[tex]\bf \begin{array}{ccll} liters&gallons\\ \cline{1-2} 1&0.26\\ 5.5&x \end{array}\implies \cfrac{1}{5.5}=\cfrac{0.26}{x}\implies x=(5.5)(0.26)\implies x=1.43[/tex]
find prob of sum 8 when two dice rolled?
[tex]|\Omega|=6^2=36\\A=\{(3,5),(5,3),(4,4),(2,6),(6,2)\}\\|A|=5\\\\P(A)=\dfrac{5}{36}\approx13.9\%[/tex]
Della’s cats weigh 9.8 and 8.25 pounds,and her dog weighs 25 pounds.How much more does her dog weight than the total weight of both of her cats?
Answer:
6.95 pounds. Her dog weighs 6.95 more pounds than the total weight of both her cats.
Step-by-step explanation:
To find the total weight of her cats, add their weights together:
9.8+8.25
=18.05 pounds
Then to find the difference between the weight of her dog and the weight of her cats' total weight, you subtract the weight of the cats from the weight of the dog:
25-18.05
=6.95 pounds
BEDE
Which of the following equations represents a line that is perpendicular to
Y = -4x+9 and passes through the point, (4, 5)?
A. y =1/4×+6
B. y = 3x+4
C. y = 1/4×+5
D. y = -4x+ 4
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+4}[/tex]
Step-by-step explanation:
[tex]Let:\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\============================\\\\\text{We have the equation of the line:}\ y=-4x+9\to m_1=-4.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-4}=\dfrac{1}{4}.\\\\\text{Put the value of the slope and the coodrdinates of the given point (4, 5)}\\\text{to the equation of a line}\ y=mx+b:\\\\5=\dfrac{1}{4}(4)+b\\\\5=1+b\qquad\text{subtract 1 from both sides}\\\\4=b\to b=4\\\\\text{Finally:}\\\\y=\dfrac{1}{4}x+4[/tex]
input x 2,4,6,8 output y 1, 2, 3, 4 compare the table with the relation f(x) =3x-10. Which relation has a greater value when x= 8
Answer:
The function f(x)=3x-10 has the greater value at x=8.
Step-by-step explanation:
In the table, x=8 corresponds to y=4.
In the function f(x)=3x-10 when x=8, y corresponds to f(8)=3(8)-10=24-10=14.
SInce 14>4 , the the function f(x)=3x-10 has a greater value at x=8 than the table does.
A spinner has 20 equally sized sections, 8 of which are yellow and 12 of which are blue. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on blue and the coin is tails?
Answer:
3/10
Step-by-step explanation:
These two events are independent, so the overall probability is the product of the individual probabilities.
12 blue sections out of 20
p(blue) = 12/20 = 3/5
There is an equal probability of the coin landing on heads or tails.
p(tails) = 1/2
p(blue & tails) = 3/5 * 1/2 = 3/10
What is the vertex form of Y = x2 - 6x + 6?
Answer:
[tex]\large\boxed{y=(x-3)^2-3}[/tex]
Step-by-step explanation:
The vertex form of a quadratic equation y = ax² + bx + c:
y = a(x - h)² + k
(h, k) - coordinates of a vertex
We have the equation y = x² - 6x + 6.
Convert to the vertex form:
[tex]y=x^2-2(x)(3)+6\\\\y=\underbrace{x^2-2(x)(3)+3^2}_{(*)}-3^2+6\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\y=(x-3)^2-9+6\\\\y=(x-3)^2-3\to h=3,\ k=-3[/tex]
If f of x equals 3x plus 2, find f of 4
Answer:
f(4) = 14
Step-by-step explanation:
f(x) = 3x+2
Let x=4
f(4) = 3(4)+2
= 12+2
= 14
What is the factored form of the polynomial?
x2 − 15x + 36
(x − 4)(x − 9)
(x − 3)(x − 12)
(x + 4)(x + 9)
(x + 3)(x + 12)
Answer:
(x - 3)(x - 12)
Step-by-step explanation:
Given
x² - 15x + 36
Consider the factors of the constant term (+ 36) which sum to give the coefficient of the x- term (- 15)
The factors are - 3 and - 12, since
- 3 × - 12 = + 36 and - 3 - 12 = - 15, hence
x² - 15x + 36 = (x - 3)(x - 12) ← in factored form
The factored form of the polynomial x² − 15x + 36 is (x − 3)(x − 12). This can be obtained by using the steps of splitting the middle term method.
