Answer:
$70
Step-by-step explanation:
x = 200 - 10 · 13
x = 200 - 130
x = 70
The designers of a water park have sketched a preliminary drawing of a new slide. The length of the ladder is I - 40 feet, and its angle of elevation is 60 (segure). 60 (a) Find the height of the slide. (Round your answer to two decimal places) - (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance ander travels (c) Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30°. Find an interval for how far ander travels hortzontally (round me values to one decimal place. Enter your answer using interval notation
The interval for horizontal distance is
(59.9 ,74.2) ( ranging from 59.9 feet to 74.2 feet)
As per given in the question,
The length of the ladder (l) is 40feet
The angle of elevation in the triangle is [tex]60^0[/tex]
a) In a Δ ABC
One angle is given as 60 and the one side length (length of ladder) is given as 40 feet
The height of the slide is
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]sin60^0[/tex] = [tex]\frac{h}{40}[/tex] where the value of ( [tex]sin60^0={\frac{\sqrt{3} }{2} }[/tex])
=> [tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{h}{40}[/tex]
=> h = 20[tex]\sqrt{3}[/tex]
Approximately the height of the slide is 34.64 feet
b) In Δ DEF,
[tex]\theta = tan^{-1} \frac{h}{d}[/tex] ----( 1)
=> [tex]Tan^{-1} (\frac{34.6}{d} )[/tex]
c) the angle of depression is [tex]\theta=25^0[/tex] and [tex]\theta=30^0[/tex]
first for the value [tex]\theta=30^0[/tex]
substitute the value of [tex]\theta[/tex] in equation (1)
[tex]tan30^0=(\frac{34.63)}{d})[/tex] where the value of ( [tex]Tan 30^0=\frac{1}{\sqrt{3} }[/tex])
=> [tex]\frac{1}{\sqrt{3} } =\frac{34.63}{d}[/tex]
=> d = 59.99
now
substitute the value [tex]\theta=25^0[/tex] in equation (1)
[tex]tan25^0=(\frac{34.6}{d} )[/tex]
=> d = 74.28
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write and find the general solution of the differential equation that models the verbal statement. evaluate the solution at the specified value of the independent variable. the rate of change of p is proportional to p. when t
When t = 3869, the rate of change of p is proportional to p.
What is differential equation?A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.
Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three. Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.
The primary focus of studying differential equations is on the solutions—the collection of functions that satisfy each equation—as well as the characteristics of those solutions.
Only the most basic differential equations can be solved using explicit formulas, but many features of a particular differential equation's solutions can be deduced without doing an exact calculation.
When a closed-form expression is used, it is common for.
According to our question-
The revised equation is then
P=5000exp(-0.0513t)
Find P at t=5 now.
P=5000 exp(-0.0513×5)
P=5000 ×exp(-0.25647) (-0.25647)
P=5000 × 0.77378
P=3868.89.
P = 3869. Roughly
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When a company sales x units of a product, its profits P can be determined
using the profit function
P(x) =
-2x² + 40x + 280
a) How many units must be sold to maximize profit?
b) What is the maximum profit?
(a) There are 10 units must be sold to maximize profit.
(b) The maximum profit is 480.
what is profit?
A profit is an income that is given to the owner in an efficient market production process in accounting. The owner's primary interest in the income-formation process of market production is profit, which is a measure of profitability. Different profit metrics are frequently employed.
Given:
A company sales x units of a product, its profits P can be determined
using the profit function P(x) = -2x² + 40x + 280 ..(1)
We have to find the maximum profit.
Differentiate equation (1) w.r.t x
P'(x) = -4x +40 ..(2)
-4x + 40 = 0
4x = 40
x = 10
Again differentiate equation (2) w.r.t x
P''(x) = -4 which is negative.
Hence, there are 10 units must be sold to maximize profit.
Now, to find the maximum profit.
Plug x = 10 in equation (1)
P(10) = -2(10)^2 + 40(10) + 280
= -200 + 400 + 280
P(10) = 480
Hence, the maximum profit is 480.
