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.
Answers
the graph has 12 segments so angle enclosed by each segment is [tex] {2\pi\over 12}=\frac{\pi}6[/tex]
anti-clockwise is taken as positive, so if you want positive q, you need to rotate 8 segments [tex] q=8\frac,{\pi}6=\frac{4\pi}3 [/tex] , and and 8 circles or units so r=8
and for a negative angle, you need to rotate clockwise
Which is 4 segments from the horizontal line. so [tex]q=-\frac{2\pi}3[/tex] and r will be same, 8 units.
[not sure about -r so I won't include it in answer]
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 )
Related Questions
Solve 5(2x + 4) = 15. Round to the nearest thousandth.
Answers
[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]
Answer:
[tex]\huge\boxed{x=-0.5}[/tex]
Step-by-step explanation:
[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]
Which of the following is equivalent to –2i(6 – 7i)?
Answers
Answer:
[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
Answer = A
what number has 7 ten thousands, 1 thousand, 1 hundred, and no ones?
Answers
Answer:
[tex]71,100[/tex]
Step-by-step explanation:
If you are trying to find a number that is written in word form, we can just use place values to find what goes where.
A number is broken down into this:
Ten thousands, thousands, hundreds, tens, ones.
If they have 7 ten thousands, the first digit will be a 7.
If they have 1 thousand, the second digit will be a 1.
If they have 1 hundred, the third digit will be a 1.
Since nothing is stated about tens, we assume it's value is 0.
And since there are no ones, it's value is 0.
So:
71,100.
Hope this helped!
A particular country has total states. If the areas states are added and the sum is divided by , the result is square kilometers. Determine whether this result is a statistic or a parameter.
Answers
Answer:
Some texts are missing from the question, I found a possible match, and here it is:
A particular country has total of 45 states. If the areas of 35 states are added and the sum is divided by 35, the result is 135,600 square kilometres. Determine whether this result is a statistic or a parameter.
Answer:
The result is a statistic because the data involved are samples.
Step-by-step explanation:
A Parameter is a numerical representation of an entire population. That is they are numbers summarizing data for an entire population. In this case, if all the 45 states were measured, the result would have been a parameter.
On the other hand, statistics are numbers that are subsets (representative portions) of an entire population. Since 35 states were chosen out of 45 states, the average area of the 35 states is a statistic and not a parameter.
What value of x makes this equation true?
17 5 - 7 = -4
x=
y Su
What value of x makes this equation true? X/6-7=-4
Answers
Answer:
x=18
Step-by-step explanation:
x/6 - 7 = -4
x/6 = 3
(x/ 6) * 6 = 3*6
x = 18
In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find m∠NMC.
Answers
Answer:
∠NMC = 50°
Step-by-step explanation:
The interpretation of the information given in the question can be seen in the attached images below.
In ΔABC;
∠ A + ∠ B + ∠ C = 180° (sum of angles in a triangle)
∠ A + 70° + 50° = 180°
∠ A = 180° - 70° - 50°
∠ A = 180° - 120°
∠ A = 60°
In ΔAMN ; the base angle are equal , let the base angles be x and y
So; x = y (base angle of an equilateral triangle)
Then;
x + x + 60° = 180°
2x + 60° = 180°
2x = 180° - 60°
2x = 120°
x = 120°/2
x = 60°
∴ x = 60° , y = 60°
In ΔBQC
∠a + ∠e + ∠b = 180°
50° + ∠e + 40° = 180°
∠e = 180° - 50° - 40°
∠e = 180° - 90°
∠e = 90°
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
∠i = 50° - 40° = 10°
In ΔNQC
∠f + ∠i + ∠j = 180°
90° + 10° + ∠j = 180°
∠j = 180° - 90°-10°
∠j = 180° - 100°
∠j = 80°
From line AC , at point N , ∠y + ∠c + ∠j = 180° (sum of angles on a straight line)
60° + ∠c + ∠80° = 180°
∠c = 180° - 60°-80°
∠c = 180° - 140°
∠c = 40°
Recall that :
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
Then In Δ NMC ;
∠d + ∠h + ∠c = 180° (sum of angles in a triangle)
∠d + 90° + 40° = 180°
∠d = 180° - 90° -40°
∠d = 180° - 130°
∠d = 50°
Therefore, ∠NMC = ∠d = 50°
The time between consecutive uses of a vending machine is exponential with an average of 15 minutes. a)Given that the machine has not been used in the previous 5 minutes, what is the probability that the machine will not be used during the next 10 minutes
Answers
Answer5
Step-by-step explanation:
These girts stasts jogging from the same point around
acircular track and they complete one round in 24
Seconds 36 seconds and 48 seconds respectively,
After.
