The length and width of a rectangle must have a sum of 36 feet. Find the dimensions of the rectangle whose area is as large as possible.

The value of the resistor needed in this scenario is approximately 1.2 ohms.

To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.

Using Ohm's Law, we have the formula:

V = I * R

Where:

V is the voltage across the resistor (12 volts in this case),

I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),

R is the resistance of the resistor (which we need to find).

Rearranging the formula, we have:

R = V / I

Plugging in the values:

R = 12 volts / 10 amps

R = 1.2 ohms

Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.

It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.

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Answer: C) 24

Step-by-step explanation:

first we take down the information given to us

sports shop sells rackets in

4 different weights

2 types of strings

3 grip sizes

Now to get the number of different rackets they could sell, you simply take the  multiplication of the number of racket gripe sizes, the types of strings and different weights they sell

so

4 * 2 * 3 = 24

therefore the sport shop could sell up to 24 different rackets .

Answer:

24

Step-by-step explanation: got it right on my test

Answer:

48

Step-by-step explanation:

480x0.1=48

The assumption in answering the question is that no student scored 0

From the question, we have the following parameters that can be used in our computation:

The bar chart

On the bar chart, we hae

Students that score more than 8 = 5

Students in the class = 33

The (b) is calculated by considering all students that score more than 0 from the histogram

This means that the assumption is that no student scored 0

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Step-by-step explanation:

\( \frac{24.60}{2870} = 0.00857142857 = \frac{3}{350} \)

Answer:

( x + y + z )( x^2 + y^2 + z^2 - xy - yz - zx )

Step-by-step explanation:

Use Identity to factor this long expression.

Hope this helps.

The given information tells us that Terry's wins-to-races ratio is 2:3, but we cannot determine the exact number of races he has won without additional information about the total number of races he has participated in.

If the ratio of the number of times Terry has won to the number of races he has swum in is 2:3, we can set up a proportion to determine the number of races he has won.

Let's denote the number of times Terry has won as x, and the total number of races he has swum in as y. According to the given ratio, we have:

x/y = 2/3

To find the value of x, we need to solve for x when y is known. Since y represents the total number of races, we don't have that information in the given problem. Therefore, we cannot determine the exact number of races Terry has won without knowing the total number of races he has participated in.

The ratio tells us the relationship between the number of wins and the total number of races, but without knowing the denominator (total races), we cannot find a specific value for the numerator (number of wins). We can only determine the ratio between the two quantities.

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Answer:

Step-by-step explanation:

A: 2/3 divided by 3

B: 6/7 divided by 3

C: 2/5 divided by 4

D: 5/6 divided by 5

E: 10/8 divided by 5

F: 4/7 divided by 4

G: 5/8 divided by 10

H: 20/6 divided by 2

Answer:

4 m/s

Step-by-step explanation:

This is just a simple ratio question

35N=7M/s

20=Xm/s

We see that 7 is 1/5 of 35

20 is 4/7 of 35

4/7 of 7 is 4

Answer:

(a) 9.18% of people have an intraocular pressure lower than 12 mm Hg.

(b) 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Step-by-step explanation:

We are given that the distribution of intraocular pressure in the general population is approximately normal with mean 16 mm Hg and standard deviation 3 mm Hg.

Let X = intraocular pressure in the general population

So, X ~ Normal(\(\mu=16,\sigma^{2} = 3^{2}\))

The z score probability distribution for normal distribution is given by;

                             Z  =  \(\frac{ X-\mu}{\sigma } }\)  ~ N(0,1)

where, \(\mu\) = population mean = 16 mm Hg

           \(\sigma\) = standard deviation = 3 mm Hg

(a) Percentage of people have an intraocular pressure lower than 12 mm Hg is given by = P(X < 12 mm Hg)

       P(X < 12) = P( \(\frac{ X-\mu}{\sigma } }\) < \(\frac{ 12-16}{3 } }\) ) = P(Z < -1.33) = 1 - P(Z \(\leq\) 1.33)

                                                   = 1 - 0.9082 = 0.0918 or 9.18%

The above probability is calculated by looking at the value of x = 1.33 in the z table which has an area of 0.9082.

(b) We have to find that 80% of adults in the general population have an intraocular pressure that is greater than how many mm Hg, that means;

        P(X > x) = 0.80      {where x is the required intraocular pressure}

        P( \(\frac{ X-\mu}{\sigma } }\) > \(\frac{ x-16}{3 } }\) ) = 0.80

        P(Z > \(\frac{ x-16}{3 } }\) ) = 0.80

Now, in the z table the critical value of z which represents the top 80% of the area is given as -0.842, that is;

                           \(\frac{ x-16}{3 } } = -0.842\)

                           \(x -16 = -0.842 \times 3\)

                           x = 16 - 2.53 = 13.47 mm Hg

Therefore, 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Answer:

22 1/2

Step-by-step explanation:

Step-by-step explanation:

Triangle

\( \frac{10 \times 4}{2} - \frac{5 \times 3}{2} = \\ = \frac{40}{2} - \frac{15}{2} = \\ = \frac{25}{2} \)

Circle

\( {4}^{2} \pi - {2}^{2} \pi = \\ = 16\pi - 4\pi = \\ = 12\pi\)

Using the scale factor given, the amount of fence, to the nearest foot, that they will have to purchase is: 297 feet.

Let P be the perimeter of your yard. We know that P = 339 feet.

