Answer:
Explained below.
Step-by-step explanation:
(a)
It is provided that the price function for 1000 TVs is,
p (1000) = 400.
Also provided that if rebate of $10 is given then sale increases by 100 per week.
Let x be the number of unit sold per week then (x − 1000) is the increase in the number of units sold.
Then the price function is:
[tex]p(x)=400-\frac{1}{10}(x-1000)[/tex]
[tex]=400-\frac{x}{10}+100\\\\=500-\frac{x}{10}[/tex]
Thus, the demand function is, [tex]p(x)=500-\frac{x}{10}[/tex].
(b)
The revenue function is:
[tex]R(x)=x\cdot p(x)[/tex]
[tex]=x[500-\frac{x}{10}]\\\\=500x-\frac{x^{2}}{10}[/tex]
Maximize the revenue as follows:
[tex]\frac{d}{dx}(R(x))=0[/tex]
[tex]\frac{d}{dx}[500x-\frac{x^{2}}{10}]=0[/tex]
[tex]500-\frac{x}{5}=0[/tex]
[tex]\frac{x}{5}=500[/tex]
[tex]x=2500[/tex]
Observe that R'(x) > 0 for 0 ≤ x < 2500 and R'(x) < 0 for x > 2500. Hence, first derivative test will lead to the conclusion that maximum occurs at x = 2500.
Compute the value p (2500) as follows:
[tex]p(2500)=500-\frac{2500}{10}=500-250=250[/tex]
Then the rebate to maximize the revenue should be: $400 - $250 = $150.
(c)
The weekly cost function is,
[tex]C(x) = 73000 + 110x[/tex]
Compute the profit function as follows:
[tex]P(x)=R(x)-C(x)[/tex]
[tex]=500x-\frac{x^{2}}{10}- 73000 - 110x\\\\=390x-\frac{x^{2}}{10}- 73000[/tex]
Compute the marginal profit as follows:
[tex]\text{Marginal profit}=P'(x)\\=\frac{d}{dx}P(x)\\=\frac{d}{dx}[390x-\frac{x^{2}}{10}- 73000]\\=390-\frac{x}{5}[/tex]
Compute the value of x for P'(x) = 0 as follows:
[tex]P'(x)=0\\\\390-\frac{x}{5}=0\\\\x=390\times 5\\\\x=1950[/tex]
Observe that P'(x) > 0 for 0 ≤ x < 1950 and P'(x) < 0 for x > 1950. Hence, first
derivative test will lead to the conclusion that maximum occurs at x = 1950.
Compute the value p (1950) as follows:
[tex]p(1950)=500-\frac{1950}{10}=500-195=305[/tex]
Then the rebate to maximize the profit should be: $400 - $305 = $95.
Find the area of the shaded region.
Round to the nearest tenth.
Answer:
Area shaded blue = 294.5 m^2 (to the nearest tenth)
Step-by-step explanation:
Refer to the attached figure.
Consider sector patterned in orange
radius = 11.1 m
angle of sector = 360-130 = 230 degrees
area of sector = (angle / 360) * area of complete circle
A1 = (230/360)*pi * 11.1^2
= 78.7175 pi
= 247.298 m^2
Area of right triangle with hypotenuse, L, and one of the angles, x, known
= (Lsin(x))*L(cos(x)/2
= L^2 sin(2x)/4
A2 = 2* (11.1^2 sin(130/2)/4)
= 11.1^2 * sin(65) / 2
= 47.192 m^2
Area shaded blue
= A1+A2
= 247.298 + 47.192
= 294.49 m^2
Which algebraic expression represents this word description?
The quotient of four and the sum of a number and three
Answer:
4÷(6+3)
Step-by-step explanation:
6+3 is the sum of a number and 3, and you divide 4 by that.
The algebraic expression represents the statement The quotient of four and the sum of a number and three is 4÷(x + 3).
