Both the length and width of the rectangle are approximately 31.62 m each.
The Area of a rectangle is calculated by multiplying the length by the width.
A = L x W
We have given that area of rectangle is 1,000 m²
1000 = W× L => W = 1000/L ---(1)
The circumference of rectangle is twice the sum of the dimensions. That is,
P = 2L + 2(1000/L)
Now, it is provided that perimeter is minimum so, we differentiate perimeter with respect to L then put first order derivative equal to zero.
dP/dL = 2 + 2000(-1/L²) = 0
=> 2-2000/L²=0
=>2000/L²=2
=> L²=2000/2
=> L²= 1000
=> L= 31.622
putting value of L in (1) we get , W= 31.622m
Therefore the length and width of the rectangle are both approximately 31.622m .
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to exercises 4.141 and 4.137. suppose that y is uniformly distributed on the interval (0, 1) and that a > 0 is a constant. a give the moment-generating function for y. b derive the moment-generating function of w
The moment-generating function for y is given as eⁿᵇ - eⁿᵃ / n(b-a) and derivation of moment-generating function of y is e-1/t
Given that,
The interval (0, 1) is covered by a uniform distribution of y, and a > 0 is a constant.
The moment generating function is eⁿᵇ - eⁿᵃ / n(b-a)
The given interval is (0,1)
Here a =0;
b=1;
Now substitute the values of a and b in the above moment generating function we get,
y=eⁿᵇ - eⁿᵃ / n(b-a)
y=e^1-e^0/t(1-0)
y= e-1/t
Therefore, the derivation of the moment generating function is e-1/t
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PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
That's a lot of exclamation marks :DDDDD
Rate of change, Δ often said as "delta" or also known as slope of a line. Rate of change is much easier when it's a line
it's just the slope of the line.
I see that the line in the picture... so the graph of the line.... is going down 1 after it goes over 4... so rate of change is rise over run..
-1 / 4
see how I got that?
so B) looks good
Reduce -34/87 to the lowest terms.
The value of the fraction -34/87 to the lowest term is still -34/87 as there's no common factor.
How to reduce to lowest term?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
To reduce to lowest term, divide the numerator and denominator by the greatest common factor to reduce a fraction to its simplest terms.
The steps involved are:
Divide the numerator (top number) and the denominator (bottom number) into prime factors.Remove any commonalities.Multiply the remaining numbers to get the numerator and denominator with the reduced numerator and denominator.In this case, there is no common factor and the value is still the same as -34/87.
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what is the probability that in seven rolls of a six-sided die, the result of 2 appears exactly 4 times?
1/6 is the probability that in seven rolls of a six-sided die, the result of 2 appears exactly 4 times
Define Probability
Probability can be defined as the likelihood or chance of an event occurring.
Probability is a branch of Mathematics that deals with the calculation on the chances of happening of a particular event.
The probability of getting some number in a cube corresponds to 1/6, the cube has six sides.
P(1) =1/6
P(2) =1/6
P(3)=1/6
P(4)= 1/6
P(5)=1/6
P(6)= 1/6
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The ratio of donuts to muffins at the restaurant is 10:6. If the total number of breakfast treats 48, how many muffins are there?
Answer:
Step-by-step explanation:
there would be 18 muffins.
if you multiply each number by 3 then add them it will end up at 48.
6x3=18
10x3=30
30+18=48
30:18
round off to the nearest 10 "728.35"
Answer:
730:35
Step-by-step explanation:
that's the answer
8
17) A hot-air balloon is at a height of 2,250 feet. It begins to descend at a rate of 150 feet per
minute. Write an expression to model its height after m minutes. Then evaluate the expression for 2,
4, 6, 8, and 10 minutes.
A hot-air balloon is at a height of 2,250 feet. It begins to descend at a rate of 150 feet per minute.
In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.
