Whats this? Conjugate???

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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\(y = 4x + 2 \\ = > y - 2 = 4x \\ = > x = \frac{y - 2}{4} \)

\(y = - 8x + 8 \\ = > y = - 8( \frac{y - 2}{4} ) + 8 \\ = > y = \frac{ - 8y + 16}{4} + 8 \\ = > y = \frac{ - 8y + 16 + 32}{4} \\ = > y = \frac{ - 8y + 48}{4} \\ = > 4y = - 8y + 48 \\ = > 4y + 8y = 48 \\ = > 12y = 48 \\ = > y = 4\)

\(y = 4x + 2 \\ = > 4 = 4x + 2 \\ = > 4x = 4 - 2 \\ = > 4x = 2 \\ = > x = \frac{2}{4} = \frac{1}{2} \)

Answer:

\(x = \frac{1}{2} \\ y = 4\)

Hope you could understand.

If you have any query, feel free to ask.

\(\\ \sf\longmapsto y=4x+2\)

\(\\ \sf\longmapsto y=-8x+8\)

If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.

In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.

Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:

The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.

There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.

There are 3 dots above the 9.5 minutes per problem tick mark.

Now, let's calculate the total time Mira spent:

(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.

Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.

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Answer:

7

Step-by-step explanation:

Rs 150- Rs 75=Rs 75 remaining

Rs 75/10= 7 as whole

Step-by-step explanation:

given,

total amnt =rs.150

cost of pen= rs.75

now,

left money =150_75

=rs.75

now,cost of 1 copy=10

then , no. of copies=75/10

=7.5

so he can buy 7 copies.

inGiven that the slope,s, is

Also given that:

To find the slope from the given values of x and corresponding values of y

Taking two values of x and y

Taking another values of x and y

The slope is the same at the two instances. Hence, the slope is 3

The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

According to the question,

We have the following information:

Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.

We know that the following formula is used to find the area of rectangle:

Length*width = 18

Length*3 = 18

Length = 18/3

Length of the rectangular garden = 6 meters

Now, perimeter of the rectangular garden:

2(length+width)

2(6+3)

2*9

18 meters

Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

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The angle formed by the two hands have a measure less than 1/4 turn

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

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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Answer:

50 degrees.

(B) is correct

.............................

y = 1/3x - 21 is the equation of the line in slope-intercept form.

What is a slope?

Slope is a measure of the steepness or incline of a line. It describes how much the dependent variable (usually y) changes for a given change in the independent variable (usually x).

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the slope is 1/3 and that the line passes through the point (3, -20). We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes, and m is the slope. Plugging in the values we have:

y - (-20) = 1/3(x - 3)

Simplifying this equation:

y + 20 = 1/3x - 1

Subtracting 20 from both sides:

y = 1/3x - 21

This is the equation of the line in slope-intercept form.

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Split the integral at \(x=0\). In the integral over \(\left[-\frac\pi2,0\right]\), substitute \(x\mapsto-x\) to get

\(\displaystyle \int_{-\pi/2}^0 \frac{\cos(x)}{1 + \cos^{\tan(x)}(x)} \, dx = \int_0^{\pi/2} \frac{\cos(x)}{1 + \cos^{-\tan(x)}(x)} \, dx\)

Then we have

\(\displaystyle \int_{-\pi/2}^{\pi/2} \frac{\cos(x)}{1 + \cos^{\tan(x)}(x)} \, dx \\\\ ~~~~~~~~ = \left\{\int_0^{\pi/2} + \int_{-\pi/2}^0\right\} \frac{\cos(x)}{1 + \cos^{\tan(x)}(x)} \, dx \\\\ ~~~~~~~~= \int_0^{\pi/2} \cos(x) \left(\frac1{1+\cos^{\tan(x)}(x)} + \frac1{1 + \cos^{-\tan(x)}(x)}\right) \, dx \\\\ ~~~~~~~~ = \int_0^{\pi/2} \cos(x) \left(\frac1{1 + \cos^{\tan(x)}(x)} + \frac{\cos^{\tan(x)}(x)}{1 + \cos^{\tan(x)}(x)}\right) \, dx \\\\ ~~~~~~~~ = \int_0^{\pi/2} \cos(x) \, dx = \boxed{1}\)

Answer:

a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C

a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C

b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C

b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C

Answer:

Step-by-step explanation:

Not completly sure what your looking for but it X would be any number lower then 12 (11,10,9,8,7,6,5,4,3.2,1)

Answer:

1-11

Step-by-step explanation:

its less than 12!

hope this is correct! c:

The proof that P(n; r1, r2, . . . , rm) = n!/( r1! r2! · · · rm!) is true is done by induction, which shows that the numerator of the i-th combination cancels with the denominator of the (i − 1)-st combination in the product of combinations for each i from 1 to m.

