Answers
Answer:
[tex](x+\frac{b}{2a})^2+(\frac{4ac}{4a^2}-\frac{b^2}{4a^2})=0[/tex]
[tex](x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}[/tex]
[tex]x=\frac{-b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a}[/tex]
Step-by-step explanation:
[tex]x^2+\frac{b}{a}x+\frac{c}{a}=0[/tex]
They wanted to complete the square so they took the thing in front of x and divided by 2 then squared. Whatever you add in, you must take out.
[tex]x^2+\frac{b}{a}x+(\frac{b}{2a})^2+\frac{c}{a}-(\frac{b}{2a})^2=0[/tex]
Now we are read to write that one part (the first three terms together) as a square:
[tex](x+\frac{b}{2a})^2+\frac{c}{a}-(\frac{b}{2a})^2=0[/tex]
I don't see this but what happens if we find a common denominator for those 2 terms after the square. (b/2a)^2=b^2/4a^2 so we need to multiply that one fraction by 4a/4a.
[tex](x+\frac{b}{2a})^2+\frac{4ac}{4a^2}-\frac{b^2}{4a^2}=0[/tex]
They put it in ( )
[tex](x+\frac{b}{2a})^2+(\frac{4ac}{4a^2}-\frac{b^2}{4a^2})=0[/tex]
I'm going to go ahead and combine those fractions now:
[tex](x+\frac{b}{2a})^2+(\frac{-b^2+4ac}{4a^2})=0[/tex]
I'm going to factor out a -1 in the second term ( the one in the second ( ) ):
[tex](x+\frac{b}{2a})^2-(\frac{b^2-4ac}{4a^2})=0[/tex]
Now I'm going to add (b^2-4ac)/(4a^2) on both sides:
[tex](x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}[/tex]
I'm going to square root both sides to rid of the square on the x+b/(2a) part:
[tex]x+\frac{b}{2a}=\pm \sqrt{\frac{b^2-4ac}{4a^2}}[/tex]
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2-4ac}}{2a}[/tex]
Now subtract b/(2a) on both sides:
[tex]x=\frac{-b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a}[/tex]
Combine the fractions (they have the same denominator):
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Related Questions
A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:
f(n) = 9(0.7)n
What does the number 0.7 represent?
The ball bounces to 30% of its previous height with each bounce.
The height at which the ball bounces at the nth bounce is 0.3 feet.
The ball bounces to 70% of its previous height with each bounce.
The height from which the ball was dropped at the nth bounce is 0.7 feet.
Answers
Answer:
The ball bounces to 70% of its previous height with each bounce.
Step-by-step explanation:
In physics terminology, the number 0.7 is the coefficient of restitution. It is the ratio of the height of bounce (n+1) to the height of bounce (n).
The meaning of the number is that the ball bounces to 70% of the height of the previous bounce.
Answer:
The ball bounces to 70% of its previous height with each bounce.
Step-by-step explanation:
A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:
f(n) = 9(0.7)n
The number 0.7 represents that the ball bounces to 70% of its previous height with each bounce.
What are some ways tanθ=sinθ/cos θ can be expressed?
Answers
Answer:
See explanation
Step-by-step explanation:
We can express
[tex] \tan( \theta) = \frac{ \sin \theta}{ \cos \theta } [/tex]
in so many ways using trigonometric identities.
Let us rewrite to obtain:
[tex]\tan( \theta) = \frac{1}{ \cos \theta } \times \sin \theta[/tex]
This implies that
[tex]\tan( \theta) = \sec \theta \sin \theta[/tex]
When we multiply the right side by
[tex] \frac{ \cos \theta}{ \cos \theta} [/tex]
we get:
[tex]\tan( \theta) = \frac{ \sin \theta \cos \theta }{ \cos ^{2} \theta } [/tex]
[tex]\tan( \theta) = \frac{ \sin 2\theta }{ 2 - 2\sin^{2} \theta } [/tex]
Etc
In the xy-plane, a parabola defined by the equation y=(x-8)^2 intersects the line defined by the equation y=36 at two points, P and Q. What is the length of PQ?
A) 8
B) 10
C) 12
D) 14
Answers
Answer:
12
Step-by-step explanation:
Alright so we are asked to find the intersection of y=(x-8)^2 and y=36.
So plug second equation into first giving: 36=(x-8)^2.
36=(x-8)^2
Take square root of both sides:
[tex]\pm 6=x-8[/tex]
Add 8 on both sides:
[tex]8 \pm 6=x[/tex]
x=8+6=14 or x=8-6=2
So we have the two intersections (14,36) and (2,36).
We are asked to compute this length.
