The area of a rectangle is 36x⁷y5. If the length of the rectangle is 9x⁴y, which expression represents the width of the rectangle in yards?​

The hypotenuse and the known leg are squared. Subtract the squared length of the hypotenuse from the squared length of the leg. Finally, compute the result's square root.

A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. Triangle ABC represents a triangle with three vertices: A, B, and C. Any three non-collinear points constitute a unique triangle and, by extension, a unique plane in Euclidean geometry. Triangles are polygons with three vertices that have three sides. The triangle's angles are constructed by joining the three sides end to end at a point. The triangle's three angles add up to 180 degrees.

Here,

Square the hypotenuse and the known leg. Subtract the squared length of the leg from the squared length of the hypotenuse. Finally, compute the square root of the result.

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The correct option is for the value of c,  such that f(c) is the average value of the function on the interval [0, 2], is D.

The average value of a function on an interval [a, b] is given by:

R = (f(b) - f(a))/(b - a)

Here the interval is [0, 2], then:

f(2) = √(2 + 2) = 2

f(0) = √(0 + 2) = √2

Then here we need to solve the equation:

√(c + 2) = (f(2) - f(0))/(2 - 0)

√(c + 2) = (2 + √2)/2

Solving this for c, we will get:

c = [ (2 + √2)/2]² - 2

c = 0.9

Them tjhe correct option is D.

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The expected utility of Marlee with the ticket from Fony is 28.

The utility function of Marlee is given by u(x) = x+k. Here, k equals 100 if Marlee gets to go to the concert and equals 0 otherwise.

Marlee has $100 to buy tickets to the Fleet Foxes concert in Atlanta. She found two different websites selling tickets, Fony Front Seats and Best Tickets. If she buys a $20 ticket from Fony, there is a 60% chance that the ticket is fake, but she won't know until she gets to the concert.

If she buys a $60 ticket from Best Tickets, the ticket is certainly real. The seat placements for both tickets are identical and it costs $10 in gas to get to the concert.

Marlee's utility function is given as u(x) = x+k, where k equals 100 if Marlee gets to go to the concert and equals 0 otherwise. Her goal is to maximize her utility function.

Marlee is facing a trade-off between the cost of the ticket and the probability of getting a real ticket.

If she buys a $20 ticket from Fony, there is a 60% chance that the ticket is fake, but she won't know until she gets to the concert. Thus, there is a 40% chance that the ticket is real.

So, the expected utility of Marlee with the ticket from Fony is given by,

0.6u(0)+0.4u(100-20-10)=0.6(0)+(0.4)(70)=28

Therefore, the expected utility of Marlee with the ticket from Fony is 28. This indicates that Marlee will not be able to go to the concert if she buys the ticket from Fony Front Seats.

If she buys a $60 ticket from Best Tickets, the ticket is certainly real. Therefore, the expected utility of Marlee with the ticket from Best Tickets is,

u(100-60-10)=u(30)=30+100=130

Therefore, the expected utility of Marlee with the ticket from Best Tickets is 130.

This indicates that Marlee should buy the ticket from Best Tickets to get the maximum utility.

Therefore, Marlee should buy her ticket from Best Tickets because she will receive the maximum utility if she buys the ticket from Best Tickets.

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Answer:

a=-5, k=31

Step-by-step explanation:

Determine a and k so the given points are on the graph of the function:

(1,11) (2,-14)

\(y=a(x+1)^2+k\)

To find the required values, we substitute the points into the equation:

\(11=a(1+1)^2+k\)

\(-14=a(2+1)^2+k\)

Operating:

\(11=a(2)^2+k\)

\(-14=a(3)^2+k\)

Simplifying:

\(11=4a+k\)

\(-14=9a+k\)

Subtract the second equation from the first equation:

\(11+14=4a-9a\)

Simplifying:

\(25=-5a\)

Solving:

\(a=25/(-5)=-5\)

a=-5

Use this equation to find k:

\(11=4a+k\)

\(11=4(-5)+k\)

\(11=-20+k\)

k=31

a=-5, k=31

Answer:

a = -5

k = 31

Plz Mark brainliest!!!

Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Answer:

B hope this helps!

Step-by-step explanation:

Trust <3

Answer:

The first thing you should do is draw the points in the Cartesian plane and then join them to find the polygon.

The searched polygon can be seen in the attached image.

The area of the polygon will be the area of the square plus the area of the triangle.

At = (6) * (8) + (1/2) * (5) * (8) = 68

At = 68

answer

the area of the polygon is 68units ^ 2

Answer:

h = -3y + 2x

Step-by-step explanation:

Add 4x to both sides of the equation.

