Find the measure of the arc. *
X
42°
V
W
?
O 42 degrees
84 degrees
0 21 degrees
O 81 degrees

The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.

The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.

A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.

If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.

Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.

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a. The exact value of the sum of -12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3)  is 12/7.

b.The exact value of the sum of∑ (1/3)ⁿ = 6*1/3⁶(1/3¹¹-1)/(1/3-1)  is 3/2.

A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - …

This is an infinite geometric series with first term a = -12 and common ratio r = 4/(-3). The sum of an infinite geometric series is given by:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = (-12) / [1 - (4/(-3))]

Simplify the denominator by multiplying both numerator and denominator by (-3):

S = (-12) / [-3 - 4]

S = (-12) / (-7)

S = 12/7

Therefore, the exact value of the sum is 12/7.

B. 6*1/3⁶(1/3¹¹-1)/(1/3-1)

This is a geometric series with first term a = 1 and common ratio r = 1/3. The sum of a geometric series with n terms is given by:

S = a (1 - rⁿ) / (1 - r)

As n approaches infinity, rⁿ approaches zero and the sum converges to:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = 1 / (1 - 1/3)

S = 3/2

Therefore, an expression that gives the exact value of the sum is 3/2.

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In order to expect a return on $400 from across all policies of a similar nature, the insurance firm should charge the policy for about $501.88.

Return[expr] leaves control structures that are present during a function's definition and returns the value expression for the entire function. Even if it comes inside other functions, yield takes effect as quickly as it is evaluated. Functions like Scan can use Return inside of them.

Since p is the chance that the 28-year-old woman survives the year and is given as 0.99962, we can enter this number into the equation for n as follows: n = 400(0.99962)/500,400 n 0.799

In light of this, the insurance provider should impose a premium of: Premium = 400/n

$501.88 is the premium ($Premium = 400/0.799)

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The trapezoid has a surface area of 480 square units.

So, a trapezoid measured in feet offers an area in square feet; one measured in millimetres gives an area in square centimetres; and so on. If it's simpler for you, you can add the lengths of the bases and then divide the total by two. Keep in mind that multiplication by 12 is equivalent to dividing by 2.

We must apply the formula for a trapezoid's area to this issue in order to find a solution:

[tex]A = (1/2) * (a + b) * h[/tex]

where h is the trapezoid's height (or altitude) and a and b are the lengths of its parallel sides.

The values for a, b, and h are provided to us, allowing us to change them in the formula:

A = (1/2) * (20 + 60) * 12

A = (1/2) * 80 * 12

A = 480 square units

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Each subsequent jump will be exactly one unit longer in length than the one before it after the initial jump, which can be one unit in length. Each jump has the option of going either left or right.

The translation of the question is

A robot jumps on a number line starting at zero. The rules of the game are the following if you look at your right hand, the length of each jump is expressed with a positive number and, if facing your left hand, with a negative number.

Also: if you jump straight ahead (that is, in the direction you are facing), the number number of jumps is expressed as a positive number, and if you jump backwards (i.e., on the opposite direction to the one you are looking at), the number of hops is considered with a negative number. Observe the following jumps of the robot, its final position in each case and answer in your notebook the questions

When closely examined, it is simple to conclude that:

If you have consistently jumped in the appropriate direction, you will arrive at point p = 1 + 2 + 3 + 4 +... + n after n jumps.

You would be at point p - 2k in any of these n leaps if you leapt left in the kth hop (k=n) rather than right.

Moreover, after n leaps, you can be anywhere between n * (n + 1) / 2 and -(n * (n + 1) / 2) with the same parity as n * (n + 1) / 2 by carefully selecting which jumps to go left and which to go right.

The trick is to imitate jumping while keeping the aforementioned facts in mind. Always jump to the right, and if at some time you arrive at a location that has the same parity as X and is at or beyond X, you'll know the answer.

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Answer:

235.65

Step-by-step explanation:

Answer:

3x - (4x - 11) = 3x - 4x + 11 = -x + 11

Step-by-step explanation:

The probability that a randomly selected student likes coconut is 0.6.

Step-by-step explanation:

Given that,

Now we have to find the probability that a randomly selected student likes coconut.