The distance formula is:
[tex]\sqrt{(14-2)^2+(36-36)^2}[/tex]
[tex]\sqrt{14-2)^2+(0)^2[/tex]
[tex]\sqrt{14-2)^2[/tex]
[tex]\sqrt{12^2}[/tex]
[tex]12[/tex].
I could have just found the distance from 14 and 2 because the y-coordinates were the same. Oh well. 14-2=12.
Marco is studying a type of mold that grows at a fast rate. He created the function f(x) = 345(1.30)x to model the number of mold spores per week. What does the 1.30 represent? How many mold spores are there after 4 weeks? Round your answer to the nearest whole number
Answers
Answer:
1.30 is the growth factor per week985 mold spores after 4 weeksStep-by-step explanation:
The base of the exponential factor in a growth formula is the growth factor. Here, that is 1.30. It represents the multiplier of the number of spores each week.
Putting 4 into the formula, we find ...
f(4) = 345×1.30^4 ≈ 985 . . . . mold spores after 4 weeks
Answer:
george floyd
Step-by-step explanation:
cmon start bouncing
In the figure below, if arc XY measures 116 degrees, what is the measure of angle ZYX?
Answers
Answer:
∠ZYX = 58°
Step-by-step explanation:
The measure of an inscribed angle or a tangent- chord angle is one half the measure of the intercepted arc.
arc XY is the intercepted arc, hence
∠ZYX = 0.5 × 116° = 58°
Answer: [tex]ZYX=58\°[/tex]
Step-by-step explanation:
It is important to remember that, by definition:
[tex]Tangent\ chord\ Angle=\frac{1}{2}Intercepted\ Arc[/tex]
In this case you know that for the circle shown in the figure, the arc XY measures 120 degrees, therefore you can find the measure of the angle ZYX. Then you get that the measure of the this angle is the following:
[tex]ZYX=\frac{1}{2}XY\\\\ZYX=\frac{1}{2}(116\°)\\\\ZYX=58\°[/tex]
"the fromula for the perminter of a rectangle is given by P= 2L +2W where l is the length and w is the width. Assume the ermiter of a rectangular plot of land is 480 ft. The length is twice the width. Find the length of rectangular plot of land
Answers
Answer:
The length of rectangular plot of land is 160 ft.
Step-by-step explanation:
L = 2 W (the length is twice the width)
P = 480 ft. (perimeter of rectangular plot of land)
L = ?
2. 2W + 2W= 480 ft >>> (2 times twice width=L) + 2W=480 ft.
4W + 2W= 480 ft >>>> 6W= 480 ft.
W= 80 ft.
L = 2. 80 = 160 ft. (Length is twice the width)
P= 2L + 2W (formula for the perimeter)
2. 160 + 2. 80 = 480 ft.
Write an equation in slope-intercept form for the line passing through the pair of points.
(-1, 2), (4, -3)
A) y = -x + 1
B) y = 0x - 1
C) y = -x - 1
D) y = 0x + 1
Answers
Answer:
A) y= -x + 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
==========================================
We have the points (-1, 2) and (4, -3).
Calculate the slope:
[tex]m=\dfrac{-3-2}{4-(-1)}=\dfrac{-5}{5}=-1[/tex]
Put the value of the slope an the coordinates of the point 9-1, 2) to the equation of a line:
[tex]2=(-1)(-1)+b[/tex]
[tex]2=1+b[/tex] subtract 1 from both sides
[tex]1=b\to b=1[/tex]
Finally:
[tex]y=-x+1[/tex]
Answer:
A line in form of y = ax + b passes (0, 2)
=> 2 = 0x + b => b = 2
This line also passes (4, 6)
=> 6 = 4x + 2 => x = 1
=> Equation of this line: y = x + 2
=> Option C is correct
Hope this helps!
:)
Step-by-step explanation:
What are the two requirements for a discrete probability distribution?
Answers
Answer:
[tex]1.\ \ p(x)\geq0 & \text{ for all values of x.}\\\ 2.\ \sum\ p(x)=1[/tex]
Step-by-step explanation:
There are two requirements for a discrete probability distribution that must be satisfied as :-
1. Each probability must be greater than equals to zero.
2. Sum of all probabilities should be equals to 1.
The above conditions are also can be written as :
[tex]1.\ \ p(x)\geq0 & \text{ for all values of x.}\\\ 2.\ \sum\ p(x)=1[/tex]
A discrete probability distribution must satisfy two conditions: each individual outcome probability must be between 0 and 1, and the total of all outcome probabilities must equal to 1.
