Answer:
A. H: mu1< mu2
Step-by-step explanation:
Given that :
Mean amount of time per domestic cars = mu1
Mean amount of time per foreign cars = mu2
Automobile technicians claim :
The mean amount of time (in hours) per domestic car repair is more than that of foreign cars. This will be the Null hypothesis.
Null hypothesis : mu1 > mu2
The alternative hypothesis will negate the Null hypothesis and will hence be the opposite. This can this be expressed as :
Alternative hypothesis : mu1 < mu2
Solve x≤0 or x≥−4 and write the solution in interval notation.
Answer: [tex](-\infty, \infty)[/tex]
=================================================
Explanation:
Draw out a number line. Plot 0 and -4 on the number line.
Shade to the left of x = 0, and have a filled in circle at the endpoint. This is the graph of [tex]x \le 0[/tex]
Then graph [tex]x \ge -4[/tex] by plotting a filled in circle at -4, and shading to the right.
Note how the two graphs overlap to cover the entire real number line
So if we have [tex]x \le 0 \ \text{ or } \ x \ge -4[/tex] then we're basically saying x is any real number. To write this in interval notation, we write [tex](-\infty, \infty)[/tex]
This is the interval from negative infinity to positive infinity (or just infinity). We exclude each endpoint because we can't actually reach infinity itself. Infinity is not a number. Infinity is a concept.
-------------
Side note: if you change the "or" to "and", then the solution to [tex]x \le 0 \ \text{ and } \ x \ge -4[/tex] would be [tex][-4, 0][/tex] to indicate the interval from x = -4 to x = 0, including both endpoints. This is the region where the two graphs overlap.
Use Green's Theorem to evaluate the line integral along the given positively oriented curve.
∫C (3y + 7e^sqrt(x)) dx + (8x + 5 cos y^2) dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2
Answer: ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA = 5/3
Step-by-step explanation:
Given that;
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy)
Green's Theorem is given as;
∫c (P(x,y)dx + Q(x,y)dy) = ∫∫ₐ { (-β/βy) P(x,y) + (β/βy) Q(x,y) } dA
Now our P(x,y) = 3y + 7e^(√x) and our Q(x,y) = 8x + 5 cos (y²)
Since we know this, therefore; we substitute
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ { (-β/βy) (3y + 7e^(√x)) + (β/βy) (8x + 5 cos (y²)) } dA
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ ( 8-3) dA
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA
from the question, our region is defined by a lower bound: y = x² and an upper bound of y = √x
going from x = 0 to x = 1
Now calculating ∫∫ₐ 5dA by means of the description of the region, we say;
∫∫ₐ 5dA = 5¹∫₀ ₓ²∫^(√x) dydx
∫∫ₐ 5dA = 5¹∫₀ (y)∧(y-√x) ∨(y-x²) dx
∫∫ₐ 5dA = 5¹∫₀ (√x-x²) dx
∫∫ₐ 5dA = 5 [ ((x^(3/2))/(3/2)) - x³/3]¹₀ NOW since ∫[f(x)]ⁿ dx = ([f(x)]ⁿ⁺¹ / n+1) + C
then
∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3) - ((0^(3/2))/(3/2)) - 0³ / 3) ]
∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3)
∫∫ₐ 5dA = 5/3
Therefore ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA = 5/3
In this exercise we have to use green's theorem to calculate the values of the curve through the integers, so we will find that:
[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]
First, the integral given in this exercise corresponds to:
[tex]\int\limits_C {((3y+7e{\sqrt{x}} dx) + (8x+5cos(y^2)) } \, dy[/tex]
Green's Theorem is given as;
