Simplify
3x + 1-4x + 4

The Mean absolute deviation and the mean are not same.

Given,

The mean;-

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Mean absolute deviation;-

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset contains.

Therefore,

The Mean absolute deviation and the mean are not same.

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The probability that exactly one roll results in a sum of 12 when rolling a pair of fair dice 24 times is 2/3, or approximately 0.6667.

To find the probability that exactly one roll results in a sum of 12 when rolling a pair of fair dice 24 times, we need to calculate the probability of a single roll resulting in a sum of 12 and then multiply it by the number of ways we can choose one roll out of the 24 rolls.

The probability of a single roll resulting in a sum of 12 can be determined by counting the favorable outcomes. In this case, there is only one favorable outcome: rolling a 6 on one die and a 6 on the other die.

Since each die has 6 sides, the total number of outcomes for rolling two dice is 6 * 6 = 36.

Therefore, the probability of a single roll resulting in a sum of 12 is 1/36.

Now, we need to consider the number of ways we can choose one roll out of the 24 rolls. This can be calculated using the combination formula:

Number of ways = 24 choose 1 = 24

Finally, we multiply the probability of a single roll resulting in a sum of 12 by the number of ways we can choose one roll:

Probability = (1/36) * 24 = 2/3

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Answer:

C) 99 + 3x

Step-by-step explanation:

Since it's always going to cost 99, it'll stay like that since it's a constant

Since it's 3 PER person, that means 3 will have a variable: 3x

Answer:

alternate exterior

The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is

x sin⁻¹x + √(1 - x²) + C.

Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as

x sin⁻¹x + √(1 - x²) + C.

where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.

Integral of Sin Reverse proof by integration by parts :

f(x) = sin⁻¹x, g(x) = 1

d(sin⁻¹x)/dx = 1/√(1 - x²)

Using these equations and facts,

∫sin⁻¹x dx = ∫sin⁻¹x.1 dx

= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx

= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx

= x sin⁻¹x - ∫x/√(1 - x²) dx

= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]

= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx

= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}

= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C

= x sin⁻¹x + (1 - x²)1/2 + C

= x sin⁻¹x + √(1 - x²) + C

Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.

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The average value of f(x, y) = 4x² + y² over the rectangle with vertices (0, -2), (2, -2), (0, 1), and (2, 1) is 17/3.

To find the average value of the function over the given rectangle, follow these steps:

1. Determine the area of the rectangle: A = (2 - 0) * (1 - (-2)) = 2 * 3 = 6.
2. Set up the double integral for the average value: (1/A) * ∬[f(x, y) dA], where dA = dx dy.
3. Integrate f(x, y) = 4x² + y² over the rectangle limits, x = 0 to 2 and y = -2 to 1: ∬[4x² + y² dx dy].
4. Perform the integration with respect to x and then y.
5. Multiply the result by (1/A), which is (1/6) in this case.

Following these steps, the average value of the function over the given rectangle is found to be 17/3.

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Answer:

look for patterns also, Ann purchased 12 apples

Step-by-step explanation:

x apples

1/3 of x, (x - x/3) = (3x - x) /3 = 2x/3

Number of people who shared (2x/3) = 4 with each getting 2Total number shared = 4 * 2 = 8Fraction shared = total shared2x/3 = 8Multiply both sides by 3(2x/3) * 3 = 8 * 32x = 24x = 12

The line of code needed below to complete the factorial recursion method is: return x * fact(x-1);

This will recursively call the fact method with x-1 as the parameter until x reaches 1, and then it will start multiplying all the values from x down to 1 to get the factorial value.

To complete the factorial recursion method using the terms you provided, you can add the following line of code:

```java
public int fact(int x) {
   if (x <= 1) {
       return 1;
   }
   return x * fact(x - 1);
}
```

This code checks if x is less than or equal to 1, and if so, returns 1. Otherwise, it returns x multiplied by the factorial of x-1, allowing for the proper recursive calculation of the factorial.

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(a) The equation of the line in point-slope form is y + 1 = 2x + 6.

(b) The equation of the line in slope-intercept form is y = 2x + 5.

