Find all complex solutions of 2x^2+x+6=0. (If there is more than one solution, separate them with commas.)
Answer:
x=-1/4+i*sqrt(47)/4 and x=x=-1/4-i*sqrt(47)/4
Step-by-step explanation:
Using quadratic formula, x=(-1±sqrt(1-48))/4.
x=-1/4+i*sqrt(47)/4 and x=x=-1/4-i*sqrt(47)/4
Answer:
If you do not understand any steps, please feel free to comment down below.
A motel has a policy of booking as many as 150 guests in a building that holds 140. Past studies indicate that only 85% of booked guests show up for their room. Find the probability that if the motel books 150 guests, not enough seats will be available.
Answer:
0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].
150 guests booked:
This means that [tex]n = 150[/tex]
85% of booked guests show up for their room.
This means that [tex]p = 0.85[/tex]
Is the normal approximation suitable:
[tex]np = 150(0.85) = 127.5[/tex]
[tex]n(1-p) = 150(0.15) = 22.5[/tex]
Both greater than 10, so yes.
Mean and standard deviation:
[tex]\mu = E(X) = np = 150*0.85 = 127.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.85*0.15} = 4.3732[/tex]
Find the probability that if the motel books 150 guests, not enough seats will be available.
More than 140 show up, which, using continuity correction, is [tex]P(X > 140 + 0.5) = P(X > 140.5)[/tex], which is 1 subtracted by the p-value of Z when X = 140.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140.5 - 127.5}{4.3732}[/tex]
[tex]Z = 2.97[/tex]
[tex]Z = 2.97[/tex] has a p-value of 0.9985.
1 - 0.9985 = 0.0015.
0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.
If a triangular pyramid has a base area of 10ft and a height of 6ft, what is the volume?
. 20ft^3
. 40ft^3
.60ft^3
.80ft^3
.120ft^3
Answer: 20 ft³
Step-by-step explanation:
volume of triangular pyramid = [tex]\frac{1}{3} bh[/tex]
b = base area = 10 fth = height = 6 ftTherefore, the volume is:
[tex]\frac{1}{3} *10*6=\frac{1}{3}*60=\frac{60}{3}=20[/tex]
Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.
A. AE || CB
B. AD|| CB
C. none of these
D. AC|| CD
9514 1404 393
Answer:
C. none of these
Step-by-step explanation:
The given information tells us ΔACD is isosceles, but gives no information about any lines that might conceivably be parallel.
Find the equation of the line that contains the point (4, -2) and is perpendicular to the line y = - 2x + 5.
y = 2x - 10
y = - 2x + 6
y = - 1/2x
y = 1/2x - 4
Answer:
It's option D. y = 1/2x - 4
Step-by-step explanation:
I used Desmos to find the answer, hope the graph helps!
Abigail plans to repaint some classroom bookcases. She has 6/25
gallons of paint. All of the bookcases are the same size and each requires 2/3
gallon of paint. How many bookcases will the custodian be able to repaint with that amount of paint?
Answer:
Step-by-step explanation: Hello! Do
C 89. What is the power of 5, so that 1 its value become ? (५ को घाताङ्क 25 कति हुदा त्यसको मान 25 हुन्छ ?) .7
C 89. What is the power of 5, so that 1 its value become ?
The power is 0. because if 0 is tge powwe of any variable or letters the value becomes 1.
Which expression is equivalent to (4x^(3)y^(5))(3x^(5)y)^(2)
Answer:
[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]
Step-by-step explanation:
Given
[tex](4x^3y^5)(3x^5y)^2[/tex]
Required
The equivalent expression
We have:
[tex](4x^3y^5)(3x^5y)^2[/tex]
Expand
[tex](4x^3y^5)(3x^5y)^2 = 4x^3y^5*9x^{10}y^2[/tex]
Further expand
[tex](4x^3y^5)(3x^5y)^2 = 4*9*x^3*x^{10}y^5*y^2[/tex]
Apply laws of indices
[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]
Which points lie on the graph of f(x) = loggx?
Check all that apply.