[tex]\int\limits_C {(P(x,y)dx + Q(x,y)dy)} \, = \int\limits \int\limits_a { (-\beta/ \beta_y) P(x,y) + (\beta/ \beta_y) Q(x,y) } dA \,[/tex]
Now our:
[tex]P(x,y) = 3y + 7e^{(\sqrt{x} )} \\ Q(x,y) = 8x + 5 cos (y^2)[/tex]
Since we know this, therefore; we substitute:
[tex]\int\limits_C {((3y + 7e^{(\sqrt{x} )} dx + (8x + 5 cos (y^2)) dy)} = \int\limits \int\limits_a {(-\beta / \beta_y) (3y + 7e^{(\sqrt{x} )} + (\beta / \beta_y) (8x + 5 cos (y^2))} \, dA\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {( 8-3) dA}\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {5 dA}\\[/tex]
From the question, our region is defined by:
lower bound: [tex]y = x^2[/tex] upper bound: [tex]y = \sqrt{x}[/tex]
Now calculating by means of the description of the region, we say;
[tex]\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 \int\limits^{\sqrt{x} }_{x^2} {x^2} \, dydx\\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {y^{\sqrt{x} } \, dx \\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {{\sqrt{x} -x^2} \, dx\\\int\limits \int\limits_a {5} \, dA = 5 [ ((x^{3/2})/(3/2)) - x^3/3][/tex]
Knowing the formula:
[tex]\int\limits {[f(x)]^n} \, dx = ([f(x)]^{n+1} / n+1) + C[/tex]
Applying the values in the presented formula we find that:
[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]
See more about Green's Theorem at brainly.com/question/15062695
In each of the following
[tex]find \: \frac{dy}{dx}\: [/tex]
[tex]a)\: \: y = \sin ^ - 1 \sqrt{x} + ln( \sqrt{x} ) [/tex]
[tex]b) {e}^{y} = {2}^{x} log(x) - {e}^{2x} [/tex]
(a) Recall that
[tex]\dfrac{\mathrm d[\sin^{-1}x]}{\mathrm dx}=\dfrac1{\sqrt{1-x^2}}[/tex]
[tex]\dfrac{\mathrm d[\ln x]}{\mathrm dx}=\dfrac1x[/tex]
[tex]\dfrac{\mathrm d[\sqrt x]}{\mathrm dx}=\dfrac1{2\sqrt x}[/tex]
Then by the chain rule,
[tex]y=\sin^{-1}(\sqrt x)+\ln(\sqrt x)[/tex]
[tex]\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm d[\sin^{-1}(\sqrt x)+\ln(\sqrt x)]}{\mathrm dx}[/tex]
[tex]=\dfrac1{\sqrt{1-(\sqrt x)^2}}\dfrac{\mathrm d[\sqrt x]}{\mathrm dx}+\dfrac1{\sqrt x}\dfrac{\mathrm d[\sqrt x]}{\mathrm dx}[/tex]
[tex]=\dfrac1{2\sqrt x\sqrt{1-x}}+\dfrac1{2(\sqrt x)^2}[/tex]
[tex]=\dfrac1{2\sqrt{x-x^2}}+\dfrac1{2x}[/tex]
[tex]=\boxed{\dfrac{x+\sqrt{x-x^2}}{2x\sqrt{x-x^2}}}[/tex]
(b) I'll assume [tex]\log x[/tex] refers to the logarithm of base [tex]e[/tex]. Recall that
[tex]\dfrac{\mathrm d[e^x]}{\mathrm dx}=e^x[/tex]
[tex]2^x=e^{\log2\,x}\implies\dfrac{\mathrm d[2^x]}{\mathrm dx}=e^{\log2\,x}\dfrac{\mathrm d[\log2\,x]}{\mathrm dx}=\log2\cdot2^x[/tex]
Then using the chain rule and implicit differentiation, we get
[tex]e^y=2^x\log x-e^{2x}[/tex]
[tex]\implies e^y\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm d[2^x]}{\mathrm dx}\log x+2^x\dfrac{\mathrm d[\log x]}{\mathrm dx}-e^{2x}\dfrac{\mathrm d[2x]}{\mathrm dx}[/tex]
[tex]e^y\dfrac{\mathrm dy}{\mathrm dx}=\log2\cdot2^x\log x+\dfrac{2^x}x-2e^{2x}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\log2\cdot2^x\log x+\frac{2^x}x-2e^{2x}}{e^y}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\log2\cdot2^x\log x+\frac{2^x}x-2e^{2x}}{2^x\log x-e^{2x}}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\boxed{\dfrac{\log2\cdot2^xx\log x+2^x-2xe^{2x}}{x(2^x\log x-e^{2x})}}[/tex]
If instead [tex]\log x=\log_{10}x[/tex] denotes the base 10 logarithm, you need only make the following adjustment:
[tex]\log x=\dfrac{\ln x}{\ln 10}\implies\dfrac{\mathrm d[\log_{10}x]}{\mathrm dx}=\dfrac1{\ln10\,x}[/tex]
where [tex]\ln x[/tex] is logarithm of base [tex]e[/tex].