(a) To write the equation of the line in point-slope form, we use the formula:

y - y1 = m(x - x1),

where m is the slope and (x1, y1) is a point on the line.

Given that the slope (m) is 2 and the point is (-3, -1), we substitute these values into the formula:

y - (-1) = 2(x - (-3)).

Simplifying the equation gives:

y + 1 = 2(x + 3).

Thus, the equation of the line in point-slope form is:

y + 1 = 2x + 6.

(b) To convert the equation to slope-intercept form (y = mx + b), where b represents the y-intercept, we need to isolate y on one side of the equation.

Starting from the point-slope form equation:

y + 1 = 2x + 6,

we can subtract 1 from both sides:

y = 2x + 6 - 1.

Simplifying further gives:

y = 2x + 5.

Therefore, the equation of the line in slope-intercept form is:

y = 2x + 5.

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Answer:

\(A = 15\pi\)

Step-by-step explanation:

1. 150 degrees is 5/12 of a circle

2. Find area but divide by 5/12:

\(A = \frac{5}{12} \pi (6)^2\)

3. Solve

\(A = \frac{5}{12} \pi (36)\)

4. Simplify

\(A = 15\pi\)

Answer:

12.04

Step-by-step explanation:

the distance between two points in the x-axis

15-3 = 12

the distance between two points in the y-axis

7-6=1

using Pythagorean theory

a²+b²=c²

12²+1²=c²

144+1=c²

145=c²

√145=√c²

12.04=c

Answer:

C. No, because it fails the vertical line test.

Step-by-step explanation:

The vertical line test a method used to check if a graph represents a function.

if you move a vertical line along the graph the line always crosses one point at a time however if the line touches two points at the same time then it is not a function .

The graph fails the vertical line test, it does not represent a function

C. No, because it fails the vertical line test

The vertical line test is a graphical test used to determine if a graph represents a function.

According to the vertical line test, if any vertical line intersects the graph in more than one point, then the graph does not represent a function.

In the graph provided, we see that there a vertical line will intersect the graph in more than one point.

Since the graph fails the vertical line test, it does not represent a function. Therefore, option C is the correct answer: "No, because it fails the vertical line test."

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Answer:gamble that,on average,will leave a person with the same amount of money.

Step-by-step explanation:

The period of simple harmonic motion for a mass of 4 pounds attached to a spring with a spring constant of 16 lb/ft is 1 second.

The spring constant (k) for a 20-kilogram mass with a frequency of 2π/or cycles/s is 10 N/m. When the mass is replaced with an 80-kilogram mass, the frequency of simple harmonic motion becomes 0.5/or cycles/s.

To find the period of simple harmonic motion, we can use the formula:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the spring constant.

Given that the mass is 4 pounds (lb) and the spring constant is 16 lb/ft, we need to convert the mass to slugs (1 slug = 32.174 lb) and the spring constant to lb/s^2.

m = 4 lb / 32.174 lb/slug ≈ 0.124 slug

k = 16 lb/ft × 1 ft/s^2 / 32.174 lb/slug ≈ 0.497 lb/s^2

Plugging these values into the formula, we get:

T = 2π√(0.124 slug / 0.497 lb/s^2) ≈ 1 second

Therefore, the period of simple harmonic motion is 1 second.

The frequency of simple harmonic motion (f) is related to the spring constant (k) and the mass (m) by the formula:

f = (1/2π)√(k/m)

We are given that the frequency is 2π/or cycles/s. To find the spring constant, we can rearrange the formula as follows:

k = (4π^2f^2)m

Given that the mass is 20 kilograms (kg) and the frequency is 2π/or cycles/s, we can calculate the spring constant:

k = (4π^2 × (2π/or)^2) × 20 kg ≈ 40π^2 N/m ≈ 1256.6 N/m

When the mass is replaced with an 80-kilogram mass, we can find the new frequency by using the same formula:

f' = (1/2π)√(k/m')

where m' is the new mass.

m' = 80 kg

f' = (1/2π)√(1256.6 N/m / 80 kg) ≈ 0.5/or cycles/s

Therefore, when the original mass is replaced with an 80-kilogram mass, the frequency of simple harmonic motion becomes approximately 0.5/or cycles/s.

