complex numbers
simplify.
\left(\sqrt{-5}+2\sqrt{20}\right)\left(-\sqrt{-5}\right)
Answer:
-5+ 20i
Step-by-step explanation:
just distribute: \((\sqrt{-5})(2\sqrt{20}+\sqrt{-5})\)---> \((2\sqrt{-100}) -5\) and because 100 is the perfect square of 10 you get -5+20i
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area of 130 square feet is 5,200 pounds when the plane is going at 150 miles per hour. Find the lifting force if the speed is 220 miles per hour. Round your answer to the nearest integer if necessary.
The lifting force if the speed is 220 miles per hour is F' = 708.53 N.
The force of light, or simply light, is the sum of all forces on an object that cause the object to move perpendicular to the direction of flow.
The most common type of lift is the wing lift. But there are many other common uses, such as propellers on airplanes and ships, rotors on helicopters, fan blades, sails on sailboats, and wind turbines.
We have,
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. It, means that,
\(F=kAv^{2}\)
Where
k is constant
If, A = 190 Ft², v = 220 mph, F = 950 pounds
Now, find k first from the above data. So,
\(k=\frac{F}{Av^{2} }\)
⇒ \(k=\frac{950}{190* (220)^2}\)
⇒ k = 0.0001033
It is required to find the lifting force on the wing if the plane slows down to 190 miles per hour.
Let F' is a new force. So,
F' = 0.0001033 × 190 × (190)²
⇒ F' = 708.53 pounds.
So, the lifting force is 708.53 pounds if the plane slows down to 190 miles per hour.
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Suppose J is between H and K. Use the Segment Addition Postulate to solve for x. Then find the length of each segment. If HJ=x+10 JK=9x KH=14x−58 a) Draw a sketch of the segments described above b) Write an equaation using the segment addition postulate that will help you solve the problem ___+ ___= c) combine like terms ( x terms on one side of the equal sign and numbers in the other side of the equal sign) ____ = ____ d) x= __ HJ= __ JK= __ HK= __
Answer:
x= 17
HJ= 27
JK= 153
HK= 180
Step-by-step explanation:
If HJ=x+10
JK=9x
KH=14x−58
a) The diagram of sketch of the segments described above is attached to this answer.
b) KH = HJ + JK
14x - 58 = (x + 10) + 9x
14x - 58 = x + 10 + 9x
c)
14x - 58 = x + 10 + 9x
14x - 58 = 10x + 10
Collect like terms
14x - 10x = 10 + 58
4x = 68
Divide both sides by 4
4x/4 = 68/4
x = 17
d)
x= 17
HJ= x + 10
= 17 + 10
= 27
Hence, HJ = 27
JK= 9x
= 9 × 17
= 153
Hence, JK = 153
HK=14x −58
HK = 14 × 17 - 58
= 238 - 58
= 180
Hence, HK = 180
At a customer service center, the call rate is believed to be 2 calls per minute, and governed by a Poisson process. (a) Find the probability the service center will receive more than 4 calls in a 1-minute period. (b) The service center opens at 8:00 am. Find the probability the first call is received between 8:01 and 8:02 am. (c) A service representative complains to her supervisor that they are receiving many more calls, on average, than 2 per minute. The supervisor designs a significance test (level 0.05) by counting the number of calls arriving during a 1-minute interval. If too many calls are received, she will reject the hypothesis of 2 calls per minute, on average. How many calls is too many? Regardless of the number of calls received, 20% of all calls are complaints, and the remaining 80% are requests for assistance. (d) If the center receives exactly 3 calls, find the probability that exactly 2 of them will be (e) Let X be the total number of calls received in a 5 minute period. Let Y be the number of complaints received in a 5 minute period. Construct the joint PMF of X and Y. If you choose to write the PMF as a table of values, complete the table only through X = 2 and Y = 2. (See below.) 0 1 N 3... X Y 0 1 2 3...
The probability that the service center will receive more than 4 calls in a 1-minute period is 0.2061. The probability that the first call is received between 8:01 and 8:02 am is approximately 0.2381.
(a) Let X be the number of calls in a 1-minute period. Then, X ~ Poisson(2). We need to find P(X > 4). Using the Poisson probability formula:
P(X > 4) = 1 - P(X ≤ 4) = 1 - ∑(k=0 to 4) e^(-2) * 2^k / k!
Calculating the sum, we get:
P(X > 4) = 1 - (e^(-2)*2^0/0! + e^(-2)*2^1/1! + e^(-2)*2^2/2! + e^(-2)*2^3/3! + e^(-2)*2^4/4!)
