how do I get the answer to 4.5 × 2.4 ?​

Answer:

The coordinate of the circumcenter of the given triangle is (4, -1)

Step-by-step explanation:

The circumcenter is found by the intersection of the perpendicular bisectors of a triangle as follows;

The vertices of triangle ΔABC are A(1, 1), B(1, -3), and C(7, -3)

The coordinates of the midpoint of segment AB is 1/2(1 + 1, 1 + (-3)) = (1, -1)

The slope of segment AB = ∞, therefore, the slope of the perpendicular to segment AB = -1/∞ = 0

The line representing the perpendicular to segment AB is y = -1

The coordinates of the midpoint of segment BC is 1/2(1 + 7, (-3) + (-3)) = (4, -3)

The slope of segment BC = 0, therefore, the slope of the perpendicular to segment BC = ∞, which is a vertical line parallel to the y-axis with equation, x = 4

Therefore, the coordinate of the circumcenter is the intersection of the lines y = -1, and x = 4, which is the point (4, -1).

Standard deviation = 0.314315

Mean = 0.466275Standard deviation = 0.314315

Using random numbers given below, we are to compute the mean and standard deviation.

0.931806 0.398110 0.216843 0.826248 0.323101 0.235342 0.105300 0.203744 0.973537 0.1813430.848380 0.602418 0.013789 0.495464 0.3657860.027959 0.782500 0.232680 0.913043 0.689042 0.399642 0.982936 0.724617 0.088320 0.152830 0.303524 0.706177 0.076412 0.937273 0.3670350.155910 0.003958 0.442786 0.769659 0.098387 0.995570 0.953256 0.497222 0.428427 0.531733 0.895690 0.717929 0.257446 0.478400 0.810417 0.666180 0.071199 0.876201 0.545347 0.159312

Let us first find the sum of all the given numbers:

Sum of all the given numbers = 22.824475The mean is equal to the sum of all the given numbers divided by the number of values or data points.

Mean = Sum of all the given numbers/Number of values= 22.824475/49= 0.466275 (to 6 decimals)For Standard Deviation:Calculate the deviations of each data point from the mean.

Deviation = data value - meanDeviation

0.931806-0.466275

= 0.4655310.39811-0.466275

= -0.0681650.216843-0.466275

= -0.2494320.826248-0.466275

= 0.3599730.323101-0.466275

= -0.1431740.235342-0.466275

= -0.2309330.1053-0.466275

= -0.3609750.203744-0.466275

= -0.2625310.973537-0.466275

= 0.5072620.181343-0.466275

= -0.2849320.84838-0.466275

= 0.3821050.602418-0.466275

= 0.1361430.013789-0.466275

= -0.4524860.495464-0.466275

= 0.0291890.365786-0.466275

= -0.1004890.027959-0.466275

= -0.4383160.7825-0.466275

= 0.3162250.23268-0.466275

= -0.2335950.913043-0.466275

= 0.4467680.689042-0.466275

= 0.2227670.399642-0.466275

= -0.0666330.982936-0.466275

= 0.5166610.724617-0.466275

= 0.2583420.08832-0.466275

= -0.3779550.15283-0.466275

= -0.3134450.303524-0.466275

= -0.1627510.706177-0.466275

= 0.2399020.076412-0.466275

= -0.3898630.937273-0.466275

= 0.4709980.367035-0.466275

= -0.099240.15591-0.466275

= -0.3103650.003958-0.466275

= -0.4623170.442786-0.466275

= -0.0234890.769659-0.466275

= 0.3033840.098387-0.466275

= -0.3678880.99557-0.466275

= 0.5292950.953256-0.466275

= 0.4869810.497222-0.466275

= 0.0309470.428427-0.466275

= -0.0378480.531733-0.466275

= 0.0654580.89569-0.466275

= 0.4294150.717929-0.466275

= 0.2516540.257446-0.466275

= -0.2088290.4784-0.466275

= 0.0121250.810417-0.466275

= 0.3441420.66618-0.466275

= 0.1999050.071199-0.466275

= -0.3950760.876201-0.466275

= 0.4099260.545347-0.466275

= 0.0790720.159312-0.466275

= -0.306963

Squared deviations are obtained by squaring the deviations.