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Given f(t) = (2.6+61)³, represents the population size with respect to time in hours.

We have to calculate the average rate of change between time 0 and 1, time 0 and 0.1, time 0 and 0.01, time 0 and 0.001, time 0 and 0.0001 and make a guess for the instantaneous rate of change at time 0 using the above information.

\(Average rate of change between time 0 and 1= [f(1) - f(0)] / (1-0)f(t) = (2.6+61)³= (63.6)³= 256896.96 f(1) = (2.6+61)³= (63.6)³= 256896.96 f(0) = (2.6+61)³= (63.6)³= 256896.96\)

\(Therefore, the Average rate of change between time 0 and 1 = [f(1) - f(0)] / (1-0)= [256896.96-256896.96] / (1-0)= 0\)

\(Average rate of change between time 0 and 0.1= [f(0.1) - f(0)] / (0.1-0)f(t) = (2.6+61)³= (63.6)³= 256896.96 f(0.1) = (2.6+6.1)³= (8.7)³= 658.503 f(0) = (2.6+61)³= (63.6)³= 256896.96\)

\(Therefore, the Average rate of change between time 0 and 0.1 = [f(0.1) - f(0)] / (0.1-0)= [658.503-256896.96] / (0.1-0)= -2562.335\)

\(Average rate of change between time 0 and 0.01= [f(0.01) - f(0)] / (0.01-0)f(t) = (2.6+61)³= (63.6)³= 256896.96 f(0.01) = (2.6+0.61)³= (3.21)³= 32.951 f(0) = (2.6+61)³= (63.6)³= 256896.96\)

\(Therefore, Average rate of change between time 0 and 0.01 = [f(0.01) - f(0)] / (0.01-0)= [32.951-256896.96] / (0.01-0)= -25630700\)

\(Average rate of change between time 0 and 0.001= [f(0.001) - f(0)] / (0.001-0)f(t) = (2.6+61)³= (63.6)³= 256896.96 f(0.001) = (2.6+0.061)³= (2.661)³= 19.904 f(0) = (2.6+61)³= (63.6)³= 256896.96\)

\(Therefore, the Average rate of change between time 0 and 0.001 = [f(0.001) - f(0)] / (0.001-0)= [19.904-256896.96] / (0.001-0)= -2569096000\)

\(Average rate of change between time 0 and 0.0001= [f(0.0001) - f(0)] / (0.0001-0)f(t) = (2.6+61)³= (63.6)³= 256896.96 f(0.0001) = (2.6+0.0061)³= (2.6061)³= 18.374 f(0) = (2.6+61)³= (63.6)³= 256896.96\)

\(Therefore, the Average rate of change between time 0 and 0.0001 = [f(0.0001) - f(0)] / (0.0001-0)= [18.374-256896.96] / (0.0001-0)= -256979200000\)

Now, we can see the Average rate of change is decreasing, which means the instantaneous rate of change will also be decreasing.

So, the guess for the instantaneous rate of change at time 0 using the above information is the instantaneous rate of change at time 0 is zero.

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Given that `f(t) = (2.6 + 61)³` represents a population size with respect to time in hours.We can see that, `

f(t) = 63.6³`. Average rate of change is the change in output variable divided by the change in input variable.

It represents the slope of the line connecting two points.

The average rate of change of f(t) between time `t1` and `t2` is given by;

`(f(t2) - f(t1))/(t2 - t1)`

Calculation of the average rate of change between time 0 and 1:`

t1 = 0,

t2 = 1`

Therefore, `

f(0) = 63.6³,

f(1) = 64.6³`

Average rate of change between time 0 and 1 is given by;

`(f(1) - f(0))/(1 - 0)` `= (64.6³ - 63.6³)/1``= 1422.9`

Calculation of the average rate of change between time 0 and 0.1:`

t1 = 0,

t2 = 0.1`

Therefore,

`f(0) = 63.6³,

f(0.1) = 63.80296³`

Average rate of change between time 0 and 0.1 is given by;`(f(0.1) - f(0))/(0.1 - 0)` `= (63.80296³ - 63.6³)/0.1``

