Answers
Answer:
[tex]\displaystyle A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta[/tex]
Step-by-step explanation:
The shaded area is the area of the curve bounded by θ = π and θ = 7π/6.* A differential of area in polar coordinates is ...
dA = (1/2)r^2·dθ
So, the shaded area is ...
[tex]\displaystyle\boxed{A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta}[/tex]
_____
* We found these bounds by trial and error using a graphing calculator to plot portions of the curve.
Related Questions
For this year's fundraiser, students at a certain school who sell at least 75 magazine subscriptions win a prize. If the fourth grade students at this school sell an average (arithmetic mean) of 47 subscriptions per student, the sales are normally distributed, and have a standard deviation of 14, then approximately what percent of the fourth grade students receive a prize
Answers
Answer:
The percentage is k = 2.3%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the percent of the fourth grade students receive a prize is mathematically represented as
[tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]
[tex]P(X > 75) = P(Z > 2)[/tex]
From the standardized normal distribution table
[tex]P(Z > 2) =0.023[/tex]
=> [tex]P(X > 75) = 0.023[/tex]
The percentage of the fourth grade students receive a prize is
k = 0.023 * 100
k = 2.3%
If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or Ace
Answers
Answer:
[tex]P(A\ or\ H) = \frac{4}{13}[/tex]
Step-by-step explanation:
Given
Number of Cards = 52
Required
Determine the probability of picking a heart or ace
Represent Ace with Ace and Heart = H
In a standard pack of cards; there are
[tex]n(A) = 4[/tex]
[tex]n(H) = 13[/tex]
[tex]n(A\ and\ H) = 1[/tex]
[tex]Total = 52[/tex]
Because the events are non mutually exclusive
[tex]P(A\ or\ H) = P(A) + P(H) - P(A\ and\ H)[/tex]
Where
[tex]P(A) = \frac{n(A)}{Total} = \frac{4}{52}[/tex]
[tex]P(H) = \frac{n(H)}{Total} = \frac{13}{52}[/tex]
[tex]P(A\ and\ H) = \frac{n(A\ and\ H)}{Total} = \frac{1}{52}[/tex]
Substitute these values in the above formula
[tex]P(A\ or\ H) = P(A) + P(H) - P(A\ and\ H)[/tex]
[tex]P(A\ or\ H) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]
Take LCM
[tex]P(A\ or\ H) = \frac{4 + 13 - 1}{52}[/tex]
[tex]P(A\ or\ H) = \frac{16}{52}[/tex]
Reduce fraction to lowest term
[tex]P(A\ or\ H) = \frac{4}{13}[/tex]
Hence, probability of a heart or ace is 4/13
Suppose a triangle has two sides of length 33 amd 37, and that the angle between these two sides is 120°. What is the length of the third side of the triangle
Answers
Answer:
c = 60.65 cm
Step-by-step explanation:
Given that,
The two sides of a triangle are 33 cm and 37 cm.
The angle between these two sides is 120°.
We need to find the length of the third side of the triangle. Let c is the third side. Using cosine rule,
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
a = 33 cm, b = 37 cm and C is 120°
So,
[tex]c^2=(33)^2+(37)^2-2\times 33\times 37\cos (120)\\\\c=60.65\ cm[/tex]
So, the length of the third side of the triangle is 60.65 cm.
what are the next terms in the number pattern -11, -8, -5, -2, 1
Answers
Answer:
4, 7, 10, 13
Step-by-step explanation:
Hey there!
Well in the given pattern,
-11, -8, -5, -2, 1
we can conclude that the pattern is +3 every time.
-11 + 3 = -8
-8 + 3 = -5
-5 + 3 = -2
-2 + 3 = 1
And so on
4, 7, 10, 13Hope this helps :)
f(x) = -3x + 7
What is f (0)?
Answers
f(0) = 7
Answer:
f(0) = 7
Step-by-step explanation:
f(x) = -3x + 7
Let x =0
f(0) = -3*0 + 7
f(0) = 7
Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?
Answers
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = [tex]\$(\dfrac{300}x)[/tex]
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]
Profit on each book= $1.50
Profit = selling price - cost price
[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]
[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]
Number of books cannot be negative.
So, there are 75 books.
Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]
So price of each book = $4.
find the total area of the prism
Answers
Answer:
63.5
Step-by-step explanation:
How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns 6% interest compounded monthly. (could anyone do this whole problem out?
Answers
Answer:
$3,717
Step-by-step explanation:
Hello, in 1 year there are 12 months.
