Find the area. Round to the nearest hundredth when necessary. Area - 28.6 ft ----- ft2

The number of suspects had less than two prior arrests are 3.

Given that, While reviewing the previous day’s arrest report.

Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.

Here, x+y=5 -----(i)

2x+3y=12 -----(ii)

From equation (i), x=5-y in equation (ii), we get

2(5-y)+3y=12

10-2y+3y=12

10+y=12

y=2

Substitute y=2 in equation (i), we get

x+2=5

x=3

Therefore, the number of suspects had less than two prior arrests are 3.

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Using the shell method, the volume of the solid generated when R is revolved about the y-axis is V= 324π cubic units.

The shell method refers to a method of finding volumes of the solid by decomposing a solid of revolution into cylindrical shells. It is one of the methods to find the volume of the solid. This solid is generated when region R is rotated about an axis or the y-axis. In case it is y-axis then the following formula is used:

V= ∫_a^b▒〖2πx [f(x)-g(x)]dx〗

Where y = f(x), y = g(x), and the interval is considered as [a,b].

The given curves are: y = 11 − x, y = 0, x = 3, x = 9

V= ∫_3^9▒〖2πx [11-x-0]dx〗

V= 2π∫_3^9▒〖(11x-x^2)dx〗

V= 2π[11/2 x^2-  1/3 x^3]

V= 2π[11/2 9^2-  1/3 9^3-  11/2 3^2+  1/3 3^3]

V= 2π[891/2-  729/3-  99/2+  27/3]

V= 2π[729/2-  702/3]

V= 2π[396-234]

V= 2π[162]

V= 324π cubic units

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Reason: Split the angle 155 in half to get 155/2 = 77.5

AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.

In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.

Therefore, we can conclude as saying:

C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

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Answer;

Explanation;

Here, we want to get the solution a pair of linear equation which we are to solve simultaneously by the graphical method

We need to plot the graphs of these two lines; The point at which the lines meet will represent the solution to the system of linear equations

The general equation of a straight line is;

where m is the slope and b is the y-intercept

To plot the lines, we need the x-intercepts and the y-intercepts

This refer to the point at which the line touches the x and y axes respectively

Let us take the lines one after the other;

The y-intercept here is -4; so the point is (0,-4)

To get the x-intercept value, we simply set y to zero and get the value of x

So the x-intercept is (-4/3,0)

To plot the line; we simply join (0,-4) and (-4/3,0)

For the second line;

We have the y-intercept as -2

So the point is (0,-2)

To get the x-intercept, we simply set y to 0 and solve for x

So, the x-intercept point is (-2,0)

We can now join (0,-2) and (-2,0) to represent the second line

Proceeding, we get the lines on the cartesian grid

This is shown in the attachment below;

As we can see from the plot, the lines touch at the point (-1,-1) and that represents the solution to the equation

There 211 number of coffee creamers left at the end of the week.

What is number ?

The arithmetic value of a number is one that is used to denote amount. As a result, a number is a mathematical concept used for counting, measuring, and labeling. As a result, mathematics is based on numbers.

An arithmetic value known as a number is used to represent a quantity and do calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.

Numerology comes in a variety of forms. Organic Numbers entire numbers Integers Realistic Numbers Unreasonable Numbers True numbers complicated numbers Organic numbers numbers beginning with "1".

x will be equal to

x = 275 - 64

  = 211

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Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

0.350

Step-by-step explanation:

Confidence interval = point estimate ± margin of error

Point estimate = Confidence interval - margin of error

To get the margin of error, we will take the average of the difference of the interval given. Given the confidence interval 0.325<p<0.375

Margin of error = 0.375-0.325/2

Margin of error = 0.050/2

Margin of error = 0.025

Using the interval of 0.375

Point estimate = 0.375 - 0.025

Point estimate = 0.350

Answer:

y = -3/2x +10

Step-by-step explanation:

y = mx+b where m is the slope and b is the y intercept

y = 2/3x +b

The slope is 2/3

We want a line perpendicular

Slopes of perpendicular lines multiply to -1

m * 2/3 = -1

Multiply by 3/2

m * 2/3 * 3/2 = -1 * 3/2

m = -3/2

The slope of the perpendicular line is -3/2

We have the slope and a point (4,4)

y = -3/2 x +b

4 = -3/2(4) +b

4 = -6+b

Add 6 to each side

4+6 = -6+6+b

10 =b

y = -3/2x +10

The values of derivatives are:

The derivative is the instantaneous rate of change of a function with respect to one of its variables.

