Euler's formula immediately gives
[tex]8e^{i\cdot16\pi}=8\cos(16\pi)+8i\sin(16\pi)=8[/tex]
and the equation above lists, from left to right, the polar, trigonometric, and rectangular forms.
What is the remainder when 19x^2 + 15x + 12 is divided by x - 2?
Answer:
R = 118
Step-by-step explanation:
Given
Represent the polynomial with P and the divisor with D
[tex]P = 19x^2 + 15x + 12[/tex]
[tex]D = x -2[/tex]
Required
Determine the remainder
We start by equating the divisor to 0
i.e.
[tex]D = 0[/tex]
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
Substitute 2 for x in the polynomial.
This gives remainder (R)
[tex]R = 19*2^2 + 15*2 + 12[/tex]
[tex]R = 19*4 + 15*2 + 12[/tex]
[tex]R = 76 + 30 + 12[/tex]
[tex]R = 118[/tex]
Hence, the remainder is 118
the research director at NASA must choose five experiments for the next space shuttle. Twelve experiments are proposed. in how many ways can this decision be made if order does not matter.. how many ways can this be arranged?
Answer:
95040Step-by-step explanation:
This is the combination of 5 experiments out of 12
Formula to find the combination:
P(n,r) = n!/(n-r)!P(12,5) = 12!/(12-5)! = 12!/7! = 12*11*10*9*8 = 95040So this can be arranged in 95040 ways
There are 36 doughnuts in 3 boxes.
How many doughnuts are in 7 boxes?
Answer:
x=84
Step-by-step explanation:
[tex]\frac{36}{3}=\frac{x}{7}[/tex]
(cross multiply)
252=3x
(divide both sides by 3)
x=84
PLZ HELP ASAP (This is not a text or an exam)
Answer:
x=4
Step-by-step explanation:
As the two angles are clearly congruent because of the bisector, we set them equal to each other:
7x=3x+16
4x=16
x=4
Therefore, the value of x is 4 and not 9
Homer is 30 feet below sea level and Marge is 45 feet above sea level. Bart’s elevation is at the exact midpoint of those two values. What is the expression that model this problem, and which is Bart’s elevation?
Answer:
14.5 feet
Step-by-step explanation:
the midpoint is halfway from 30 to 45 so be(bart elevation) b.e = 45 - 30 / 2
7.5 m above sea level
__________________________________________________________
Step-by-step explanation:We are given:
The elevation of Homer = -30 feet [30 feet below sea level]
The elevation of Marge = +45 feet [45 feet above sea level]
The elevation of Bart is at the exact mid-point of the elevations of Homer and Marge
The elevation of Bart:
We are given that the elevation of Bart is at the exact mid-point of the elevations of Homer and Marge
So, Half the distance between the elevation of Homer and Marge is the elevation of Bart
Elevation of Bart (with respect to the elevation of Homer) =
(elevation of Marge - Elevation of Homer) / 2
replacing the variables with the suitable values:
(+45 - (-30))/2
(45 + 30) / 2
75 / 2
Elevation of Bart (w.r.t. Homer) = 37.5 feet
Since this is the elevation of Bart with respect to Homer, we can say that Bart is 37.5 m above Homer
So, we can say that:
Elevation of Bart (w.r.t Homer) = Elevation of Bart - Elevation of Homer
replacing the values
37.5 = Elevation of Bart -(-30)
37.5 = Elevation of Bart + 30
Elevation of Bart = 7.5 m above sea level [subtracting 30 from both sides]
Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.
f(x) = −one twelfth(x − 5)2 + 2
f(x) = one twelfth(x − 5)2 + 2
f(x) = −one twelfth(x + 5)2 + 2
f(x) = one twelfth(x + 5)2 + 2
Answer:
The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].
Step-by-step explanation:
From statement we understand that parabola has its axis of symmetry in an axis parallel to y-axis. According to Analytical Geometry, the minimum distance between focus and directrix equals to twice the distance between vertex and any of endpoints.
If endpoints are (-5, 5) and (-5, -1), respectively, then such distance ([tex]r[/tex]), dimensionless, is calculated by means of the Pythagorean Theorem:
[tex]r = \frac{1}{2}\cdot \sqrt{[-5-(-5)]^{2}+[5-(-1)]^{2}}[/tex]
[tex]r = 3[/tex]
And the location of the vertex ([tex]V(x,y)[/tex]), dimensionless, which is below the focus, is:
[tex]V(x,y) = F(x,y)-R(x,y)[/tex] (1)
Where:
[tex]F(x,y)[/tex] - Focus, dimensionless.