Which is the better buy, 36 cans for $3.32, or 9 cans for $0.91 ?
O They are the same.
O 9 cans for $0.91
36 cans for $3.32
Answer:
36 cans for $3.32
Step-by-step explanation:
36 cans = $3.32
1 can =$ 0.092
9 cans = $0.91
1 can = $0.01
0.09 and 0.1 the cheaper is 0.09 dollars so 36 cans for $3.32 is better
Which of the following is NOT a solution to the inequality graphed below?
Graph:
(-2, -4)
(-1, -5)
(0, -3)
(2, -1)
Greetings from Brasil...
The point (-2; -4) is in the blue area, so it is the solution to the equation;
The point (-1; -5) is in the blue area, so it is the solution to the equation;
The point (0; -3) is in the blue area, so it is the solution to the equation;
The point (2; -1) is exactly on the function line. As this line is dashed, it does not include its values, so this point is not a solution (no point on the dashed line is a solution)
Based on a survey, assume that 28% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when consumers are randomly selected, exactly of them are comfortable with delivery by drones. Identify the values of n, x, p, and q. 28
Question:
Based on a survey, assume that 28% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly three of them are comfortable with delivery by drones.
Identify the values of n, x, p, and q.
Answer:
[tex]n = 5[/tex]
[tex]x = 3[/tex]
[tex]p = 0.28[/tex]
[tex]q = 0.72[/tex]
Step-by-step explanation:
Given
Proportion of customers that prefer drone = 28%
Selected customers= 5
Customers expected to prefer drone = 3
Required
Determine the value of n, x, p and q
In probability; n represents the selected sample;
So;
[tex]n = 5[/tex]
The expected number of people to prefer drone is represented by x;
So;
[tex]x = 3[/tex]
In probability, opposite probabilities add up to 1
i.e.
[tex]p + q = 1[/tex]
Where p is the given probability;
[tex]p = 28\%[/tex]
Convert to decimal
[tex]p = 0.28[/tex]
Substitute 0,28 for p in the above equation
[tex]p + q = 1[/tex] becomes
[tex]0.28 + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - 0.28[/tex]
[tex]q = 0.72[/tex]
Question 6 of 20 :
Select the best answer for the question.
6. The sum of 1/6, 2/3, and 1/4 is
O A. 2172, or 1/36
B. 11/12
O C. 4/12 or 13.
OD. 13/12 or 11/12
Answer:
OD. 13/12 or 1 1/12
Step-by-step explanation:
[tex] \frac{1}{6} + \frac{2}{3} + \frac{1}{4} \\ lcm = 12 \\ = \frac{2 + 8 + 3}{12} \\ [/tex]
[tex] = \frac{13}{12 } \\ 13 \div 12 = 1r1 \\ = 1 \frac{1}{12} [/tex]
A four pack of batteries cost 5.16 at this price what is the cost of
Answer:
1.29 for 1 pack
Step-by-step explanation:
5.16/4=1.29
1/2(6+18)-2²
Help me my good ppl it asks to evaluate
Answer:
8
Step-by-step explanation:
1/2(6+18)-2^2
=1/2(24)-4
=12-4
=8
You bought 8 dvds for $22 each and 4 dvds for $13 each.
What is the average price you paid for each movie? *
Answer:
the average is
add 22 8 times and add 13 4 times
8×22=176
4×13=52
52+176=228
The average price you paid for each movie will be $19.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean.
It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
You bought 8 DVDs for $22 each and 4 DVDs for $13 each.
Then the total number of the DVDs will be
Total DVDs = 8 + 4 = 12
The total amount of dollars spent will be
Total amount = 22 x 8 + 13 x 4
Total amount = $228
Then the average price you paid for each movie will be
Average = $228 / 12
Average = $19
The average price you paid for each movie will be $19.
More about the mean link is given below.
https://brainly.com/question/521501
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A customer at a restaurant leaves $80 on the table to pay for the food, a 15% tip, and 8% sales tax. If both tip and sales tax were calculated from
the cost of the food, which of the following was the cost of the food, rounded to the nearest cent?
Answer:
$65.04
Step-by-step explanation:
Given:
Total amount left by the customer on table = $80
It contains cost of the food + 15% tip + 8% sales tax.
Sales tax and tip are calculated from the cost of food.
To find:
Cost of the food = ?