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start by thinking of the number 22 as divided into 22 individual items and the variables x1, x2, and x3 as three categories into which these items are placed. since each xi is a positive correct: your answer is correct. integer, start by placing one item in each category and distribute the remaining items among the categories. the number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. thus, the answer is 20 incorrect: your answer is incorrect. .
The number of solution to the equation is 210 when consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃.
Given that,
Consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃ . acting as the three categories into which these items are sorted. Since each x is a true affirmative, your response is accurate. Put one item in each category to begin with, then divide the remaining items across the categories. The number of classification schemes for all the objects is the number of solutions to the equation satisfying the given criteria. In light of this, your response of 20 is erroneous.
We know that,
Number 22 is divided into 22 individual items ,
The three categories in which these items are placed are x₁, x₂ and x₃ .
x₁+x₂+x₃=22----->equation(1)
(x₁-1)+(x₂-1)+(x₃-1)=22-3=19
Let
a=x₁-1,
b=x₂-1 and
c=x₃-1.
So,
a+b+c= 19 ----->equation(2)
So , the number of ways of arranging 21 characters in which 19 are same(A) and 2 are same (J)
= 21!/(2! × 19!)
= 21×10 = 210
Therefore, the number of solution to the equation is 210 when consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃.
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2. A gas in a flexible container with volume 8L has a temperature of 400 K. If the temperature of the gas changes to 200 K, what is the expected new volume of the gas?
A. 2 L
B. 4 L
C. 16 k
D. 32 L
The volume of the gas becomes 4L. Option B is correct.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
From the ideal gas equation, we know that,
Volume is directly proportional to the temperature,
So,
V₁ / V₂ = T₁ / T₂
Where,
V₁ and T₁ are the initial pressure and temperature,
V₂ and T₂ are the final pressure and temperature.
Substitute the values,
8 / V₂ = 400 / 200
V₂ = 4
Thus, the volume of the gas becomes 4L. Option B is correct.
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1. Assume there are 5 red balls, 6 blue balls, and 4 green balls. If the balls are removed from the box one at a time, in how many different orders can the balls be removed assuming two balls of the same type are indistinguishable.
2. Give a recursive definition of the set of all even positive integers not divisible by 3.
Please write clearly so I can study from it! Try not to skip steps as much as you can.
Thank you!
There are 1307674368000 possible methods to remove each ball from the box one at a time.
what is probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. examination of events subject to probability.
given,
the quantity of balls inside a box ,
four red balls
6 balls in blue
four green balls
The variety of ways the balls can be taken out of the box one at a time must be determined.
Here,
Combination is possible because order is imperceptible;
mixture formula; nCr is equal to n!/r1(n-r)!
Here, There are 15 balls in the box overall (5 + 4 + 6 balls).
Then.
¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000
that is
There are 1307674368000 ways in which we can take the balls out of the box one at a time.
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Which expression is equivalent to 3√x^5y^?
The equivalent expression for the given expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression ∛x⁵y.
expression is equivalent to ∛x⁵y is
[tex](x^5y)^{\frac{1}{3} }[/tex]
= [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]
The equivalent expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.
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(c) Solve by Completing the Square (Round answers to the nearest tenth)
x²+10 x+2=2 x+5
After solving the equation by Completing the square , the answer is x = 0.4 , x = -8.4 .
In the question ,
it is given that ,
the equation is x² + 10x + 2 = 2x + 5,
rewriting the equation ,
we get ,
x² + 8x - 3 = 0
adding 3 to both sides ,
we get ,
x² + 8x = 3 ,
For the method of completing the square ,
we take half of the second term's coefficient, and square it, then add it to both sides.
that is 8/2 = 4 .
the equation becomes ;
x² + 2*x*4 + 4² = 3 + 4²
(x + 4)² = 3 + 16
(x + 4)² = 19
taking root on both the sides ,
we get ,
x + 4 = ±√19
So , x = -4 + √19 or x = -4 - √19
Simplifying further ,
we get ,
x = 0.35889 or x = -8.35889
rounding to the nearest tenth we get
x = 0.4 or x = -8.4 .