What is an expression?A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Given:
The quotient of four and the sum of a number and three,
The above statement can be written as,
4÷(x + 3)
Here, x is the number
To know more about the expression:
https://brainly.com/question/13947055
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Simplify the expression 2(-2x+4-5-3)
Answer:2 (-2x + 4 - 5 - 3)
2(-2x -4)
-4x - 8
show all steps when completing the square to solve 2x^2 - 4x - 5 = 25
Answer:
x = 5, -3
Step-by-step explanation:
2x² - 4x - 5 = 25
add 5 to each side
2x² - 4x = 30
factor out the 2
2(x² - 2x) = 30
divide both sides by 2
x² - 2x = 15
divide b by 2, square it -- (b/2)², and add it to both sides
-2/2 = -1 → -1² = 1
x² - 2x + 1 = 15 + 1
factor the expression on the left -- this will be [x - (b/2)]²
(x - 1)² = 16
find the square root of both sides
x - 1 = ±4
add 1 to both sides
x = 4 + 1
x = -4 + 1
solve
x = 5, -3
The digit \greenD88start color #1fab54, 8, end color #1fab54 in which number represents a value of 888 thousandths?
Question:
The digit 8 in which number represents a value of 8 thousandths?
Answer:
See Explanation
Step-by-step explanation:
The question requires options and the options are missing.
However, the following explanation will guide you
Start by representing 8 thousandths as a digit
[tex]\frac{8}{1000} = 0.008[/tex]
i.e.
8 thousandths implies 0.008
Next;
Replace the 0s with dashes
_ . _ _8
Note that there are two dashes after the decimal point and before 8
PS: The dashes are used to represent digits
This implies that thousandths is the 3rd digit after the decimal point
Typical examples to back up this explanation are:
17.008, 1.1489, 0.008 and so on...
Prove that if four numbers are chosen from the set {l, 2, 3, 4.5.6}, at least one pair of the selected numbers must add up to 7
Answer:
Step-by-step explanation:
GIven that:
The set is : {l, 2, 3, 4.5.6}
To Prove that:
If four numbers are to be chosen , at least one pair of the selected numbers must add up to 7
From the data set given, this set has three pairs of number which can add up to 7. These are:
{1, 6} i.e 1 + 6 = 7
{2,5} i.e 2+ 5 = 7
{3,4} i.e 3 + 4 = 7
So, if four number are chosen from the set that contains six numbers, then that the possibility for such to occur is either by selecting two pairs out of the three pairs or one pair and two numbers.
Thus, in both cases, at least one pair of the selected numbers must add up to 7.
Steven travel for 10 hours at a constant rate of 53 miles per hour Stephanie traveled the same distance at a constant rate of 48 miles per hour how long did it take Stephanie to travel the same distance as Steven write your plan to solve in the correct order.
Answer:
11.04hrs
Step-by-step explanation:
Since Steven traveled 530 miles (number of hrs times mph) we would just divide 530 and 48 which is 11.04 hrs
Which digit in 2,385,679 has a value that is greater than 10 times the value of the first digit to its right?
A-8
B-5
C-7
D-2
Answer:
Hey there!
8 is the correct answer.
It is 16 times greater than the digit to it's right.
Let me know if this helps :)
SUPER HARD QUESTION (I POSTED THE DIAGRAM) In the diagram of.....
Answer:
A
Step-by-step explanation:
Since m∠JOK is 1/5th of the measure of the full circle (we know this because 72° is 1/5th of 360° and 360° is the measure of the whole circle), we know that the measure of minor arc JK will be 1/5th of the circumference of the circle. C = 2πr and we know that r = 5 so the circumference is 10π. 1/5th of that is 2π.
One consequence of the popularity of the internet is that it is thoughout to reduce television watching. Suppose that a random sample of 55 individuals who consider themselves to be avid Internet users results in a mean time of 2.10 hours watching television on a weekday.
Required:
Determine the likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours.
Complete Question
One consequence of the popularity of the internet is that it is throughout to reduce television watching. Suppose that a random sample of 55 individuals who consider themselves to be avid Internet users results in a mean time of 2.10 hours watching television on a weekday. The standard deviation is [tex]\sigma = 1.93[/tex]
Required:
Determine the likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours.