2h = −6y + 4x

Divide each term in 2h = −6y + 4x by 2 and simplify.

Divide each term in 2h = −6y + 4x by 2.

2h/2 = -6y/2 + 4x/2

Simplify the left side.

h = −6y/2 + 4x/2

Simplify the right side.
Simplify each term.
Cancel the common factor of −6 and 2.

h = -3y+2(2x)/2

Cancel the common factors.
Factor 2 out of 2.

h = -3y+2(2x)/2(1)
Cancel the common factor

h = -3y+2(2x)/2(1)
Rewrite the expression
h = -3y + 2x/1

Divide 2x by 1.
h = -3y + 2x

hopefully its right LOLZ

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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The correct option is C, the slope is −4 throughout the line.

We can see that the same linear equation is the hypotenuse of both triangles.

So, if there is a single line, there is a single slope, then the slopes that we can make with both triangles are equal.

To get the slope we need to take the quotient between the y-side and x-side of any of the triangles, using the smaller one we will get:

slope = -4/1 = -4

Then the true statment is C, the slope is -4 throughout the line.

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Answer: 21 c^16 + 24c^9+ 21 c^8

Step-by-step explanation: To multiply exponents with the same base, add them.

Answer:

3c^3(7c^8+8c+7)

=(3c^3)(7c^8+8c+7)

=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)

=21c^11 + 24c^4 + 21c^3

Step-by-step explanation:

Remember....  ^ is for power

EXPLANATION

Given that we need to consider the bartering system, we can apply the following reasoning:

10 carrot sticks -----1 apple

1 apple ------- 20 potato chips

(1/2 grab bag) --- 1/2 pudding cup

1 grab bag ---1 pudding cup

Constraint: apples ad pudding cups may not be divided.

Juliana ---->

15 carrot sticks + 1 apple

As 1 apple is equivalent to 1/2 pudding cup, but the pudding cups can not be divided, we need to add a half more fraction in order to get the pudding cup.

Also, as 10 carrot sticks are equivalent to 1/2 pudding cup, we can trade 1 apple and 10 carrot stick for a pudding cup.

In conclusion, she should give 1 apple and 10 carrot sticks in order to get 1 pudding cup.

Answer:

G=-2t+14

Step-by-step explanation:

The slope of the function is -2 which reveals the number of gallons of gas used per hour driven.

there's the correct answer!^^

Let's determine the height of the building using ratios and proportions.

Where,

h = height of the building

We get,

Therefore, the height of the building is approximately 105 m.

The difference between the maximum value of g(x) to the maximum value of f(x) is 11. The maximum value of g(x) is -5 and f(x) is 6.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given,

f(x) = -(x - 5)² + 4

At x = -3

f(-3) = -(-3 - 5)² + 4

f(-3) = -81 + 4 = -77

At x = 2

f(2) = -(2 - 5)² + 4

f(2) = -9 + 4 = -5 (maximum)

Now,

g(x) = 6 (maximum)

6 - (-5) = 11

Hence "The difference between the maximum value of g(x) to the maximum value of f(x) is 11. The maximum value of g(x) is -5 and f(x) is 6".

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The best predicted value given that a person has an IQ of 91 is 94.03.

Here, we are given that-

sample size n = 20

sample mean for the independent value x = 100.39

sample mean for the dependent value y = 103.6

coefficient of correlation r = 0.925

The general expression for representing a linear model is given by-

y = β₀ + β₁x

where β₀ is the intercept and β₁ is the slope

For the above given case, the linear model will be given as-

y = -3.34 + 1.07x

where -3.34 is the intercept and 1.07 the slope.

To find the best predicted value when X = 91, we substitute the value of x as 91 in the equation as follows-

y = -3.34 + 1.07(91)

y = 94.03

Thus, the best predicted value given that a person has an IQ of 91 is 94.03.

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Answer:

a = 19

Step-by-step explanation:

a+5/3 (Note: this means a+5 over 3, as in a fraction.)

3 x 8 = a + 5

24 = a + 5

24 + (-5) = (a + 5) + (-5)

19 = (a + 5) - 5

19 = a + 5 - 5

19 = a

a = 19

Hope this helped!

In this scenario, a player spins two spinners, and each spinner can land on 1, 2, or 3.

The expected value of x, denoted as E(x), is equal to 5/3. Hence, the answer is option (b) 5/3.

In this scenario, a player spins two spinners, and each spinner can land on 1, 2, or 3. The random variable x is defined as the maximum of the two numbers on the spinners.

The probability distribution of x is as follows:

To find the expected value of x, we multiply each possible value of x by its corresponding probability and sum them up:

E(x) = 1(1/9) + 2(4/9) + 3(6/9) = 2 + 2/3 = 8/3.