Let k be the scale factor for your friend's yard. We know that the perimeter of your friend's yard is 7/8 times the perimeter of your yard, so the perimeter of your friend's yard is:

7/8 * P = 7/8 * 339 = 296.625 feet

Since your friend's yard is similar to yours, the ratio of corresponding sides is k. Since the perimeter is the sum of all sides, we can write:

k * P = 296.625

Solving for k, we get:

k = 296.625 / P = 296.625 / 339 = 0.875

So the scale factor for your friend's yard is 0.875.

Now we can use the scale factor to find the length of fence your friend will need to purchase. The length of fence for your yard is P, so the length of fence for your friend's yard is:

k * P = 0.875 * 339 = 296.625 feet

Therefore, your friend will need to purchase approximately 297 feet of fence.

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Sarah spends reading 30 min + \(0.05 min^{2}\).

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

The problem is in a mathematical expression.

30 min+3s min did Sarah spend reading

Convert s to min

.30min+3s min× 1min/60s

Cancel the common units and simplify.

Cross-cancel units.

30 min + \(0.05 min^{2}\)

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Evaluating the composition of functions in x = 1 gives:

f(g(1)) = 28

Here we have the two functions:

f(x) = 4x

g(x) = 2x + 5

And we want to find to find the composition f(g(x)), we will get:

f(g(x)) = 4*g(x)

Replacing g(x) there we will get:

f(g(x)) = 4*(2x + 5)

         = 8x + 20

Now we can evaluate that in x = 1, then we will get:

f(g(1)) = 8*1 + 20 = 28

That is what we wanted to find.

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Answer:

Step-by-step explanation:

1/3 x 5/2 = 5/6

Answer:

man thats really hard i think youve gotta ask a professional for that

Step-by-step explanation:

Answer:

1+4=5

1-4=-3 (3)

1 x 4= 4

1/4 =4

Step-by-step explanation:

Answer:

Question 1: 21

Question 2: 6

Question 3: -3

Question 4: 9

The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

<95141404393>

Answer:

5≤x≤7

Step-by-step explanation:

For a given function f(x), the average rate of change in a given interval:

a ≤ x ≤ b

is given by:

\(r = \frac{f(b) - f(a)}{b - a}\)

Here we have:

f(x) = 4*log(x + 2)

And we want to see which interval has the smallest average rate of change, so we just need fo find the average rate of change for these 4 intervals.

1)  1≤x≤3

here we have:

\(r = \frac{f(3) - f(1)}{3 - 1} = \frac{4*log(3 + 2) - 4*log(1 + 2)}{2} = 0.44\)

2)  5≤x≤7

\(r = \frac{f(7) - f(5)}{7 - 5} = \frac{4*log(7 + 2) - 4*log(5 + 2)}{2} = 0.22\)

3) 3≤x≤5

\(r = \frac{f(5) - f(3)}{5 - 3} = \frac{4*log(5 + 2) - 4*log(3 + 2)}{2} = 0.29\)

4) −1≤x≤1

\(r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4*log(1 + 2) - 4*log(-1 + 2)}{2} = 0.95\)

So we can see that the smalles average rate of change is in 5≤x≤7

Answer:

-1 or 7

Step-by-step explanation:

brainliest plss

Answer:

C. 7°F

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

The length and width of the rectangle are 11 and 78 respectively.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, the length of a rectangle is 4 inches more than its width.

let x be the width of a rectangle.

thus, length = 4 + width

From the general formula of area and perimeter:

Area of rectangle = length*width

Perimeter of rectangle = 2(length + width)

In our case,

Area = x * (4 + x)

Area = x² + 4x

Perimeter = 2( 4 +x+ x)

Perimeter = 8 + 4x

Since the area of the rectangle is equal 5 inches more than 2 times the perimeter.

Thus,

x² + 4x = 5 + 2(8 + 4x)

x² + 4x = 5 + 16 + 8x

x² + 4x = 21 + 8x

x² + 4x -8x -21 = 0

x² - 4x -21 = 0

x = 7 and -3

Thus,

the width of the rectangle = 7

and the length of the rectangle = 11

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Complete question:

length of a rectangle is 4 inches more than its width. the area of the rectangle is equal 5 inches more than 2 times the perimeter. find the length and width.

Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

Answer:

43 3/4 cups of cheese

8 3/4 cups of olives

26 1/4 cups of sausage

Step-by-step explanation:

Answer:

43 3/4 cup of cheese

26 3/4 cups of olives

Exact value:  \(c = \frac{-11+\sqrt{165}}{22}\)

Approximate value:    c = 0.08387

Round the approximate value however you need to

==============================================

Work Shown:

Let x = 1+c

\(\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\\)

We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.

Each new term is found by multiplying the previous term by 1/x.

Assuming -1 < r < 1 is true, the infinite geometric sum is

\(S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\\)

Plug in S = 11 and solve for x

\(S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\\)

Use the quadratic formula to find the two solutions

\(x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\\)

Using these x values, we find that the corresponding r values are

r = 1/x = 1/(1.08387) = 0.92262

r = 1/x = 1/(-0.08387) = -11.92321

The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387

----------------------------------------------

Using the solution that corresponds to x = 1.08387, we find the value of c is

\(x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\\)

The expected gain of this company by the policy that they have here is given as $77.

The stated probability about a person dying is given as 0.0023

This tells us that out of this 10000, the number of people that would die would be 10000*0.0023 = 23 persons

Out of these 23, each of the number that would get the $10000 form the company.

23 * 10000 = $230000

Amount of policy sold at unit price is $100 for 10000

= 100 * 10000

= $1000000

The net earning = 1000000 - 230000

= 770000

The total earning = 770000/10000

= $77

Hence the expected gain of this company is going to be $77.

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It looks like you have provided a formula for a function called C(x) but it is missing some information. What would you like to know or what information do you have for the function?