Answer:
The likelihood is [tex]P(X \le 2.10 ) = 0.08931[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 55[/tex]
The population mean is [tex]\mu = 2.45 \ hours[/tex]
The random mean considered [tex]\= x = 2.10 \ hours[/tex]
Generally the standard error of mean is mathematically represented as
[tex]\sigma _{\= x } = \frac{\sigma }{ \sqrt{n} }[/tex]
=> [tex]\sigma _{\= x } = \frac{1.93 }{ \sqrt{55} }[/tex]
=> [tex]\sigma _{\= x } = 0.2602[/tex]
The likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours is mathematically represented as
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - P( \frac{X - \mu }{\sigma_{\= x }} > \frac{ 2.10 - 2.45}{ 0.2602} )[/tex]
Generally [tex]\frac{X - \mu }{\sigma_{\= x }} = Z(The \ standardized \ value \ of \ X )[/tex]
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - P( Z > -1.345 )[/tex]
From the z-table the value of
[tex]P( Z > -1.345 ) = 0.91069[/tex]
So
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - 0.91069[/tex]
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 0.08931[/tex]
[tex]P(X \le 2.10 ) = 0.08931[/tex]
A function f, defined on the set of positive integers, has f(1) = 2 and f(2) = 3. Also f(f(f(n))) = n + 2 if n is even and f(f(f(n))) = n + 4 if n is odd. What is f(777)?
pls answer, I'm really confused
Answer:
f(777) = 390
Step-by-step explanation:
f(1) = 2 . . . . given
f(2) = f(f(1)) = 3 . . . . given
f(3) = f(f(f(1))) = 1+4 = 5
f(5) = f(f(3)) = f(f(f(2))) = 2+2 = 4
f(4) = f(f(5)) = f(f(f(3))) = 3+4 = 7
f(7) = f(f(4)) = f(f(f(5))) = 5+4 = 9
Then the sequence of sequential function values is ...
2, 3, 5, 4, 7, 9, 6, 11, 13, ... (pattern repeats in groups of 3)
__
Each odd number of the form 4n+1 is the function value f(4n-1) = 4n+1.
Similarly, the next function value is f(4n+1) = (4n+1+3)/2.
Since 777 is 4(194) +1, we have ...
f(777) = (777+3)/2
f(777) = 390
Which choice is the solution to the inequality below?
x/10>7
O A. X>7
O B. x> 1.43
O c. X>70
D. x < 70
Answer: C. x>70
Step-by-step explanation:
x/10>7
x/10 × 10>7 × 10
x>70
Hope this helps!! :)
Which distribution is used to test the claim that women have a higher mean resting heart rate than men?
This question is incomplete, the complete question is;
Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that women have a higher mean resting heart rate than men?
A.t
B.F
C.Normal
D. Chi-square
Answer:
A) t test
Step-by-step explanation:
A t-test uses sample information to assess how plausible it is for the population means μ1 and μ2 to be equal.
The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on the assumption of having an equal variance or not.
If the variances are assumed to be not equal,
he formula is:
t = (bar X₁ - bar X₂) / √( s₁²/n₁ + s₂²/n₂ )
If the variances are assumed to be equal, the formula is:
t = (bar X₁ - bar X₂) / √ (((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)) ( 1/n₁ + 1/n₂)
it called t-test for independent samples because the samples are not related to each other, in a way that the outcomes from one sample are unrelated from the other sample.
hence option A is correct. t test
A website reports that 70% of its users are from outside a certain country, and 60% of its users logon the website every day. Suppose that for its users from inside the country, that 80% of them log onevery day. What is the probability that a person is from the country given that he logs on the websiteevery day? Has the probability that he is from the country increased or decreased with the additionalinformation?
Answer:
The value is [tex]P (I | L ) = 0.63[/tex]
The probability has increased
Step-by-step explanation:
From the question we are told that
The percentage that are from outside the country is [tex]P(O) = 0.70[/tex]
The percentage that logs on everyday is [tex]P(L) = 0.60[/tex]
The percentage that logs on everyday that are from the inside the country is [tex]P(L | I) = 0.80[/tex]
Generally using Bayes' Rule the probability that a person is from the country given that he logs on the website every day is mathematically represented as
[tex]P (I | L ) = \frac{P(I)* P(L|I)}{ P(O) *P(L|O) + P(I) *P(L|I) }[/tex]
Where [tex]P(I)[/tex] is the percentage that are from inside that country which is mathematically represented as
[tex]P(I) = 1 - P(O)[/tex]
[tex]P(I) = 1 - 0.70[/tex]
[tex]P(I) = 0.30[/tex]
And [tex]P(L| O)[/tex] is percentage that logs on everyday that are from the outside the country which is evaluated as
[tex]P(L| O) = 1- P(L| I)[/tex]
[tex]P(L| O) = 1- 0.80[/tex]
[tex]P(L| O) = 0.20[/tex]
[tex]P (I | L ) = \frac{ 0.3* 0.80 }{ 0.7 *0.20 + 0.3 * 0.8 }[/tex]
[tex]P (I | L ) = 0.63[/tex]
Given that the percentage that are from inside that country is [tex]P(I) = 0.30[/tex]
and that the probability that a person is from the country given that he logs on the website every day is [tex]P (I | L ) = 0.63[/tex]
We see that the additional information increased the probability
5/1-6i = (simplified)
Answer:
5/37+30/37*i
Step-by-step explanation:
we multiply by 1+6i
so 5*(1+6i)/(1^1-36i^2)=(5+30i)/37=
5/37+30/37*i
What is the radius of a circle with a diameter of 9 meters? Enter as a decimal number.