Squared Deviation

0.216548295 0.004637516 0.062216904 0.129554124 0.020491426 0.053184018 0.130515481 0.068973147 0.257270145 0.081111189 0.145998825 0.018532791 0.204814163 0.000849691 0.010099712 0.191979424 0.099977778 0.054573104 0.199406948 0.049550262 0.004452173 0.266797063 0.066566605 0.142963461 0.098098804 0.026526768 0.057547573 0.057523157 0.151011985 0.060334873 0.220807229 0.003184658 0.096166054 0.213734313 0.092657256 0.134059226 0.250037803 0.236149271 0.000918616 0.064068937 0.00624095 0.305417694 0.237333383 0.04779582 0.120453688 0.006914376 0.006493958 0.017708226The variance is the average of the squared deviations.

Variance = (Sum of squared deviations) / (Number of values - 1)Variance = 5.426947 / 48= 0.113123 (to 6 decimals)

Standard deviation is equal to the square root of the variance.

Standard deviation = sqrt(Variance)= sqrt(0.113123)= 0.314315 (to 6 decimals)

Therefore,Mean = 0.466275

Standard deviation = 0.314315

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The value of 11√11 in form of √a is √1331.

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } ​square root of, end square root . Finding the square root of a number is the opposite of squaring a number.

Given:

11√11, we have to write in the form of √a.

First, anything that comes out of the root have a pair when turns inside the root like (2 x 2 x 2) then only one '2' comes outside the root which can be seen as 2√2.

Now, 11√11 can be written as

= √11 x 11 x 11

= √1331.

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Answer:

the range is -5>-9    

the domain is 44

Step-by-step explanation:

To determine if each relation is a function, we need to check if each input value (x-coordinate) is associated with only one output value (y-coordinate).

For the given relation:

(2,4),(1,3),(-3,-1),(4,6)

We can see that each unique x-coordinate is paired with a unique y-coordinate. There are no repeated x-values, meaning that each x-value has a unique y-value associated with it.

Therefore, this relation is a function because each input value (x-coordinate) is associated with only one output value (y-coordinate). No x-value has multiple y-values assigned to it.

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Answer:

it should be B.

Step-by-step explanation:

Answer: I think it’s 8

Step-by-step explanation: because it can’t be the other ones

Answer:

37

Step-by-step explanation:

Answer:

40 inches

Step-by-step explanation:

Answer: 4 hours

Step-by-step explanation: After 4 hours, they will both cost $340.

If angle2 is congruent to angle6, angle2 must have the same measure as angle6.

Congruent angles have the same measure, meaning their angles are equal. If angle2 is congruent to angle6, it implies that both angles have the same measure. This means that if angle6 has a measure of, for example, 45 degrees, then angle2 must also have a measure of 45 degrees. Congruent angles can be thought of as identical twins in terms of their measures. So, if angle2 is congruent to angle6, it simply means that angle2 and angle6 have the same measure.

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The many square inches of plastic wrap were used to wrap the container is 2.4π square inches. Option B

The formula for calculating the area of the cylinder is expressed as;

A = 2πrh + 2πr²

Given that the parameters are;

Diameter = 2radius

Radius = 1.6/2 = 0. 8 inches

Substitute the values, we get;

Area = 2π×0. 8 × 0.7 + 2 × π × 0. 8²

find the squares and multipy, we have;

Area = 1. 12π + 1.28π

Add the values, we get;

Area = 2.4π square inches

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Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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Answer: The area of the region enclosed by the curves y=x, y=2x, x=y^2, x=4y^2 in the first quadrant is 119/5 square units.

Step-by-step explanation:

Let's begin by sketching the region in the first quadrant enclosed by the given curves:

We can see that the region is bounded by the lines y=x and y=2x, and the parabolas x=y^2 and x=4y^2.

To get the area of this region, we can use the change of variables u=y and v=x/y. This transformation maps the region onto the rectangle R={(u,v): 1 ≤ u ≤ 2, 1 ≤ v ≤ 4} in the uv-plane. To see why, note that when we make the substitution y=u and x=uv, the curves y=x and y=2x become the lines u=v and u=2v, respectively.

The curves x=y^2 and x=4y^2 become the lines v=u^2 and v=4u^2, respectively.Let's determine the Jacobian of the transformation. We have:

J = ∂(x,y) / ∂(u,v) =

| ∂x/∂u ∂x/∂v |

| ∂y/∂u ∂y/∂v |

We can compute the partial derivatives as follows:∂x/∂u = v

∂x/∂v = u

∂y/∂u = 1

∂y/∂v = 0

Therefore, J = |v u|, and |J| = |v u| = vu.