Explanation:There are two key requirements that a set of data must meet to be considered a discrete probability distribution:
The probabilities of all outcomes must be between 0 and 1 (inclusive). This means that for any random variable X, the probability P(X) is such that 0 ≤ P(X) ≤ 1.The sum of the probabilities of all possible outcomes must be equal to 1. This is based on the law of total probability. For example, if we denote the random variable's outcomes as x, and their corresponding probabilities as p(x), then the sum of all p(x) should equal 1, denoted mathematically as: ∑ p(x) = 1.Learn more about Discrete Probability Distribution here:https://brainly.com/question/33727484
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Arthur is comparing the prices of two rental car companies. Company A charges $22 per day and an additional $5 as service charges. Company B charges $20 per day and an additional $16 as service charges.
Answers
21
Step-by-step explanation:
Answer:
company A because its less money
Step-by-step explanation:
please help im confused
Answers
Answer:
m∠1 = 43°27'm∠2 = 136°33'm∠4 = 136°33'Step-by-step explanation:
Angles 1 and 3 are vertical angles, so are equal:
m∠1 = m∠3 = 43°27'
Angles 2 and 3 are a linear pair, so are supplementary:
m∠2 = 180° - m∠3 = 180° - 43°27' = 136°33'
Angles 2 and 4 are also vertical angles, so are equal:
m∠4 = m∠2 = 136°33'
_____
There are 60 minutes in a degree, so 180° is the same as 179°60'. Subtraction can proceed in the usual way after this rewrite:
180° - 43°27' = 179°60' -43°27'
= (179 -43)° +(60 -27)' = 136°33'
The double number line shows that in 3 seconds an ostrich can run 63 meters . Based on the ratio shown in the double number line how far can the ostrich run in 5 seconds
Answers
then, 1 second for 21 meters
therefore, 5 seconds for 105 meters
Answer:
Ostrich can run in 5 second = 105 meter .
Step-by-step explanation:
Given : The double number line shows that in 3 seconds an ostrich can run 63 meters .
To find : Based on the ratio shown in the double number line how far can the ostrich run in 5 seconds.
Solution : We have given
ostrich can run in 3 second = 63 meter .
Let ostrich can run in 5 second = x meter .
By the Ratio : 63 : 3 :: x : 5
[tex]\frac{63}{3} =\frac{x}{5}[/tex]
On cross multiplication
63 * 5 = 3 * x
315 = 3 x
On dividing both sides by 3
x = 105 meter .
Therefore, ostrich can run in 5 second = 105 meter .
Mahnoor randomly selects times to walk into a local restaurant and observe the type of music being played. She found that the restaurant was playing country 111111 times, rock & roll 171717 times, and blues 888 times. Use the observed frequencies to create a probability model for the type of music the restaurant is playing the next time Mahnoor walks in. Input your answers as fractions or as decimals rounded to the nearest hundredth.
Answers
Answer:
Outcome : A(Country) B(Rock & roll) C(blues)
Probability : [tex]\dfrac{11}{36}[/tex] [tex]\dfrac{17}{36}[/tex] [tex]\dfrac{1}{9}[/tex]
Step-by-step explanation:
A probability model is a mathematical display of a random situation S contain various sets .
Let A be the event that they play a country music, B be the event that they play rock & roll and C be the event that they play blues.
Then , n (A) = 11, n(B)=17 and n(C)=8
Let S be the combined set of number of times music played in local restaurant.
Then , [tex]n(S)=11+17+8=36[/tex]
Then , [tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{11}{36}[/tex]
[tex]P(B)=\dfrac{n(B)}{n(S)}=\dfrac{17}{36}[/tex]
[tex]P(C)=\dfrac{n(C)}{n(S)}=\dfrac{8}{36}=\dfrac{1}{9}[/tex]
Now, the required probability model:-
Outcome : A(Country) B(Rock & roll) C(blues)
Probability : [tex]\dfrac{11}{36}[/tex] [tex]\dfrac{17}{36}[/tex] [tex]\dfrac{1}{9}[/tex]
Answer:
country = 0.31
rock and roll =0.47
Blues = 0.22
Step-by-step explanation: Here we go :O
Let's put the count of each type of music from the sample into a table.
country = 11
Rock and roll= 17
blues = 8
Total = 36
We get the probabilities by dividing the frequencies by the total. (Remember to round to the nearest hundredth.)
11/36 = country
17/36 = rock and roll
8/36 = blues
Divide these
country = 0.31
rock and roll =0.47
Blues = 0.22
In circle A below, if angle BAC measures 30 degrees, what is the measure of arc BC?