Answer:
4.5 m
Step-by-step explanation:
The diameter is twice the radius
d = 2r
Divide each side by 2
d/2 = r
9/2 = r
4.5 = r
Answer:
4.5 meters
Step-by-step explanation:
radius is half of the diameter
In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Find the angle A.
Answer:
17°
Step-by-step explanation:
Using trigonometrical ratios we have a triangle with opposite of A° as 7cm and adjacent A° as 24cm as drawn in the above diagram.
Using trigonometry the value to be used is Tangent due to the availability of only the opposite and adjacent sides.
tan = opp/adj
tan x(x is the angle) = 7/24
tan x = 0.2917 ~= 0.3
tan x = 0.3
x = tan^-1 0.3
x = 16.7 ~= 17°.
Find the partial derivative of the function f(x,y)=Integral of cos(-7t^2-6t-1)dt. Find fx(x,y) and fy(x,y)
Answer:
[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]
[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]
Step-by-step explanation:
Given that :
[tex]f(x,y) = \int ^x_y cos (-7t^2 -6t-1) dt[/tex]
Using the Leibnitz rule of differentiation,
[tex]\dfrac{d}{dt} \int ^{b(t)}_{a(t)} f(x,t) dt= f(b(t),t) *b'(t) -f(a(t),t) * a' (t) + \int^{b(t)}_{a(t)} \dfrac{\partial f}{\partial t} \ dt[/tex]
To find: fx(x,y)
[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial }{\partial x} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]
[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial x}{\partial x} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial x} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial x} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]
[tex]\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1) -0+0[/tex]
[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]
To find: fy(x,y)
[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial }{\partial y} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]
[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial x}{\partial y} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial y} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial y} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]
[tex]\dfrac{\partial f}{\partial y}= 0 - cos ( -7y^2 -6y-1)+0[/tex]
[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]
Divide and write answer in standard complex form ( a + bi) 10+20i/4+2i
Answer:
[tex]4+3i[/tex]
Step-by-step explanation:
=[tex]\frac{(10+20i)}{4+2i} \\\\\frac{10+20 i}{4+2i}[/tex]x [tex]\frac{(4-2i)}{(4-2i)}[/tex]
=[tex]\frac{(10+20i)(4-2i)}{(4^{2}-2i^{2}) } \\\frac{40-20i+80i+40}{16+4}\\ \frac{80+60i}{20}\\ 4+3i[/tex](Taking 20 common from both numerator and deniminator)
Enter the correct value so that each expression is a perfect square trinomial
Answer:
12x
Step-by-step explanation:
This is b/2^2, so basically you take the square root of 36 and multiply that value by 2.
so [tex]\sqrt{36}[/tex] = 6(2)=12
Hope this makes sense!
Step-by-step explanation:
First, let's look at some examples of what a perfect square trinomial looks like. [tex]x^2 + 16x + 64[/tex]
This trinomial is made from:
[tex](x+8)^2[/tex]
So for your second question (x^2 + ___x + 36), we need to work backwards, starting with the last number of the trinomial, 36. Think of two identical numbers that would make 36 if they got multiplied together. Or: √36. Either way, we get 6. So we can put this as a squared binomial.
[tex](x+6)^2[/tex]
Then, we could solve the binomial to get our middle number. (Use FOIL: Multiply the First terms, then Outer terms, then Inner terms, and Last terms)
[tex](x+6)(x+6)[/tex]
[tex]x^2+6x+6x+36\\x^2+12x+36[/tex]
As you can see, our middle number is 12x, and that is what goes into the blank.