Given:

y = 1/ (x+2)

y= \((x + 2)^{-1}\)

On differentiating w.r.t 'x' is

y' = (-1) \((x+2)^{-2}\)

y' = -1/(x+2)²

Now, y'(5) = -1 / (5+2)²

y'(5) = -1/49

at x= -4

dy/dx = -1/(-4+2)²

dy/ dx =-1/4

At x= -1

y' = -1/ (-1+2)²

y' = -1

At x= 2

dy/dx = 1/(2+2)²

=1/16

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Answer:

7.5 seconds

Step-by-step explanation:

\(h = - 16 {t}^{2} + 120t \\ \because \: we \: have \: to \: find \: the \: time \: required \: \\ for \: the \: object \: to \: return to \: its \: \\ point \: of departure. \\ \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\ \therefore \: 0 = - 16 {t}^{2} + 120t \\ \therefore \:16 {t}^{2} - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \: \: or \: \: (2t - 15) = 0 \\ \therefore \:t = \frac{0}{8} \: or \: t = \frac{15}{2} \\ \therefore \:t = 0 \: or \: t = 7.5 \\ \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{ \therefore \: t = 7.5 \: seconds}}\)

Thus, the time required for the object to return to its point of departure is 7.5 seconds.

Yes,The law of large number says that if you take sample of larger and larger size forming population than the mean of the sampling distribution u-x tend to get closer to true population.

As a sample size increases, the sample mean and standard deviation will be closer in value to the population mean μ and standard deviation σ.Very large samples tend to transform small differences into statistically significant differences.

There are following steps for finding sample mean

Add up the sample items. Firstly we will need to count how many sample items you have within a data set and add up the total amount of items.

Divide sum by the number of samples.

The result is the mean.

Use the mean to find the variance.

Use the variance to find the standard deviation.

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how

how you get 800 in 8000000 to 87777

Answer:

(a) x=5

(b) x= -1 1/3

(c) x= 1

Step-by-step explanation:

(a)                       (b)                        (c)

2(x-3)=4           −3(2x+1)=5          a(bx+c)=d

x−3=4/2           2x+1= −  5/3          d^1−1

x−3=2               2x= -5/3-3/3        d^0

x=2+3                 2x= -5-3/3           x=1

x=5                    2x= -8/3*2

                          x= -8/6

                          x= -4/3

The matrix resulting from the multiplication of matrices B and C is given as follows:

[-92, -730; 3350, 19648]

The matrices in this problem are defined as follows:

For the product of the matrices, the row of matrix B multiplies the column of matrix C.

Then the element at the first row and the first column of the product matrix is given as follows:

2 x 4 - 10 x 10 = -92

The element at the first row and the second column of the product matrix is given as follows:

2 x -25 - 10 x 68 =  -730.

The element at the second row and the first column of the product matrix is given as follows:

60 x 4 + 311 x 10 = 3350.

The element at the second row and the second column of the product matrix is given as follows:

60 x -25 + 311 x 68 =  19648.

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\(f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54\)

Answer:

4/5

find a common factor that can divide evenly into 12 and 15 in this case its 3

12÷3=4

15÷3=5

so therefore the answer is 4/5.

I hope this helps!

Answer:

4/5

Step-by-step explanation:

The complete equality will be;

⇒ 1 / 2 = 3 / 6 = 4 / 8

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

By using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true.

Now,

All the numbers from 1 to 9 are;

= 1, 2 ,3 , 4, 5, 6, 7, 8, 9

Let a proportion = 1 / 2

Hence, The equivalent ratio of 1/2 are;

= 3 / 6 and 4 / 8

Thus, The complete equality will be;

⇒ 1 / 2 = 3 / 6 = 4 / 8

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The length of the arc KL in the given circle is 3.49 units

In a circle whose radius is R, the length of an arc defined by an angle x is given by:

Length = (x/360)*2*3.14*R

Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:

Length = (100/360)*2*3.14*2

Lenght = 3.49 units.

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Answer:

Step-by-step explanation:

Since EF = 20 and E is at 4

F is at:

The smallest integer that Pearl wrote down is -12.Let's assume the smallest integer that Pearl wrote down is represented by the variable "x."

According to the given information, the sum of the seven consecutive integers is equal to $\frac{21}{4}$ times the largest integer.

The sum of consecutive integers can be expressed as the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is x and the last term is x + 6 (since there are seven consecutive integers). Therefore, the sum of the integers can be written as:

Sum = (7/2)(x + (x + 6))

Simplifying the equation:

(7/2)(2x + 6) = (21/4)(x + 6)

Multiplying both sides by 4 to eliminate the fractions:

14x + 42 = 21x + 126

Subtracting 14x from both sides:

42 = 7x + 126

Subtracting 126 from both sides:

-84 = 7x

Dividing both sides by 7:

-12 = x.

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Answer:

Mean = 16.5

Variance = 35.55

Step-by-step explanation:

           x      P(x)        x. P(x)     x²            x². P(x)

          6      0.10          0.6      36            3.6

         12     0.35          4.2       144           50.4

        18     0.25           4.5       324            81

        24     0.30          7.2        576         172.8

                  ∑x P (x)  16.5         ∑x² P (x) 307.8

The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.

Mean is given by  E(X)=  ∑x P (x) =  16.5

Similarly the variance is also calculated using the expected value of X and X².

Variance is given= E(X)²-  [E(X)]²= 307.8- (16.5)²=  307.8-272.25 = 35.55

Answer:

E- don't report this one-

Step-by-step explanation:

The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)

a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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