Find the factored form using splitting the middle term:Given the polynomial, x² − 15x + 36
Step 1:First we should multiply first term and last term, x²×36=36x²Step 2:This product ,that is 36x², should be slit such that the factors sum is the middle term, -15x.(-3x)×(-12x)=36x² and (-3x)+(-12x)= - 15x
-3x and -12x are the required factors of 36x²
Step 3:Substitute the factors in the place of middle term,x² - 3x - 12x+36
Step 4:Take common terms from the first two terms and last two terms,x² - 3x - 12x+36 = x(x - 3) - 12(x - 3)
=(x - 3)(x - 12)
Hence the factored form of the polynomial x² − 15x + 36 is (x − 3)(x − 12).
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How do I solve questions 1,2 and 6?
Answer:
1. P = 13.2542. P = 6.64 + 2x6. P = 10Step-by-step explanation:
[tex]1.\\\text{The length of semicircle:}\\\\l=\dfrac{1}{2}d\pi\\\\d-diameter\\\\d=2.2\\\\\text{substitute:}\\\\l=\dfrac{1}{2}(2.2)\pi=1.1\pi\approx(1.1)(3.14)=3.454\\\\\text{The perimeter of the figure:}\\\\P=2(3.8)+2.2+3.454=13.254[/tex]
[tex]2.\\P=2(3.32)+2x=6.64+2x[/tex]
[tex]6.\\\text{Look at the picture.}\\\\P=4(2)+2(1)=8+2=10[/tex]
The equation represents Function A, and the graph represents Function B:
Function A
f(x) = x − 9
Function B
graph of line going through ordered pairs negative 1, negative 3 and 2, 3
Which equation best compares the slopes of the two functions?
Slope of Function B = 2 x Slope of Function A
Slope of Function A = Slope of Function B
Slope of Function A = 2 x Slope of Function B
Slope of Function B = − Slope of Function A
Answer:
Slope of Function B = 2 x Slope of Function A
Step-by-step explanation:
step 1
Find the slope of the function A
we have
[tex]f(x)=x-9[/tex]
This is the equation of the line into point slope form
[tex]y=mx+b[/tex]
where m is the slope
b is the y-intercept
therefore
The slope of the function A is
[tex]m=1[/tex]
step 2
Find the slope of the function B
we have the points
(-1,-3) and (2,3)
The slope m is equal to
[tex]m=(3+3)/(2+1)=6/3=2[/tex]
step 3
Compare the slopes
[tex]SlopeA=1\\ SlopeB=2[/tex]
therefore
The slope of the function B is two times the slope of the function A
Answer:
slope of function a = -2
slope of function b = (1 + 5)/(2 + 1) = 6/3 = 2
slope of function b = - slope of function a.
Step-by-step explanation:
Which rule describes the translation below?
Answer: A is correct, (x-5, y-3) Hope this helps, mark brainliest please :)
Step-by-step explanation:
The green triangle is the original, and the blue is the duplicated translation, you know this by the ' mark on the blue S.
You can count the squares from one spot to the next to find how many it moved. It clearly is moved to the left and down though, which means it was subtracted from in both directions.
Answer:A
Step-by-step explanation:
Which system is equivalent to y = -2x , y = x-2 ?
The given system of equation can be solved if x = 2/3 and y = -4/3.
So we need to find another system which can be solved by these values.
From the given 4 options lets find out which can be solved by x = 3/2 and y = -4/3
1.
y = -2y^2 -2 , x = y - 2
lets put the value of y here
y = -2(16/9)-2 = -32/9-2= -50/ 9
So not an equivalent equation.
2.
y = -2y^2 + 2 , x = y + 2
y = -2(16/9)+2=-32/9+2=-14/9
So not an equivalent system.
3.
y = -2y^2 - 8y - 8 , x = y + 2
y = -2(16/9)-8(-4/3)-8 = -32/9+32/3-8=64/9-8=-8/9
So not an equivalent system.
4.
y = -2y^2 + 8y - 8 , x = y -2
y = -2(16/9)+8(-4/3)-8=-32/9-32/3-8=-128/9-8=-22.22
So this is not an equivalent equation too
Answer:
C. [tex]\left \{ {{y=-2y^{2}-8y-8 } \atop {x=y+2}} \right.[/tex]
Step-by-step explanation:
Edge 2020
If f(x) = 3x + 2 and
g(x) = 2x- 2,
what is (f - g)(x)?