Solution:
Let the cost of food = $[tex]x[/tex]
As per given question statement:
Tip = 15% of [tex]x[/tex]
Sales Tax = 8% of [tex]x[/tex]
Money left on table = Cost of food + Tip + Sales tax
$80 = [tex]x[/tex] + 15% of [tex]x[/tex] + 8% of [tex]x[/tex]
Now, let us solve the equation:
[tex]\$80 = x + 15\%\ of\ x + 8\%\ of\ x\\\Rightarrow 80 = x + \dfrac{15}{100} \times x + \dfrac{8}{100} \times x\\\Rightarrow 80 = \dfrac{100x + 15\times x + 8\times x}{100}\\\Rightarrow 80 = \dfrac{123x}{100}\\\Rightarrow 80 \times 100= 123x\\\Rightarrow x = \dfrac{8000}{123}\\\Rightarrow \bold{x = \$65.04}[/tex]
Therefore, the cost of food, rounded off to nearest cent is $65.04.
Answer:
Step-by-step explanation:
The cost of the food as x, the tips as 0.15, and the tax as 0.08x. Then setting up and solving the equation x+0.15x+0.08x=80.
Solve for x please
1/6x=10
Answer:
x=60
Step-by-step explanation:
1/6x=10
multiply both sides by 6 to get x
x=60
Answer:
x=60
Step-by-step explanation:
In order to solve for x, we must isolate x on one side of the equation.
The equation given is:
[tex]\frac{1}{6}x=10[/tex]
1/6 and x are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 1/6
[tex]\frac{1}{6}x/\frac{1}{6}=10/\frac{1}{6}[/tex]
When dividing by a fraction, you can multiply by the reciprocal of the fraction instead.
To find the reciprocal, flip the numerator and denominator.
1/6 ⇒ flip top number and bottom number ⇒ 6/1=6
Replace the division by 1/6 with multiplication by 6.
[tex]\frac{1}{6}x * 6=10*6[/tex]
[tex]x= 10 *6[/tex]
[tex]x=60[/tex]
The solution to this equation is x=60
today the city madsion has a population of 6.34 million residents. in 19114, the population was just 1.9 million residents. by how many residents has the population increased since 1914
Subtract starting population from current one:
6.34 - 1.9 = 4.44
The population increased by 4.44 million.
An artist makes a scale drawing of a parallelogram-shaped sculpture. The scale is 10 cm on the drawing? Show your work. PLEASE HELP ME-
Answer:
Area of parallelogram = 25.2 m²
Step-by-step explanation:
Given:
Base = 6 m
Height = 4.2 m
Find:
Area of parallelogram
Computation:
Area of parallelogram = Base × Height
Area of parallelogram = 6 × 4.2
Area of parallelogram = 25.2 m²
can you please help me this homework?
Answer & Step-by-step explanation:
Working from the inner circle out:
Natural Numbers: 1,2,3,4
These are the numbers you would use to count
Whole Numbers: 0,1,2,3
The natural numbers and zero
Integers: -3,-2,-1,0,1,2,3
The natural numbers, their opposites, and zero
Rational Numbers: [tex]-\frac{1}{2}, 0.22222222....,1,2,\frac{2}{3} ,\frac{5}{4} ,6.1[/tex]
-are all numbers that you can write as a quotient of integers [tex]\frac{a}{b}, b\neq 0[/tex]
-include terminating decimals. For example, [tex]\frac{1}{8}=0.125[/tex]
-include repeating decimals. For example, [tex]\frac{1}{3}=0.333333...[/tex]
In the rectangle:
Irrational Numbers: [tex]\sqrt{2} ,\pi[/tex]
-have decimal representations that neither terminate nor repeat. For example, [tex]\sqrt{2} =1.414213...[/tex]
-cannot be written as quotients of integers
Which expression is equivalent to 4/9×7
Answer:
Step-by-step explanation:
if the fraction is (4/9)*7 then the answer =28/9
if the fraction is 4/(9*7) then the answer is 4/63
How would you write a word phrase for the algebraic expression d/5+2? The difference between the quotient of d and 5 and 2? The sum of 2 and the product of d and 5? The difference between 2 and the product of d and 5? The sum of the quotient of d and 5 and 2?
Answer: The word phrase for this expression is the last option, "The sum of the quotient of d and 5 and 2." d is being divided by 5, so we would use "quotient of d and 5" for that part, and then we would add the "sum" because d/5 is being added to 2.
