Hello,
A:
[tex]\begin{array}{c|ccc|c}&x^3&x^2&x&1\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&-a-b+c-1\\\end{array}\\\\\\\begin{array}{c|ccc|c}&x^3&x^2&x&1\\&1&-a&b&c\\x=2&&2&-2a+4&-4a+2b+8\\---&---&---&---&---\\&1&-a+2&-2a+b+4&-4a+2b+c+8\\\end{array}\\\\\\\\-a-b+c-1=-4a+2b+c+8\\\\\boxed{b=a-3}\\[/tex]
B:
[tex](2x-1)^3+6(3+4x^2)\\\\=8x^3-12x^2+6x-1+18+24x^2\\\\=8x^3+12x^2+6x+17\\\\\\\begin{array}{c|ccc|c}&x^3&x^2&x&1\\&8&12&6&17\\x=-\dfrac{1}{2} &&-4&-4&-1\\---&---&---&---&---\\&8&8&2&16\\\end{array}\\\\\\(2x-1)^3+6(3+4x^2)=(2x+1)(4x^2+4x+1)+16[/tex]
I need help ASAP !!!!
Find the intersection point between the lines of equations:
x+y-2=0 and 3x-y+4=0
Answer:
(-0.5,2.5)
Step-by-step explanation:
The given equations are ,
[tex]\implies x + y - 2 = 0 [/tex]
[tex]\implies 3x - y +4 = 0 [/tex]
The point of intersection will be the solution of the given system of equations. Adding both , y will get cancelled . So that ,
[tex]\implies 4x +2 = 0 [/tex]
Now solve for x , we have ,
[tex]\implies 4x = -2 \\\\\implies x =\dfrac{-2}{4}\\\\\implies x = -0.5 [/tex]
Now put this value in any equation and solve out for y , we have ,
[tex]\implies -0.5 + y - 2 = 0 \\\\\implies y = 2.5 [/tex]
Therefore , the point of intersection will be ,
[tex]\implies\underline{\underline{ Point = (-0.5,2.5 ) }}[/tex]
he time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places. (a) What is the probability that more than three aircraft arrive within an hour? Enter your answer in accordance to the item a) of the question statement (b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals? Enter your answer in accordance to the item b) of the question statement
Answer:
A) 0.019
B) 0.563
Step-by-step explanation:
a) We will use Poisson distribution formula to solve this;
The formula is given as;
P(X = x) = ((e^-λ) × (λˣ))/x!
Mean is 1. Thus;
λ = 1 aircraft/hour.
Thus, the probability that more than three aircrafts will arrive within an hour is written as; P(X > 3)
Thus;
P(X > 3) = 1 - P(X ≤ 3)
Thus;
1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
Solving through online calculator, we have;
P(X > 3) = 1 - 0.98101
P(X > 3) = 0.01899
To 3 decimal places, we have; P(X > 3)= 0.019
b) Probability of one 1-hour interval not containing more than 3 arrivals is, let's first find;
P(X ≤ 3) = 1 - P(X > 3)
P(X ≤ 3) = 1 - 0.01899
P(X ≤ 3) = 0.98101
Since there are 30 one-hour intervals, then we have;
Probability that none of the thirty 1-hour intervals will contain more than 3 arrivals;
(P ≤ 3) = (0.98101)³⁰
(P ≤ 3) = 0.5626
Approximating to 3 decimal places, we have;
(P ≤ 3) = 0.563
Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality
7.2b + 6.5 > 4.8b – 8.1.
Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.
Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.
Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6.
Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.
Which student’s first step was incorrect, and why?
Amelia’s, because the variable term must be isolated on the left side
Luis’s, because he flipped the inequality sign when he subtracted
Shauna’s, because she did not apply the subtraction property of equality properly
Clarence’s, because the terms he added together were not like terms
Answer:
Luis’s, because he flipped the inequality sign when he subtracted
Step-by-step explanation:
Given:
7.2b + 6.5 > 4.8b – 8.1.
Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.
Amelia:
7.2b + 6.5 - 7.2b > 4.8b – 8.1 - 7.2b
6.5 > -2.4b - 8.1
Correct
Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.
7.2b + 6.5 - 4.8b > 4.8b – 8.1 - 4.8b
2.4b + 6.5 > -8.1
Incorrect
Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6
7.2b + 6.5 - 6.5 > 4.8b – 8.1 - 6.5
7.2b > 4.8b - 14.6
Correct
Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.
