The diameter of a circle is 6 cm. What is the area of the circle to the nearest square meter?

Answer:

10

Step-by-step explanation:

Use the distance formula.

\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

We have x1 = 2; y1 = 0; x2 = -6; y2 = 6.

\( d = \sqrt{(-6 - 2)^2 + (6 - 0)^2} \)

\( d = \sqrt{(-8)^2 + 6^2} \)

\( d = \sqrt{64 + 36} \)

\( d = \sqrt{100} \)

\( d = 10 \)

Answer: 10

Answer:

There are 366 acres of old-growth trees

Step-by-step explanation:

61000 x 0.006 = x (x represents acres of old-growth trees)

x = 366

tadah!

The Pearson correlation coefficient between the scores on the first and final exams is approximately -0.165. This indicates a weak negative correlation between the two variables.

What is correlation coefficient?

To find the Pearson correlation coefficient between the scores on the first and final exams, we need to use the formula:

r = ΣZxZy / √(ΣZx² * ΣZy²)

Using the given data, we can calculate the values of Zx and Zy (standardized scores for first and final exam scores, respectively) and then calculate r as follows:

ΣZxZy = (0.481)(-0.345) + (-0.102)(0.366) + (1.720)(-0.548) + (-0.904)(-0.548) + (0.189)(-0.041) + (-0.612)(-0.650) + (0.991)(0.670) + (1.280)(1.280) + (-1.767)(-0.410) = -0.023

ΣZx² = 0.723 + 0.011 + 2.958 + 0.818 + 0.036 + 0.374 + 0.982 + 1.638 + 3.127 = 10.667

ΣZy² = 0.119 + 0.135 + 0.302 + 0.302 + 0.002 + 0.423 + 0.449 + 1.638 + 3.125 = 6.695

r = -0.023 / √(10.667 * 6.695) = -0.165

Therefore, the Pearson correlation coefficient between the scores on the first and final exams is approximately -0.165. This indicates a weak negative correlation between the two variables.

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Answer:

y ≤ x-2

y > -x + 5

y ≤ 3

y ≥ 0

Step-by-step explanation:

all answers have y ≥ 0 and y ≤ 3

next, we want to figure out if y < -x + 5 or y > -x + 5

plotting the line with a few points (e.g. (0,5), (5,0)), we can tell the red dotted line is y = -x + 5. the shaded area is above it, so we can say that y > -x + 5

similarly, we can tell the blue line is y = x-2. the shaded values are below it, so we can say that y ≤ x-2

Answer:

-\(\frac{9}{2}\) = -4.5

Step-by-step explanation:

-9 ÷ 2

Fraction \(\frac{-9}{2}\) can be written as \(-\frac{9}{2}\) by extracting the negative sign.

\(-\frac{9}{2}\)

Factor:

\(\frac{(-1)x3^{2} }{2}\) = -4.5

Answer:

I cant answer, but I can help, divide 100 by 16, than multiply what you get from that with 24, it'll look like this:

(100÷16)x24=A

Answer:

200 students vote in the election

Step-by-step explanation:

We know

120 votes = 60%

1% = 2 votes

To find how many students vote in the election, we take

2 x 100 = 200 votes

So, 200 students vote in the election

Answer:

c because its right trust

Step-by-step explanation:

The measure of variability that is used when the statistic with the greatest stability is sought is the Standard Deviation.

The Standard Deviation takes into account the dispersion of data points from the mean and provides a measure of the average distance between each data point and the mean. It is widely used in statistical analysis and is considered a robust measure of variability, providing a more precise and stable measure compared to other measures such as Mean Deviation, Quartile Deviation, or Range.

The Standard Deviation is a statistical measure that quantifies the dispersion or variability of a dataset. It takes into account the differences between individual data points and the mean of the dataset. By calculating the average distance between each data point and the mean, it provides a measure of how spread out the data is.

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Answer:

1. 7 Nickels, 13 Dimes

2. 30 Nickels, 15 Quarters

3. 74 Girls, 106 Boys

4. 180 tickets bought before and 113 bought at the gate

Step-by-step explanation:

Answer:

Step-by-step explanation:

1)

Nickel: n = 5c, Dime: d = 10c

Equations as per given:

Substitute d:

2)

Nickels: n = 5c, Quarters: q = 25c

Equations as per given:

Substitute n:

3)

Boys = b

Girls = g

Equations as per given:

Substitute b:

4)

Tickets purchased at the gate: g = $15

Tickets purchased before the concert: b = $10

Equations as per given:

Substitute b:

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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Answer:

im not sure about the 1st one but sec one is 162 i think and im  i dont know the last eaither srry  

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

16 ÷ 12 = 1.33 (rounded to 2 decimal places)

1.33 = scale factor

1.33² = area scale factor

1.33² × 36 = 64 (rounded to a whole number)

Answer: 64 would be the area

Step-by-step explanation:

Answer:

Step-by-step explanation:

NO i think

Answer:

∠BAD ≅ ∠BCD

Step-by-step explanation:

The complete equation is attached.