Let's note I the Initial amount.
So, after 1 month we will get the following, because we compute the interest amount for one month only.
I * ( 1 + 6% * (1/12) )
And the next month, we will have interest of the amount available from previous month so it gives
[tex]I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2[/tex]
... and after n months ...
[tex]I*(1.005)^n[/tex]
8 years is 8*12 = 96 months. so we are looking for I such that
[tex]I*(1.005)^{96}=6000\\\\<=> I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}[/tex]
Thank you.
musah stands at the center of a rectangular field . He first takes 50 steps north, then 25 step west and finally 50 steps on a bearing of 315°. How far west and how far north is Musah final point from the center?
Answers
Answer:
85.36 far north from the center
10.36 far east from the center
Step-by-step explanation:
The extra direction taken in the north side is x
X/sin(360-315)=50/sin 90
Sin 90= 1
X/sin 45= 50
X= sin45 *50
X= 0.7071*50
X= 35.355 steps
X= 35.36
Then the west direction traveled
West =√(50² - 35.355²)
West = √(2500-1249.6225)
West= √1250.3775
West= 35.36 steps
But this was taken in an opposite west direction
From the center
He is 35.36 +50
= 85.36 far north from the center
And
25-35.36=-10.36
10.36 far east from the center
I need help please help me!
Answers
Answer:
36ft³
Step-by-step explanation:
Bottom rectangular prism: 2x2x6=24
Top rectangular prism: 2x2x3=12
24+12=36ft³
Answer:
[tex]\boxed{36ft^3}[/tex]
Step-by-step explanation:
Hey there!
Well to solve for V we need to find the volume of the 2 rectangular prism's given.
Rec#1: 2•3•2 = 12
Rec#2: 6•2•2 = 24
Rec#1 + Rec#2 = V
12 + 24 = 36ft³
Hope this helps :)
A buoy floating in the sea is bobbing in simple harmonic motion with amplitude 13 in and period 0.25 seconds. Its displacement d from sea level at time t=0 seconds is 0in, and initially it moves downward. (Note that downward is the negative direction.)Required:Give the equation modeling the displacement d as a function of time t.
Answers
Answer:
The equation is [tex]x(t) = -13 cos (8 \pi t )[/tex]
Step-by-step explanation:
From the question we are told that
The amplitude is [tex]A = 13 \ in[/tex]
The period is [tex]T = 0.25[/tex]
Generally the displacement function for a simple harmonic motion is mathematically represented as
[tex]x(t) = A cos (wt )[/tex]
Here [tex]w[/tex] is the angular frequency which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 \pi }{ 0.25}[/tex]
[tex]w = 8\pi[/tex]
Given that at t = 0 the displacement is equal to 0 it means that there is no phase shift and also we are told that it is initially moving downward which implies that its Amplitude is [tex]A = -13\ in[/tex]
So the equation modeling the displacement d as a function of time t is mathematically represented as
[tex]x(t) = -13 cos (8 \pi t )[/tex]
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x+12=48,where x represents the cost of a. Ticket.how much is one ticket
Answers
Answer:
x=9; one ticket is $9
Step-by-step explanation:
4x+12=48
4x=48-12
4x=36
x=36/4
x=9
In the multiplication below, each of A, B and
C represents a different digit. What is ABC?
A B C
X
3
В В В
Answers
Answer:
ABC = 148, 3*148 = 444
Step-by-step explanation:
We know that 111 = 3* 37, so all numbers of the form BBB has the factor 37.
So we need a multiple of 37 such thant when multiplied, we get three digits the same as the middle digit.
Try 4*37 = 148, 148*3 = 444, bingo, we got the right combination.
So ABC is 148.
We want to model the daily movement of a particular stock (say Amazon, ticker = AMZN) using a homogeneous markov-chain. Suppose at the close of the market each day, the stock can end up higher or lower than the previous day’s close. Assume that if the stock closes higher on a day, the probability that it closes higher the next day is .65. If the stock closes lower on a day, the probability that it closes higher the next day is .45.
(a) What is the 1-step transition matrix? (Let 1 = higher, 2 = lower)
(b) On Monday, the stock closed higher. What is the probability that it will close higher on Thursday (three days later)
Answers
Answer:
See the explanation and attached images for the answers.
Step-by-step explanation:
a) 1-step transition matrix:
See the attached image for transition matrix.
Let the matrix be M
if the stock closes higher on a day, the probability that it closes higher the next day is 0.65.