Therefore , the solution of the given equation is x = 0.4 , x = -8.4 .
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problem 1.save and preview only -- answers not submitted for grading (5 points) Find the equation in x and y for the line tangent to the curve in polar coordinates r-2 sin θ at the value θ-- Leave your answer in exact form
The equation in x and y for the line tangent to the curve is x - √3y - √3 = 0
A given curve can be defined by both its cartesian coordinates that is in x-y form or in polar coordinates that is in terms of r and θ there exists a relationship between two sets of coordinates
x = r cosθ
y = r sinθ
The tangent to any curve f(x) is defined by f'(x) . In order to find tangent to a given terms of r and θ , we can calculate from the above to expressions f'(x)
f'(x) = dy/dx = dx/dθ ÷ dy/dθ
It is given in the question that
r = 2 sinθ
Replacing the value of r to the standard equation,
x = (2 sinθ )cosθ = sin2θ
At θ = π/3 , x = √3 / 2
y = (2 sinθ)sinθ = 2sin²θ
At θ = π/3 , y = 3/2
Differentiating both w.r.t θ
=> dx / dθ = 2cosθ
=> dy/dθ = 4sinθcosθ
So, dy/dx = 2cosθ / 4sinθcosθ
=> 1 / 2sinθ
Therefore , slope of tangent : m = 1/2sinθ ( θ = π/3)
=> m = 1 / 2sin(π/3)
=> m = 2 / 2√3
=> m = 1 /√3
Hence , the equation of line is
( y - 3/2 ) = 1 /√3 (x - √3 / 2)
=> √3y - 3√3/2 = x - √3/2
=> x - √3y - √3 = 0
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592 x 43 in standard algorithm
Answer:
25456
Step-by-step explanation:
592 over 43
592
x 43
multiply 3 by 2, 9 and 5. 3 by 2 is 6. 3 by 9 is 27. 3 by 5 is 15.
add a zero at the second row then,
multiply 4 by 2, 9, 5. 4 by 2 is 8. 4 by 9 is 36. 4 by 5 is 20.
if you aligned them properly, when you add them you should get 25456
I'll try to include a picture of my work, hopefully you can see it**
The table shows the heart rates of different animals...
Animal
Cat
Cow
Hamster
Horse
Cat:
Heart Rate (beats/min)
Cow:
150
65
Find the unit rates for each animal in mass per heart rate
Horse:
450
Input: xx-x/x g/ xxx beat per min (i.e. 300-1/4 g/ 1 beat per min)
44
Hamster: (Put answer as a decimal to the nearest hundredth [2 places behind the decimal])
Mass (9)
2000
800,000
60
1,200,000
POSSIBLE POINTS: 1
B
The unit rates for each animal in mass per heart rate (beats/minute) are as follows:
Animal Unit RateCat 13.33g/1 beat per min
Cow 12,307.69g/1 beat per min
Hamster 1.36g/1 beat per min
Horse 2,666.67g/1 beat per min
What is the unit rate?The unit rate is the ratio of two different variables expressed in a common denominator.
The unit rate is the quotient of the division operation between, for instance, the mass of an animal and its heart rate.
In this instance, the mass of the animal is the numerator with the heart rate used as the denominator.
Animal Heart Rate Mass (g) Unit Rate
(beats/min) (mass per heart rate)
Cat 150 2,000 13.33g/1 beat per min (2,000/150)
Cow 65 800,000 12,307.69g/1 beat per min (800,000/65)
Hamster 44 60 1.36g/1 beat per min (60/44)
Horse 450 1,200,000 2,666.67g/1 beat per min (1,200,000/450)
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107 km Big Goldtown. 805km Little Goldtown. 107km Old Goldtown The distance between Little Goldtown and Old Goldtown is A) 805km+107km. B) 805km-107km. C) 107km+107km+805km
The distance between Little Gold town and Old Gold town is 805km-107km.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common usage can refer to a physical length or an estimation based on other factors.