7.2b + 6.5 + 8.1 > 4.8b – 8.1 + 8.1
7.2b + 14.6 > 4.8b
Correct
Differentiate
[tex]y = 3x {}^{3} + 8x - 7[/tex]
Answer:
y=9x^2 + 8
Step-by-step explanation:
using the power rule, we will differentiate each term separately
d/dx of 3x^3 = (3)(3)x^(3-1) = 9x^2
d/dx of 8x = 8x^(1-1) = 8
d/dx of -7 = 0
combining them we get the derivative which is y = 9x^2 + 8
Answer:
9x² + 8
Step-by-step explanation:
The given function to us is ,
[tex]\implies y = 3x {}^{3} + 8x - 7[/tex]
And we need to differentiate the given function with respect to x . Taking the given function and differenciating wrt x , we have
[tex]\implies y = 3x^3 + 8x - 7 [/tex]
Recall that , the derivative of constant is 0 . Therefore ,
[tex]\implies \dfrac{dy }{dx}= \dfrac{d}{dx}(3x^3 + 8x - 7) \\\\\implies\dfrac{dy }{dx}= \dfrac{d}{dx}(3x^3)+\dfrac{d}{dx}(8x) + 0 \\\\\implies\dfrac{dy }{dx}= 3\times 3 . x^{3-1} + 8\times 1 . x^{1-1} \\\\\implies\underline{\underline{\dfrac{dy }{dx}= 9x^2+8}} [/tex]
Hence the derivative of given function is 9x² + 8 .
Consider a binomial experiment. If the number of trials is increased, what happens to the expected value
Answer:
The expected value is an expression of the weighted average and can be taken as the (arithmetic) mean
As the number of trials is increased in a binomial experiment, the expected values obtained, in each of the set of trials continuously tend to the theoretical expected value
Step-by-step explanation:
somebody help me please
Answer:
x=-4
Step-by-step explanation:
:Distribute 2 to 9.7 and -4.8x
3.4+19.4-9.6x=61.2
:combine 3.4 and 19.4
22.8-9.6x=61.2
: subtract 22.8 from both sides
-9.6x=61.2-22.8
:divide both sides by -9.6
-9.6x/-9.6=38.4/-9.6
x=-4
A body is projected from aa point such that the horizontal and vertical components of its velocity are [tex]640ms^-^1[/tex] and [tex]480 ms^-^1[/tex] respectively . (Take g = [tex]10ms^-^1[/tex] )
i. Calculate the greatest height attained above the point of projection
A.600m B.1215 m C.1521 m D. 11520m E. 20480m
D. 11520m
Answer:
Solution given:
initial velocity[u]=480m/s
g=10m/s²
maximum height=?
now
we have
maximum height=[tex]\frac{u²sin²\theta}{2g}[/tex]
where
[tex]\theta=90°[/tex]
=[tex]\frac{480²*sin90}{2*10}=11520m[/tex]
What is the mean absolute deviation? 6,5,7,2,4,8
Answer:
To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean: |data value – mean|
Step-by-step explanation:
finding the answer (solution) for z!
Answer:
z = 83/(6-c-t)
Step-by-step explanation:
-cz +6z = tz +83
Subtract tz from each side
-cz +6z -tz = 83
Factor out z
z(6-c-t) = 83
Divide by (6-c-t)
z(6-c-t) /(6-c-t) = 83/(6-c-t)
z = 83/(6-c-t)
Quadrilateral ABCD is a rectangle. FindBD ifAO = 6x - 22 and OC = 2x + 6.
40 units
20 units
7 units
10 units
true or false
is this a function 0 goes to 0 4 goes to 1 8 goes to 2 and 12 goe to 3
Answer:
Step-by-step explanation:
True. The function appears to be f(x) = x/4.
This year, Carlos planted 6 more than one-third of the cucumber plants he planted last year. How many cucumber
plants did he plant this year if last year he planted 12 plants?
06
09
O 10
12
Answer:
10
Step-by-step explanation:
last year he planted 12.
1/3 of that is 12/3 = 4.
6 more than that is 4 + 6 = 10.
Answer: C.) 10
Step-by-step explanation:
The vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
Find the equation of the perpendicular bisector of the side QR
Answer:
Step-by-step explanation:
Find the slope of QR. From that we can find the the slope of the line perpendicular to QR.
Q(-2, -5) & R(8,1)
[tex]Slope \ = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-[-5]}{8-[-2]}\\\\=\frac{1+5}{8+2}\\\\=\frac{6}{10}\\\\=\frac{-3}{5}[/tex]
So, the slope of the line perpendicular to QR = -1/m - 1÷ [tex]\frac{-5}{3} = -1*\frac{-3}{5}=\frac{3}{5}[/tex]
Bisector of QR divides the line QR to two half. We have find the midpoint of QR.
Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
[tex]=(\frac{-2+8}{2},\frac{-5+1}{2})\\\\=(\frac{6}{2},\frac{-4}{2})\\\\=(3,-2)[/tex]
slope = 3/5 and the required line passes through (3 , -2)
y - y1 = m(x-x1)
[tex]y - [-2] = \frac{3}{5}(x - 3)\\\\y + 2 = \frac{3}{5}x-\frac{3}{5}*3\\\\y=\frac{3}{5}x-\frac{9}{5}-2\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{2*5}{1*5}\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{10}{5}\\\\y=\frac{3}{5}x-\frac{19}{5}[/tex]
If the ordered pairs(a,3)and (2,b) belong to the set {(x,y):y=2x-3},find the value of a,b
Answer:
a=3
b=1
Step-by-step explanation:
3=2a-3 => a=3
b=2*2-3 = 1
what is the measure of the angle formed by a side of the given angle and the given angle's bisector:27?
Answer:
Step-by-step explanation:
An angle is cut in half by the bisector.