The proof that P(n; r1, r2, . . . , rm) = n!/( r1! r2! · · · rm!) is true is done by induction. We show that for each i from 1 to m, the numerator of the i-th combination cancels with the denominator of the (i − 1)-st combination in the product of combinations.

To start, we assume that the result holds for i = 1. We then have:

\(P(n; r1, r2, . . . , rm) = C(n, r1) * C(n-r1, r2) * ... * C(n-r1-r2-...-rm+1, rm) = n!/(r1!(r2!(...(rm-1)!rm!)...)\)

Now, to prove the result for i = 2, we have to show that the numerator of C(n-r1, r2) cancels with the denominator of C(n, r1). This is done by showing that:

\((n-r1)!/r2! = (n!/(r1!(n-r1)!))/r2! = (n!/(r1!r2!(n-r1-r2)!))\)

which is the required result. The same process can be repeated for each i from 1 to m, and hence the result follows for all values of i. Thus the proof is complete.

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Answer:

m = 2

Step-by-step explanation:

8m + 5 + 13m - 5 = 42

The 5s cancel each other out

8m + 13m = 42

21m = 42

Divide both sides by 21

m = 42/21

m = 2

the least common multiple is...

(32,28,24) = 2^5 * 3 * 7 = 672

Answer:

D: 2

Step-by-step explanation:

1(1/3) = 4/3

(4/3)/(2/3) = 4/3 * 3/2 = 12/6

12/6 simplified = 2.

Let me know if you have any questions

Answer:

2

Step-by-step explanation:

So i would reccomend using desmos calculator for problems like this because it has many symbols and there are different types if calculators to so it was easier to divide 1 1/3 by 2/3. hope this helps

Answer:

https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php try this website, it shows a step by step solution, and is a calculator for your problem <3

Step-by-step explanation:

Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.

To calculate the population size after 4 hours, we can use the formula for exponential growth:

Population size = Initial population * \((1 + growth rate)^t^i^m^e\)

Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:

Population size = 3.3 million *\((1 + 0.4465)^4\)

Calculating the exponent first:

\((1 + 0.4465)^4 = 1.4465^4\) ≈ 1.7879

Now, we can substitute this value back into the formula:

Population size = 3.3 million * 1.7879

Calculating the population size:

Population size = 5.892 million

Therefore, the population size after 4 hours is approximately 5.892 million cells.

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Step-by-step explanation:

True

and the more mass the object had the greater gravitational force it is

P. S my opinion

Answer:

Step-by-step explanation:

To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:

n! ≈ (n/e)^n √(2πn)

where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.

Using this approximation, we can rewrite (n!)^(1/n) as:

(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)

Taking the limit as n approaches infinity, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)

Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:

lim [√(2πn)]^(1/n) = 1

For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:

lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1

Therefore, combining the two terms, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1

Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.

Answer:1

Step-by-step explanation:

The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C

From the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.

The amount of 150 dollars would then be added to the debt that has the second highest rate.

Hence the amount of debt that would be paid off first would be the first debt based on the stack method.

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Answer:

commutative property of addition

Answer:

43%

Step-by-step explanation:

29% red = 29 out of 100, or 29/100

28% white = 28 out of 100, or 28/100

Take 100, subtract 28 and 29 from it and you're left with 43 out of 100, or 43%

Answer:

So if every day the Car place makes u pay 45 dollars, all you gotta do is add 45 twice and then add it to 135, which is 225

Step-by-step explanation:

1) The mass remaining after 0 years is; m(0) = 460 grams

2) The mass remaining after 45 years is; m(45) = 0.1054 grams

Exponential decay functions are defined as functions that reduce in value as the input value increases.

We are given the decay function as;

m(t) = 460e^(-0.05t)

where;

m(t) is the mass (in grams) remaining after t years

We want to find the mass at time t = 0 years

Thus;

m(0) = 460e^(-0.05 * 0)

m(0) = 460 grams

Now, after 45 years, the amount of mass remaining is;

m(45) = 460e^(-0.05 * 45)

m(45) = 0.1054 grams

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