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.
Given: 107 km Big Gold town. 805km Little Gold town. 107km Old Gold town.
We have to find the distance between little gold town and old gold town.
Here, 805km Little Gold town. 107km Old Gold.
Hence, the distance between Little Gold town and Old Gold town is 805km-107km.
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The mortgage amount of a new home 170,000. The bank required a 8.6% down payment.
What was the original price before the down payment was made?
Answer: 15,507.44.
Step-by-step explanation: To find the original price of the home before the down payment was made, you need to use the following formula:
Original price = Mortgage amount / (1 - Down payment percentage)
Plugging in the values given in the question, you get:
Original price = $170,000 / (1 - 8.6%)
The original price of the home before the down payment was made is $<<170000/(1-.086)=185507.44>>185,507.44.
This means that the down payment amount was $185,507.44 - $170,000 = 185507.44-170000=15,507.44.
What is 7/2 with a denominator of 10
Answer: 35/10
Step-by-step explanation:
if you have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.
7 by 5 35
2 by 5 10
The value of 7/2 with a denominator of 10 is 35/10
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
(we used the identity [tex](b-c)(b+c) = b^2 - c^2 )[/tex]
We actually rationalize just for the use of that later denominator or numerator
We have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.
7 × 5 = 35
2 × 5 = 10
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Find the volume of the composite solid (STEP BY STEP PLEASE) 15 POINTS
Answer: 226.19
Step-by-step explanation:
Using the formula for a cyclinder{ V=πr2h} and inputing the values given in the diagram, (the radius and height given) you get 28.27.
Then adding the cone's volume (V=πr2h/3) and inputing that values in the diagram (the radius and height) you get 197.92.
Adding those values you got from the cyclinder and cone together, you get the volume of the composite solid.
During surgery, patient's circulatory system requires at least 50 milligrams of an anesthetic: The amount of anesthetic present hours after 70 milligrams of anesthetic administered given by the following T(t) 70(0.727)t (a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system 30 minutes after the anesthetic is administered? (b) How long_ to the nearest minute can the operation last if the patient does not recelve additional anesthetic?
63 mg of anesthetic is present in the patient’s circulatory system.
The operation can last for 20 minutes.
During surgery, a patient’s circulatory system requires at least 50 mg of an anesthetic. The amount of anesthetic present t hours after 70 mg of anesthetic is administered is given by the following,
T(t) = 70 × (0.727) ^t
Time = 1/3 hours
T (1/3) = 70 × (0.727) ^1/3
= 70 × ∛ 0.727
= 70 × 0.899176
= 62.94232
To the nearest mg: 63mg
Now,
63 = 70 × (0.727) ^t
63/70 = (0.727) ^t
0.9 = (0.727) ^t
Log0.9 = log (0.727) ^t
Log0.9 = t × log (0.727)
T = log0.9 / log0.727
T = 0.330461
T = 0.330461 hours
= 20 minutes
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Determine which integer in the solution set will make the equation true
Answer:
2
Step-by-step explanation:
First, we must add 14 to both sides to put the variable and coefficient alone.
4s - 14 = -6
+14 +14
4s = 8
s = 2
Find the area of the shape.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
Area = [tex]\pi x^{2}[/tex] For a full circle. This is 1/4 of a circle
A= [tex]\frac{\pi 2^{2} }{4}[/tex] = [tex]\frac{\pi 4}{4}[/tex] = [tex]\pi[/tex]
Answer : The area of the shape is, 111.02 units 2
A population is made up of r disjoint subgroups. Let Pi denote the proportion of the population that is in sub- group i,i = 1,...,7. If the average weight of the members of subgroup i is w;,i = 1, ...,r, what is the average weight of the members of the population?