Therefore, the expected value of x, E(x), is equal to 5/3. Hence, the answer is (b) 5/3.

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The area of the field is 10,765.44 square meters.

Given that:

Diameter, d = 72 m

Width, W = 72 m

Length, L = 93 m

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the field is calculated as,

A = (π/4)d² + W·L

A = (3.14 / 4) x 72² + 72 x 93

A = 4,069.44 + 6,696

A = 10,765.44 square meters

The area of the field is 10,765.44 square meters.

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Answer:

x < 3

Step-by-step explanation:

Step 1: Write inequality

4x + 8 > 2(3x + 1)

Step 2: Solve for x

Here we see that any value smaller than 3 will be a solution.

The function f(x) = \(x^2 e^{(-x^2)}\) has a maximum value at x = 0, which is a relative maximum point.

To find the relative maximum of the function f(x) =\(x^2 e^{(-x^2)}\), we can take its first derivative, set it to zero, and solve for x.

f(x) = \(x^2 e^{(-x^2)}\)

f'(x) = \(2x e^{(-x^2)} - 2x^3 e^{(-x^2)}\)

Setting f'(x) = 0, we get:

\(2x e^{(-x^2)} - 2x^3 e^{(-x^2)} = 0\)

\(2x e^{(-x^2)} (1 - x^2) = 0\)

This equation is true when either \(2x e^{(-x^2)} = 0\) or \(1 - x^2 = 0\).

Solving \(2x e^{(-x^2)} = 0\), we get x = 0.

Solving \(1 - x^2 = 0\), we get x = 1 or x = -1.

Now, we need to determine whether these values of x correspond to relative maximum, minimum, or inflection points.

To do this, we can use the second derivative test. The second derivative of f(x) is:

f''(x) = \(2e^{(-x^2)} - 4xe^{(-x^2)} - 4x^2e^{(-x^2)}\)

At x = 0, f''(0) = 2, which is positive. This means that f(x) has a relative minimum at x = 0.

At x = 1, f''(1) = \(-6e^{(-1)}\), which is negative. This means that f(x) has a relative maximum at x = 1.

At x = -1, f''(-1) = \(-6e^{(-1)}\), which is negative. This means that f(x) has a relative maximum at x = -1.

Therefore, the answer is (D) -1 and 1 only, as these are the only values of x at which f(x) has a relative maximum.

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The number of bags of candy and cookies sold by the drama club is 4 and 10 respectively

let

The equation:

8.50x + 4.50y = 79

y = x + 6

Substitute x = y + x into

8.50x + 4.50y = 79

8.50x + 4.50(x + 6) = 79

8.50x + 4.50x + 27 = 79

8.50x + 4.50x = 79 - 27

13x = 52

x = 52/13

x = 4

Recall,

y = x + 6

y = 4 + 6

y = 10

Therefore, the number of bags of candy and cookies sold by the drama club is 4 and 10 respectively.

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Answer:

160 in ^2

Step-by-step explanation:

First we need to find the area of each shape and add them together

1. Triangles:

The formula for a triangle is (base x height)/2, so we can replace them as (5 * 4)/2 * 2( Because there are two triangles), so therefore the two triangles will add up to 20 inches

2. The Rectangles

The Big Rectangle:

The big rectangle is just l x w or 5 * 20 which is 100

The small rectangle:

To find the width of the small rectangle you have to do 20 - (5 + 5) because we are not including the triangles. 20 - (5 +  5) = 10, so that would be 10 * 4 = 40.

3.Add them together

20 + 100 + 40 = 160 inches ^2

Hope this helps!!!

The measure of a central angle of a regular polygon with 24 sides is 15°. There is no need to round the answer as it is already in whole degrees.

The measure of a central angle of a regular polygon with 24 sides. A central angle is formed by two radii drawn from the center of the polygon to two consecutive vertices. In a regular polygon, all the sides and angles are equal.

To find the measure of a central angle, you can use the formula: Central Angle = (360°) / (Number of Sides) In this case, the regular polygon has 24 sides.

So the formula would be: Central Angle = (360°) / (24) Now, we can solve for the central angle: Central Angle = 15° So, the measure of a central angle in a regular polygon with 24 sides is 15 degrees. Since the result is already in whole degrees, there's no need to round it to the nearest tenth of a degree

To find the measure of a central angle of a regular polygon with 24 sides, you can use the formula:

Central angle = (360°) / (number of sides)

In this case, the number of sides is 24, so the formula becomes:

Central angle = (360°) / 24

Central angle = 15°

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Answer:

c = 0.85 ; $1.7 ; c = 0.79p

Step-by-step explanation:

Given :

Cost per pound of supply shipped = $0.85

Total cost, c to ship p pounds of horse supply

Total cost = cost per pound * pound of supply

c = 0.85 * p

c = 0.85p

Cost of shipping 2 pounds :

c = 0.85 * 2

c = $1. 7

B.)