[tex]R(x,y)[/tex] - Vector distance, dimensionless.
If we know that [tex]F(x,y) = (-5,5)[/tex] and [tex]R(x,y) = (0,3)[/tex], then the location of the vertex is:
[tex]V(x,y) = (-5,5)-(0,3)[/tex]
[tex]V(x,y) =(-5,2)[/tex]
In addition, we define a parabola by the following expression:
[tex]y-k = \frac{(x-h)^{2}}{4\cdot r}[/tex] (2)
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.
[tex]r[/tex] - Distance of the focus with respect to vertex, dimensionless.
If we know that [tex]h = -5[/tex], [tex]k = 2[/tex] and [tex]r = 3[/tex], then the equation of the parabola is:
[tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex]
The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].
About 50% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.(a) Is the experiment a binomial experiment?⪠Yes⪠No(b) What is a success in this experiment?⪠This is not a binomial experiment.⪠Baby recovers⪠Baby doesn't recover(c) Specify the value of n.A. n = _____B. This is not a binomial experiment.(d) Specify the value of p.A. p = _____B. This is not a binomial experiment.
Answer:
a. yes it is a binomial experiment
b. success is that baby recovers
c. n = 6
d. p = 0.5
e. q = 0.5
f. X: 0,1,2,3,4,5,6
Step-by-step explanation:
a.
the answer is yes this is a binomial experiment. This is true because we have a finite number of babies and these babies are independent of each other. there are two possible outcomes. 1. baby recovers 2. baby does not recover.
b.
success: baby recovers
c.
n = number of babies born with ailment. n = 6
d.
p = 50% = 0.5
e.
q = 1-p = 1-0.5
q = 0.5
f.
possible values of X: 0,1,2,3,4,5,6
3(x+5) +2(2x+3)=0 solveeeeeeeeeeeedddddddddedddddd
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf 3 (x+5)+2 (2x+3)=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3x+15+4x+6=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3x+4x+15+6=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 7x+21=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 7x=-21 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {-21}{7}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=-3 [/tex]
[tex]\maltese{\underline{\boxed{\bf {x=-3}}}}[/tex]
What is the difference between an expression and an any quality
Answer:
A expression is a number, variable, or a combination of numbers and variables and operation symbols. A equality is a relationship between 2 quantities or more . Hope it helps:)))
Step-by-step explanation:
answer in percent 20/80 = x/100
y - 2/5 = 1 3/5 (plz show work)
Answer:
y=2
Step-by-step explanation:
that's the answer hope u understand it
Answer:
[tex]y = 2[/tex]
Step-by-step explanation:
Sure.
[tex]y - \frac{2}{5} = 1 \frac{3}{5} \\[/tex]
Convert to improper fraction
[tex]y - \frac{2}{5} = \frac{8}{5}[/tex]
Combine like terms
[tex]y - \frac{2}{5} = \frac{8}{5} \\[/tex]
[tex]+\frac{2}{5}[/tex] from both sides
[tex]y = \frac{8}{5} + \frac{2}{5} \\y = 2[/tex]
Love from Nepal :)
In the graph above what is the average speed for the object?
a. 0.4m/s
b. 2.5m/s
c. 3m/s
d. 0.8m/s
Answer:
c
Explanation:
Just because
I WILL GIVE BRAINLIEST
Rewrite 12x + 3y = 6 in slope-intercept form. Give the slope and y-intercept.
y =
m =
b =
Answer:
12x + 3y = 6 in slope-intercept form.y = -4x+2m = -4b =(0,2)PLEASE
Solve for x and y by graphing the system of linear equations.
y=-7/2x+3
y=-3/2x-1
Answer:
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).
Step-by-step explanation:
hope its right
ucjvlvjcyxgxjglhlchzfzhckcj
Answer:
Huhuhuhhuh?!!!
Step-by-step explanation:
LOL.. What's that?
Answer: approximately oihfviauegfvyabgfiubaqvuoa
Step-by-step explanation:
first you gotta ohgnvailuerfhivlugehiuvlh the fepoghvapirugv93hrv9igp
then once thats done you edjfahuilurevh the p8eufhavipuhgfv8i7uh to the rfugvhligauerhgiuvlwhreaoiuvh
finally, you ifujevhoaiug the iujhfliauerhgifu with the oifuhewiuasrhfi and uirjewg it to the iudfhvailkvkaebrfvilhjb, and you get your answer
what is the slope and the y-intercept for the equation y = -3 + 6x?