P (student likes coconut) = the number of students who liked coconut / total number of students

= 60/100

= 0.6

Therefore, the probability that a randomly selected student likes coconut is 0.6.

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The phone is worth $128 after 2 years, which is option C.

What is exponential decay ?

Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.

Calculating the worth of the phone :

The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.

Let's use the formula for exponential decay: [tex]A = A_0(1 - r)^t[/tex], where A is the final amount, [tex]A_0[/tex] is the initial amount, r is the decay rate, and t is the time elapsed.

In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:

[tex]A = 800(1 - 3/5)^2[/tex]

[tex]A = 800(2/5)^2[/tex]

[tex]A = 800(4/25)[/tex]

[tex]A = 128[/tex]

Therefore, the phone is worth $128 after 2 years, which is option C.

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The number 10 is 30% of the following number: 33.33.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the whole number which 10 is 30%, we would apply the following mathematical expression (formula);

Quantity = percent × number

Substituting the given parameters into the percentage and quantity formula, we have the following;

10 = 30/100 × number

10 = 0.3  × number

Number = 10/0.3

Number = 33.33.

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sum area = -3x - 6y + 12 and product area = -36x - 72y.

what is rectangle?

A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.

The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:

Sum:

Area = length x width

Area = (-3x - 6y) + 12

Area = -3x - 6y + 12

Product:

Area = length x width

Area = (-3x - 6y) x 12

Area = -36x - 72y

Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.

Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.

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Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year when compounded.

Simple interest is computed just using the principle, which is the initial sum borrowed or put into an investment. The interest rate is constant throughout time and solely applies to the principal sum. Short-term loans or investments frequently employ simple interest.

The given situation can be modeled as a linear equation given by:

y = mx + c

For Jerry we have:

y = 50x + 125

For 3 years = 36 months we can substitute x = 36:

y = 50(36) + 125

y = 1825

For x = 10:

y = 50(120) + 125

y = 6125

Hence, Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year.

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According to Chebyshev's theorem, at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.

Chebyshev's theorem states that for any set of data, regardless of its distribution, a certain percentage of the data lies within a certain number of standard deviations from the mean. Specifically, Chebyshev's theorem states that for any data set, at least 1 – 1/k² of the data values will lie within k standard deviations of the mean, where k is any number greater than 1. If k=2, at least 75% of the data values lie within 2 standard deviations of the mean. If k=3, at least 89% of the data values lie within 3 standard deviations of the mean.

Therefore, for a data set with a mean of 63.6 minutes and a standard deviation of 2.5 minutes, we can use Chebyshev's theorem to determine that at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.

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Answer:

29.12 square cm

Step-by-step explanation:

     Side = a = 8.2 cm

    [tex]\boxed{\bf Area \ of \ equilateral \ triangle = \dfrac{\sqrt{3}}{4}a^2}[/tex]

                                                       [tex]\sf = \dfrac{\sqrt{3}}{4}*8.2*8.2\\\\= \sqrt{3}*4.1 * 4.1\\\\= 1.732 * 4.1 *4.1\\\\= 29.12 \ cm^2[/tex]

The answer of the given question based on finding the m∠LKM from the given circle the answer is the measure of ∠LKM is 140° degrees.

In geometry,  diameter of circle is  line segment that passes through  center of  circle and has both endpoints on circle. The diameter is the longest chord (line segment connecting two points on  circumference) of  circle. The length of  diameter is twice the length of radius, which is distance from the center of  circle to any point on  circumference.

The diameter i important property of a circle and is used to calculate other properties, like the circumference and area of the circle

Since MK is a diameter of the circle, it passes through the center of the circle, which we can label as point O. Therefore, ∠LKM is an inscribed angle that intercepts arc LM.

By the Inscribed Angle Theorem, we know that the measure of an inscribed angle is equal to half the measure of the arc that it intercepts. Therefore, to find the measure of ∠LKM, we need to find the measure of arc LM.

We are given that the measure of arc LK is 100° degrees. Since arc LM is the sum of arcs LK and KM, and MK is a diameter (so arc KM is also a semicircle with a measure of 180 degrees), we can write:

m(arc LM) = m(arc LK) + m(arc KM) = 100 + 180 = 280° degrees

Therefore, the measure of ∠LKM is:

m∠LKM = 1/2 * m(arc LM) = 1/2 * 280 = 140° degrees

So the measure of ∠LKM is 140° degrees.