Answers
Answer:
30°
Step-by-step explanation:
The measure of the arc is the same as the measure of the central angle that intercepts it, hence
m AC = ∠BAC = 30°
Answer: The measure of arc BC is 30°
Step-by-step explanation:
It is important to remember that, by definition:
[tex]Central\ angle = Intercepted\ arc[/tex]
Therefore, in this case, knowing that the angle BAC (which is the central angle) in the circle provided measures 30 degrees, you can conclude that the measure of arc BC (which is the intercepted arc) is 30 degrees.
Then you get that the answer is:
[tex]BAC=BC[/tex]
[tex]BC=30\°[/tex]
The coordinates of the vertices of a regular polygon are given. Find the area of the polygon to the nearest tenth.
A(0, 0), B(2, -2), C(0, -4), D(-2, -2)
Answers
Answer:
The area is equal to [tex]8\ units^{2}[/tex]
Step-by-step explanation:
we have
A(0, 0), B(2, -2), C(0, -4), D(-2, -2)
Plot the figure
The figure is a square (remember that a regular polygon has equal sides and equal internal angles)
see the attached figure
The area of the square is
[tex]A=AB^{2}[/tex]
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]AB=\sqrt{(-2-0)^{2}+(2-0)^{2}}[/tex]
[tex]AB=\sqrt{(-2)^{2}+(2)^{2}}[/tex]
[tex]AB=\sqrt{8}[/tex]
[tex]AB=2\sqrt{2}\ units[/tex]
Find the area of the square
[tex]A=(2\sqrt{2})^{2}[/tex]
[tex]A=8\ units^{2}[/tex]
If in right triangle ABC with right angle C, sin A = 3/5 then what is the value of sin B?
Answers
Check the picture below.
For this case we have to define trigonometric relationships in rectangular triangles that the sine of an angle is given by the leg opposite the angle, on the hypotenuse of the triangle.
If we have to:
[tex]Sin A = \frac {3} {5}[/tex]
So:
Leg opposite angle A is: 3
The hypotenuse is: 5
If we apply the Pythagorean theorem, we find the value of the other leg:
[tex]x = \sqrt {5 ^ 2-3 ^ 2}\\x = \sqrt {25-9}\\x = \sqrt {16}\\x = 4[/tex]
So, the Sine of B is given by:
[tex]Sin B = \frac {4} {5}[/tex]
Answer:
[tex]SinB = \frac {4} {5}[/tex]
Please help!! math question below!!! pic
Answers
Answer:
about 32,000
Step-by-step explanation:
You are being asked to evaluate the quartic for x=7.
f(7) = (((-0.022·7 +0.457)7 -2.492)7 -5279)7 +87.419
= ((.303·7 -2.492)7 -5.279)7 +87.419
= (-0.371·7 -5.279)7 +87.419
= -7.876·7 +87.419
= 32.287
The number of dolls sold in 2000 was approximately 32,000.
A biologist is researching the population density of antelopes near a watering hole. The biologist counts 32 antelopes within a radius of 34 km of the watering hole. What is the population density of antelopes? Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest whole number.
Answers
Answer:
18 antelopes/km^2
Step-by-step explanation: Took the test ;)
Final answer:
The population density of antelopes near the watering hole is approximately 9 antelopes per km² when rounded to the nearest whole number.
Explanation:
The concept of population density is fundamental in ecology and refers to the number of individuals of a species per unit of area.
To calculate population density for the population of antelopes the biologist is studying, we first need to determine the area covered, which is a circle with a radius of 34 km.
Using the given value of pi (3.14), the area (A) is calculated with the formula A = πr², where r is the radius.
The area is therefore 3.14 × (34 km)² = 3.14 × 1,156 km² = 3,629.44 km².
Next, the population density (D) is determined by dividing the number of individuals (N) by the area (A), which in this case is D = N / A = 32 antelopes / 3,629.44 km² ≈ 0.00 88 antelopes per km².
Rounding the final value to the nearest whole number gives us a population density of 9 antelopes per km².
Swaziland has the highest HIV prevalence in the world : 25.9% of this country’s population is infected with HIV. The ELISA test is one of the first and most accurate tests for HIV. For those who carry HIV, the ELISA test is 99.7% accurate. For those who do not carry HIV, the ELISA test is 92.6% accurate. 1. If an individual from Swaziland has tested positive, what is the probability that he carries HIV ? 2. If an individual from Swaziland has tested negative, what is the probability that he is HIV free ?