= 1 - (0.4060 + 0.2707 + 0.0902 + 0.0225 + 0.0045)
= 0.2061
Therefore, the probability that the service center will receive more than 4 calls in a 1-minute period is 0.2061.
(b) Let Y be the time (in minutes) between the opening of the center and the first call received. Then, Y ~ Exponential(2). We need to find P(1 < Y ≤ 2). Using the Exponential probability formula:
P(1 < Y ≤ 2) = ∫(1 to 2) 2e^(-2y) dy
Evaluating the integral, we get:
P(1 < Y ≤ 2) = e^(-2) - e^(-4) ≈ 0.2381
Therefore, the probability that the first call is received between 8:01 and 8:02 am is approximately 0.2381.
(c) Let X be the number of calls in a 1-minute period. We want to find the number of calls that is too many, such that if the center receives that many calls, the supervisor will reject the hypothesis of 2 calls per minute, on average, at a significance level of 0.05. This is equivalent to finding the critical value of X for a Poisson distribution with λ = 2 and a right-tailed test with α = 0.05. Using a Poisson distribution table or a calculator, we find that the critical value is 5.
Therefore, if the center receives 6 or more calls in a 1-minute period, the supervisor will reject the hypothesis of 2 calls per minute, on average, at a significance level of 0.05.
(d) Let X be the number of calls in a 1-minute period. We want to find P(2 out of 3 calls are complaints). Since each call is a complaint with probability 0.2 and a request for assistance with probability 0.8, the distribution of X is a Binomial(3, 0.2). Therefore:
P(2 out of 3 calls are complaints) = P(X = 2) = (3 choose 2) * 0.2^2 * 0.8^1 = 0.096
Therefore, the probability that exactly 2 out of 3 calls are complaints is 0.096.
(e) Let X be the total number of calls in a 5-minute period, and let Y be the number of complaints in a 5-minute period. Then, X ~ Poisson(10) and Y ~ Binomial(25, 0.2), since there are 25 independent 1-minute periods in a 5-minute period, and each call is a complaint with probability 0.2.
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Plzzz helppppppp meee
Answer:
-3
Step-by-step explanation:
H = -3
J = -1
J = -1
M=2
(-3+-1)+(-1+2)=-3
need help , if you can answer it pls do . thank you
Answer:
9
Step-by-step explanation:
14-5=9
therefore TV=9
hope this helped
bir basamaklı en küçük pozitif tam sayı
Answer:
Step-by-step explanation:
jjjjjjjj
The distance between (−1,−2) and (5,−2) is how many units?
Answer:
6 units right I believe
Step-by-step explanation:
HELP PLEASE 60 POINTS
Deshaun has a deck of 10 cards numbered 1 through 10. He is playing a game of chance.
This game is this: Deshaun chooses one card from the deck at random. He wins an amount of money equal to the value of the card if an even numbered card is drawn. He loses $3.50 if an odd numbered card is drawn.
A) Find the expected value of playing the game.
(b) What can Deshaun expect in the long run, after playing the game many times?
(He replaces the card in the deck each time.)
A. Deshaun can expect to gain money.
How much per draw?
B. Deshaun can expect to lose money.
How much per draw?
C. Deshaun can expect to break even (neither gain nor lose money).
Answer:
C
Step-by-step explanation:
I'm pretty sure if he does he can't gain nor.loose
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 907.46 square feet? Use 3.14 for π
Answer:
The number of feet away from the sprinkler where it could spread water would be the radius of the circle in which it is spraying.
The Area of a circle is
πr2=808.64
(3.14)r2=808.64
Divide both sides by 3.14
r2=257.5286624
Square root both sides to get radius
r=16 feet
7 feet away from the sprinkler can it spread water if the area formed by the watering pattern is 907.46 square feet
Area of circle:What information do we have?
Area of watering pattern = 907.46 square feet
Area of watering pattern = Area of circle
Area of watering pattern = πr²
907.46 = (3.14)r²
r² = 289
r = 17
Length = 17 feet
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What is the vertex of the function f(x) = x2 + 12x?
O (-6, -36)
O (-6,0)
O (60)
O (6,-36)
Answer:
es la tercera amiga yo pienso
The vertex of the function f(x) = x² + 12x is,
⇒ Vertex = (- 6, - 36)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = x² + 12x
Now, We can change the function into the form,
f (x) = (x - h)² + k
Where, (h, k) is vertex.