The weighted average of the average weights of each individual subgroup, where the weights represent the population proportions in each subgroup, provides the average weight of the population's constituents.
This can be mathematically represented as: average population weight = _(i=1) r P i * w i, where P i is the population's share of subgroup I and w i is the weight of the subgroup's average members.
For instance, if the population is divided into three subgroups with proportions of P1 = 0.2, P2 = 0.5, and P3 = 0.3, and the subgroups' average weights are P1 = 150 lbs, P2 = 200 lbs, and P3 = 175 lbs, respectively, then the population's average weight is P1 * 150 lbs 180 lbs is equal to +0.5 * 200 lbs + 0.3 * 175 lbs.
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6x+6y=90 9x+2y=79 What pair of numbers solves the system?
Answer:
(7, 8)
Step-by-step explanation:
equation 1: [tex]6x+6y=90[/tex]
equation 2: [tex]9x+2y=79[/tex]
This system of equations can be solved for using the elimination method.
First, multiply both sides of the first equation by 3/2 to match the number of x's in both equations so that when we subtract the first equation from the second, the x's cancel and we can solve for y.
[tex]\left(\dfrac{3}{2}\right)\left(6x+6y\right)=(90)\left(\dfrac{3}{2}\right)[/tex]
[tex]9x + 9y = 135[/tex]
Next, subtract this from the second equation.
[tex]9x+2y=79[/tex] ← eq. 2
[tex]\underline{- (9x+9y=135)}[/tex] ← modified eq. 1
[tex]0 - \, 7y \, = -56[/tex]
Then, solve for y by dividing by 7.
[tex]7y = 56\\\overline{\, 7 \ } \ \ \ \ \overline{\ 7 \: }[/tex]
[tex]y=8[/tex]
So, the y-coordinate of the solution pair is 8.
Now that we've solved for the y, all we have to do to get x is plug the solved y-value back into one of the equations. I'll use the first equation.
[tex]6x+6y=90[/tex]
[tex]6x + 6(8) = 90[/tex]
↓ multiplying out 6 and 8
[tex]6x + 48 = 90[/tex]
↓ subtracting 48 from both sides
[tex]6x = 90 - 48[/tex]
[tex]6x = 42\\\overline{\: 6 \: } \ \ \ \ \, \overline{\: 6 \: }[/tex]
[tex]x = 7[/tex]
So, the x-coordinate of the solution pair is 7.
Finally, put the x- and y-coordinates together into an ordered pair in the form [tex](x, y)[/tex].
(7, 8)
Answer:
(7, 8) is the required pair of numbers---------------------------
Given system6x + 6y = 90, 9x + 2y = 79.Solve it by substitutionFirst, simplify the first equation by dividing all terms by 6:
x + y = 15Then solve it for y:
y = 15 - xNow, substitute this into the second equation:
9x + 2(15 - x) = 799x + 30 - 2x = 797x = 79 - 307x = 49x = 7Finally, find the value of y:
y = 15 - 7y = 8The pair of numbers is (7, 8).
Find the maximum area of a rectangle that is inside of the triangle forms by the x-axis and the lines y=-3x+12 and y=3x+12. The base of the triangle is on the x-axis and the two upper verticies are on the lines y=-3x+12 and y=3x+12.
With this question. Obviously the are of the rectangle is lw or xy... I have figured out that x = (8-2x) and y=(12-y). Im not sure of the next step.. Could someone help?
The maximum area of rectangle is 24, that can be calculated using the derivatives.
The area of rectangle = length * breadth,
The length of the rectangle is 2x units and the breadth is 3x+12 units,
So, A(x)=2x*(-3x+12)
=2x(-3x+12)
=-6x^2+24x
The derivative A'(x)=0
-12x+24=0
x=+2
Therefore, x=+2 is the critical point.
The second derivative.