Since the given angle is 172, its bisector creates 2 equal angles.
2x = 172 Divide both sides by 2
x = 172/2
x = 86
expand and simplify (2x-3)(3x
+1)
Answer:
6x^2+2x-9x-3
=6x^2-7x-3
What is 2/3 divided by 1/6
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
When we divide fractions, we are essentially multiplying by the reciprocal of the fraction.
2/3 ÷ 1/6
= 2/3 × 6
= 12/3
= 4
find the angles of the triangle if they are proportainal to 3, 4, 5. The angles are?
Answer:
Because it is a right triangle one angle is obviously 90°. The other two are approximately 36.87° and 53.13°.
hope it helps you
have a good day
plz mark me as brainliest
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
Answer:
There is no actual question here, this is just a statement.
re-read the question .... i assume it says "what is the highest that she will get during a dive?"
highest point is at t = 33/32
– 16(33/32)^2 + 33(33/32) + 4 =
62.015625
Step-by-step explanation:
Lindsey will be 30 feet in the air at approximately 1.09 seconds and 2.48 seconds.
To find the time at which Lindsey will be 30 feet in the air, we need to solve the quadratic equation y = -16x² + 33x + 45 for x when y = 30.
Setting y equal to 30, we have:
30 = -16x² + 33x + 45
Rearranging the equation, we have:
16x² - 33x - 15 = 0
To solve this quadratic equation, we can factor or use the quadratic formula. In this case, factoring might be more challenging, so we'll use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values from our equation, we have:
x = (-(-33) ± √((-33)² - 4(16)(-15))) / (2(16))
Simplifying, we get:
x = (33 ± √(1089 + 960)) / 32
x = (33 ± √(2049)) / 32
Calculating the square root of 2049, we have:
x = (33 ± √(2049)) / 32
x ≈ 1.09 or x ≈ 2.48
To learn more about quadratic equation click on,
https://brainly.com/question/27958207
#SPJ2
Complete question is:
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x² + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
At what time will Lindsey be 30 feet in air?
10. The sum of the digits of a two digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27 . find the number
Answer:
Step-by-step explanation:
Let "ab" represent the digits of the number. The value of "ab" is 10a+b.
a+b = 7
The value of "ba" is 10b+a
(10b+a) - (10a+b) = 9b-9a = 27
b-a = 3
a+b = 7
b-a = 3
------------
2b = 10
b = 5
a = 2
The number is 25.
PLEASE HELP!! You are playing a game in which you must flip a coin and then roll a die. What is the probability of flipping a tails and then rolling a five?
===========================================================
Explanation:
1/2 is the probability of flipping tails because we have one side labeled tails out of 2 sides total.
1/6 is the probability of rolling a 5, because there's one side we want out of 6 total.
The two events (flipping the coin and rolling the die) are independent, allowing us to multiply those previously mentioned fractions:
(1/2)*(1/6) = (1*1)/(2*6) = 1/12
Review your answers to Question 4. What happens to the coordinates of a shape when the shape reflects about the line y = x? Explain.
Answer:
The x and y coordinates swap position
Step-by-step explanation:
Given
Reflection across: [tex]y = x[/tex]
Required
What happens to the coordinate
When a point is reflected about [tex]y = x[/tex], the x and y coordinates swap position
i.e.
[tex](x,y) \to (y,x)[/tex]
Answer:
When the shape reflects about the line y = x, the x-coordinate and the y-coordinate of each point are swapped.
Step-by-step explanation:
What is the range of the given function ?
{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)}
Answer:
{0,-3,-9,5,7}
Step-by-step explanation:
range = all y values
function =(x,y)
so all the second values are ranges
Choose the smallest number 3 1/8 or 10/3
Answer:
10/3
Step-by-step explanation:
31/8= 3.8
10/3= 3.3
if 5 miles is 8km . Convert 33.7 km into miles
Answer:
20.94021
Step-by-step explanation:
mark me brainlist
Answer:
53.92
Step-by-step explanation:
5 miles = 8 km
1 miles = 1.6 km
33.7 x 1.6 = 53.92
What is the slope of the line? What is the y-intercept of the line? y = 1/2x + 7
Answer:
slope= 1/2
y-intercept= 0,7
Answer:
slope = 1/2 or 0.5, the y-intercept is (0,7)
Step-by-step explanation:
What is the value of x?
Enter your answer, as a decimal, in the box.
Answer:
x = 50.6
Step-by-step explanation:
Find the missing side. Round to the nearest tenth. (ITS DUE IN THE MORNING PLEASE HELP)
24.
A) 14.2
C) 13.8
B) 9.2
D) 15.7.
25.
A) 37.6
B)30.8
C) 45.1
D)5.5
Answer:
24. A)14.2
25. D)5.5
Step-by-step explanation:
I hope it help for you keep safe
A : B = 5 : 7 and B : C = 3 : 5 what is the ratio of A : B : C ?
Answer:
15:21:35 (I'm not sure, but this is my best guess)
Step-by-step explanation:
15:21 = A:B (plugging in 3 as a test)
21:35 = B:C
15:21:35 = A:B:C (can't simplify)