A. x+4
B. x-2
C. x
D. 5x – 2
E. x-4
Answer:
A. x + 4Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) = 3x + 2, g(x) = 2x - 2.
Substitute:
(f - g)(x) = (3x + 2) - (2x - 2) = 3x + 2 - 2x - (-2) = 3x + 2 - 2x + 2
combine like terms
(f - g)(x) = (3x - 2x) + (2 + 2) = x + 4
Angie, a student in an advanced statistics course, was given an algebra test and she scored
80%. Is this an accurate predictor of how well students in the algebra class will perform on
the test? (2 points)
Answer:
C. No because Angie is not representative of the population in the algebra class
Step-by-step explanation:
I just took the test and this was correct
No, this is not an accurate predictor
Accurate predictor:Since Angie is the student of an advanced statistics course but she gives the algebra test and scored 80%. We know that the advanced statistics is the higher level of math so it is not an accurate predictor.
An accurate predictor should be applied when the person is 100% confirmed to the related thing. So in the given situation, the student is not 100% confirm.
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Select the correct answer.
What is the equation of the parabola shown in the graph?
Answer:
x=y2/8+y/2+9/2
Step-by-step explanation:
Given:
directrix: x=2
focus = (6,-2)
Standard equation of parabola is given by:
(y - k)2 = 4p (x - h)
where
directrix : x=h-p
focus=(h + p, k)
Now comparing the give value with above:
(h + p, k)= (6,-2)
k=-2
h+p=6
h=6-p
Also
directrix: x=h-p
h-p=2
Putting value of h=6-p in above
6-p-p=2
6-2p=2
-2p=2-6
-2p=-4
p=-4/-2
p=2
Putting p=2 in h-p=2
h=2+p
h=2+2
h=4
Putting k=-2, p=2, h=4 in standard equation of parabola we get:
(y - k)2 = 4p (x - h)
(y-(-2))^2 = 4(2) (x - 4)
(y+2)^2 = 8 (x - 4)
y2+4y+4=8x-32
y2+4y+4+32=8x
x=y2/8+4y/8+36/8
x=y2/8+y/2+9/2!
the point slope equation of a line is?
Answer:
[tex]\text{The point-slope equation of a line is:}[/tex]
[tex]C.\ y-y_0=m(x-x_0)[/tex]
[tex]m-\text{slope}\\\\(x_0,\ y_0)-\text{point on a line}[/tex]
A bird is flying at a height of 2 meters above the sea level. The angle of depression from the bird to the fish it sees on the surface of the ocean is 15∘. Find the distance the bird must fly to be directly above the fish. Round to the nearest ten
See the attached picture:
Helppppppppppping me please
Answer:
8. D) 2x + 89. C) 6x + 32 = 15810. 50 ftStep-by-step explanation:
Look at the picture.
9. The perimeter of the rectangle l × w:
P = 2l + 2w
Substitute l = 2x + 8 and w = x + 8:
P = 2(2x + 8) + 2(x + 8) use the distributive property
P = (2)(2x) + (2)(8) + (2)(x) + (2)(8)
P = 4x + 16 + 2x + 16 combine like terms
P = (4x + 2x) + (16 + 16)
P = 6x + 32
10. Solve the equation:
6x + 32 = 158 subtract 32 from both sides
6x = 126 divide both sides by 6
x = 21
Put the value of x to the expression 2x + 8:
2(21) + 8 = 42 + 8 = 50
Given WXYZ what is the measure of Z
Answer: 35
Step-by-step explanation:
The measure of ∠Z is 35°
The correct answer is an option (D)
What is parallelogram?"It is a quadrilateral in which opposite sides are parallel and equal in length.""The opposite angles of parallelogram are equal.""The adjacent angles of the parallelogram are supplementary."For given question,
We have been given a parallelogram WXYZ.
The measure of angle X is 35°
We know that, the opposite angles of parallelogram are equal.
⇒ ∠X = ∠Z
⇒ ∠Z = 35°
Therefore, the measure of ∠Z is 35°
The correct answer is an option (D)
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Which of the following is the simplified form of ^7 radical x • ^7 radical x • ^7 radical x
For this case we must find an expression equivalent to:
[tex]\sqrt [7] {x} * \sqrt [7] {x} * \sqrt [7] {x}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, rewriting the given expression we have:
[tex]x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} =[/tex]
To multiply powers of the same base we put the same base and add the exponents:
[tex]x ^ {\frac {1} {7} + \frac {1} {7} + \frac {1} {7}} =\\x ^ {\frac {3} {7}}[/tex]
Answer:
Option 1
Answer: Option 1.