Reduction in shipping cost :

Reduced cost = $0.85 - $0.06 = $0.79

Total cost = cost per pound * pound of supply

c = 0.79 * p

c = 0.79p

10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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Answer:

−10−1(−2)^3−1(−2)(−11)

● −10−1(−8)−1(−2)(−11)

●−10+8−1(−2)(−11)

●−10+8−22

●−10+8−22

☆Answer:-24

○●○●○●○●○●○

Hope it helps

Have a great day!!

The relationship between the capacity and fluid ounce is; that capacity is the measurement while the fluid ounce is the measuring unit.

Since Capacity of a substance or object is the greatest quantity it can hold, whereas its volume is the amount of space it takes up.

We also know that fluid ounce is a volume measurement unit that is commonly used to measure liquids.

The Capacity is the amount of something that could be held by an object, while the Fluids ounces are one type of measurement of capacity. A few of examples of fluid ounces are:

2 pints= 1 quart

4 quarts= 1 gallon

8 fluid ounces = 1 cup

2 cups=1 pint

We can conclude that the relationship between the capacity and fluid ounce is that capacity is the measurement while the fluid ounce is the measuring unit.

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Therefore, the differential equation is obtained to be\(c(t) + 2e^{(-t)} - e^{(-2t)} + 3sin(t) + \big(\frac{1}{\sqrt{3}}\big)sin(\sqrt(3)t) = r(t)\).

What is differential equation?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

The transfer function G(s) = C(s)/R(s) is given by:

\(G(s) = \frac{(s^5 + 2s^4 + 4s^3 + s^2 + 3)}{(s^6 + 7s^5 + 3s^4 + 2s^3 + s^2 + 3)}\)

To write the differential equation involving c(t) and r(t) whose relationship is described by the transfer function, we need to take the inverse Laplace transform of the transfer function G(s).

We can use partial fraction decomposition to simplify the expression -

\(G(s) = \frac{(s^5 + 2s^4 + 4s^3 + s^2 + 3)}{(s^6 + 7s^5 + 3s^4 + 2s^3 + s^2 + 3)} = \frac{1}{s} - \frac{2}{(s+1)} - \frac{1}{(s+2)} + \frac{3}{(s^2+1)} - \frac{1}{(s^2+3)}\)

Taking the inverse Laplace transform of each term, we obtain -

\(c(t) = r(t) - 2e^{(-t)} - e^{(-2t)} + 3sin(t) - \big(\frac{1}{\sqrt{3}}\big)sin(\sqrt(3)t)\)

Therefore, the differential equation involving c(t) and r(t) is -

\(c(t) + 2e^{(-t)} - e^{(-2t)} + 3sin(t) + \big(\frac{1}{\sqrt{3}}\big)sin(\sqrt(3)t) = r(t)\)

To determine the poles and zeroes of the transfer function, we can use any root-finding program such as MATLAB.

Using the MATLAB command "pzmap", we get the following plot -

The poles of the transfer function are located at approximately -6.167, -1.149, -0.4587 ± 0.7175i, and 0.2155 ± 0.9605i.

The zeroes of the transfer function are located at approximately ±1.316i.

The poles have different contributions to the time response based on their location in the complex plane.

The pole at -6.167 contributes an exponentially decaying term \(e^{(-6.167t)}\) to the time response.

The poles at -1.149, -0.4587 ± 0.7175i, and 0.2155 ± 0.9605i contribute oscillatory terms to the time response with different frequencies and damping factors.

Therefore, the differential equation is \(c(t) + 2e^{(-t)} - e^{(-2t)} + 3sin(t) + \big(\frac{1}{\sqrt{3}}\big)sin(\sqrt(3)t) = r(t)\).

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Using fractional operation, since Jack ate ¹/₂ of the delicious pizza with ¹/₆ left, Jill ate ¹/₃ of it.

The fractional operations involve mathematical operations using fractions, which are parts or portions of the whole value or quantity.

Some of the mathematical operations include addition, subtraction, multiplication, and division.

The fraction ate by Jack = ¹/₂

The fraction of the pizza left over after Jack and Jill have eaten = ¹/₆

The fraction or portion that Jill ate = ¹/₃ [1 - (¹/₂ + ¹/₆)]

Thus, we can conclude that Jill ate ¹/₃ of the delicious pizza.

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