Answer: 12x
Round the whole number 4,205 to the tens place
The tens place has a 0 in that digit. One spot to the right is 5. Since this is 5 or larger, we round up to the nearest ten.
The 0 bumps up to 1. The 5 is replaced with 0
4205 becomes 4210
In the diagram of O, m∠JOK = 60° and OJ = 6 in. What is the exact area of the shaded region?
Answer: 6π
Step-by-step explanation:
Area of a circle is π r².
Area of a section of a circle is π r² × the section of the circle.
[tex]A=\pi r^2\bigg(\dfrac{\theta}{360^o}\bigg)[/tex]
Given: r = 6, Ф = 60°
[tex]A=\pi (6)^2\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =\pi (6)^2\bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =6\pi[/tex]
Find the points of intersection of the graphs of the equations. r = 1 + cos θ r = 1 − sin θ r ≥ 0, 0 ≤ θ < 2π
This question is based on the point of intersection.Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
Given:
Equations: r = 1 + cos θ ...(1)
r = 1 − sin θ ...(2)
Where, r ≥ 0, 0 ≤ θ < 2π
We need to determined the point of intersection of the graphs of the equations.
To obtain the points of intersection, Equate the two equations above as follows;
r = 1 + cos θ = 1 - sin θ
=> 1 + cos θ = 1 - sin θ
Solve further for θ. We get,
1 + cos θ = 1 - sinθ
cos θ = - sinθ
Now dividing both sides by - cos θ and solve it further,
[tex]\dfrac{cos\;\theta}{-cos\;\theta} =\dfrac{-sin\;\theta}{-cos\;\theta}\\\\tan\;\theta=-1\\\\\theta=tan^{-1}(1)\\\\\theta=45^{0}=\dfrac{-\pi }{4}[/tex]
To get the 2nd quadrant value of θ, add π ( = 180°) to the value of θ. i.e
[tex]\dfrac{-\pi }{4} +\pi =\dfrac{3\pi }{4} \\[/tex]
Similarly, to get the fourth quadrant value of θ, add 2π ( = 360° ) to the value of θ. i.e
[tex]\dfrac{-\pi }{4} +2\pi =\dfrac{7\pi }{4} \\[/tex]
Therefore, the values of θ are 3π / 4 and 7π / 4.
Now substitute these values into equations (i) and (ii) as follows;
[tex]When \;\theta=\dfrac{3\pi }{4},[/tex]
[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{3\pi }{4} =1+\dfrac{-\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]
[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{3\pi }{4} =1-\dfrac{\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]
[tex]When\; \theta=\dfrac{7\pi }{4}[/tex]
[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{7\pi }{4} =1+\dfrac{\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]
[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{7\pi }{4} =1-\dfrac{-\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]
Represent the results above in polar coordinates of the form (r, θ). i.e
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
Therefore, at the pole where r = 0, is also one of the points of intersection.
Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
For further details, please prefer this link:
https://brainly.com/question/13373561
Which of the following is the solution to 4/5 = 20/(x-5)?
Answer:
x=30
Step-by-step explanation:
[tex]\frac{4}{5}=\frac{20}{x-5} \\\\4(x-5)=20*5\\\\4x-20=20(5)\\\\4x=20(5)+20(1)\\\\4x=20(5+1)\\\\4x=20(6)\\\\x=\frac{20(6)}{4} \\\\x=5*6\\\\x=30[/tex]
[tex] \frac{4}{5} = \frac{20}{(x - 5)} [/tex]
By Cross-multiplication
[tex] \implies4 \times (x - 5) = 20 \times 5[/tex]
[tex] \implies4x - 20 = 100[/tex]
[tex] \implies4x = 100 + 20[/tex]
[tex] \implies4x = 120[/tex]
[tex] \implies \: x = \cancel \frac{120}{4} [/tex]
[tex] \implies \: x = 30[/tex]
How long will it take you to drive 135 miles at a speed of 45 miles per hour?
Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 − 5x y2 = 0
Answer: Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]
Step-by-step explanation:
Thiis is quite straightforward, so I will be gudiding you through the process.
we have that;
y1 = x² -5x
and y² = 0
Taking Limits:
y1 = x² -5x, y2 = 0
x² - 5x = 0;
so x(x - 5) = 0
this gives x = 0 and x = 5
∴ 0≤x≤5
This is to say that the graph intersets at x = 0 and x = 5 and y2 is the upper most function.
