x 2= 100
Total = $1600
Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets
2.5*1000= $2,500
Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600
Then the expected profit is = $2,500-$1600= $900
1. What is the difference between an exponential growth and exponential decay? 2. What is an example equation for expoential growth and an example equation for exponential decay?
Answer: see below
Step-by-step explanation:
The standard form of an exponential equation is: y = a(b)ˣ where
a is the initial valueb is the rateGrowth:
Exponential growth is where the final value (y) is greater than the initial value (a).
An example would be the spreading of a rumor:
You tell 1 person (a = 1) who then tells 2 people each minute (b = 2). How many people will they have spread the rumor to after 5 minutes (x = 5)?
y = 1(2)⁵
= 32
Decay:
Exponential decay is where the final value (y) is less than the initial value (a).
An example would be the decrease of bacteria in a person:
A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2). How many bacteria will the person have after 2 hours (x = 2)?
[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]
It keeps saying my answer is wrong after i identified the GCF as 3 but maybe I typed it wrong.
Answer:
3(9t^5-7p^4)(9t^5+7p^4)
Step-by-step explanation:
243 t^10 - 147 p^8
3 ( 81 t^10-49 p^8 )
Then we need to factor what is in the parentheses
3 ( ( 9t^5) ^2 - ( 7p^4) ^2)
This is the difference of squares ( a^2 -b^2) = ( a-b) (a+b)
3(9t^5-7p^4)(9t^5+7p^4)
Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25
x y
1 5
2 20
3 45
4 80
5 125
x y
1 5
2 25
3 125
4 625
5 3125
x y
1 2
2 4
3 7
4 16
5 32
Answer:
The first table on the list:
x 1 2 3 4 5
y 5 10 15 20 25
Step-by-step explanation:
A linear equation is when the slope is the exact same between each point. The way we find slope is by finding the change in "y" over the change in "x".
x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5
x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5
x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5
x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5
The slope for each change in points is 5, which means that this table represents a linear function.
The only table that represents a linear function is; Table 1
Linear functionA linear function is one that has the same slope for every coordinate point.
Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;
At x = 1, y = 5 and;Slope = 5/1 = 5
At x = 2; y = 10 and;Slope = 10/2 = 5
At x = 3, y = 15 and;Slope = 15/3 = 5
At x = 4, y = 20 and;Slope = 20/4 = 5
At x = 5, y = 25 and;slope = 25/5 = 5
In conclusion, only table 1 represents a linear function.
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PLEASE HELPPPP
A standard I.Q. test produces normally distributed results with a mean of 100 and a standard deviation of 15 for the city of New York. Out of approximately 8,400,000 citizens, how many of these people would have I.Q.s below 67?
Answer:
approx 193200
Step-by-step explanation:
As known for normal distribution is correct the rule 95.4% of the results are situation within mean+-2*s ( where s is a standard deviation)
So the border is 100+-2*15=70 and that is approx=67.
95.4% of 84000000 citizens are= 8 400 000*0.954=8013600 persons
So the residual number of the citizens =8400000-8013600=386400 citizens
Because of the simmetry of normal distribution to find the number of the citizens that have IQ below 67 we have to divide 386400 by 2.
N=386000/2=193200
The perpendicular bisectors of ΔKLM intersect at point A. If AK = 25 and AM = 3n - 2, then what is the value of n?
Answer:
n = 9 is the answer.
Step-by-step explanation:
Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.
AK = 25 units and
AM = 3n -2
To find:
Value of n = ?
Solution:
First of all, let us learn about perpendicular bisectors and their intersection points.
Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.
And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.
We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.
i.e.
Circumcenter of a triangle is equidistant from all the three vertices of the triangle.
In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].
Please refer to the attached image for the given triangle and sides.
The distance of A from all the three vertices will be same.
i.e. AK = AM
[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]
Therefore, n = 9 is the answer.
In a small town 68% of the people owned television 72% on radio and 12% owned neither television nor radio (1)represent the information on a Veen diagram.
(2)what percentage of the population owned television.
Answer:
See attachment for Venn diagram
Percentage of only TV owners is 16%
Step-by-step explanation:
Given
[tex]TV\ Owners = 68\%[/tex]
[tex]Radio\ Owners = 72\%[/tex]
[tex]None = 12\%[/tex]
Required
Represent with a Venn Diagram
What percentage owned television
From the Venn Diagram and In sets theory; we have that
Total = (TV Owners - Radio and TV Owners) + (Radio Owner - Radio and TV Owners) + Radio and TV Owners + None
Represent Radio and TV Owners with y
[tex]Total = (TV\ Owners - y) + (Radio\ Owner - y) + y + None[/tex]
Substitute 68% for TV Owners, 72% for Radio Owners, 12& for None:
[tex]Total = 68\% - y + 72\%- y + y + 12\%[/tex]
Collect Like Terms
[tex]Total = 68\% + 72\%+ 12\%- y + y - y[/tex]
[tex]Total = 152\% - y[/tex]
In Sets, Total represents 100%; So, we have
[tex]100\% = 152\% - y[/tex]
Make y the subject of formula
[tex]y = 152\% - 100\%[/tex]
[tex]y = 52\%[/tex]
The percentage of only TV owners is calculated by subtracting y from TV owners
[tex]\%P = 68\% - 52\%[/tex]
[tex]\%P = 16\%[/tex]
Answer:
The answer is 90%
Step-by-step explanation:
