Answer:
(a) Increasing:[tex]\frac{\pi}{2}< x< \frac{3\pi}{2}[/tex] and Decreasing:[tex]0< x< \frac{\pi}{2}\ \text{or}\ \frac{3\pi}{2}< x< 2\pi[/tex]
(b) The local minimum and maximum values are -16 and 16 respectively.
(c) The inflection points are [tex](\frac{\pi}{6},\ -2)\ \text{and}\ (\frac{5\pi}{6},\ -2)[/tex]
Step-by-step explanation:
The function provided is:
[tex]f(x)=8cos^{2}(x)-16sin( x);\ 0\leq x\leq 2\pi[/tex]
(a)
[tex]f(x)=8cos^{2}(x)-16sin( x);\ 0\leq x\leq 2\pi[/tex]
Then, [tex]f'(x)=-16cos(x)sin(x)-16cos(x)=-16cos(x)[1+sin(x)][/tex]
Note, [tex]1+sin(x)\geq 0\ \text{and }\ sin(x)\geq 1\\[/tex]
Then, [tex]sin(x)=-1\Rightarrow x=\frac{3\pi}{2}[/tex] for [tex]0\leq x\leq 2\pi[/tex].
Also [tex]cos(x)=0[/tex].
Thus, f (x) is increasing for,
[tex]f'(x)>0\\\Rightarrow cos(x)<0\\\Rightarrow \frac{\pi}{2}< x< \frac{3\pi}{2}[/tex]
And f (x) is decreasing for,
[tex]f'(x)<0\\\Rightarrow cos(x)>0\\\Rightarrow 0< x< \frac{\pi}{2}\ \text{or}\ \frac{3\pi}{2}< x< 2\pi[/tex]
(b)
From part (a) f (x) changes from decreasing to increasing at [tex]x=\frac{\pi}{2}[/tex] and from increasing to decreasing at [tex]x=\frac{3\pi}{2}[/tex].
The local minimum value is:
[tex]f(\frac{\pi}{2})=8cos^{2}(\frac{\pi}{2})-16sin(\frac{\pi}{2})=-16[/tex]
The local maximum value is:
[tex]f(\frac{3\pi}{2})=8cos^{2}(\frac{3\pi}{2})-16sin(\frac{3\pi}{2})=16[/tex]
(c)
Compute the value of f'' (x) as follows:
[tex]f''(x)=16sin(x)[1+sin(x)]-16cos^{2}(x)\\\\=16sin(x)+16sin^{2}(x)-16[1-sin^{2}(x)]\\\\=32sin^{2}(x)+16sin(x)-16\\\\=16[2sin(x)-1][sin (x)+1][/tex]
So,
[tex]f''(x)>0\\\Rightarrow sin(x)>\frac{1}{2}\\\Rightarrow \frac{\pi}{6}<x<\frac{5\pi}{6}[/tex]
And,
[tex]f''(x)<0\\\\\Rightarrow sin(x)<\frac{1}{2}\ \text{and}\ sin (x)\neq -1\\\\\Rightarrow 0<x<\frac{\pi}{6}\ \text{or} \frac{5\pi}{6}<x<\frac{3\pi}{2}\ \text{or}\ \frac{3\pi}{2}<x<2\pi[/tex]
Thus, f (x) is concave upward on [tex](\frac{\pi}{6},\ \frac{5\pi}{6})[/tex] and concave downward on [tex](0,\ \frac{\pi}{6}), (\frac{5\pi}{6},\ \frac{3\pi}{2})\ \text{and}\ (\frac{3\pi}{2},\ 2\pi)[/tex].
If [tex]x=\frac{\pi}{6}[/tex], then f (x) will be:
[tex]f(\frac{\pi}{6})=8cos^{2}(\frac{\pi}{6})-16sin(\frac{\pi}{6})=-2[/tex]
If [tex]x=\frac{5\pi}{6}[/tex], then f (x) will be:
[tex]f(\frac{5\pi}{6})=8cos^{2}(\frac{5\pi}{6})-16sin(\frac{5\pi}{6})=-2[/tex]
The inflection points are [tex](\frac{\pi}{6},\ -2)\ \text{and}\ (\frac{5\pi}{6},\ -2)[/tex].
No clue how to graph this any help would be greatly appreciated
Answer:
First, you can graph the y-intercept. The y-intercept would be (0,3) or in your equation, the number 3. Next, you could create a table by substituting values for x such as 1, 2, 3, or 4. This will give you easy numbers to graph. Instead of creating a table, perhaps you want to graph this by plotting the slope. Since the slope is 3/2, is means that it is going up, because the number is positive. An easy way to start would be starting at your y-intercept, (0,3), you could go two to the right and three up. That is a point. Then you could go the way down; two to the left and three down. Finally, you can draw a line connecting the points together.
I hope this helped you! Have a great rest of your day!
For the rational function f(x)=x-2/3x^2+x-2, solve f(x)=2
Answer:
When f(x) = 2, x = 1/2, -2/3
Step-by-step explanation:
Step 1: Set equation equal to 2
[tex]2 = \frac{x-2}{3x^2 +x -2}[/tex]
Step 2: Multiply both sides by denominator
2(3x² + x - 2) = x - 2
Step 3: Distribute
6x² + 2x - 4 = x - 2
Step 4: Isolate everything to one side
6x² + x - 2 = 0
Step 5: Factor
(2x - 1)(3x + 2) = 0
Step 6: Find roots
x = 1/2, -2/3
Given h(x)=5x-5, find h(2)
Answer:
5
Step-by-step explanation:
h(2)=5(2)-5
5 x 2 = 10
10 - 5 = 5
The value of the function h(x) = 5x - 5 at x = 2 will be 5.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The function is given below.
h(x) = 5x - 5
Then the value of the function at x = 2 will be
h(2) = 5 (2) - 5
h(2) = 10 - 5
h(2) = 5
The value of the function h(x) = 5x - 5 at x = 2 will be 5.
More about the value of expression link is given below.
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A car travels an average speed of 45km per hour. What distance does it cover in 12 hours?
Answer:
540 kilometers
Step-by-step explanation:
The car travels 45 kilometers every 1 hour.
In 12 hours, 45 × 12 = 540
The car will have covered a distance of 540 kilometers.
If car travels an average speed of 45km per hour, the car covers a distance of 540 kilometers in 12 hours.
To calculate the distance covered by the car in 12 hours, we can use the formula:
Distance = Speed × Time
Given that the average speed of the car is 45 km per hour and it travels for 12 hours, we can plug these values into the formula:
Distance = 45 km/h × 12 hours
Distance = 540 km
The formula for calculating distance is straightforward: it multiplies the speed (rate of motion) by the time taken. In this case, the car travels at a constant speed of 45 km/h, which means it covers 45 kilometers every hour.
By traveling for 12 hours, it accumulates a total distance of 540 kilometers. This calculation is useful for determining how far an object, in this case, a car, will travel given its speed and the duration of its journey.
To learn more about distance/speed click on,
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Point is the center of this circle. What is m< BCA?
Answer:
62°
Step-by-step explanation:
∠BOA is the supplement to the angle marked 56°, so is 124°. ∠BCA is an inscribed angle subtending the same arc (AB), so has half the measure of the arc.
m∠BCA = (1/2)(124°)
m∠BCA = 62°
Find the distance between the points B and B′ if ΔABC is reflected across line l followed by a reflection across line m.
A.)10 units
B.)14 units
C.)7 units
D.)17 units
Answer:
¿Consideras que la gente que discrimina por aspectos como el color de la piel, clase social, por el género, etc., no saben lo que las personas valen y por eso no las valoran?
Answer:
14 units
Step-by-step explanation:
If l and m are two parallel lines and a point X is reflected across line l followed by a reflection across line m, then the distance between
X and X′ is 2d, where d is the distance between l and m. Since d = 7, the distance between B and B′′ is 2(7) = 14 units.
A circle has been dissected into 16 congruent sectors. The base of one sector is 1.17 units, and its height is 2.94 units. Using the area of a triangle formula, what is the approximate area of the circle?
Answer:
The approximate area of the circle is 27.5184∧2
Step-by-step explanation:
In order to calculate the approximate area of the circle we would have to calculate the following formula:
approximate area of the circle=approximate area of one triangle*number of congruent sectors
number of congruent sectors=16
approximate area of one triangle=1/2*base*height
base=1.17 units
height=2.94 units
Therefore, approximate area of one triangle=1/2*1.17*2.94
approximate area of one triangle=1.7199 units∧2
Therefore, approximate area of the circle=1.7199 units∧2*16
approximate area of the circle=27.5184∧2
Answer:
27.52 rounded to the nearest 10th
Step-by-step explanation:
est the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Upper H 0 : p equals 0.89 versus Upper H 1 : p not equals 0.89 n equals 500 comma x equals 430 comma alpha equals 0.01 Is np 0 (1 minus p 0 )greater than or equals 10? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. No, because np 0 (1 minus p 0 )equals nothing. B. Yes, because np 0 (1 minus p 0 )equals 48.95. Your answer is not correct. Now find ModifyingAbove p with caret.
Answer:
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population proportion significantly differs from 0.89.
The requirements for the test are satisfief.
n(1-p)=70>10
Step-by-step explanation:
This is a hypothesis test for a proportion.
There are 3 requirements to have a valid test of proportion: random sample, independence and normal.
For the first two (random and independent sample) we don't have details, but we assume the sampling has been random.
The latter can be verified by calculating np and n(1-p):
[tex]np=430>10\\\\n(1-p)=70>10[/tex]
Both are bigger than 10, so the normal approximation can be considered appropiate.
The claim is that the population proportion significantly differs from 0.89.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.89\\\\H_a:\pi\neq 0.89[/tex]
The significance level is 0.01.
The sample has a size n=500.
The sample proportion is p=0.86.
[tex]p=X/n=430/500=0.86[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.89*0.11}{500}}\\\\\\ \sigma_p=\sqrt{0.000196}=0.014[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.86-0.89+0.5/500}{0.014}=\dfrac{-0.029}{0.014}=-2.072[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z<-2.072)=0.038[/tex]
As the P-value (0.038) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population proportion significantly differs from 0.89.
The following table shows the number of medals won in the 2008 Olympics for swimming by the top five countries. Country Number of Medals USA 31 Australia 20 Great Britain 6 China 6 France 6 How many degrees will the USA section be in a circle graph? 31° 45° 162° 184°
Answer:
Of the total 31 + 20 + 6 + 6 + 6 = 69 medals, the USA won 31 of them. 31/69 as a percentage is about 45%. Since there are 360° in a full circle, 45% of that is 0.45 * 360 = 162°.
Answer:
How many degrees will the USA section be in a circle graph?
31°
162°
45°
184°
Step-by-step explanation:
162° THIS ONE IS RIGHT
PLEASE GIVE ME A Brainiest PLEASE AND THX
HOPE IT HELP
If P and Q are two sets such that P U Q has 40 elements,P has 22 elements and Q has 28 elements,how many elements does P intersection Q have
Answer:
[tex]\boxed{10 elements}[/tex]
Step-by-step explanation:
[tex]n(P) = 22[/tex]
[tex]n(Q) = 28\\[/tex]
n(P∪Q) = 40
Using Formula
n(P∪Q)=n(P)+n(Q)−n(P∩Q)
For, n(P∩Q), it becomes
=> n(P∩Q)=n(P)+n(Q)−n(P∪Q)
So,
=> n(P∩Q) = 22+28-40
=> n(P∩Q) = 50-40
=> n(P∩Q) = 10 elements
HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
X^2 3*3=9
X^2 2*2=4
Hope this helps. I've done something like this before. (: Good luck
Answer:
B: x^2-9/x^2-4
Step-by-step explanation:
numerator:
(x+3)(x-3) = x^2-3x+3x-9 = x^2 - 9
denominator:
(x+2)(x-2) = x^2-2x+2x-4 = x^2 - 4
final answer:
x^2-9 /x^2-4
Solve each equation.
13x+9] = 30
12x+ 1 = -13
|X+2+4= 11
x = 5
x = 7
O x = 1, -19
no solution
0 x = -7
no solution
o
no solution
O x=-14, 12
Ox=5,-9
OX= 7, -11
O x = 7, -13
O x= -7,6
DONE
DONE
DONEM
Answer:
13x+9=30
13x=30+9
13x=39
divide both sides by 13
x=3
12x+1=-13
12x=-13-1
12x=-14
divide both sides by 12
x=7/6
x+2+4=11
x+6=11
x=11_6
x=5
The solution {x} for each function is -
{x} = 21/13{x} = -7/6{x} = 5What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is to solve each of the functions given.
.
{ 1 } -
13x + 9 = 30
13x = 21
{x} = 21/13
{ 2 } -
12x + 1 = - 13
12x = - 14
x = -14/12
{x} = -7/6
{ 3 } -
x + 2 + 4= 11
x = 11 - 2 - 4
{x} = 5
Therefore, the solution {x} for each function is -
{x} = 21/13{x} = -7/6{x} = 5To solve more questions on functions, visit the link below-
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To dilute a solution that is 40% saline, a chemist combines it with a solution that is 15% saline. How much of each solution should she use if she needs 150 mL of a solution that is 25% saline? Hint: solve by using system of equations
Answer:
60 ml of 40% saline and 90 ml of 15% saline
Step-by-step explanation:
We can call the amount of 40% solution x and the amount of 15% solution y.
x + y = 150 -- (1)
0.40x + 0.15y = 150 * 0.25 -- (2) --- 150 * 0.25 = 37.5
40x + 15y = 3750 (Multiply (2) by 100 to get rid of decimals)
15x + 15y = 2250 -- (3) (Multiply (1) by 15)
25x = 1500 (Subtract (3) from (1)
x = 60
y = 150 - 60 = 90
Answer:
[tex] 37.5= 0.4 x +0.15 y[/tex]
We can solve for x and we got:
[tex] x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]
And replacing into the water condition we have:
[tex] 112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]
Solving for y we got:
[tex] 112.5= 56.25 -0.225 y+0.85 y[/tex]
[tex] y = \frac{112.5-56.25}{0.625}= 90[/tex]
And then solving for x we got:
[tex] x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]
So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution
Step-by-step explanation:
We can solve this problem with the following system of equations:
[tex] 150*0.25 = x*0.4 + y *0.15[/tex] salt
[tex] 150*(1-0.25)= x(1-0.4) +y(1-0.15)[/tex] water
With x the ml of solution for 40% concentration and y the ml of solution at 15% of concentration
From the salt condition we have:
[tex] 37.5= 0.4 x +0.15 y[/tex]
We can solve for x and we got:
[tex] x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]
And replacing into the water condition we have:
[tex] 112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]
Solving for y we got:
[tex] 112.5= 56.25 -0.225 y+0.85 y[/tex]
[tex] y = \frac{112.5-56.25}{0.625}= 90[/tex]
And then solving for x we got:
[tex] x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]
So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution
Victor always runs out of money by the end of the month, so he wants to start keeping a budget. Last month, he spent a total of $176.47 on groceries, $78.66 for phone, and $62.37 on gas. Estimate his monthly total for groceries, phone, and gas by first rounding to the nearest $10.
Answer:
Yearly budget= $3840
Monthly budget= $320
Step-by-step explanation:
His budget will be calculated first by rounding off to the nearest$10 all his monthly spending.
For groceries= $176.47
Round off=$ 180.00
For phone =$ 78.66
Round off = $80.00
For gas = $62.37
Round off= $60.00
His total round off = $180+$80+$60
His total round off = $320
Before the round off, his total spending was $176.47+$78.66+$62.37
= $317.5
So his monthly budget should be $320
And yearly budget =$ 320*12
Yearly budget= $3840
Express 2x+1/(x-2)(x²+1) as a partial fraction
Answer:
2x+1/(x-2)(x²+1)= 1/(x-2) + (-2x )/(x²+1)
Step-by-step explanation:
2x+1/(x-2)(x²+1) = a/(x-2) + (bx+c)/(x²+1)
Multiplying with the denominators
2x+1= a(x²+1) +( bx+c)(x-2)
Let x = 2
2(2) + 1 = a(2² + 1) + 0
5 = a5
a = 1
Then let's expand the brackets
2x +1= ax² + a + bx² -2bx + cx - 2c
Comparing co-efficients
ax² + bx² = 0
a + b = 0 equation 1
a -2c = 1 equation 2
-2bx + cx = 2x
-2b + c = 2 equation 3
Let's remember a= 1
a + b = 0
1 + b= 0
b = -1
a -2c = 1
1 - 2c = 1
c= 0
-2b + c = 2
-2(-1) + 0 = 2
2= 2. Verified.
a/(x-2) + (bx+c)/(x²+1)
= 1/(x-2) + (-2x )/(x²+1)
2x+1/(x-2)(x²+1)= 1/(x-2) + (-2x )/(x²+1)
Neil places £2000 in a bank account that pays 1.5% simple interest per year.How much interest will he earn in 6 years?
Answer:
£ 180Solution,
Principal( P)= £ 2000
Rate (R)= 1.5%= 1.5/100
Time (t)= 6 years
Interest=?
Now,
[tex]interest = principal \times rate \times time \\ \: \: \: \: = 2000 \times \frac{1.5}{100} \times 6 \\ \: \: = 180[/tex]
Therefore, he will earn £ 180 in 6 years.
Hope this helps..
Good luck on your assignment..
PLEASE HELP!!
What is the volume of the cylinder shown below?
A. 150 cu. units
B. 100 cu units
C. 2250 cu units
D. 1500 cu units
Answer:
V = 150 pi units ^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = pi 10^2 * 15
V = 1500 pi units ^3
Explanation: Notice that the figure shown here is a cylinder.
To find the volume of a cylinder, start with the formula
for the volume of a cylinder which is v = πr²h.
Here, notice that our cylinder has a radius of 10 and a height of 15.
So we have (π)(10)²(15).
Start by simplifying the exponent.
(10)² is (10)(10) or (100 units²).
So we have (π)(100 units²)(15).
Now, (100 units²)(15) is 1,500 units³.
So we have 1,500π units³.
So your answer is D.
can someone help me plzz!
Answer:
126.6Option A is the right option.
Step-by-step explanation:
Sum of angles in triangle= 180°
[tex]85 + 53 + m < a = 180 \\ or \: 138 + m < a = 180 \\ or \:m < a = 180 - 138 \\ m < a = 42[/tex]
Applying sine rule:
[tex] \frac{sin \: a \: }{a} = \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: (85)}{b} = \frac{sin(42)}{85} \\ 85 \: sin \: (85) = \: b \: sin \: (42) \\ b = \frac{85 \: sin \: (85)}{sin \: 42} \\ ac = 126.6[/tex]
Hope this helps....
Good luck on your assignment...
there is 54 g of fruits in a smoothie. If the ratio of strawberry and blueberry in the smoothie is 5:4, how much of each fruit is there in the smoothie?
Answer:
strawberry: 30 gblueberry: 24 gStep-by-step explanation:
The total number of ratio units is 5+4 = 9, so each of them represents ...
(54 g)/9 = 6 g
of fruit. Multiplying the ratio by this value shows you the amount of each kind of fruit:
strawberry : blueberry = 5 : 4 = 5(6 g) : 4(6 g)
strawberry : blueberry = 30 g : 24 g
There are 30 g of strawberry and 24 g of blueberry in the smoothie.
One number is 5 more than another. The difference between their squares is 105. What are the numbers?
Answer: 8 & 13
Step-by-step explanation:
13 squared is 169 and 8 squared is 64, and the difference of those two squares would be 169 - 64 = 105. Hope this helps!
Which function has an inverse that is also a function?
A: (-1,-2),(0,4),(1,3),(5,14),7,4)
B: (-1,2),(0,4),(1,5),(5,4),(7,2)
C: (-1,3),(0,4),(1,14),(5,6),(7,2)
D: (-1,4),(0,4),(1,2),(5,3),(7,1)
Answer:
Option (C)
Step-by-step explanation:
Option (A):
(-1, -2),(0, 4), (1, 3), (5, 14), (7, 4)
In these ordered pairs (4, 4) and (7, 4) have the same y-value.
This function is not a one-to-one function.
Therefore, this function will have no inverse function.
Option (B):
(-1, 2), (0,4), (1, 5), (5, 4), (7, 2)
(-1, 2) and (7, 2) have the same output values for input values -1 and 7.
This function is not a one-to-one function.
Therefore, this function will have no inverse function.
Option (C).
(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)
For every input value there is a different output value in these pairs.
So the function is one-to-one function.
Therefore, inverse of this function will be a function.
Option (D).
(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)
Here (-1, 4) and (0, 4) show the same y-value which shows, the given function is not a one-to-one function.
Therefore, inverse of this function will not be a function.
Please help me and say thanks , will give brainiest answer
Answer:
Ivy's definition matches the comment that starts with "Sorry, this is incorrect. An ellipse..." because she didn't specify that the points that belong to the circle must be the same distance away from the center point. According to Ivy's definition, any curved and closed shape would be a circle but that's not true. For example, like the teacher said, an ellipse would match her circle definition but an ellipse is not a circle, it's more like an oval-ish shape. Ethan's definition is correct. Ebuka's definition matches the comment that starts with "Your definition is close..." because he/she didn't say that the shape must be closed. According to Ebuka's definition, an incomplete curve could count as a circle but that's not true, for example, as the teacher said, a semicircle is not a circle.
Answer: brainliest plz:)
ivy is the 3
ethan is correct
ebuka is close
Step-by-step explanation:
ivy is not even close to the correct
ethan got it right on and the last one was really close but not quite
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is: Compute E(Y) Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is:
y | P(Y)
0 | 0.50
1 | 0.20
2 | 0.25
3 | 0.05
Compute E(Y)
Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
Answer:
The expected value E(Y) is
[tex]E(Y) = 0.85[/tex]
The expected amount of the surcharge is
[tex]E(100Y^2) = 165[/tex]
Step-by-step explanation:
Let Y be the number of moving violations for which the individual was cited during the last 3 years.
The given probability mass function (pmf) of Y is
y | P(Y)
0 | 0.50
1 | 0.20
2 | 0.25
3 | 0.05
Compute E(Y)
The expected value E(Y) is given by
[tex]E(Y) = \sum Y \cdot P(Y) \\\\E(Y) = 0 \cdot 0.50 + 1 \cdot 0.20 + 2 \cdot 0.25 + 3 \cdot 0.05 \\\\E(Y) = 0.85[/tex]
Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
The expected amount of the surcharge is given by
[tex]E(100Y^2) = 100E(Y^2)[/tex]
Where
[tex]E(Y^2) = \sum Y^2 \cdot P(Y) \\\\E(Y^2) = 0^2 \cdot 0.50 + 1^2 \cdot 0.20 + 2^2 \cdot 0.25 + 3^2 \cdot 0.05\\\\E(Y^2) = 1.65[/tex]
So, the expected amount of the surcharge is
[tex]E(100Y^2) = 100E(Y^2) \\\\E(100Y^2) = 100 \cdot 1.65 \\\\E(100Y^2) = 165[/tex]
The sum of two odd integers is an even integer.
1. True
2. False
Answer:
True.
Step-by-step explanation:
Try out some numbers:
3 + 3 = 6
5 + 5 = 10
11 + 11 = 22
(7k-4)(7k^2+4k-1) mulityply the polynomials
Answer:
49k^3 -23k -4
Step-by-step explanation:
The distributive property is your friend.
[tex](7k-4)(7k^2+4k-1)=7k(7k^2+4k-1)-4(7k^2+4k-1)\\\\=49k^3+28k^2-7k-28k^2-16k+4\\\\=49k^3+k^2(28-28)+k(-7-16)-4\\\\=\boxed{49k^3-23k-4}[/tex]
ABCD is a rectangle. Rectangle A B C D is shown. All angles are right angles. The length of A D is 5 and the length of D C is 12. Use the diagram to answer the questions. The length of AB is 12 . The length of BC is 5 . The length of AC is .