Answers
Answer:
1. If an individual from Swaziland has tested positive, what is the probability that he carries HIV ?
P=0.8249 or 82.49%
2. If an individual from Swaziland has tested negative, what is the probability that he is HIV free ?
P=0.9988 or 99.88%
Step-by-step explanation:
Make the conditional probability table:
Individual
Infected Not infected
ELISA
Positive
Negative
Totals
The probability of an infected individual with a positive result from the ELISA is obtained from multiplying the probability of being infected (25.9%) with the probability of getting a positive result in the test if is infected (99.7%), the value goes in the first row and column:
P=0.259*0.997=0.2582 or 25.82%
Individual
Infected Not infected Totals
ELISA
Positive 25.82%
Negative
Totals
The probability of a not infected individual with a negative result from the ELISA is obtained from multiplying the probability of not being infected (100%-25.9%=74.1%) with the probability of getting a negative result in the test if isn't infected (92.6%), the value goes in the second row and column:
P=0.741*0.926=0.6862 or 68.62%
Individual
Infected Not infected Totals
ELISA
Positive 25.82%
Negative 68.62%
Totals
In the third row goes the total of the population that is infected (25.9%) and the total of the population free of the HIV (74.1%)
Individual:
Infected Not infected Totals
ELISA
Positive 25.82%
Negative 68.62%
Totals 25.9% 74.1%
Each column must add up to its total, so the probability missing in the first column is 25.9%-25.82%=0.08%, and the ones for the second column is 74.1%-68.62%=5.48%.
Individual
Infected Not infected Totals
ELISA
Positive 25.82% 5.48%
Negative 0.08 68.62%
Totals 25.9% 74.1%
Individual
The third column is filled with the totals of each row:
Infected Not infected Totals
ELISA
Positive 25.82% 5.48% 31.3%
Negative 0.08 68.62% 68.7%
Totals 25.9% 74.1% 100%
The probability A of tested positive is 31.3% and the probability B for tested positive and having the virus is 25.82%, this last has to be divided by the possibility of positive.
P(B/A)=0.2582/0.313=0.8249 or 82.49%
The probability C of tested negative is 68.7% and the probability D for tested negative and not having the virus is 68.62%, this last has to be divided by the possibility of negative.
P(D/C)=0.6862/0.687=0.9988 or 99.88%
What is the value of x in trapezoid ABCD? x=15 x=20 x=45 x=60
Answers
Answer:
A. X = 15 is the correct answer.
Step-by-step explanation:
It's the only one that really makes sense.
Hope this helped :)
The value of the variable x will be 15. Then the correct option is A.
What is a trapezoid?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.
The trapezoid is an isosceles trapezoid.
An isosceles trapezoid is the form of trapezoid on which the non-parallel sides are of equal length.
In the isosceles trapezoid, the sum of the opposite angles is 180 degrees.
Then the sum of the angle B and angle D will be 180°.
∠B + ∠D = 180°
9x + 3x = 180
12x = 180°
x = 180°
x = 15°
Thus, the value of the variable x will be 15.
Then the correct option is A.
The question was incomplete, but the complete question is attached below.
More about the trapezoid link is given below.
https://brainly.com/question/22607187
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Find the minimum value of the region formed by the system of equations and functions below.
y ≥ x - 3
y ≤ 6 - 2x
2x + y ≥ - 3
f(x, y) = 3x + 4y
A. -12
B. -4.5
C. 9
D. 24
Answers
Answer:
A. -12
Step-by-step explanation:
A graph shows the vertices of the feasible region to be (0, 6), (3, 0) and (0, -3). Of these, the one that minimizes f(x, y) is (0, -3). The minimum value is ...
f(0, -3) = 3·0 + 4(-3) = -12
_____
Comment on the graph
Here, three regions overlap to form the region where solutions are feasible. By reversing the inequality in each of the constraints, the feasible region shows up on the graph as a white space, making it easier to identify. The corner of the feasible region that minimizes the objective function is the one at the bottom, at (0, -3).
The minimum value of the function f(x,y) = 3x+4y in the feasible region defined by the given system of inequalities is -19, which unfortunately does not match any of the given options. The steps involve graphing the inequalities, finding the vertices of the feasible region, and substituting those points into the function to find the minimum value.
Explanation:This problem includes finding the minimum value of the given function in a defined region dictated by the system of inequalities. I will guide you step by step on how to reach the solution. This is basically an optimization problem dealing with linear programming. The system of inequalities yields a feasible region, and the function you want to minimize is the given f(x, y) = 3x + 4y.
Your first step is to graph the inequalities and find the feasible region, this will give you the points (vertices) that we need. The inequalities are: y ≥ x - 3, y ≤ 6 - 2x and 2x + y ≥ - 3. By graphing these inequalities, the intersection points are: (3,0), (1,-2), and (-1,-4).