So for this, since the rate is linear we will be using the slope-intercept form, which is y = mx+b (m = slope/rate of change, b = y-intercept)
Since the rate of change "descends 150 ft per min", the m variable is -150.
The y-intercept is, in this case, the height of the balloon at 0 mins, or the starting height. Since the balloon "is at a height of 2250 ft", the b variable is 2250.
Putting our equation together, its y = -150x + 2250.
Since time is our independent variable, plug in 6, 8, and 10 mins into the x variable to solve for their heights:
y = -150(6)+2250
y = -900+2250
y = 1350
y = -150(8)+2250
y = -1200+2250
y = 1050
y = -150(10)+2250
y = -1500+2250
y = 750
Hence the answer, In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.
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a landscaping company ordered 17 plants and 8 trees for a total $ 964. if plants are $ 12 each, write and solve a linear equation to find the cost for each tree
Answer:
$95
Step-by-step explanation:
If 1 plant is $12 each, 17 plants will be
= 17($12)
= $204
Substitute the number of trees for x
The total cost of both is $964
Hence,
17($12) + 8(x) = $964
$204 + 8x = $964
Collect like terms
8x = $964 - $204
8x = $760
Divide both sides by 8
8x/8 = 760/8
x = $95
Can anyone help me with this proof
What was the winner's speed during last year's race? (3 points for speed, 2 points for conversion to knots).
Given: 6076 feet/nautical mile.
The winner's time was 16.5 minutes.
(distance unknown)
Part VIII of 2.11.2 Project: Performance Task: The Parrallax Problem apex
The speed of the winner based on the information is 368.24 mile per minutes
How to calculate the speed ?It should be noted that speed is calculated as the distance divided by the time given.
The following can be deduced from the information given:.
Distance = 6076 feet/nautical mile.
Time =16.5 minutes.
Speed = Distance / Time
Speed = 6076 / 16.5
Speed = 368.24 mile per minutes
The speed is 368.24 mile per minutes.
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if you had to serve six persons equally from a standard 750-ml. bottle of champagne, how many oz. could you serve each of them?
If you were serving a metric standard 750 ml bottle of champagne to 6 people equally, you would need to pour 4.2 fl oz to each one of them to get 6 equal serving.
A bottle of champagne with a metric unit of volume of 750 ml divided equally among 6 people will give each of them a 125 ml serving of champagne by volume.
750/6=125
Converting metric system to imperial unit of volume of US fluid ounce, with 1 fl oz = 29.57 ml, you will get:
125/29.57=4.23
Hence you will be pouring each one of them 4.2 fl oz serving of champagne.
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i need help, image attached. thanks ahead of time :)
The value of x's in the equation of angles are :-
1. 4.729
2. 7
3. 13
4. 10
What are parallel line ?In geometry, lines are categorized into different types such as: Parallel lines, vertical lines, intersecting lines, non-intersecting lines, etc. For lines that do not intersect, you can draw special lines called horizontal lines that intersect these lines at different points. In this article, we will discuss parallel lines in detail. Two parallel lines that meet at infinity can also be called parallel lines. For a line to be horizontal, two or more lines must intersect at different points. Angle relationship between parallel lines and horizontal linesDifferent angle pairs are created when a horizontal line crosses two or more parallel lines.Calculation1 . 25x - 5 + 12x = 180
37x = 175
x = 4.729...
2. 15x - 7 = 14x
x = 7
3. 5x +39 = 8x
3x = 39
x = 13
4 . 4x + 12x + 20 = 180
16x = 160
x = 10
now put the values of each x in the equations of angle to find the angle .
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Kelly drank .86 of her Gatorade and John drank 7/8 of his Ginger Ale. Who drank less?
The area of a rectangle and its length, if its width is 2cm
Use the value of the discriminant to determine whether the quadratic equation has two rational solutions, two irrational solutions, one repeated real solution, or two complex solutions that are not real.
3z² +3z +10=0
Choose the correct answer below.