= 8028.85`

Calculation of the average rate of change between time 0 and 0.01:

`t1 = 0,

t2 = 0.01`

Therefore, `f(0) = 63.6³, f(0.01) = 63.6423039480016³`

Average rate of change between time 0 and 0.01 is given by;

`(f(0.01) - f(0))/(0.01 - 0)` `= (63.6423039480016³ - 63.6³)/0.01`

`= 806.341`

Calculation of the average rate of change between time 0 and 0.001:

`t1 = 0,

t2 = 0.001`

Therefore, `f(0) = 63.6³, f(0.001) = 63.6000234192395³`

Average rate of change between time 0 and 0.001 is given by;`

(f(0.001) - f(0))/(0.001 - 0)` `= (63.6000234192395³ - 63.6³)/0.001

``= 80.6548`

Calculation of the average rate of change between time 0 and 0.0001:`

t1 = 0,

t2 = 0.0001`

Therefore, `f(0) = 63.6³, f(0.0001) = 63.6000000002344³

`Average rate of change between time 0 and 0.0001 is given by;`

(f(0.0001) - f(0))/(0.0001 - 0)` `= (63.6000000002344³ - 63.6³)/0.0001``

= 8.06541

`From the above calculations, we can see that the average rate of change is decreasing with a decrease in time interval size.

Thus, we can make a guess that the instantaneous rate of change at time 0 is zero.

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Answer:

\(2x + 7 + 8x + 12 \\ collecting \: like \: terms \: \\ 2x + 8x + 7 + 12 \\ 10x + 19\)

Answer:

The correct option is (4).

Step-by-step explanation:

The complete question is:

Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(275)?

Solution:

The function f (p) is defined as the average number of days a house stays on the market before being sold for price p in $1,000s.

The function provided is: f (275)

That is, p = $275,000.

So, the function  (275) describes the average number of days a house stays on the market before being sold for price $275,000.

Thus, the correct option is (4).

In a case whereby a ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the time the ball is thrown will it strike the​ ground at t = 2.5 or -3.5.

Height of building = 140 ft

Initial velocity, u = 16 ft/sec

the equation given is

h = -16t² -16t +140

h(t) = -16t² -16t +140

AT h(t) = 0 , We can divide by -2 and have

(8t² + 8t - 70) = 0

8t² + 8t - 70 = 0

Then if we solve with quadratic equation formula where  a=8, b=8, c=- 70 then the root will be -7/2 and 5/2 then  t = 2.5 or -3.5

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complete question;

A ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the height of the ball h in feet after t seconds is given by the equation h equals negative 16 t squared minus 16 t plus 140. how long after the ball is thrown will it strike the​ ground?

Answer:

3x+5x=40

=8x=40

=x=5

then no.of boys= 3×5 = 15

and no. of girls= 5×5=25

girls more than boys= 25-15=10

mark me brainliest

pls it takes too much time to solve this

Answer:

There will be 10 more girls than boys in the class.

Step-by-step explanation:

5x+3x=40

8x = 40

8x/8 = 40/8

x = 5

5*2 = 10

For the limit limx→0 sin(2x)/(3x), based on a table of values, the estimated limit is 0.20772.

For the limit limx→1 f(x), where f(x) = {7+cos(πx), x<1; 2x+4, x>1}, based on a table of values, the estimated limit is 7.

For the first question, we can create a table of numerical values to estimate the limit:

x                    sin(2x)/(3x)

0.1                   0.21221

0.01                 0.20790

0.001               0.20772

0.0001             0.20772

0.00001           0.20772

Based on the values in the table, as x approaches 0, the values of sin(2x)/(3x) seem to approach approximately 0.20772.

Hence, we estimate the limit as x approaches 0 of sin(2x)/(3x) to be  0.20772.

For the second question, we can create a table of values to estimate limx→1 f(x):

x                      f(x)

0.9               6.99985

0.99            6.99999

0.999          7.00000

1.001            7.00001

1.01               7.00015

1.1                  7.00436

Based on the values in the table, as x approaches 1 from both sides, the values of f(x) appear to approach approximately 7..