Step-by-step explanation:
f(x)=log(x)
=d(log(x)/dx)
=>y=1/x
what is the tan invers of 3i/-1-i
z = 3i / (-1 - i )
z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )
z = (3i × (-1 + i )) / ((-1)² - i ²)
z = (-3i + 3i ²) / ((-1)² - i ²)
z = (-3 - 3i ) / (1 - (-1))
z = (-3 - 3i ) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have
arg(z) = arctan((-3/2)/(-3/2)) - π
arg(z) = arctan(1) - π
arg(z) = π/4 - π
arg(z) = -3π/4
where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.
PLEASE HELP!! WHOEVER HELPS FIRST AND GETS IT CORRECT GETS BRAILIEST!! By the way, TWO people need to answer so I can mark brainliest.
Answer:
what's is the question anyway
What error, if any, did Noah make?
Answer:
breathing, jk buddy
Step-by-step explanation:
Given $f(x) = \frac{\sqrt{2x-6}}{x-3}$, what is the smallest possible integer value for $x$ such that $f(x)$ has a real number value? Please show steps. Thank you!
(I rewrote the question without the symbols, they are the same question)
Given f(x) = {2x-6}/{x-3}, what is the smallest possible integer value for x such that f(x) has a real number value? Thank you!
===========================================================
Explanation:
The given function is
[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}[/tex]
which is the same as writing f(x) = ( sqrt(2x-6) )/(x-3)
The key for now is the square root term. Specifically, the stuff underneath. This stuff is called the radicand.
Recall that the radicand cannot be negative, or else the square root stuff will result in a complex number. Eg: [tex]\sqrt{-4} = 0+2i[/tex]
The question is basically asking: what is the smallest x such that [tex]\sqrt{2x-6}[/tex] is a real number?
Well if we made 2x-6 as small as possible, ie set it equal to 0, then we can find the answer
[tex]2x-6 = 0\\\\2x = 6\\\\x = 6/2\\\\x = 3\\\\[/tex]
I set the radicand equal to 0 because that's as small as the radicand can get (otherwise, we're dipping into negative territory).
So 2x-6 set equal to 0 leads to x = 3.
This means x = 3 produces the smallest radicand (zero) and therefore, it is the smallest allowed x value for that square root term.
But wait, if we tried x = 3 in f(x), then we get...
[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}\\\\f(3) = \frac{\sqrt{2*3-6}}{3-3}\\\\f(3) = \frac{\sqrt{0}}{0}\\\\[/tex]
which isn't good. We cannot have 0 in the denominator. Dividing by zero is not allowed. The result is undefined. It doesn't even lead to a complex number. So we'll need to bump x = 3 up to x = 4. You should find that x = 4 doesn't make the denominator 0.
----------------
In short, we found that x = 3 makes the square root as small as possible while staying a real number, but it causes a division by zero error with f(x) overall. So we bump up to x = 4 instead.
Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 121212 by 121212 inches, with 0.750.750, point, 75 inch margins on all 444 sides. India measures 3{,}2143,2143, comma, 214 kilometers from north to south and 2{,}9332,9332, comma, 933 kilometers from west to east. Uche wants the longest dimension of India to fit exactly in between the margins of the page. If kkk is the number of kilometers per inch in Uche's scale, which equation best models the situation
The scale ratio of a point A to another point B is the division of the length of B by the length of A. The best equation that models the situation is: [tex]10.5k= 3214[/tex]
The page dimension is:
[tex]Length = 12[/tex]
[tex]Width = 12[/tex]
The length and the width of Uche's book are equal; this means the pages of Uche's book have the shape of a square
The margin of 0.75 on either sided means the usable dimension is:
[tex]Length = 12 - 2 * 0.75 =10.5[/tex]
The dimension of India is:
[tex]Length = 3214[/tex]
[tex]Width =2933[/tex]
The longest side in India's dimension is:
[tex]Longest = 3214[/tex]
From Uche's book, the longest dimension is:
[tex]Longest = 10.5[/tex]
So, the scale equation is:
k * longest length of Uche's book = longest side of India
This gives:
[tex]k * 10.5 =3214[/tex]
[tex]10.5k =3214[/tex]
Read more about scale ratio at:
https://brainly.com/question/16192120
please help
Evaluate 3^x for x = −2, x = 1, and x = 3.
A)1∕3, 0, 9
B) 9, 3, 27
C) 1∕9, 3, 27
D)1∕9, 9, 27
Step-by-step explanation:
1/3,0,9
9,3,27
1/9,3,27
$88 tickets to the San Francisco 49ers game are offered at a 15%
discount. What is the sale price?