O A. one repeated real solution
OB. two irrational solutions
OC. two rational solutions
OD. two complex solutions that are not real
Answer:
D
Step-by-step explanation:
discriminant = 9 - 4(10 * 3)
9 - 4 * 30
9 - 120 = -111
Is negative so the equation has two complex solutions
NO LINKS!! Please help me with this polynomial function activity 6. Also make a graph.
Answer:
x-intercepts: -4, -2, 1 and 3
y-intercept: 24
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]y=(x+4)(x+2)(x-1)(x-3)[/tex]
The x-intercepts are the points at which the curve intersects the x-axis, so when the function equals zero.
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Therefore, to find the x-intercepts, set each factor of the given polynomial equal to zero and solve for x:
Therefore:
[tex]\implies (x+4)=0 \implies x=-4[/tex]
[tex]\implies (x+2)=0 \implies x=-2[/tex]
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-3)=0 \implies x=3[/tex]
Therefore, the x-intercepts are -4, -2, 1 and 3.
The y-intercept is the point at which the curve intersects the y-axis, so when x is zero.
To find the the y-intercept, substitute x = 0 into the given polynomial:
[tex]\implies y=(0+4)(0+2)(0-1)(0-3)[/tex]
[tex]\implies y=(4)(2)(-1)(-3)[/tex]
[tex]\implies y=(8)(-1)(-3)[/tex]
[tex]\implies y=(-8)(-3)[/tex]
[tex]\implies y=24[/tex]
Therefore, the y-intercept is 24.
To find the other points on the graph, substitute each value of x into the polynomial and solve for y:
[tex]\begin{aligned}x=-5 \implies y&=(-5+4)(-5+2)(-5-1)(-5-3)\\&=(-1)(-3)(-6)(-8)\\&=(3)(-6)(-8)\\&=(-18)(-8)\\&=144\end{aligned}[/tex]
[tex]\begin{aligned}x=-3 \implies y&=(-3+4)(-3+2)(-3-1)(-3-3)\\&=(1)(-1)(-4)(-6)\\&=(-1)(-4)(-6)\\&=(4)(-6)\\&=-24\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies y&=(2+4)(2+2)(2-1)(2-3)\\&=(6)(4)(1)(-1)\\&=(24)(1)(-1)\\&=(24)(-1)\\&=-24\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies y&=(4+4)(4+2)(4-1)(4-3)\\&=(8)(6)(3)(1)\\&=(48)(3)(1)\\&=(144)(1)\\&=144\end{aligned}[/tex]
Therefore:
[tex]\large\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]
Consider a case where 400 fish are tagged and released during a first outing. During a second outing in the same area, 400 fish are again caught and released, of which half are already tagged. Estimate N, the total number of fish in the entire sampling area.
The total number of fish in the entire sampling area is 600
Sampling:
The process of selecting the group that you will actually collect data from in your research is called sampling.
Given,
Consider a case where 400 fish are tagged and released during a first outing. During a second outing in the same area, 400 fish are again caught and released, of which half are already tagged.
Here we need to find the total number of fish in the entire sampling area.
Let us consider N be the number of fish in the entire sampling area.
While looking through the given question,
We have identified the following,
Number of fish tagged = 400
Next time number of fish caught = 400
We know the half of them are tagged, so the untagged fishes are
=> 400/2
=> 200
Therefore, the total number of fishes is
=> 400 + 200
=> 600
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Members of a lacrosse team raised $2863.50 to go to a tournament. They rented a bus for $1087.50 and budgeted $74 per player for meals. Which equation or tape diagram could be used to represent the context if xx represents the number of players the team can bring to the tournament?
write the equation for the line which is perpendicular to the line y=-3/2+1 and which passes through the point (-6,-9)
Using the formula of equation of perpendicular line, the new equation is y = 2/3x - 5
Equation of Perpendicular LineA perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.