The 2d derivative measures the immediately rate of alternate of the 1st derivative. The signal of the second derivative tells us whether or not the slope of the tangent line to is growing or decreasing.
A"(x)=-12<0
By the second derivative test, A(x) has maximum value at x=+2
Thus, the maximum are is
A(x)=2x(-3x+12)
A(2)=2(2)(-3(2)+12)
=4(6)
=2
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pdf state the number of complex zeros the possible number of real and imaginary zeros and the possible rational zeros for each function
First possibility: 2 positive roots 0 negative roots 4 imaginary roots
Second possibility: 0 positive 0 negative 6 imaginary
Let f(x) = 4x6-4x3+8
f(x) has 2 sign changes. So, by Descartes's Rule of Signs, f(x) has either 2 positive roots or none.
f(-x) = 4(-x)6-4(-x)3+8 = 4x6+4x3+8
f(-x) has no significant changes. So, by Descartes's Rule of Signs, f(x) has no negative roots.
f(x) has degree 6. So, by counting multiplicities, there are a total of 6 roots.
First possibility: 2 positive roots 0 negative roots 4 imaginary roots
Second possibility: 0 positive 0 negative 6 imaginary
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Suppose you observed the following sample:
6.2, 7.4, 9.6, 11.5, 13.5
Compute the 2nd sample moment. (please type in the exact number, do not round your answer)
449.86
To compute the moment of the second sample, we need to compute the sum of the squares of the sample values.
This formula is:
Sum = ∑(x_i^2)
After inserting the example values:
Sum = 6.2^2 + 7.4^2 + 9.6^2 + 11.5^2 + 13.5^2
Simplifying this formula to:
Total = 38.44 + 54.76 + 92.16 + 132.25 + 181.25
Adding these terms gives us the following final result:
Total = 449.86
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PLEASE HELP
Simplify the expression 4x³ × 2x³
3
A) 8x^6
B) 8x⁹
C)2x^6
D) 2x⁹
Answer:it isA
Step-by-step explanation:
Answer:
8x^6
Step-by-step explanation:
Add the exponents and multiply the numbers
Can someone explain what division algorithm is? I’m not sure I understand this?
Answer:
The division algorithm is an algorithm that specifies how to perform the division of one number (called the dividend) by another number (called the divisor) to obtain the quotient and the remainder.
For example, if we want to divide 15 by 4, we can use the division algorithm to find the quotient and remainder. In this case, we have:
15 = 4 * 3 + 3
So, the quotient is 3 and the remainder is 3.
If it's not clear for you yet, you can wait for another answer, maybe better explained.
Easier example (the classic one with apples):
Imagine you have a bunch of apples, and you want to divide them equally among a group of friends. The division algorithm can help you figure out how many apples each friend gets, and how many apples are left over.
Here's an example, let's say you have 15 apples, and you want to divide them among 4 friends. Using the division algorithm, we can figure out that each friend gets 3 apples, and there will be 3 apples left over.
To use the division algorithm, you start by dividing the number of apples (15) by the number of friends (4). This gives us the number of apples each friend gets, which is called the "quotient." In this case, the quotient is 3.
Then, we take the remainder, which is the number of apples that are left over after we divide them evenly among the friends. In this case, the remainder is 3.
So, each friend gets 3 apples, and there are 3 apples left over.
a nail is measured with a ruler and its length is reported as 5.46 cm. select all the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
If the nail is measured with a ruler and its length is 5.46 cm , then the correct statements are :
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ;
(b) The uncertainty is in the final digit of the measurement .
The Uncertainty of a number helps to estimates in comparison of experimental numbers .
it is given that , the reported length of the ruler is = 5.46 cm ;
we know that ,
the uncertainty In any number , is present in last digit only ,
the place value of the last digit in 5.46 is 0.01 .
So , uncertainty can be expressed by reporting measurement as 5.46 ± 0.1 cm
Therefore , the correct statements about the certainty and uncertainty are (a) and (b) .