Step-by-step explanation:
We need to remember that:
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
Then, having the expression:
[tex]\sqrt[7]{x}*\sqrt[7]{x} *\sqrt[7]{x}[/tex]
We can rewrite it in this form:
[tex]=x^{\frac{1}{7}}*x^{\frac{1}{7}} *x^{\frac{1}{7}}[/tex]
According to the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then, the simplied form of the given expression, is:
[tex]=x^{(\frac{1}{7}+\frac{1}{7}+\frac{1}{7})}=x^\frac{3}{7}[/tex]
6 1/4% interest on $150 is how much money?
$9.38
0.0625×150=$9.38
Have a good day
You have 2 jugs(and only 2 jugs), one can hold 3 gallons of water and the other can hold 5. You need exactly 4 gallons of water. Assume the jugs have no markings, you have no measuring equipment, and you have infinite water.
Answer:
See below.
Step-by-step explanation:
You fill the 5 gallon up to the top then you pour 3 gallons into the 3 gallon jug, leaving 2 gallons in the bigger jug.
You throw the contents of the 3 gallon jug away then transfer the 2 gallons from the bigger jug into the 3 gallon jug. So you have 2 gallons in the 3 gallon jug.
You then fill the 5 gallon jug and pour 1 gallon into the 3 gallon jug, so you are left with 4 gallons of water in the 5 gallon jug.
The function f(x) = 4x + 5,000 represents the amount of money a television is being sold for, where x is the number of televisions being manufactured.
The function g(x) = 20x − 500 represents the cost of production, where x is the number of televisions being manufactured.
What is (f − g)(100)? Explain.
a. $6.9K is the profit made from 100 TVs
b. $3.9K is the profit made from 100 TVs
c. $6.9K is the cost of manufacturing 100 TVs
d. $3.9K is the cost of manufacturing 100 TVs
Answer:
The opción b
Step-by-step explanation:
the profit is defined by
[tex]Profit=Gain-cost[/tex]
In this case [tex](F-g)(100)=[/tex] is the profit to sell 100 television and is calculated
[tex]F(x)-g(x)=4x+5000-(20x-500)=4x-20x+5000+500=-16x+5500=-16*(100)+5500=3900[/tex]
[tex]3900=3.9k[/tex]
Answer:
The answer You're looking for is B)$3.9K is the profit from 100 TV's
Step-by-step explanation:
explain why angle d must be a right angle
Pls help
Answer:
see explanation
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.
Consider the right triangle on the right and calculate n
n² + 2² = 3²
n² + 4 = 9 ( subtract 4 from both sides )
n² = 5 ( take the square root of both sides )
n = [tex]\sqrt{5}[/tex]
If the triangle on the left is right then the square of the longest side must equal the sum of the squares on the other 2 sides.
The longest side is n = [tex]\sqrt{5}[/tex] ⇒ n² = ([tex]\sqrt{5}[/tex] )² = 5 and
([tex]\sqrt{2}[/tex] )² + ([tex]\sqrt{3}[/tex] )² = 2 + 3 = 5
Hence D is a right angle
6. Benjamin has to wear a uniform to school. His uniform is made up of tan or blue pants and a blue or white collared shirt.
Benjamin has 2 pair of blue pants, 2 pair of tan pants, 3 white shirts, and 2 blue shirts. How many combinations can be made
with the clothes Benjamin has to choose from? What is the probability that he will wear his favorite combination, tan pants
and a white shirt?
(SHOW WORK)
Answer:
Probably of getting both = 3/10 *100 = 30%
Step-by-step explanation:
According to the given statement we have four possible combinations:
Blue pants/white shirt, tan pants/white shirt, blue pants/blue shirt, blue pants/white shirt
.probability of getting tan pants = 2/4
probability of getting white shirt = 3/5
probably of getting both = 2/4 x 3/5 = 6/20 = 3/10
probably of getting both = 3/10 *100 = 30% ...
a bottle holds 64 fluid ounces of lemonade. How much is this in pints?
Answer:
there are 4 pints
Step-by-step explanation:
64 / 16 = 4
64 fluid ounces of lemonade equals to 4 pints. This is done by dividing the total fluid ounces by the number of fluid ounces in one pint.