how much time will they meet atone point?
Answers
Answer:
2hrs 24mins
Step-by-step explanation:
Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.
Ans LCM(24, 36, 48) = 144 mins
= 2hrs 24mins
Answer:
The answer is 2 hours and 24 minutes
Step-by-step explanation:
Hope you get this right:)
Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
Answers
200 would be a better guess
Fiona wrote the linear equation y = y equals StartFraction 2 over 5 EndFraction x minus 5.x – 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s? x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 2 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 2 EndFraction.y =
Answers
Answer:
D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{2}{5}x - 5[/tex]
Required
Determine its equivalent
From the list of given options, the correct answer is
[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]
This is shown as follows;
[tex]y = \frac{2}{5}x - 5[/tex]
Multiply both sides by [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]
Open Bracket
[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]
[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]
Subtract x from both sides
[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]
[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]
Multiply both sides by -1
[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]
[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]
Reorder
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Hence, the correct option is D
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Answer:
The 4th option
Step-by-step explanation:
An urn contains 9 red marbles, 6 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Find the probability all three marbles are the same color
Answers
Answer:
P(identical colours) = 160/1771 (0.0903 to four decimals)
Step-by-step explanation:
Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)
Choose three without replacement.
Need probability three identical colours.
Use the multiplication rule.
P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253
P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771
P(BBB) = 8/23 * 7/22 * 6/21 = 8/153
Probability of getting identical colours
= P(RRR)+P(WWW)+P(BBB)
= 160/1771 (0.0903 to four decimals)
Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.
-----------------
A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the marbles are chosen is not important, and they are also chosen without replacement, which means that the combination formula is used to find the number of outcomes.-----------------
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
-----------------
The desired outcomes can be:
3 from a set of 9(all red).3 from a set of 6(all white).3 from a set of 8(all blue).Thus:
[tex]D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160[/tex]
-----------------
The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:
[tex]T = C_{23,3} = \frac{23!}{3!20!} = 1771[/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{160}{1771} = 0.0903[/tex]
0.0903 = 9.03% probability all three marbles are the same color.
A similar problem is given at https://brainly.com/question/10896842
Five more than the square of a number Five more than twice a number Five less than the product of 3 and a number Five less the product of 3 and a number Twice the sum of a number and 5 The sum of twice a number and 5 The product of the cube of a number and 5 The cube of the product of 5 and a number. 5 + x2 5 + 2x 5 - 3x 3x - 5 2x + 5 2(x + 5) 5x3 (5x)3 WILL MARK BRAINLIEST AND DON'T PUT A FAKE ANSWER TO GET POINTS EITHER CUS I NEED HELP
Answers
Answer:
BelowStep-by-step explanation: Let all unknown no be x
Five more than the square of a number
= [tex]5 + x^2[/tex]
Five more than twice a number ;
[tex]5+2x\\= 2x+5[/tex]
Five less than the product of 3 and a number ;
[tex]5- 3x\\= 3x-5[/tex]
Twice the sum of a number and 5 ;
[tex]2(x+5)\\[/tex]
The sum of twice a number and 5 ;
[tex]2x+5[/tex]
The product of the cube of a number and 5;
[tex]x^3 \times 5\\=5x^3[/tex]
The cube of the product of 5 and a number ;
[tex](5\times x)^3\\(5x)^3[/tex]
A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?