The equation of perpendicular line is given as
(y - y₁) = m(x - x₁)
m = slope of the line.
But the slope of a perpendicular line is given as
m₁m₂ = -1
-3/2m₂ = -1
m₂ = 2/3
The slope of the new equation is 2/3
Using equation of a perpendicular line;
(y - y₁) = m(x - x₁)
y - (-9) = 2/3(x -(-6))
y + 9 = 2/3(x + 6)
y + 9 = 2/3x + 4
y = 2/3x - 5
The equation of perpendicular line is y = 2/3x - 5
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Mario purchased a storage cube with a volume of 27 cubic feet. he wants to sit it on a shelf that is 4 feet wide wide. volume: 27ft³ Will the cube fit on the shelf? Explain how you know
Answer:
No, the cube will not fit on the shelf because it is too big. The shelf is only 4 feet wide, but the cube is 27 cubic feet, which is much bigger.
What is the sum of (3x + 4) + (9x – 10)?
Step-by-step explanation:
(3x+4)+(9x-10)
= 3x+4+9x-10
=3x+9x+4-10
=12x-6
ANSWER IS 12X-6
Answer:
The solution is 12x-6
Step-by-step explanation:
(3x+4)+(9x-10)
We remove the brackets
= 3x+4+9x-10
= 3x+9x+4-10
= 12x-16
a spherical balloon is inflated so that its volume is increasing at the rate of 3.7 ft3/min. how rapidly is the diameter of the balloon increasing when the diameter is 1.5 feet?
Using Sphere geometry formulas , 2.45 ft/min is increasing rate of spherical ballon when the diameter is 1.5 feet.
Sphere is a three dimensional form of circle .
let V and D be volume and diameter of the sphere. we have given that ,
Volume increasing rate of spherical ballon (dV/dt)
= 3.7 ft³/min
diameter of sphere at time of increasing = 1.5 feet
the increasing rate of spherical ballon is dD/dt.
Now, Volume of sphere (V) = 4/3π³ ft³
or we know that D = r/2 so,
V = 4/3 π (D)³×8 ft³
differentating both sides we get ,
dV/dt = 32/8π 3D³dD/dt
=> 3.7 = 32/3 (3.14)(1.5)²dD/dt
=> dD/dt= 2.45 feet/min
Hence, 2.45 ft/min is the rate of the diameter of the balloon increasing when the diameter is 1.5 feet.
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help please.................................................
Answer:
[tex]8 \sqrt{2} [/tex]
Step-by-step explanation:
This is a special right triangle with angle measures 45°-45°-90°
and side lengths represented with a-a-a√2 respectively
a is given as 8 here so a√2 would be 8√2 the answer is c.
Describe the type of association between x and y for each set of data. Explain.
3. The table below shows the temperature of an oven, in degrees Fahrenheit, t minutes
after it is turned on.
Oven Temperature
Time, t
(in minutes)
0
3
5
Temperature, F
(in °F)
70
160
220
10
370
An equation for a line of best fit for these data is F = 30t + 70. What is the slope of this
line, and what does it represent?
The slope of this line, and what it represent is: The slope is 30, and it represents the increase in temperature, in degrees Fahrenheit, each minute the oven is on.
How to identify and interpret the slope?Mathematically, the standard form of the equation of a line can be calculated by using this equation:
y = mx + c .......equation 1.
Where:
m represents the slope.x and y represent the variables.c represents the y-intercept.From the information provided, we have the following equation of line:
F = 30t + 70 ..........equation 2.
Comparing equation 1 and equation 2, we have:
Slope, m = 30, which is the increase in temperature of the oven in degrees Fahrenheit.
y-intercept, c = 70, which also represents the initial temperature of the oven in degrees Fahrenheit.
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Complete Question:
The table below shows the temperature of an oven, in degrees Fahrenheit, t minutes after it is turned on. An equation for a line of best fit for these data is F = 30t + 70. What is the slope of this line, and what does it represent?
answer choices
The slope is 30, and it represents the initial temperature, in degrees Fahrenheit, of the oven.