Answer:
slope-6
y-intercept-(0,-3)
Step-by-step explanation:
oredr -3/4, 3/8, -1 1/8, - 1/2 from least to greatest.
Answer: -1 1/8 -3/4 -1/2 3/8
Erica makes $27 an hour how much does ahe make in 140 hours
Answer:
$3,780
Step-by-step explanation:
27*140=3780
Simplify each expression, Help plz
Answer:
I believe that the answer is the second one.
Step-by-step explanation:
What is the factored form of the equation 4x^2-11+6=0
Answer:
(4x−3)(x−2)=0
Step-by-step explanation:
Step-by-step explanation:
4x²-11+6=0
4x²-5=0
x²=5
4
x=√5
4
hope it help u
Sammy deposits $200 in an account at his bank.The simple interest rate is 8%.How much interest will he earn in three years
Answer:
$48
Step-by-step explanation:
Multiply 200 by 0.08 or 8%. That is how much interest he will earn in a year. Then multiply the product by 3.
A commuter train travels 45 miles in 34 minutes. What is its speed in miles per hour?
What type of transformation has occurred?
A Translation
B Dilation
C Reflection
D Rotation
Answer:
B dilation
Step-by-step explanation:
the shape didnt move but it got bigger
You are given the explicit formula below. Identify if will produce an arithmetic or geometric sequence. Also identify the common difference or common ratio
f(n) = 25(4)^n-1
1. Geometric, common ratio of 1/4
2. Geometric, common ratio of 4
3. Arithmetic, common ratio of 25
4. Arithmetic, common ratio of 4
Answer:
2. Geometric, common ratio of 4Step-by-step explanation:
Given is the exponential function which is a geometric sequence
It has common ratio of 4
Correct answer option:
2. Geometric, common ratio of 4Bella measured the heights of her corn stalks in centimeters. The heights are 81, 88, 69, 65. 87.
What is the mean height of Bella's corn stalks?
A 69 cm
B. 75 cm
C. 78 cm
D. 80 cm
E. 81 cm
Answer:
d
Step-by-step explanation:
.................have a great day
What is the simplest form of 1.764?
0 21
0 42
0 3²(7²)
22(32)(74)
please explain why because I don’t want someone to guess this is kinda important, ty
Answer:
[tex]1764 = 2^2 \times 3^2 \times 7^2[/tex]
Step-by-step explanation:
Divide by the prime numbers in increasing order until you find all the prime factors.
The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17
1764/2 = 882
882/2 = 441
441/3 = 147
147/3 = 49
49/7 = 7
7/7 = 1
[tex]1764 = 2^2 \times 3^2 \times 7^2[/tex]
2/v+1/w+1/2 solve for v
Answer:
look go search Math - way its a calculator and type in your question ir really helps gives you the answer
Step-by-step explanation:
How many metres and centimetres are in 3080mm
Answer:
3080mm = 3.08 meters
3080mm = 308 centimeters
Step-by-step explanation:
1 meter = 1000 mm
3080mm = 3080/1000 = 3.08 meters
1 centimeter = 10 mm
3080mm = 3080/10 = 308 centimeters
On average, 2.8 babies are born each day at a local hospital. Assuming the Poisson distribution, what is the probability that no babies are born today?
Answer:
The probability is [tex]P(X = 0) = 0.6997[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 2.8[/tex]
Generally the Poisson distribution constant [tex]\lambda[/tex] is mathematically represented as
[tex]\lambda = \frac{1}{\mu }[/tex]
=> [tex]\lambda = \frac{1}{2.8 }[/tex]
=> [tex]\lambda = 0.3571[/tex]
Generally the probability distribution for Poisson distribution is mathematically represented as
[tex]P(X = x) = \frac{(\lambda t)^x e^{-t \lambda}}{x!}[/tex]
Here t = 1 day
Generally the probability that no babies are born today is mathematically represented as
[tex]P(X = 0) = \frac{(0.3571 * 1 )^0 e^{-1 * 0.3571}}{0!}[/tex]
=> [tex]P(X = 0) = 0.6997[/tex]
is x= 3 a solution to the equation 2(2x +1) + x = 8x +2-3x
I think u got right answer...