Two triangles are congruent to each other if all their three sides are equal to each other and all their three angles are equal to each other.

The angle side angle (ASA) congruence theorem states that two triangles are congruent if two angles of one triangle is equal to two angles of the other triangle and also if their included side are equal.

Since AB = BC, ∠ABD = ∠CBD. For ∠ABD ≅ ∠CBD based on ASA then ∠BAD ≅ ∠BCD

Answer:

3π, 6π

Step-by-step explanation:

12π*1/4=3π

16π*135/360=6π

the length of arc:

\(\tt =\dfrac{\alpha }{360}\times 2\pi.r\)

5.

\(\tt \dfrac{90}{360}\times 2\pi6= 3\pi~yd\)

7.

\(\tt \dfrac{135}{360}\times 2\pi.8=6\pi~km\)

a)Pˣ =  \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\)  in matrix form, using eigen-values.

b)state 2 is 0.75; state 5 is 0 and ;state 6 is 0.25.

a)In order to calculate the value of Pˣ, follow the below-given steps:

Step 1: Compute the eigen-values of the matrix P.

Here, we get λ = 1, λ = 0.6, λ = 0.4, λ = 0.1, λ = 0, λ = 0.

Step 2: Compute the eigen-vectors corresponding to each eigenvalue of the matrix P.

Step 3: Compute the diagonal matrix D and the transition matrix T. \(\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\end{matrix}0.6\)

\(\begin{matrix}0.58 & 0.25 & 0.72 & 0 & 0 & 0\end{matrix}0.4.\)

\(\begin{matrix}0.07 & 0 & 0.04 & 0.7 & 0 & 0\end{matrix}0.1.\)

\(\begin{matrix}0.35 & 0.75 & 0.56 & 0 & 1 & 0\end{matrix}0.\)

\(\begin{matrix}0 & 0 & 0 & 0.3 & 0 & 1\end{matrix}\)

Pˣ = T . Dˣ . T⁻¹

We get the following matrix as a result.  

Pˣ =  \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\)  

b)If the process starts in state 3,

the probability that it will be absorbed in state 2 is 0.75,

the probability that it will be absorbed in state 5 is 0, and

the probability that it will be absorbed in state 6 is 0.25.

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There are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

To find the number of unique 4-digit integers (excluding leading zeros) where the sum of the digits is 6, we can use a combinatorial approach.

Let's consider the four digits as four distinct positions: A, B, C, and D. The sum of the four digits is 6, so we need to distribute these six units among these four positions.

We can solve this problem using stars and bars. Imagine we have six stars (representing the six units) and three bars (representing the three dividers between the positions). The bars help us separate the units into four distinct positions.

For example, if we have the configuration "* | * * | * * | *," it represents the digits 1, 2, 2, and 1. The sum of these digits is 6.

The number of ways to arrange the six stars and three bars is given by the binomial coefficient (6 + 3 choose 3). Using the formula for combinations, we have:

(6 + 3) C 3 = (9 C 3) = 9! / (3! * (9 - 3)!) = 84.

So, there are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

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The probability that the randomly selected point is in the bullseye is: 1/3

We are told that there are two concentric circles.

Now, the circles that have a common centre are referred to as concentric circles and have different radii. In other words, it is defined as two or more circles that have the same centre point. The region between two concentric circles are of different radii is known as an annulus.

Now, the bulls eye diameter of 4 cm since the radius is 2 cm

Meanwhile, the outer part forms a diameter of 8 cm.

Thus:

Probability of hitting the bulls eye = 4/12 = 1/3

Probability of hitting the outer part = 8/12 = 2/3

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The orthogonal complement w⊥ of w has a basis given by {v1, v2} = {(1, 0, 0), (0, 1, 2)}.

To find the orthogonal complement w⊥ of w, we need to find the set of all vectors that are orthogonal (perpendicular) to w.

