Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.

Exponential equation S is 40,000(1.04)^8, and Salary after 8 years: S is $64,735.20.

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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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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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.

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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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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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

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

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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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.

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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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.

Mathematically, the standard form of the equation of a line can be calculated by using this equation:

y = mx + c          .......equation 1.

Where:

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.

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

Answer:

730:35

Step-by-step explanation:

that's the answer

Answer:

79?

Step-by-step explanation:

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]

The required verbal expression : Twice of a variable x when added with 7 will give a constant equal to 35

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.

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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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

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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The conditional probability that a Philadelphian who got the flu got a flu shot is of:

0.4375 = 43.75%.

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:

In the context of this problem, the events are described as follows:

The probability of people who got the flu is obtained as follows:

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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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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Using the formula of equation of perpendicular line, the new equation is y = 2/3x - 5

A 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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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

The value of the fraction -34/87 to the lowest term is still -34/87 as there's no common factor.

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:

In this case, there is no common factor and the value is still the same as -34/87.

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The value of x's in the equation of angles are :-

1. 4.729

2. 7

3. 13

4. 10

1 . 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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The speed of the winner based on the information is 368.24 mile per minutes

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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