Here, The function is,
⇒ f (x) = x² + 12x
⇒ f (x) = x² + 12x + 36 - 36
⇒ f (x) = (x + 6)² - 36
⇒ f (x) = (x - (- 6))² + (- 36)
Hence, By comparing,
Vertex = (h, k) = (- 6, - 36)
Thus, The vertex of the function f(x) = x² + 12x is,
⇒ Vertex = (- 6, - 36)
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What determines where the graph will cross the x-axis?.
The graph will cross the x-axis if the multiplicity of the real root is odd.
What is polynomial?
In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Main body:
For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)
(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)
(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)
(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.
The graphs: (a) black, (b) red, (c) green
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please help, i need to know this answer!!
Answer:
It is d
Step-by-step explanation:
tep 1: –10 8x < 6x – 4step 2: –10 < –2x – 4step 3: –6 < –2xstep 4: ________what is the final step in solving the inequality –2(5 – 4x) < 6x – 4?x < –3 x > –3x < 3x > 3
The final step in solving the inequality -2(5 - 4x) < 6x - 4 is x > 3. This means that for the given The final step in solving the inequality -2(5 - 4x) < 6x - 4 is x > 3. This means that for the given inequality to hold true, the value of x must be greater than 3.
Let's go through the steps to solve the inequality:
Step 1: Distribute the -2 to the terms inside the parentheses: -2 * 5 + 2 * 4x < 6x - 4
Simplifying: -10 + 8x < 6x - 4
Step 2: Move the terms involving x to one side and the constant terms to the other side: -10 < 6x - 8x - 4
Simplifying: -10 < -2x - 4
Step 3: Combine like terms: -10 < -2x - 4
Step 4: To isolate x, we need to move the constant terms to the other side by adding 4 to both sides: -6 < -2x + 4
To solve for x, we divide both sides by -2, remembering to flip the inequality sign because we are dividing by a negative number: -6/-2 > -2x/-2 + 4/-2
Simplifying: 3 > x + 2
Finally, subtract 2 from both sides to isolate x: 3 - 2 > x + 2 - 2
Simplifying: 1 > x
Therefore, the final step in solving the inequality -2(5 - 4x) < 6x - 4 is x > 3.
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Theoretically, the standard error of the mean decreases as the sample size increases measures the variability of the sample mean from sample to sample is never larger than the standard deviation of the population All of the Above
Answer: All of the above
Step-by-step explanation:
The formula for the standard error of the mean is:
σM =σ/√N
where,
σM = standard error of the mean
σ = standard deviation of sample
√N = square of sample size
As the sample size of a population rises, it should be noted that the standard error of the mean will decrease. This is due to the fact that when there's an increase in sample size, there'll be cluster of the sample mean around the population mean.
Also, the the standard error of the mean measures the variability of the sample mean from sample to sample and is never larger than the standard deviation of the population.
Therefore, the answer will be "all or the above".
Caroline saved $3. 84 on a discounted item that was marked down 15% off of the
original price of the item. What was the original price of the item before the discount?
Caroline saved $3. 84 on a discounted item that was marked down 15% off of the original price of the item. What was the original price of the item before the discount, the original price of the item was $4.52 before the discount.
Let the original price of the item be $x. The item was marked down by 15%, so the discounted price is 85% of the original price. This is equivalent to saying that the discounted price is 100% - 15% of the original price. Mathematically, we can write this as: 0.85x = discounted price
Since Caroline saved $3.84 on the discounted item, we can write an equation that equates the amount she paid for the item to the discounted price minus the amount she saved. Mathematically, we can write this as:
0.85x - 3.84 = amount paid
Solving for x (the original price) requires us to rearrange the equation to isolate x. Mathematically, we can write this as:
x = (amount paid + 3.84) / 0.85
Substituting in the given values gives: x = ($0.00 + $3.84) / 0.85 = $4.52
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Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase.
Which models can be used to solve the problem?
Answer:
its C
Step-by-step explanation:
How would you solve for M in this equation?
E=\(\frac{1}{2}\)\(mv^{2}\)
Write the area A of an equilateral triangle as a function of the length s of its sides.
STEP 1: Find the base of the equilateral triangle in terms of s.
STEP 2: The height of an equilateral triangle can be found via the Pythagorean theorem. Use this information to find h in terms of s.
Write the area A of an equilateral triangle as a function of the length s of its sides. Draw the triangle; label each side "2s". Draw the altitute; it will bisect the base into s and s. ... Therefore, the area is equal to the measure of the bisected side times the measure of the altitude, quantity divided by 2.
HOPE SO IT HELPS YOU
Answer:
Step-by-step explanation:
Part A
Each side including the base is s.