The given question is incomplete , the complete question is
A nail is measured with a ruler and its length is reports as 5.46 cm.
Select ALL the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ,
(b) The uncertainty is in the final digit of the measurement ,
(c) All three digits shown in the measurement are known with certainty ,
(d) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.01 cm .
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Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. For two events M and N, P(M)=0.6, P(N|M)=0.9, and P(N|M′)=0.2. Find P(M′|N.)
For two events M and N, P(M)=0.6, P(N|M)=0.9, and P(N|M′)=0.2. Then P(M′|N.) is 0.7
This can be easily solved if we know the formula:
P(A or B) = P(A) + P(B) - P(A and B)
So, for this problem, we can modify the formula to be:
P(M or N) = P(M) + P(N) - P(M and N)
Using given information, we can solve:
P(M or N) = P(M) + P(N) - P(M and N)
P(M or N) = 0.6 + 0.2 - 0.1
P(M or N) = 0.7
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Find the standard deviation for each data set. Use the standard deviations to compare the pair of data sets. fastest recorded speeds of various large wild cats (miles per hour): 70 45 25 45 35 35 40 40 25 fasted recorded speeds of various birds in flight (miles per hour): 216 103 96 56 63 35 50 32 55 25 25 20
The standard deviation of the large wild cats is ō=
The standard deviation of the birds in flight is ō=
The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate _____ from the mean than the fastest recorded speeds of birds in flight.
A. Less
b. more
(a) The standard deviation of the large wild cats is 25.5 (b) The standard deviation of the birds in flight is 33 (c) The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight . Option A
How to determine the standard deviation?We should understand that standard deviation looks at the amount of deviation from the means of the set of data.
(a) (70+45+25+45+35+35+40+40+25)÷9 = 40
mean is = 40
(x-m) =30+5+-15+5+-5+-5+0+0+-15)
(x-m)²=(900+25+225+25+25+25+0+0+225)=1450/9
Standard deviation = √650
Standard deviation = 25.5
(b) x= (216+103+96+56+63+35+50+32+55+25+25+20)=776
Mean(m)=776/12=65
(x-m)=151+38+31+-9+-2+-30+-15+-33+-10+-40+-40+-45
Now the square of the deviations from the mean is
(x-m)²=(7396+1444+961+81+4+900+225+1089+100+1600+1600+2025)÷12
=1452
Standard deviation = √1452=33
(c) Therefore, from the calculations, the standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight
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Let X1,X2,...,Xn be a random sample of size n from a geometric distribution for which p is the probability of success.
(a) Use the method of moments to find a point estimate for p.
(b) Explain intuitively why your estimate makes good sense.
a) X1+X2 have distribution Bi(n1+n2, p)
b) P(X1 + X2 = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
Since both variables are independent but they have the same probability parameter, you can interpret that like if the experiment that models each try in both variables is the same. When you sum both random variables toguether, what you obtain as a result is the total amount of success in n1+n2 tries of the same experiment, thus X1+X2 have distribution Bi(n1+n2, p).
b)
Note that, if X2 = k, then X1+X2 = 1 is equivalent to X1 = 1-k. Since X1 and X2 are independent, then P(X1+X2 = 1| X2 = K) = P(X1=1-k|X2=k) = P(X1 = 1-k).
If k = 0, then this probability is equal to P(X1 = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X1 = 0) = (1-p)ⁿ¹
Thus,
P(X1+X2 = 1) = P(X1+X2 = 1| X2 = 1) * P(X2=1) + P(X1+X2 = 1| X2 = 0) * P(X2 = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
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3) Lourdes got a plant as a birthday gift. Her plant grows an average of 1 2/5 inches every month. How long will it take for the plant to grow a full 10 2/3
Answer:
7 13/21 months
Step-by-step explanation:
10 2/3 ÷ 1 2/5 =
= 32/3 ÷ 7/5
= 32/3 × 5/7
= 160/21
= 7 13/21
Answer: 7 13/21 months