The minimal value for the function, f(x,y), must be at one of these vertices. Substitute each of these points into the function f(x,y) = 3x+4y to see which gives the smallest result:
At (3,0), f(x,y) = 3*3+4*0 = 9.At (1,-2), f(x,y) = 3*1+4*(-2) = -5.At (-1,-4), f(x,y) = 3*(-1)+4*(-4) = -19.Therefore, the minimum value of f(x,y) in this region is -19, however, this option is not listed among your choices. It may be that there's a mistake. Ensure you've copied the questions and options accurately.
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Which of the following are binomials?
Check all that are:
A. x^4+x^2+1
B. 5/7y^3+5y^2+y
C. x^11
D. 6x^2+1/2y^3
E. x^2+3
F. 8x
Answers
Answer:
so, I believe D and E, are Binomials.
Step-by-step explanation:
Bi- is 2
Mono- is 1
Hope my answer has helped you and if not i'm sorry.
5 kilograms of coffee are going going to be shared equally among 4 people.
How many kilograms of coffee does each person get?
Choose 1 Answer:
Answers
Answer:
B: between 1 and 2
Step-by-step explanation:
Since you share 5 kg amongst 4 you need to divide it by 4.
5 / 4 = 1.25 kg
This is between 1 and 2 kg
Answer: B. Between 1 and 2 kilograms.
Step-by-step explanation: Divide the amount of coffee by the number of people.
5/4=1.25.
Each person will get 1.25 kilograms of coffee, which is between 1 and 2 kilograms.
The monthly wind speeds over a one-year period at Denver International Airport were recorded and the values for each month averaged. The average monthly wind speeds, in mph, from January to December during that time period were 9.7, 10.0, 10.8, 11.9, 11.0, 10.7, 10.3, 10.1, 9.9, 9.9, 9.6, and 10.1.
use the statistics calculator to find the statistical measures.
The median of the data set is .
The mean of the data set is .
The population standard deviation of the data set is .
Answers
Answer:
median: 10.1
mean: 10.333
SD: 0.632
The median of the data set is 10.1 mph. The mean of the data set is 10.26 mph. The population standard deviation of the data set is approximately 0.5339 mph.
Explanation:The median of a data set is the middle value when the data is arranged in ascending or descending order. To find the median of the given data set, we need to arrange the wind speeds in ascending order:
9.69.79.99.910.010.110.110.310.710.811.011.9Since we have 12 values in the data set, the median will be the average of the 6th and 7th values, which are both 10.1. Therefore, the median of the data set is 10.1 mph.
The mean or average of a data set is found by summing all the values and dividing by the number of values. For the given data set, the sum of the wind speeds is 123.1 mph (9.6 + 9.7 + 9.9 + 9.9 + 10.0 + 10.1 + 10.1 + 10.3 + 10.7 + 10.8 + 11.0 + 11.9) and there are 12 values. Dividing the sum by 12, the mean of the data set is 10.26 mph.
The population standard deviation is a measure of the spread or dispersion of the data. To calculate it, we need to subtract the mean from each value, square the result, sum them all, divide by the number of values, and take the square root. Using the given wind speeds:
(9.6 - 10.26)^2 = 0.0576(9.7 - 10.26)^2 = 0.3136(9.9 - 10.26)^2 = 0.0964(9.9 - 10.26)^2 = 0.0964(10.0 - 10.26)^2 = 0.0676(10.1 - 10.26)^2 = 0.0256(10.1 - 10.26)^2 = 0.0256(10.3 - 10.26)^2 = 0.0016(10.7 - 10.26)^2 = 0.0196(10.8 - 10.26)^2 = 0.0324(11.0 - 10.26)^2 = 0.0544(11.9 - 10.26)^2 = 2.7264Summing these values gives us 3.4368. Dividing by 12, we get 0.2864. Finally, taking the square root, the population standard deviation of the data set is approximately 0.5339 mph.
Please help me with this. I am stuck on this like glue on this problem
Answers
[tex]\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_5&10\\ s_6&10r\\ s_7&10rr\\ s_8&10rrr\\ &10r^3 \end{array}\qquad \qquad \stackrel{s_8}{80}=10r^3\implies \cfrac{80}{10}=r^3\implies 8=r^3 \\\\\\ \sqrt[3]{8}=r\implies \boxed{2=r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=8\\ s_8=80\\ r=2 \end{cases}\implies 80=s_1(2)^{8-1} \\\\\\ 80=s_1(2)^7\implies \cfrac{80}{2^7}=s_1\implies \cfrac{80}{128}=s_1\implies \boxed{\cfrac{5}{8}=s_1}[/tex]
Which of the following is an equation of a line that is parallel to y = 4 x + 9 ? (Choose all correct equations.)
y = 2 x + 9
y = 4 x − 7
12 x − 3 y = 6
− 20 x + 5 y = 45
Answers
Answer:
The second, third and fourth are parallel to the given equation
Step-by-step explanation:
In order to determine if the slopes are the same, put all of the equations in slope-intercept form: y = mx + b. In order for lines in this form to be parallel, the m values of each have to be the exact same number, in our case, 4. Equation 2 has a 4 in the m position, just like the given, so that one is easy. Equation 2 is parallel.