Now we can write the integral for the area of the region in terms of u and v as follows

:A = ∬[D] dA = ∫[1,2]∫[1,u^2] vu dv du + ∫[2,4]∫[1,4u^2] vu dv du

= ∫[1,2] (u^3 - u) du + ∫[2,4] 2u(u^3 - u) du

= [u^4/4 - u^2/2] from 1 to 2 + [u^5/5 - u^3/3] from 2 to 4

= (8/3 - 3/4) + (1024/15 - 32/3)

= 119/5.

Therefore, the area of the region enclosed by the curves y=x, y=2x, x=y^2, x=4y^2 in the first quadrant is 119/5 square units.

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Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

The homothet coefficients and the value of x are

The homothet coefficient by definition and in this context, is the scale factor of dilation

Using the above as a guide, we have the following:

Figure (a)

If the image of point P is P′, then

Homothet coefficient = 18/9

Homothet coefficient = 2

Also, we have

x/9 = 35/18

x = 9 * 35/18

x = 17.5

Figure (b)

If the image of point P is P′, then

Homothet coefficient = 15/9

Homothet coefficient = 5/3

Also, we have

x/10 = 15/9

x = 10 * 15/9

x = 50/3

Figure (c)

Here, we have

Homothet coefficient = 15/6

Homothet coefficient = 5/2

Also, we have

x/2 = 15/6

x = 2 * 15/6

x = 5

Hence, the value of x is 5

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Complement of set A is the set of all elements in the universal set that are not in the set .

If there is a subset of the universal set (U) called A, then the complement of set A, denoted by the symbol A', is different from the elements of set A and contains the elements of the universal set but not the elements of set A.

In this case, A' = x U: x A.

In other words, the complement of a set A is the difference between the universal set and set A.

For example: U = {1, 2, 3, 5, 7, 9, 15 ,14, 13}, A = {1, 2, 3, 5,7,9}, find the complement of A.

A' = U - A = {1, 2, 3, 5, 7, 9, 15,14,13} - {1, 2, 3, 5,7,9} = {15,14, 13}

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolised by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

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Answer:

90

Step-by-step explanation:

q

4 is the slope of the linear relationship.

An indication as to how sharp a line is its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

The ratio of the increase in elevation between two places to the run in elevation between those same two points is referred to as the slope.

Slope-related equations The "change in y" over the "change in x" of a line is referred to as the slope. By dividing (y₂ - y₁) over (x₂ - x₁) and choosing two locations on the line (x₁, y₁) and (x₂, y₂), you can get the slope.

A linear relationship is given in the table.

According to the data of the table,

x: -2  -1  0  1  2

y:  -13  -9  -5  -1  3

now, slope = (y₂ - y₁) / (x₂ - x₁)

slope = {-9 -(-13)} / {-1 -(-2)}

slope = 4

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When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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Answer: The answer I got was A) 16

Step-by-step explanation:

Hope this helps!!!!

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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The symbol of absolute value is two vertical bars (||).

The absolute value of a number is the distance between that number and zero on a number line. The absolute value of a number is always positive, regardless of the sign of the original number. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5.

In mathematical notation, the absolute value of a number is represented by placing the number between the vertical bars, like this: |x|. When the absolute value is applied to a variable or an expression, the result is the positive value of that variable or expression. For example, |-5| = 5, and |5| = 5.

The absolute value is used in many branches of mathematics, including algebra, calculus and geometry, and it is used to represent the magnitude of a number, regardless of its sign, and also it is used to define the distance between two points on a number line.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

The formula for the area of a sector of a circle is \(A = (θ/360) * π * r^2,\) where θ is the central angle in degrees, π is 3.14, and r is the radius of the circle.

Given the area of a sector of a circle is \(56 cm^2\) and the radius is 10 cm, we can solve for θ:

\(56 cm^2 = (θ/360) * 3.14 * 10^2\\56 cm^2 = (θ/360) * 314\\θ = (56 * 360) / 314\\θ = 63.6\)

Therefore, the central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

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Answer:

Step-by-step explanation:

PS =5 because PS's line is parallel to 5 the line.

So now all that is left is the angle one

m∠Q =105° we can come to this conclusion because 105° is parallel to m∠Q

If you are still confused please, let me know! :)

Answer:

20 =x

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

x+40 = 3x

Subtract x from each side

x+40-x = 3x-x

40 = 2x

Divide by 2

40/2 = 2x/2

20 =x

Answer:

x = 20

Step-by-step explanation:

3x = x + 40

2x = 40

x = 20