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Answer:

See below.

Step-by-step explanation:

a) The zeros tell us when the missiles will be at ground level after being launched.

b) h(t) = 0 = -t^2+6t = t(6-t)

The missile was in flight for 6 units minutes.

c) h'(t) = -2t+6 = 0 --> t = 3

h(3) = 9

d) 8 = -t^2+6t

t^2-6t+8 = 0

(t-2)(t-4)=0

The missile is descending at a height of 8 km at 4 minutes.

It lands at 6 minutes.  So, it will impact 2 minutes after the early warning alarm.

Answer:

3\(\sqrt{5}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Simplifying the radicals

\(\sqrt{125}\)

= \(\sqrt{25(5)}\)

= \(\sqrt{25}\) × \(\sqrt{5}\) = 5\(\sqrt{5}\)

\(\sqrt{45}\)

= \(\sqrt{9(5)}\)

= \(\sqrt{9}\) × \(\sqrt{5}\) = 3\(\sqrt{5}\)

Then

\(\sqrt{125}\) - \(\sqrt{45}\) + \(\sqrt{5}\)

= 5\(\sqrt{5}\) - 3\(\sqrt{5}\) + \(\sqrt{5}\) ← collect like terms

= 3\(\sqrt{5}\)

Using transformations, the coordinates of the points are given as follows:

The rule for a rotation of 180º degrees about the origin is given as follows:

(x,y) -> (-x, -y).

Meaning that the signal of both the x-coordinate and of the y-coordinate is exchanged.

The coordinates of point A are given as follows:

A(-1,2).

Hence the coordinates of A' are given as follows:

A'(1, -2).

The rule for a dilation with a scale factor of k is given as follows:

(x,y) -> (kx, ky).

Meaning that each coordinate is multiplied by the scale factor.

Considering the scale factor of 2, the coordinates of A'' are given as follows:

A'' (2, -4).

Those three points are plotted on the image given at the end of the answer.

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The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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The Pythagorean Theorem is used to show that the hypotenuse has a length of sqrt(2).

In a unit circle, the radius is always equal to 1 unit. Now, consider an isosceles right triangle with two equal sides of length 1 unit

By the Pythagorean Theorem, the length of the hypotenuse (c) of this triangle can be found as:

\(c^2 = 1^2 + 1^2\)

\(c^2 = 2\)

\(c = sqrt(2)\)

Now, let's consider a circle centered at the origin with a radius of sqrt(2) units. Any point on this circle has coordinates (x, y) such that:

\(x^2 + y^2 = (sqrt(2))^2\)

\(x^2 + y^2= 2\)

This equation represents the unit circle, and any point on the isosceles right triangle we considered earlier also satisfies this equation. Therefore, the isosceles right triangle is inscribed in the unit circle.

In summary, the isosceles right triangle is inscribed in the unit circle because its hypotenuse has a length of sqrt(2) units, which satisfies the equation of the unit circle \((x^2 + y^2 = 1)\). The Pythagorean Theorem is used to show that the hypotenuse has a length of sqrt(2).

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Answer:

-3

Step-by-step explanation:

Because f(x) = y so when y=3 what is input value (x)

When y is 3 x is -3

Answer:

13

Step-by-step explanation:

\(16 + \frac{24}{8} - 6 = 13\)

Answer:-1

Step-by-step explanation:

you would add 16+24

which would equal 40

the divided by 40/8-6 = -1

Answer:

Area of sphere = 576 pi ft^2

Volume of sphere = 2,304 pi ft^3

Step-by-step explanation:

Radius of great circles are the same as radius of the sphere

So let’s calculate the radius of the sphere from the area given;

Mathematically;

pi * r^2 = 144pi

r^2 = 144

r = square root of 144

r = 12 ft

Volume of sphere = 4/3 * pi * r^3

= 4/3 * pi * 12^3 = 2,304 pi ft^3

Area of sphere = 4 * pi * r^2 = 4 * pi * 12^2 = 4 * 144 * pi = 576 pi ft^2