Answers
Answer:
Total expected amount = $0.04375
Step-by-step explanation:
We need to calculate probability of getting heads on every combination of coin tosses
HHH = 1/8 = 3 heads
HHT = 1/8 = 2 heads
HTH = 1/8 = 2 heads
HTT = 1/8 = 1 head
THH = 1/8 = 2 heads
THT = 1/8 = 1 head
TTH = 1/8 = 1 head
TTT = 1/8 = 0 head
So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175
Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225
Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375
Total expected amount = 0.00375 + 0.0225 + 0.0175
Total expected amount = $0.04375
Given below are descriptions of two lines. Line 1: Goes through (-2,10) and (1,1) Line 2: Goes through (-2,8) and (2,-4)
Answers
Answer:
Option (2)
Step-by-step explanation:
1). If two lines have the same slope, lines are defined as parallel.
m₁ = m₂
2). If the multiplication of the slopes of two lines is (-1), lines will be perpendicular.
m₁ × m₂ = (-1)
Line 1 : It passes through two points (-2, 10) and (1, 1).
Slope of the line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{1+2}{10-1}[/tex]
= [tex]\frac{3}{9}[/tex]
m₁ = [tex]\frac{1}{3}[/tex]
Line 2 : It passes through two points (-2, 8) and (2, -4).
Slope of the line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{8+4}{-2-2}[/tex]
= [tex]-\frac{12}{4}[/tex]
m₂ = -3
Since, m₁ × m₂ = [tex]\frac{1}{3}\times (-3)[/tex]
= (-1)
Therefore, given lines are perpendicular to each other.
Option (2) is the correct option.
Pablo rented a truck for one day. There was a base fee of $19.99, and there was an additional charge of 80 cents for each mile driven. Pablo had to pay
$221.59 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
252 miles
Step-by-step explanation:
19.99 + .80x = 221.59
,80x = 201.60
x = 252
A clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30, while 3,000 shirts can be sold at a price of $10. Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
Answers
Answer:
p(n) = -1/100 n 40
Step-by-step explanation:
Use the two points (n, p): (1000, 30) and (3000, 10).
Now we find the equation of the line that passes through these two points.
m = (10 - 30)/(3000 - 1000)
m = -20/2000
m = -1/100
p(n) = mn + b
30 = -1/100 * 1000 + b
30 = -10 + b
b = 40
The equation is:
p(n) = -1/100 n 40
If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answers
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25
Answers
Complete Question
What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is 7.5
Answer:
The minimum sample size is [tex]n =97[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 1.25[/tex]
The standard deviation is [tex]s = 7.5[/tex]
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha =10\%[/tex]
[tex]\alpha =0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]
The minimum sample size is mathematically evaluated as
[tex]n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }[/tex]
=> [tex]n = \frac{1.645^2 * 7.5^2 }{1.25^2 }[/tex]
=> [tex]n =97[/tex]
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answers
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
one of these marbles is picked at random. what is the probability that a blue marble is picked?
A.1/3
B.2/5
C.1/2
D.1/4
Answers
Answer:
1/3
Step-by-step explanation:
there are twelve marbles total. there are 4 blue marbles.
4/12 = 1/3
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is
Answers
Complete Question
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:
A -1.645
B -2.066
C -2.000
D-1.960
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The population mean is [tex]p = 0.50[/tex]
The sample size is [tex]n = 64[/tex]
The number that met the standard is [tex]k = 24[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{24}{64}[/tex]
[tex]\r p =0.375[/tex]
Generally the standard error is mathematically evaluated as
[tex]SE = \sqrt{ \frac{p(1- p )}{n} }[/tex]
=> [tex]SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }[/tex]
=> [tex]SE = 0.06525[/tex]
The test statistics is evaluated as
[tex]t = \frac{ \r p - p }{SE}[/tex]
[tex]t = \frac{ 0.375 - 0.5 }{0.0625}[/tex]
[tex]t = -2[/tex]
Find the intersection point for the following liner function f(x)= 2x+3 g(x)=-4x-27
Answers
Answer:
( -5,-7)
Step-by-step explanation:
f(x)= 2x+3 g(x)=-4x-27
Set the two functions equal
2x+3 = -4x-27
Add 4x to each side
2x+3+4x = -4x-27+4x
6x+3 = -27
Subtract 3
6x+3 - 3 = -27-3
6x = -30
Divide each side by 6
6x/6 = -30/6
x =-5
Now we need to find the output
f(-5) = 2(-5) +3 = -10+3 = -7
Answer:
Step-by-step explanation:
big burgewr
A projectile is fired vertically upward from a height of 300
300
feet above the ground, with an initial velocity of 900
900
ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0
h
(
t
)
=
−
16
t
2
+
v
0
t
+
y
0
. Write a quadratic equation to model the projectile's height h(t)
h
(
t
)
in feet above the ground after t seconds.