Let's solve the third equation for y:
12x - 3y = 6 so
-3y = -12x + 6 and
y = 4x - 2. Equation 3 is parallel since there is a 4 in the m position.
Let's solve the fourth equation for y:
-20x + 5y = 45 so
5y = 20x + 45 and
y = 4x + 9. Equation 4 is also parallel since there is a 4 in the m position.
The amount of time (t) in minutes it takes Jeff to mow an average sized yard is related to (n) the number of yards he mows. The equation is t = 2n + 12. How many lawns does Jeff mow if it takes him 30 minutes?
Answers
Answer:
Jeff mows 9 yards of lawn in 30 minutes
Step-by-step explanation:
The equation that models the amount of time (t) in minutes it takes Jeff to mow an average sized yard is [tex]t=2n+12[/tex], where n is the number of yards he mows.
To find the number of yards Jeff mows in 30 minutes, we set the equation to 30 and solve for n.
[tex]\implies 2n+12=30[/tex]
Add -12 to both sides:
[tex]\implies 2n=30-12[/tex]
[tex]\implies 2n=18[/tex]
Divide both sides by 2
[tex]\implies \frac{2n}{2}=\frac{18}{2}[/tex]
[tex]\implies n=9[/tex]
Hence Jeff mows 9 yards of lawn in 30 minutes.
Final answer:
Jeff mows 9 lawns if it takes him 30 minutes, based on the equation t = 2n + 12
Explanation:
The question asks us to find out how many lawns Jeff mows if it takes him 30 minutes. The relationship between the amount of time (t) in minutes and the number of yards he mows (n) is given by the equation t = 2n + 12. Since we are given that t = 30 minutes, we can substitute the value of t into the equation to solve for n, the number of lawns.
30 = 2n + 12
By subtracting 12 from both sides of the equation we get:
18 = 2n
Next, we divide both sides of the equation by 2 to solve for n:
n = 9
Therefore, Jeff mows 9 lawns if it takes him 30 minutes.
Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus. (a) Which of E[X] or E[Y] do you think is larger? Why? (b) Compute E[X] and E[Y].
Answers
Answer:
E[X] is larger than E[Y]
E[X] = 39.283784 and E[Y] = 37
Step-by-step explanation:
Given data
total students = 148
bus 1 students = 40
bus 2 students = 33
bus 3 students = 25
bus 4 students = 50
to find out
E[X] and E[Y]
solution
we know bus have total 148 students and 4 bus
so E[X] is larger than E[Y] because maximum no of students are likely to chosen to bus and probability of bus is 1/4 as chosen students
and probability of 40 i.e. P(40) students = 40/148
P(33) = 33/148
P(25) = 25 / 148
P(50) = 50 / 148
first we find out i.e
E[X] = 40 P(40) + 33 P(33)+ 25 P(25)+ 50 P(50)
E[X] = 40 (40/148) + 33 (33/148)+ 25 (25/148)+ 50 (50/148)
E[X] = 39.283784
and
y is bus chosen
E[Y] = 1/4 (40+ 33 + 25 + 50)
so E[Y] = 1/4 (40+ 33 + 25 + 50)
E[Y] = 1/4 (148)
E[Y] = 37
so E[X] = 39.283784 and E[Y] = 37
The values of E[X] and E[Y] can be calculated by finding the sum of the product of each bus's student count and their respective probabilities. E[X] is expected to be less than E[Y] because students are chosen from each bus inversely proportional to the bus's total students, while for Y, each bus has equal probability of being chosen.
Explanation:The problem describes an expectation value calculation in the context of probability for two random variables X and Y. X represents a randomly selected student from 148 students who arrived at a stadium in 4 different buses and Y represents a randomly selected bus from the 4 buses and its number of students.
Let's calculate the expected value for X (E[X]) and Y (E[Y]). The expected value of a random variable is computed as a weighted average of the possible outcomes, where each outcome is weighted by its probability. The formula is E(X) = µ = Σ xP(x). Therefore, we need to find the number of students on each bus and their respective probabilities.
For bus 1, we have 40 students, for bus 2, we have 33 students, for bus 3, we have 25 students, and for bus 4, we have 50 students. These numbers represent the possible outcomes for both random variables X and Y. Now, we need to find their respective probabilities, which are determined by the number of students in each bus divided by the total number of students (148).