Explanation:The question is asking to convert 64 fluid ounces of lemonade into pints. To do this, you should know that 1 pint is equal to 16 fluid ounces. So, you can divide the total fluid ounces by the number of fluid ounces in one pint. In this situation, divide 64 by 16, which equals 4 pints. Therefore, 64 fluid ounces of lemonade equals to 4 pints.
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what is the equation of a line that contains the point (2,-5) and is parallel to the line y=3x-4
Answer:
[tex]\large\boxed{y=3x-11}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=3x-4\to m_1=3\\\\\text{Therefore}\ m_2=3.\\\\\text{We have the equation:}\ y=3x+b.\\\\\text{Put the coorsdinates of the point (2, -5) to the equation of the line}\\\\-5=3(2)+b\\-5=6+b\qquad\text{subtract 6 from both sides}\\-11=b\to b=-11[/tex]
how to solve derivative of (sin3x)/x using first principle
[tex]\dfrac{d}{dx}(\dfrac{\sin(3x)}{x})[/tex]
First we must apply the Quotient rule that states,
[tex](\dfrac{f}{g})'=\dfrac{f'g-g'f}{g^2}[/tex]
This means that our derivative becomes,
[tex]\dfrac{\dfrac{d}{dx}(\sin(3x))x-\dfrac{d}{dx}(x)\sin(3x)}{x^2}[/tex]
Now we need to calculate [tex]\dfrac{d}{dx}(\sin(3x))[/tex] and [tex]\dfrac{d}{dx}(x)[/tex]
[tex]\dfrac{d}{dx}(\sin(3x))=\cos(3x)\cdot3[/tex]
[tex]\dfrac{d}{dx}(x)=1[/tex]
From here the new equation looks like,
[tex]\dfrac{3x\cos(3x)-\sin(3x)}{x^2}[/tex]
And that is the final result.
Hope this helps.
r3t40
Answer:
[tex]\frac{3\cos(3x)}{x}-\frac{\sin(3x)}{x^2}[/tex]
Step-by-step explanation:
If [tex]f(x)=\frac{\sin(3x)}{x}[/tex], then
[tex]f(x+h)=\frac{\sin(3(x+h)}{x+h}=\frac{\sin(3x+3h)}{x+h}[/tex].
To find this all I did was replace old input, x, with new input, x+h.
Now we will need this for our definition of derivative which is:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]
Before we go there I want to expand [tex]sin(3x+3h)[/tex] using the sum identity for sine:
[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]
[tex]\sin(3x+3h)=\sin(3x)\cos(3h)+\cos(3x)\sin(3h)[/tex]
So we could write f(x+h) as:
[tex]f(x+h)=\frac{\sin(3x)\cos(3h)+\cos(3x)\sin(3h)}{x+h}[/tex].
There are some important trigonometric limits we might need before proceeding with the definition for derivative:
[tex]\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1[/tex]
[tex]\lim_{u \rightarrow 0}\frac{\cos(u)-1}{u}=0[/tex]
Now let's go to the definition:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{\frac{\sin(3x)\cos(3h)+\cos(3x)\sin(3h)}{x+h}-\frac{\sin(3x)}{x}}{h}[/tex]
I'm going to clear the mini-fractions by multiplying top and bottom by a common multiple of the denominators which is x(x+h).
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x(\sin(3x)\cos(3h)+\cos(3x)\sin(3h))-(x+h)\sin(3x)}{x(x+h)h}[/tex]
I'm going to distribute:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)\cos(3h)+x\cos(3x)\sin(3h)-x\sin(3x)-h\sin(3x)}{x(x+h)h}[/tex]
Now I’m going to group xsin(3x)cos(3h) with –xsin(3x) because I see when I factor this I might be able to use the second trigonometric limit I mentioned. That is xsin(3x)cos(3h)-xsin(3x) can be factored as xsin(3x)[cos(3h)-1].
Now the limit I mentioned:
[tex]\lim_{u \rightarrow 0}\frac{\cos(u)-1}{u}=0[/tex]
If I let u=3h then we have:
[tex]\lim_{3h \rightarrow 0}\frac{\cos(3h)-1}{3h}=0[/tex]
If 3h goes to 0, then h goes to 0:
[tex]\lim_{h \rightarrow 0}\frac{\cos(3h)-1}{3h}=0[/tex]
If I multiply both sides by 3 I get:
[tex]\lim_{h \rightarrow 0}\frac{\cos(3h)-1}{h}=0[/tex]
I’m going to apply this definition after I break my limit using the factored form I mentioned for those two terms:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)\cos(3h)-x\sin(3x)+x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)(\cos(3h)-1)+x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)(\cos(3h)-1)}{x(x+h)h}+\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
So the first limit I’m going to write as a product of limits so I can apply the limit I have above:
[tex]f’(x)=\lim_{h \rightarrow 0}\frac{\cos(3h)-1}{h} \cdot \lim_{h \rightarrow 0}\frac{x\sin(3x)}{x(x+h)}+\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
The first limit in that product of limits goes to 0 using our limit from above.