Kendall is solving this inequality. x/2 + 6 > 42 What should she do first to solve?
Answer:
see below
Step-by-step explanation:
First, she should subtract 6 from both sides of the inequality. This makes it so that the x terms are on one side and the non-x terms are on the other side so she can then solve for x by multiplying the entire inequality by 2.
The table shows the relationship between the number of calories Raquel burns while hiking and the number of minutes she hikes.
How many calories will Raquel burn in 1 minute while hiking?
Answer:
hi i have the same question and im super confused, what was your answer for that question?
Step-by-step explanation:
Answer:
5 calories
Step-by-step explanation:
A very wealthy person has 96 shirts, 90 pairs of pants and 120 pairs of
shoes but only one pair of underwear. How many different outfits can
they wear?
A. 1,630,800
B. 1,036,800
C. 1,360,800
D. 1,063,800
Answer:
B.
Step-by-step explanation:
96x90x120x1= 1,036,800
Answer:
Hey there!
The wealthy person can have 96x90x120 different outfits, and that is 1036800 combinations.
Let me know if this helps :)
Classify the AVERAGE number of students in all the math classes at Ponderosa. (Click all that apply)
Real
Irrational
Natural
Whole
Rational
Integer
Answer:
real, rational
Step-by-step explanation:
Without knowing what the average number of students is, we know the number must be a real number, and must be rational. (An average of integers is always the ratio of two integers.) It may or may not be a natural number, whole number, or integer.
Prove the cofunction Identity using the Addition and Subtraction Formulas. Tan (pi/2 - u) = cot (u) Since tan (pi/2) is undefined, use a Reciprocal Identity, and then use the Substitution Formulas to simplify. Tan (pi/2 - u) = sin/cos (pi/2 - u) = (cos (u)) - (cos (pi/2)) (sin (u))/(sod (pi/2)) (cos (u)) + (sin (pi/2)) (sin (u)) = (cos (u)) - (0) (sin (u))/(0) (cos (u)) + (1) (sin (u)) =/sin (u)
Answer:
Step-by-step explanation:
We are to prove the cofunction Identity using the Addition and Subtraction Formulas. [tex]tan(\pi/2 - u) = cot (u)[/tex]
From trigonometry identity, [tex]tan x = sinx/cosx[/tex], starting from right hand side of the equation, the expression above will become;
[tex]tan(\pi/2 - u) = \dfrac{sin(\frac{\pi}{2}-u )}{cos(\frac{\pi}{2}-u) }........ \ 1 \\\\from\ quadrant;\\\\sin(\frac{\pi}{2}-u) = cos (u) \ and \ cos(\frac{\pi}{2}-u) = sin(u)[/tex]
Substituting this trigonometry identities into equation 1 we will have;
[tex]tan(\pi/2 - u) = \dfrac{cos(u)}{sin(u)}[/tex]
Since cot(u) = 1/tan(u) = cos(u)/sin(u), hence;
[tex]tan(\pi/2 - u) = \dfrac{cos(u)}{sin(u)} = cot(u)\\\\tan(\pi/2 - u) = cot (u)\ Proved![/tex]
Katie is working on a blueprint for a fence she is designing. She will need to construct parallel lines to ensure that the second slat is parallel to the first. Which step will Katie need to do first to ensure that the second slat is parallel to the first slat in the diagram below? a line Draw a second line using a straightedge so that it intersects the first. Draw a second line using a straightedge so that it is parallel to the first. Create two arcs above the line using a compass. Create arcs above and below the line using a compass.
A. Draw a second line using a straightedge so that it intersects the first.
Step-by-step explanation:
trust me i took the test and got it right
Answer:
Draw a second line using a straightedge so that it intersects the first.
Answer above is correct, just took the test.
Step-by-step explanation:
lila compro cuatro pares de pantalones azules q $32 cada uno. cuánto dinero le pago lila al empleado?
Answer:
128
Step-by-step explanation:
32 x 4 = 128
o
32 + 32 + 32 + 32 = 128
Consider the function represented by the table.
What is f(0)?