If the stock closes lower on a day, the probability that it closes higher the next day is 0.45
if the stock closes higher on a day, the probability that it closes lower the next day is 1 - 0.65 = 0.35
if the stock closes lower on a day, the probability that it closes lower the next day is 1 - 0.45 =0.55
b)
To compute probability for 3 days later multiply matrix M (from part a) thrice i.e. M*M *M
[tex]M^{3} = \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.65 * 0.65 + 0.35 * 0.45 &0.65 * 0.35 + 0.35 * 0.55 \\0.45 * 0.65 + 0.55 * 0.45 &0.45 * 0.35 + 0.55 * 0.55 \end{array}\right] * \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.58&0.42\\0.54&0.46\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc} 0.58 * 0.65 + 0.42 x 0.45&0.58 * 0.35 + 0.42 * 0.55 \\0.54 * 0.65 + 0.46 * 0.45 &0.54 * 0.35 + 0.46 * 0.55 \end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.566&0.434\\0.558&0.442\end{array}\right][/tex]
The probability that it will close higher on Thursday is 0.566. See the transmission matrix of M³ for higher-higher. This can be interpreted as:
if the stock closed higher on Monday, the probability that it closes higher the on Thursday (three days later) is 0.566
Which polynomial represents the sum below?
Answers
Answer:
The sum is represented by the polynomial:
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
Step-by-step explanation:
Recall that polynomials are added by combining like terms. The only like terms in this addition are: 5 x and 8 x which added render: 13 x. therefore, the addition of these polynomials renders;
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
A hunter shot 7 ducks. The hunter's dog recovered 5/7 of the ducks. How many ducks were recover
Answers
Answer:
5
Step-by-step explanation:
Just multiply 5/7 by 7 since his dog retrieved 5/7 out of the 7 ducks he shot.
Answer:
5
Step-by-step explanation:
7*5/7
7 represents the # of ducks
5/7 represents the # of ducks that were recovered
The question asks the number of ducks that were recovered so you should multiply the total # of ducks there are by the fraction that were recovered.
If the average fixed cost (AFC) of producing 5 bags of rice is $20.00, the average fixed cost of producing 10 bags will be
Answers
Answer:$40.00
Step-by-step explanation:first divide 20 by 5 and the answer will be 4. now multiply 10 into 4 and you'll get the answer $40.00
What faction of a day is 5hrs 20 mine
Answers
Answer:
16/3 hours 5 1/3
Step-by-step explanation:
Answer: 5 1/3
Step-by-step explanation:
Yiadom is y
years now.
What would be
his age in the next ten
years.
Answers
Answer:
(y+10 ) years
Step-by-step explanation:
If Yiadom is y years now.
Then after 10 years, his anew age will be = (y+10) yrs
Y * 3 = 81 please i need it for today
Answers
Answer:
Y = 27
Step-by-step explanation:
Y * 3 = 81
Divide each side by 3
Y * 3/3 = 81/3
Y = 27
Help please I need help as soon as possible!all answers are appreciated! Keisha tried to evaluate an expression step by step. 3+(−4)−7
Answers
Answer:
D no mistakes
Step-by-step explanation:
3+(-4)-7 is equal to 3-4-7=-8
Answer:0
Step-by-step explanation:
3+(-4)-7 when there are parenthesis around a negative number you flip it to positive and then 4+3-7=0
A certain animal's body temperature has a mean of F and a standard deviation of F. Convert the given temperatures to z scores.
Answers
A certain animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.
a. 93.52 °F b. 95.22 °F c. 94.72 °F
Answer:
a. z = - 2.1053
b. z = 0.87719
c. z = 0
Step-by-step explanation:
Given that :
The population mean μ = 94.72
The standard deviation σ = 0.57
the formula for calculating the standard normal z score, which can be represented as:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
For a.
The sample mean [tex]\bar x[/tex] = 93.52
The z score can be computed as follows:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{-1.2}{0.57}[/tex]
z = - 2.1053
For b.
The sample mean [tex]\bar x[/tex] = 95.22
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0.5}{0.57}[/tex]
z = 0.87719
For c.
The sample mean [tex]\bar x[/tex] = 94.72
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0}{0.57}[/tex]
z = 0
Stepwise regression is a variable screening method, not a model building method.
A. True
B. False
Answers
Answer:
A. True
Step-by-step explanation:
Stepwise regression is a variable-selection method for independent variables.
Stepwise regression helps us to recognize and choose the most handy descriptive variables from a list of several reasonable independent variables.