Answers
Step-by-step explanation:
It is given that, a projectile is fired vertically upward from a height of 300 feet above the ground, with an initial velocity of 900 ft/s.
The general equation with which a projectile are modled by the function is given by :
[tex]h(t)=-16t^2+v_ot+y_o[/tex]
y₀ is the initial height above the ground
v₀ = initial velocity
So,
[tex]h(t)=-16t^2+900t+300[/tex]
This is the quadratic equation that models the projectile height in feet above the ground after t seconds.
Solve the following equation algebraically:
3x^2=12
a.+3
b. +2
C.+3.5
d. +1.5
Answers
(3x)^2 =12
9x^2= 12
X= 1.5
Answer:
Step-by-step explanation:
answer is c just took test
What is the area of a parallelogram if the coordinates of its vertices are (0, -2), (3,2), (8,2), and (5, -2)?
Answers
Answer: 20 sq. units .
Step-by-step explanation:
Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.
First we plot these points on coordinate plane, we get parallelogram ABCD.
By comparing the y-coordinate of B and C with A and D , we get
height = 2+2 = 4 units
Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units
Area of parallelogram = Base x height
= 5 x 4 = 20 sq. units
Hence, the area of a parallelogram ABCD is 20 sq. units .
A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34, 0.38]. Therefore, there is a probability of 0.98 that the proportion of Drosophola with this mutation is between 0.34 and 0.38. True or False
Answers
Answer:
False
Step-by-step explanation:
The 98% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 98% confidence that the proportion of Drosophola with his mutation is between 0.34 and 0.38.
the temp fell 3 degrees every hour for 5 hours what's the change in temperature
Answers
Answer:
-15
Step-by-step explanation:
If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees
Using the insurance company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period. Round your answer to four decimal places.
Answers
Answer: 19.2222
Step-by-step explanation:
given data;
no of tornadoes = 2,1,0 because it’s fewer than 3.
period = 14 years
probability of a tornado in a calendar year = 0.12
solution:
probability of exactly 2 tornadoes
= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )
= 0.0144 * 0.2451 * 1092
= 3.8541
probability of exac one tornado
= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )
= 0.12 * 0.2157 * 182
= 12.7109
probability of exactly 0 tornado
= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )
= 1 * 0.1898 * 14
= 2.6572
probability if fewer than 3 tornadoes
= 3.8541 + 12.7109 +2.6572
= 19.2222
Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.
Answers
Answer:
Step-by-step explanation:
Given
Garden: [tex]x^2+18x+81[/tex]
One Bag: [tex]x^2 - 81[/tex]
Requires
Determine the number of bags to cover the whole garden
This is calculated as thus;
[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]
Expand the numerator
[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]
[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]
Express 81 as 9²
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]
Evaluate as difference of two squares
[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]
[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
This table shows a linear relationship.
The slope of the line is ?
Answers
Answer:
2
Step-by-step explanation:
2,8 to 4,12 has a rise of 4 and a run of 2.
4/2 = 2
The slope is 2.
Remember rise/run!
Answer:
2
Step-by-step explanation:
We take take two points and use the slope formula
m = (y2-y1)/(x2-x1)
m = (12-8)/(4-2)
= 4/2
= 2