Let us take the formula:
Area = ∫b-a (upper curve - lower curve)
where a here represents 0 and b represents 5
the upper curve y2 = 0
whereas the lower curve y1 = x² - 5x
Area = ∫5-0 [ 0 - (x² - 5x) ] dx
This becomes the Area.
Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]
cheers i hope this helped !!!
zach invested $50 and was able to triple his money in two years. Kayla also began with in investments, and was able to cube her money in two years. Who had more money after two years? Explain
Bob and Laquisha have volunteered to serve on the Junior Prom Committee. The names of twenty volunteers,
including Bob and Laquisha, are put into a bowl. If two names are randomly drawn from the bowl without
replacement, what is the probability that Bob's name will be drawn first and Laquisha's name will be drawn
second?
Answer:
1/380
Step-by-step explanation:
Probability of Bob's name drawn first is:
1/20 as there are 20 people with equal chanceAnd probability of Laquisha's name drawn second is:
1/19 as there are 19 people left with equal chanceProbability of the two events happening is:
1/20*1/19 = 1/380 product of individual probabilitiesAnswer:
Hey there!
1/19 (1/20)=1/380, so the probability is 1/380
Let me know if this helps :)
Interpret the regression coefficients. Fill in the blanks below.
The [a. coefficient of determination b. correlation coefficient intercept
slope coefficient] is the estimated amount of a purchase if time spent viewing the online catalog were zero. The a. intercept b. coefficient of determination
c. slope coefficient d. correlation coefficient] is the estimate of amount that a purchase changes for one extra minute spent viewing the online catalog.
b. Compute the coefficient of determination and interpret its meaning. Fill in the blanks below.
The [a. proportion b. amount] of the total variation in purchases that can be explained by variation in the minutes spent viewing the? on-line catalog is equal to the coefficient of? determination, which is ____. (Round to three decimal places as needed)
State the conclusion. Fill in the blanks below. [a. Do not Reject b. Reject] the null hypothesis. There is [a. sufficient b. insufficient] evidence to support the claim that the overall model is significant.
The p-value is ____. (Round to three decimal places as needed.)
State the conclusion. Fill in the blanks below.
a.Do not Reject b. Reject c. the null hypothesis. There is a. sufficient b. insufficient
evidence to support the claim that the overall model is significant.
Determine the p-value.
The p-value is ____. (Round to three decimal places as needed.)
State the conclusion. Fill in the blanks below.
[a. Reject b. Do not Reject] the null hypothesis. There is [a. insufficient b. sufficient]
evidence to support the claim that the regression slope coefficient is not equal to zero.
Answer:
With the information given in the question, the blank spaces are filled thus:
Step-by-step explanation:
1. The intercept is the estimated amount of a purchase, if time spent viewing the online catalog was zero minutes.
2. The slope coefficient is the estimate of amount that a purchase charges/changes, for one extra minute spent viewing the online catalog.
3. The proportion of total variation in purchases that can be explained by variation in the minutes spent viewing an online catalog is equal to the coefficient of determination.
4. The p-value is the probability value
5. Reject the null hypothesis if there is sufficient evidence to support the claim that the regression slope coefficient is not equal to zero.
NOTE: In the case of number 5, the assumption is that;
Null Hypothesis: The regression slope coefficient = 0
Alternative Hypothesis: The regression slope coefficient ≠ 0
Other answers require numerical information and full data, in order to be computed or calculated.
Select the correct answer.
Given
D = {xIx is a whole number}
E = {xl x is a perfect square between 49 and 100}
F={xl x is an even number between 10 and 20}
The expression Du F means...
The expression DNF means
The expression Dn E means
The expression E N F means
The expression Dn (EU F) means
Answer:
Step-by-step explanation:
D = {x | x is a whole number}
D = {0, 1, 2, 3, 4,......}
E = {x | x is a perfect square between 49 and 100}
E = {64, 81}
F = {x | x is an even number between 10 and 20}
F = {12, 14, 16, 18}
D∪F = {x | x is whole number}
D∩F = {x | x is an even number between 10 and 20}
D∩E = {x | x is a perfect square between 49 and 100}
E∩F = {null set}
D∩(E∪F) = {12, 14, 16, 18, 64, 81}