For X or E[X], the probability of any student being chosen is inversely proportional to the number of students in each bus (since the student is being randomly chosen), while for Y or E[Y], the probability of any bus being chosen is the same (since the bus is being randomly chosen). Therefore, we can expect E[X] to be less than E[Y], as the probability distribution for Y is more weighted towards buses with more students.
To calculate E[Y] and E[X], we follow the expected value formula and multiply each outcome (each bus's number of students) by its probability for both X and Y. So, E[X] is summation over { 40 * ( 40 / 148), 33 * ( 33 / 148), 25 * ( 25 / 148), 50 * ( 50 / 148) } and E[Y] is summation over { 40 * ( 1 / 4), 33 * ( 1 / 4), 25 * ( 1 / 4), 50 * ( 1 / 4) } respectively.
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HELP ME!!
Select the correct answer from each drop-down menu.
Complete the statement.
If and θ is in quadrant III, and .
Answers
The correct answer from each drop-down menu is:
If cost 8 = 8 and tan20 = 17, then cos28 = -8/17.
To solve this problem, we can use the double angle formula for cosine:
cos2θ = 2cos²θ - 1
We know that cos20 = 17, so we can substitute this value into the formula:
cos2(20°) = 2(cos20°)² - 1
cos2(20°) = 2(17²)² - 1
cos2(20°) = -8/17
Therefore, the correct answer is cos28 = -8/17.
which graph represents the solution to 7x>21 or 6x-9<21
Answers
Answer:
3 < x OR 5 > x
Step-by-step explanation:
Divide 3 on both sides; move 9 to the other side of the inequality symbol to get 6x < 30. Then divide both sides by 6.
**NOTE: The ONLY time you reverse the inequality sign is when you are dividing\multiplying by a negative [this does not apply so no need to worry].
I am joyous to assist you anytime.
The solution to both the inequalities will lie in (3 , 5) region, this is represented by line C.
What is an Inequality?An Inequality is the statement formed when two algebraic expressions are equated using an Inequality operator.
The inequalities are
7x>21 and 6x-9<21
7x >21Dividing 7 on the both sides
x >3
6x-9 <21Adding 9 on both sides
6x < 30
Dividing 6 on both sides
x < 5
Therefore, the solution to both the inequalities will lie in (3 , 5) region, this is represented by line C.
The complete question is attached with the answer.
To know more about Inequality
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Find the value of tan( π + θ) if θ terminates in Quadrant III and sinθ = -5/13.
-5/13
-5/12
0
5/12
Answers
we know that θ is in the III Quadrant, and let's recall that on the III Quadrant sine and cosine are both negative, and since tangent = sine/cosine, that means that tangent is positive. Let's also keep in mind that tan(π) = sin(π)/cos(π) = 0/-1 = 0.
well, the hypotenuse is just a radius unit, so is never negative, since we know sin(θ) = -(5/13), well, the negative number must be the 5, so is really (-5)/13.
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a\implies \stackrel{III~Quadrant}{-12=a} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf tan(\theta )\implies \cfrac{sin(\theta )}{cos(\theta )}\implies \cfrac{~~-\frac{5}{13}~~}{-\frac{12}{13}}\implies -\cfrac{5}{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times -\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{12}\implies \cfrac{5}{12} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf tan(\pi +\theta )=\cfrac{tan(\pi )+tan(\theta )}{1-tan(\pi )tan(\theta )}\implies tan(\pi +\theta )=\cfrac{0+\frac{5}{12}}{1-0\left( \frac{5}{12} \right)} \\\\\\ tan(\pi +\theta )=\cfrac{~~\frac{5}{12}~~}{1}\implies tan(\pi +\theta )=\cfrac{5}{12}[/tex]
The value is 5/12.
To find the value of tan(π + θ) given that θ terminates in Quadrant III and sinθ = -5/13, we need to first note that in the third quadrant, both sine and tangent are negative. Since we already have the value for sine, we can use the Pythagorean identity to find the value for cosine. The identity is sin^2θ + cos^2θ = 1.
Starting with sinθ = -5/13, we square both sides to get sin^2θ = 25/169. Then, we use the Pythagorean identity to solve for cos^2θ which gives us cos^2θ = 1 - 25/169 = 144/169. Taking the positive and negative square root, since cosine is also negative in the third quadrant, we choose the negative root, cosθ = -12/13.
Now, tanθ is the ratio of sine to cosine, which is tanθ = sinθ/cosθ = (-5/13) / (-12/13). This simplifies to tanθ = 5/12. However, the question asks for tan(π + θ), not tanθ. The tangent function has a period of π, so tan(π + θ) = tanθ. Therefore, the answer is 5/12.