The slope is 70, and it represents the initial temperature, in degrees Fahrenheit, of the oven.
The slope is 30, and it represents the increase in temperature, in degrees Fahrenheit, each minute the oven is on.
The slope is 70, and it represents the increase in temperature, in degrees Fahrenheit, each minute the oven is on.
show all work
An employee receives a 4% raise once per year. If the employee’s initial salary is $40,000, what will the employee’s salary be after 8 years?
(2 points –1 writing the exponential equation, 1 salary after 8 years)
Exponential equation S is 40,000(1.04)^8, and Salary after 8 years: S is $64,735.20.
What is Exponential equation?An exponential equation is an equation that contains a variable in the form of an exponent. It is used to solve problems involving exponential growth and decay. The equation has the form y = a × b^x, where "a" is the initial value, "b" is the base of the exponent, and "x" is the exponent. This equation can be used to find the value of y, given a value for x. Exponential equations are commonly used in fields such as mathematics, physics, economics, and biology.
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2. Last year, 70% of 1 million Philadelphians got their flu shots. About 2% of people who got
their shot got sick with the flu. 6% of people who did not get their flu shot got sick. What is
the probability that a Philadelphian who got the flu got a flu shot? Using bayes rule
The conditional probability that a Philadelphian who got the flu got a flu shot is of:
0.4375 = 43.75%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the outcome of a previous event.
The formula is presented as follows:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which each probability in the formula is described as follows:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.In the context of this problem, the events are described as follows:
Event A: Got the flu.Event B: Got the flu shot.The probability of people who got the flu is obtained as follows:
2% of 70%. (got the shot).6% of 30%. (did not get the shot).Hence:
P(A) = 0.02 x 0.7 + 0.06 x 0.3 = 0.032.
The probability of both getting the flu and the shot is:
P(A and B) = 0.02 x 0.7 = 0.014.
Hence the conditional probability that a Philadelphian who got the flu got a flu shot is calculated applying the conditional probability formula as follows:
P(B|A) = P(A and B)/P(A) = 0.014/0.032 = 0.4375 = 43.75%.
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Write a verbal expression or word problem that could be represented by the following equation.
2x + 7 = 35
The required verbal expression : Twice of a variable x when added with 7 will give a constant equal to 35
What is a variable ?An unknown numerical value in an equation or algebraic expression is represented by a symbol (typically a letter) in algebra. A variable is, to put it simply, a quantity that is changeable and not fixed and is frequently represented by an alphabet.
What is a verbal expression ?A verbal statement is a mathematical problem. Algebraic 8 + 6 is an example of using numbers and numeric variables. It is necessary to be familiar with the words used to describe mathematical operations in order to translate between verbal statements and algebraic expressions.
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what is the answer to this?
Answer:
79?
Step-by-step explanation:
Alex, Stephen and Bridget share some sweets in the ratio 5:4:2. Alex gets 21 more sweets than Bridget. How many sweets are there altogether?
Alex, Stephen and Bridget have 77 sweets altogether.
According to the question,
We have the following information:
Alex, Stephen and Bridget share some sweets in the ratio 5:4:2. Bridget gets 21 more sweets than Alex. (This is the correct statement otherwise the answer will be in negative which is not possible.)
Now, let's take the number of sweets Alex has to be 5x, that of Stephen to be 4x and that of Bridget to be 2x.
Now, we have the following expression:
2x+21 = 5x
Subtracting 2x from both sides:
21 = 5x-2x
3x = 21
x = 21/3
x = 7
Now, we have the following number of sweets:
Alex = 5*7 = 35
Stephen = 4*7 = 28
Bridget = 2*7 = 14
Now, total number of sweets:
35+28+14
77
Hence, Alex, Stephen and Bridget have 77 sweets altogether.
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