O4
O 5
O 6
O 7
Answer:
6
Step-by-step explanation
The only f(0) answer in table is 6
Answer:
6
Step-by-step explanation:
f(0) = 6. That is, when the input (x) is 0, the output (y) is 6.
what is the ordered pair for y=-3x when x=0
Answer: (0,0)
Step-by-step explanation:
When x is 0 then input 0 into the equation for x and solve for y.
y = -3(0)
y = 0
So x is 0 and y will also be zero so we will have the ordered pair (0,0)
Answer:
The ordered pair is (0,0)
Step-by-step explanation:
y=-3x
Let x = 0
y = -3*0
y = 0
The ordered pair is (0,0)
what is 1 3/8 as a decimal
Answer:
1.375
Step-by-step explanation:
I recommend using a calculator. Divide 3/8. Add 1 back.
The decimal value of 1(3/8) is 1.375.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
1(3/8)
This can be written as,
11/8
Now,
11/8 = 1.375
Thus,
The decimal value of 1(3/8( is 1.375.
Learn more about fractions here:
https://brainly.com/question/24370499
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You are working as an office apprentice for bksb newcastle arena you are helping collect a customer satisfaction survey for the arena enter the following replies into the table below
To find the area of the arena, you will need to find the areas of the rectangular spaces and the 2 semicircles. Because the formulas are given, I will just substitute in the values and show the work for finding the areas.
To find the perimeter, you will look at the distances of lines that take you around the space. Because two of these spaces are half circles, you will need to find the circumference of the full circle.
Also, the answers need to be given in meters, so all units given in centimeters will be divided by 100 to convert them to meters.
Perimeter:
C= 3.14 x 20 m
C = 62.8 meters
62.8 + 8 + 25 + 8 + 5 + 8 + 10 + 8 + 40= 174.8 meters for the Perimeter
Area:
A = 25 x 8
A = 200 square meters
A = 10 x 8
A = 80 square meters
A = 20 x 40
A = 800 square meters
A = 3.14 x 10^2
A = 314 square meters
Total Area: 314 + 800 + 80 + 200= 1394 square meters
Suppose that X is a random variable with probability function x 0 1 2 3 4 5 P(x) 0.00032 0.0064 0.0512 0.2048 0.4096 0.32768 and that the random variable Y = 9X2 − 36X + 4. (a) What is the range of Y ? (b) Calculate P{Y = 4}. (c) Calculate P{Y = 0}.
(a) For each value of X we have:
[tex]X=0\quad\Rightarrow\quad Y=4\\\\X=1\quad\Rightarrow\quad Y=-23\\\\X=2\quad\Rightarrow\quad Y=-32\\\\X=3\quad\Rightarrow\quad Y=-23\\\\X=4\quad\Rightarrow\quad Y=4\\\\X=5\quad\Rightarrow\quad Y=49[/tex]
so the range of Y = {-32, -23, 4, 49}
(b)
[tex]P\{Y=4\}=P\{X=0\}+P\{X=4\}=0.00032+0.4096=\boxed{0.40992}[/tex]
(c)
Y cannot equal 0, so
[tex]P\{Y=0\}=0[/tex]
33) through: (2,-2) and (2-1)<br />
Please help
Answer:
y = 3 4 x − 25 4
Explanation:
We could use calculus but first as with all Mathematical problems one should step back and think about what the question is asking you, and in this case we can easily answer the question using knowledge of the equation, in this case:
x 2 + y 2 = 25
represents a circle of centre ( a , b ) = ( 0 , 0 ) and radius r = 5
First verify that ( 3 , − 4 ) actually lies on the circle;
Subs x = 3 oito the circle equation:
⇒ 3 2 + y 2 = 25 = y 2 = 16 ⇒ y = ± 4 So ( 3 , − 4 )
So does indeed lie on the circle. A straight line passing between that point and the centre of the circle ( 0 , 0 ) will be perpendicular to the tangent. So the gradient of the normal is given by:
m N = Δ y Δ x = − 4 − 0 3 − 0 = − 4 3 Then as the normal is perpendicular to the tangent the product of their gradients is − 1 , so then: m T = 3/4
So using the point/slope form y − y 1 = m ( x − x 1 ) the equation we seek is;
y − ( − 4 ) = 3/4 ( x − 3 )
∴ y + 4 = 3/4 x − 9/4
∴ y = 3/4 x − 25/4
We can confirm this solution is correct graphically:
If x 2 + y 2 = 25 then differentiating wrt x implicitly gives us:
2 x + 2 y d y d x = 0
∴ d y d x = − x/y
When x = 3 and y = − 4 ⇒ d y d x = − 3 − 4 = 3 4 , which is what we obtained.
Hoped I helped
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