Part B
Use 1/2 the base to find the height. The height meets the base at 90 degrees which gives you the right to use c^2 = b^2 + a^2
The hypotenuse is s
The base is 1/2s
h^2 = s^2 - (1/2s)^2
h^2 = s^2 - 1/4 s^2
h^2 = 3s^2/4
h = sqrt(3)/2 *s
Area = 1/2 * s * sqrt(3)/2 s
Area = 1/4 * s^2 * sqrt(3)
Which statement is correct for the graph of the specified function?
A) The rate of change for the linear function is 2.
B) The rate of change for the linear function is −1.
C) The maximum value of the quadratic function occurs at y = 4.
D) The minimum value of the quadratic function occurs at x = 4.
The correct statement regarding the function plotted in the graph is:
C) The maximum value of the quadratic function occurs at y = 4.
What is the rate of change of the linear function?When x = 0, y = -7, and when x = -5, y = 8, hence the rate of change(change in y divided by change in x) is given by:
R = [8 - (-7)]/-5 - 0 = 15/-5 = -3
What is the maximum value of the quadratic function?It is concave down, hence it has only a maximum value at y = 4 and not a minimum value, hence option C is correct.
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Una tienda ofrece descuentos en todos sus productos en el mismo porcentaje. Camila compró una silla de playa que costaba $26.970, pero pagó $21.576. Si además por un quitasol pagó $15.992. ¿Cuál era el precio original de este?
Answer:
Step-by-step explanation:
A store offers discounts on all its products at the same percentage. Camila bought a beach chair that cost $ 26,970, but paid $ 21,576. If he also paid $ 15,992 for a sunshade. What was the original price of this one?
Step 1
Find the percentage discount
% discount = Discount amount/ Original amount × 100
= $26,970 - $ 21,576/$26,970 × 100
= 0.2 × 100
= 20%
Onsider the provided information. Let the original price is p. Now it is given that we need to write an expression that the original price p of an item less a discount of 35%
Given :
Original price , P .
Discount given , 35 % .
To Find :
The final discounted price of the object .
Solution :
Let final price is x .
Now , x = p - (35% of p) .
\(x=p-\dfrac{35}{100}p\\\\x=0.65p\)
Therefore , final price of the object is 0.65p ,
Hence , this is the required solution .
Alicia envió cuatro correos electrónicos ayer. Si hoy envió el cuadrado de lo que mande ayer ¿cuantos correos envió durante dos días?
Alicia envió un total de 20 correos electrónicos durante dos días.
¿Cuántos correos envió Alicia en los últimos dos días?
En este problema tenemos conocimiento de que Alicia envió 4 correos electrónicos en el primer día y que al segundo día envió el cuadrado de la cantidad del día anterior. Este es un caso de serie geométrica.
En consecuencia, el total de correos electrónicos enviados por Alicia es la suma de correos enviados en aquellos dos días, es decir:
n = 4 + 4²
n = 4 + 16
n = 20
En consecuencia, Alicia envió un total de 20 correos electrónicos durante dos días.
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Three times a number is 4 more than twice the number
Answer:
3n = 2n + 4
Step-by-step explanation:
That is that as an equation.
Multiply (-6) (5.7)
show work please thanks
Answer:
-34.2
Step-by-step explanation:
5.7
x 6
___
34.2 (add negative sign cuz the bigger number is negative)
Please mark me brainliest If I help :)
5. A giraffe is twice as tall as its baby. The baby's height and the mother's height total 4.5m. How tall is the baby? How tall is the mother?
Answer:
Step-by-step explanation:
call x the mother deer, y the baby deer, we have x = 2y
x + y = 4,5 ---> x = 3, y = 3/2
Answer:
2.25
Step-by-step explanation:
4.5 / 2
Solve using substitution
Answer:
The answer should be "No Solution" as these lines never meet each other
Please help
4) -2 - p= -4 -42p+3)
Answer:
p = 1/41
Step-by-step explanation:
- 2 - p = - 4 - 42p + 3- p + 42p = - 4 + 3 + 241p = 1p = 1/41Mrs. Watson wants to buy some dresses for her trip to Houston. There are three boutiques, each offering a different deal.
Lara's Boutique 2 dresses for $32
The Dress Shop 6 dresses for $90
Marge's Dresses 8 dresses for $160
Which boutique has the best deal for dresses?
Answer
Dude my name is Lara and my fourth grade teacher was mrs. Watson..... but the dress shop is the answer.... guess my boutique just wasn’t it huh:
Step-by-step explanation:
plz solve this!!!!!!
Answer:
where is the question?......