Given w = (x, y, z) = (12t, -12t, 6t), we can find a vector v = (a, b, c) that is orthogonal to w by taking their dot product equal to zero:

w · v = 0

Substituting the values of w and v:

(12t, -12t, 6t) · (a, b, c) = 0

(12t)(a) + (-12t)(b) + (6t)(c) = 0

12at - 12bt + 6ct = 0

Now, we can solve this equation to find the values of a, b, and c that satisfy the orthogonal condition for all values of t.

12at - 12bt + 6ct = 0

Factor out t:

t(12a - 12b + 6c) = 0

For this equation to hold true for all values of t, the expression inside the parentheses must equal zero:

12a - 12b + 6c = 0

Divide by 6:

2a - 2b + c = 0

This equation represents a plane in three-dimensional space. To find a basis for w⊥, we can express this equation in the form of a linear combination of vectors. Let's solve for c:

c = 2b - 2a

Now, we can express the basis vectors for w⊥ in terms of a and b:

v = (a, b, 2b - 2a)

We can choose any values for a and b to get different vectors in the orthogonal complement w⊥. For example, we can set a = 1 and b = 0:

v1 = (1, 0, 0)

Or we can set a = 0 and b = 1:

v2 = (0, 1, 2)

These two vectors, v1 and v2, form a basis for w⊥.

Therefore, the orthogonal complement w⊥ of w has a basis given by {v1, v2} = {(1, 0, 0), (0, 1, 2)}.

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The volume of a pyramid is 60 inches.

Given that,

A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.

V1 = 35 cubic inches

A1 = 15 square inches

h1 = 7 inches

A2 = 36 inches

h2 = 5 inches

To find  : What is V2

The following formula is used to determine a pyramid's volume:

V = (Base Area × Height)/3

V2 = (36 square inches multiplied by 5)/3

V2 = 60 cubic inches

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9514 1404 393

Answer:

  C.  y = x - 4

Step-by-step explanation:

We notice that values of x are consistently 4 more than the corresponding values of y. One way this can be written is ...

  x = y + 4 . . . (matches choice D)

However, we usually consider y to be the dependent variable. Rearranging this to "y = " form, we have ...

  y = x - 4 . . . matches choice C

The value of the postfix expression 6 3 2 4 + - * is 18, which falls between 15 and 100. Therefore, the correct answer is d) Something between 15 and 100.

Here is the step-by-step  of how to evaluate the postfix expression:

1. Start with the first two numbers, 6 and 3, and the first operator, *. Multiply 6 and 3 to get 18.
2. Move on to the next two numbers, 2 and 4, and the next operator, +. Add 2 and 4 to get 6.
3. Now you have 18 and 6, and the last operator, -. Subtract 6 from 18 to get 12.
4. The final result is 12.

Therefore, the value of the postfix expression 6 3 2 4 + - * is 12, which falls between 15 and 100. The correct answer is d) Something between 15 and 100.

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Iyell will save $7.68 on a classical music CD that has a price of $23.99.

Off means in market - The actual price of the objects/things will be different from the marked price.

Coupon means in market - The actual price of the objects/things will get reduced after applying the coupon.

For example:

1. 20% off on $60.

so, the price of $60 will get reduced by 20%

20% of $60 = ( 20x60 ) /100 = $12

actual price will be $60 - $12 = $48

Here, we have given that the marked price of CD is $23.99

First the 15% off sale will apply on the CD

15% of $23.99 = (15 x 23.99 ) / 100 = $3.5985

now, the price of CD will become, $23.99 - $3.5985 = $20.3915

now, to get maximum discount Iyell will apply the coupon for 20% extra off.

20% of $20.3915 = $4.0783

then, the actual price of CD will become, $20.3915 - $4.0783 = $16.3132

Iyell have save $4.0783 + $3.5985 = $7.68

Hence, Iyell will save $7.68 on a classical music CD that has a price of $23.99.

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The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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Answer:

-2 leis.

Step-by-step explanation:

212 * 14 = 2,968 leis

2,968/30 = 99 boxes

99*30=2970

2968-2970=-2

There is a problem with the wording of this question. There isn't a total so it's really confusing...

Given, the volume of a cube is 407cm³.Let's assume that a is the length of a side of the cube. We know that the volume of a cube = a³So,

a³ = 407Take the cube root of both sides to find the value of a.

a = (407)^(1/3)≈ 7.96cm(rounded to 1 decimal place)

Hence, the length of the side of the cube rounded to 1 DP is 7.96 cm (more than 100 words).

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