The second limit goes to sin(3x)/(x+h) which goes to sin(3x)/x since h goes to 0.
Since both limits exist we are good to proceed with that product.
Let’s look at the second limit given the first limit is 0. This is what we are left with looking at:
[tex]f’(x)=\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
I’m going to write this as a sum of limits:
[tex]\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)}{x(x+h)h}+\lim_{h \rightarrow 0}\frac{-h\sin(3x)}{x(x+h)h}[/tex]
I can cancel out a factor of x in the first limit.
I can cancel out a factor of h in the second limit.
[tex]\lim_{h \rightarrow 0}\frac{\cos(3x)\sin(3h)}{(x+h)h}+\lim_{h \rightarrow 0}\frac{-\sin(3x)}{x(x+h)}[/tex]
Now I can almost use sin(u)/u goes to 1 as u goes to 0 for that first limit after writing it as a product of limits.
The second limit I can go ahead and replace h with 0 since it won’t be over 0.
So this is what we are going to have after writing the first limit as a product of limits and applying h=0 to the second limit:
[tex]\lim_{h \rightarrow 0}\frac{\sin(3h)}{h} \cdot \lim_{h \rightarrow 0}\frac{\cos(3x)}{(x+h)}+\frac{-\sin(3x)}{x(x+0)}[/tex]
Now the first limit in the product I’m going to multiply it by 3/3 so I can apply my limit as sin(u)/u->1 then u goes to 0:
[tex]\lim_{h \rightarrow 0}3\frac{\sin(3h)}{3h} \cdot \lim_{h \rightarrow 0}\frac{\cos(3x)}{(x+h)}+\frac{-\sin(3x)}{x(x)}[/tex]
[tex]3(1) \cdot \lim_{h \rightarrow 0}\frac{\cos(3x)}{(x+h)}+\frac{-\sin(3x)}{x(x)}[/tex]
So we can plug in 0 for that last limit; the result will exist because we do not have over 0 when replacing h with 0.
[tex]3(1)\frac{\cos(3x)}{x}+\frac{-\sin(3x)}{x^2}[/tex]
[tex]\frac{3\cos(3x)}{x}-\frac{\sin(3x)}{x^2}[/tex]
If sin=2/3 and tan is less than 0, what is the value of cos
tangent is less than 0 or tan(θ) < 0, is another way to say tan(θ) is negative, well, that only happens on the II Quadrant and IV Quadrant, where sine and cosine are different signs, so we know θ is on the II or IV Quadrant.
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{2}}{\stackrel{hypotenuse}{3}}\qquad \impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\bf \pm\sqrt{3^2-2^2}=a\implies \pm\sqrt{5}=a\implies \stackrel{\textit{II Quadrant}}{-\sqrt{5}=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{5}}}{\stackrel{hypotenuse}{3}}~\hfill[/tex]
Pleeaaaase hellllpppp asap
Answer:
Option B
Step-by-step explanation:
the mean is the sum of each value of P(x) multiply for x
Mean= 23x0.16 + 25x0.09 + (26x0.18) + (31x0.12)+ (34x0.24) + (38x0.21)
Mean= 30.47
Answer:
B. 30.47
Step-by-step explanation:
The mean discrete random variable tells us the weighted average of the possible values given of a random variable. It shows the expected average outcome of observations. It's like getting the weighted mean. The expected value of X can be computed using the formula:
[tex]\mu_{x}=x_1p_1+x_2p_2+x_3p_3...+x_kp_k\\\\=\Sigma x_ip_i[/tex]
Using the data given in your problem, just pair up the x and P(x) accordingly and get the sum.
[tex]\mu_{x}=x_1p_1+x_2p_2+x_3p_3+x_4p_4+x_5p_5+x_6p_6\\\\\mu_{x}=(23\times 0.16) + (25\times 0.09) + (26\times 0.18) + (31\times 0.12) + (34\times 0.24) + (38\times 0.21)\\\\\mu_{x} = 30.47[/tex]