Answer:
74.80
Step-by-step explanation:
First find the discount
88 * 15%
88*.15
13.2
Subtract the discount from the original price
88-13.2
74.80
Is x=-2 a solution for the equation below?
Answer:
no
Step-by-step explanation:
-7+x^2-3x = 9+x-10
-7+(-2)^2-3*(-2) 9+(-2)-10
-7+4+6 9-12
3 > -3
if we substitute -2 to x, answer is not equal
Answer:
x= -2
-7 +x^2 - 3x = 9 +x - 10
-7 + (-2)^2 -3×(-2) = 9 + (-2) -10
-7 +4 +6 = 9 - 2 - 10
-7+10=9-12
3 =-3
Don't blame me if this is incorrect:)
Alan's aunt gave him $95 to spend on clothes at the mall. He bought 5 shirts that cost $6 each and a pair of pants that cost $17. How much money does Alan have left to buy more clothes? (one more)
Answer:
he has 48 dollars left to spend on clothes
8 meters for every 2inches what is the area of 144 meters squared
9514 1404 393
Answer:
9 square inches
Step-by-step explanation:
The area is proportional to the square of the linear scale factor. We can use this to write the proportion ...
A/(144 m²) = ((2 in)/(8 m))²
A = (144·4/64) in² = 9 in²
The area representing 144 square meters is 9 square inches.
f (-10) = ?
Evaluate piecewise functions
Answer:
f(- 10) = 150
Step-by-step explanation:
f(- 10) with t = - 10 corresponds to t ≤ - 10 with f(t) = t² - 5t , then
f(- 10) = (- 10)² - 5(- 10) = 100 + 50 = 150
for t=-10
f(t)=t²-5tSo
f(-10)
(-10)²-5(-10)100+50150Which quadrilateral has equal diagonals
Select one:
a. trapezoid
b. rectangle
c. parallelogram
d. rhombus
Answer:
Option b: Rectangle
Explanation:
Give branliest pls ;)
Need the help thanks guys
Answer:
1/4
Step-by-step explanation:
x^2 - x
Take the coefficient of x
-1
Divide by 2
-1/2
Square it
(-1/2)^2 = 1/4
Add it
x^2 -x +1/4
I need help ASAP please
Answer:
yes how can I help you???
Amanda has 1 3/4yds of red ribbon and 7/8yds of green
ribbon. What is the total amount of ribbon that
Amanda has? (write answer as a fraction)
Answer:
21/8 yds or 2 5/8 yds
Step-by-step explanation:
First turn 1 3/4 yards into an improper fraction so you can add it to 7/8 yards.
1 3/4 as an improper fraction is 7/4 yds
7/4 yds = 14/8 yds
14/8 yds + 7/8 yds = 21/8 yds
So the total amount of ribbon Amanda has is 21/8 yds or 2 5/8 yds
which polygon will NOT tessellate a plane?
Step-by-step explanation:
the answer is regular octagon
i think
please help, will give brainliest for correct answer
ain't it just 3 for each one unless i'm missing something
Divide into two triangles in a straight line
Step-by-step explanation:
I am not sure but is this question like this
if it's not i am sorry
Circled one I need help with thank you!!
Formula-
If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}
Symbol that can be used-
The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".
Hope it helps you... pls mark brainliest if it helped you.
Cho hai tập hợp A={1;2;3;4},B={2;4;6;8} . Tập hợp nào sau đây bằng tập hợp A ∩B ?
Answer:
A∩B ={2;4}
Step-by-step explanation:
Chúc bạn học tốt
9(5x + 1) ÷ 3y
From the expression above, provide an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write "not present." (ill give brainiest and if there is any troll answers I will report and take this down )
Answer
3y(5x+1)
Step-by-step explanation:
9*(5x+1)/3y
3(5x+1)y
Answer:
Step-by-step explanation:
sum: 5x + 1
factor: 3 which divides into 9 evenly
quotient: the answer to division: 9(5x + 1)/(3y) = 3(5x +1)/y
coefficent: this depends on what you have been told. In my day, there were two kinds of coefficents
numerical: 5 and 3
literal: x and y