Answer: 13
Step-by-step explanation:
I used Pythagorean theorem to solve this problem. As DC and AD is 12 and 5, you would do 12²+5²= c². 12²= 144 and 5²= 25. 144+25= 169. It doesn't end there. Do the square root of 169 ---> √169=13.
Given that ABCD is a rectangle, if a diagonal line cuts from A to C make a two equal right angled triangles, the hypotenuse which is the length of AC is 13.
What is a rectangle?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
What is Pythagorean theorem?Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c = √( a² + b² )
Given the data in the question;
Length AB and DC = 12Length AD and BC = 5Let line AC be the hypotenuse as it cuts the rectangle into two equal right angled triangle.
From Pythagorean theorem.
c = √( a² + b² )
AC = √( AB² + BC² )
AC = √( 12² + 5² )
AC = √( 144 + 15 )
AC = √169
AC = 13
Therefore, given that ABCD is a rectangle, if a diagonal line cuts from A to C make a two equal right angled triangles, the hypotenuse which is the length of AC is 13.
Learn more about Pythagorean theorem here: https://brainly.com/question/343682
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I need help I don’t understand
Answer:
6
Step-by-step explanation:
you have to distributw the 4 to the 1/4 so essentially youre multiplying the exponents. think of it as 4*1/4 and youll have 4/4 which equals to 1. 6^1 is just 6 so thats the answer
well first you have to multiply 6 by 1/4 and then you have to do this: 1.5*1.5*1.5*1.5 to get your answer i think....
The quantities x and y are proportional.
x y
11 1 2/9
21 2 1/3
45 5
find the constant of proportionality (r) in the equation y=rx
Answer: r = 1/9
Step-by-step explanation:
y = rx --> [tex]r=\dfrac{y}{x}[/tex]
[tex]1)\ y=1\dfrac{2}{9}\rightarrow\dfrac{11}{9}\\\\.\quad x=11\\\\r=\dfrac{11}{9}\div11\\\\\\r=\dfrac{11}{9}\times \dfrac{1}{11}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]
[tex]2)\ y=2\dfrac{1}{3}\rightarrow\dfrac{7}{3}\\\\.\quad x=21\\\\r=\dfrac{7}{3}\div21\\\\\\r=\dfrac{7}{3}\times \dfrac{1}{21}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]
[tex]3)\ y=5\\\\.\quad x=45\\\\r=5\div45\\\\\\r=\dfrac{5}{45}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]
A very large batch of components has arrived at a distributor. The batch can be characterized as acceptable only if the proportion of defective components is at most .10. The distributor decides to randomly select 10 components and to accept the batch only if the number of defective components in the sample is at most 2. Let X denote the number of defective components in the sample. What is the distribution of X? Justify your answer.
Required:
What is the probability that the batch will be accepted when the actual proportion of defectives (p) is:_______
a, 0.01
b. 0.05
c. 0.10
d. 0.20
e. 0.25
Answer:
c. 0.10
Step-by-step explanation:
Hello!
To accept a batch of components, the proportion of defective components is at most 0.10.
X: Number of defective components in a sample of 10.
This variable has a binomial distribution with parameters n=10 and p= 0.10 (for this binomial experiment, the "success" is finding a defective component)
The distributor will accept the batch if at most two components are defective, symbolically:
P(X≤2)
Using the tables for the binomial distribution you can find the accumulated probability for a sample of n=10 with probability of success of p= 0.10 and number of successes x= 2
P(X≤2)= 0.9298
I hope this helps!
which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
Answer:
Measuring it with a ruler and jotting down the length.
Step-by-step explanation:
If you are copying a line segment, the best way to copy it perfectly is to take the measure of the original line segment and copy down the measurement and then construct the other line segment to the exact measure.
Answer:
Brianlliest!
Step-by-step explanation:
you must measure the current line segment and copy it with the same length and make a new one