It entails a series of steps that is drafted to locate the most handy X-variable to incorporate in a regression model. During each step of the course of action or method, each X - variable is estimated by applying a set criterion to determine if it is meant to exist in the model.
The basis for selection can be choosing a variable which satisfies the stipulated criterion or removing a variable that least satisfies the criterion. A typical illustration of such criterion is the t value.
Evaluate the polynomial when x = 3 and y = - 8
x2 + y2 + xy
Answers
Work Shown:
Replace x with 3, replace y with -8. Use order of operations PEMDAS to simplify.
x^2 + y^2 + x*y
3^2 + (-8)^2 + 3*(-8)
9 + 64 - 24
73 - 24
49
Answer:
49
Step-by-step explanation:
We are given the polynomial:
[tex]x^2+y^2+xy[/tex]
We want to evaluate when x=3 and y= -8. Therefore, we must substitute 3 for each x and -8 for each y.
[tex](3)^2+(-8)^2+(3*-8)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Solve the parentheses first. Multiply 3 and -9.
3*-8=-24
[tex](3)^2+(-8)^2 + -24[/tex]
[tex](3)^2+(-8)^2-24[/tex]
Now, solve the exponents.
3^2= 3*3 =9
[tex]9+ (-8)^2 -24[/tex]
-8^2= -8*-8= 64
[tex]9+64-24[/tex]
Add 9 and 64
[tex]73-24[/tex]
Subtract 24 from 73
[tex]49[/tex]
The polynomial evaluated for x=3 and y= -8 is 49.
6(x + 2) = 30Solve the following linear equation
Answers
Answer:
[tex]\huge \boxed{x=3}[/tex]
Step-by-step explanation:
[tex]6(x+2)=30[/tex]
[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]
[tex]x+2=5[/tex]
[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]
[tex]x=3[/tex]
Answer:
3
Step-by-step explanation:
30 = 6(x+2)
30/6 = 5
5 = x+2
5-2 = 3
3=x
This is a pretty simple question and I tried to make it as simple as possible when explaining it.
If 2 = 5, what is 2 3 − 4?
Answers
Answer:
27.5
Step-by-step explanation:
3 = 7.5
4 = 10
5*7.5=37.5-10=27.5
Seriously. 2=5 contradicts.
(5)3-4
5(3)=15
15-4=11
Name one real-world object that suggests A. Points B. Lines and C. Planes
Answers
There are many examples to pick from, one is
point = location on map
line = straight road between two locations (aka two points)
plane = flat ground (the ground cannot have any hills or valleys)
First, let's write some useful definitions:
Point: it is an entity that has a location in a given space or plane, and do not have any surface nor measure.
Line: if we have two points, we can define a line as a straight, infinite ray that connects them. Still does not have a surface
Plane: We can define a plane as a line and a point outside of it, here appears the concept of the surface.
So, the easier one is a plane, a sheet of paper could be a good representation of a plane. And in the same way that a sheet of paper can bend in different ways, also do the planes.
For the line, we could use a really straight wire.
Finally, the point, which is the hardest one to describe (notice that we used points to describe the other two, lines, and planes) so here we could choose something small, that has near to no surface and that also has a location in the space. An example of this could be an electron or any other elemental particle.
If you want to learn more, you can read:
https://brainly.com/question/17213603
simplify the expression 10 divided by 5 times 3
Answers
Answer:
= 2/3
Step-by-step explanation:
10 / (5*3)
= 10/15
= 2/3
Determine the value(s) for which the rational expression 2x^2/6x is undefined. If there's more than one value, list them separated by a comma, e.g. x=2,3.
Answers
Answer:
0
Step-by-step explanation:
Hello, dividing by 0 is not defined. so
[tex]\dfrac{2x^2}{6x}[/tex]
is defined for x different from 0
This being said, we can simplify by 2x
[tex]\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x[/tex]
and this last expression is defined for any real number x.
Thank you
A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answers
Answer:
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]Sections = 10[/tex]
[tex]n(Gray) = 5[/tex]
[tex]n(Blue) = 5[/tex]
Required
Determine P(Gray and Blue)
Using probability formula;
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
Calculating P(Gray)
[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]
[tex]P(Gray) = \frac{5}{10}[/tex]
[tex]P(Gray) = \frac{1}{2}[/tex]
Calculating P(Gray)
[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]
[tex]P(Blue) = \frac{5}{10}[/tex]
[tex]P(Blue) = \frac{1}{2}[/tex]
Substitute these values on the given formula
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