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Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the lower right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]  ( cross- multiply )

x = 4[tex]\sqrt{2}[/tex]

Answer:

$10

Step-by-step explanation:

We Know

Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.

Let C be the total cost, and x be the number of minutes she talks; we have the equation.

C = 0.05x + 10

If Terri does not make any calls, what would her bill be?

C = 0.05(0) + 10

C = $10

So, her bill will be $10

Considering flow over a flat plate, and by using the Thwaites-Walz method and the Pohlhausen method are very similar, but they differ significantly from the exact solution.

The Thwaites-Walz Method for flow over a flat plate:

          The Blasius method can be used to obtain the non-dimensional velocity distribution over a flat plate. But the computation of the shear stress and friction coefficient from this velocity distribution requires the knowledge of the second derivative of u with respect to y which is difficult to obtain.

          The Thwaites method is an alternative method for computing the friction coefficient, which avoids the computation of the second derivative of u with respect to y. This method involves the solution of an ordinary differential equation.

            This method is particularly useful for computing the friction coefficient in the early stages of the boundary layer. The equations for the Thwaites method are as follows:

                 [tex]\frac{d^2\delta}{dx^2} =\frac{\delta}{u^2}\left(1+ \frac{\delta}{2}\frac{dU/dx}{U}\right)C_f[/tex]

                                                         = [tex]\frac{0.288\delta}{Re_x}(\frac{d\delta}{dx})^{1/2}Re_x[/tex]

                                                         = [tex]\frac{\rho u(x)x}{\mu}\tau_w[/tex]

                                                         = [tex]\rho u_\infty C_f/2x[/tex]

                                                         = [tex]\frac{1}{C_f}\int_{0}^{\delta}u_\infty \left(1- \frac{u}{u_\infty}\right)dy$$[/tex]

The following are the predictions using the Thwaites-Walz method to predict d, d*, 8, and

                   [tex]Cvs x.*d = 0.375 x^(1/5)*d*[/tex]

                                    = [tex]4.91 x^(1/5)*8[/tex]

                                    = [tex]0.664 x^(3/5)*Cv[/tex]

                                    = [tex]1.328 x^(1/5)[/tex]

        The Pohlhausen method is a simple method for computing the shear stress and the friction coefficient, which is based on an approximate solution of the boundary layer equations. The Pohlhausen method is based on the assumption that the velocity distribution is a parabolic function of the distance from the wall.

             The equations for the Pohlhausen method are as follows:

                      [tex]u(x,y)= U(x)\left(1-\left(\frac{y}{\delta}\right)^2\right)\tau_w[/tex]

                                 = [tex]\rho u_\infty \frac{dU}{dx}\frac{\delta^2}{3}C_f[/tex]

                                 =  [tex]\frac{2}{3}\frac{\tau_w}{\rho u_\infty^2}x[/tex]

                                 =  [tex]\frac{1}{C_f}\int_{0}^{\delta}u_\infty \left(1- \frac{u}{u_\infty}\right)dy$$[/tex]

The following are the predictions using the Pohlhausen method to predict d, d*, 8, and

                       Cvs x.• d = 0.37 x^(1/5)• d*

                                       = 4.9 x^(1/5)• 8

                                       = 0.664 x^(3/5)• Cv

                                       = 1.328 x^(1/5)

The following are the exact solutions for flow over a flat plate. Equations (2.21) and (2.22) are for the shear stress and friction coefficient respectively.

                           [tex]$$ \tau_w = \rho u_\infty C_f/2[/tex]

                                =  [tex]\frac{0.664 \rho u_\infty^2 x^{3/5}}{Re_x^{1/5}}C_f[/tex]

                                 =   [tex]\frac{0.664}{Re_x^{1/2}}[/tex]

          The following are the predictions using the exact solutions for flow over a flat plate.

                                  [tex]*d = 0.664 x^(3/10)*d*[/tex]

                                        = [tex]4.91 x^(1/5)*8[/tex]

                                       = [tex]0.664 x^(3/5)*Cv[/tex]

                                       = [tex]1.328 x^(1/5)[/tex]

         Hence, the predictions using the Thwaites-Walz method and the Pohlhausen method are very similar, but they differ significantly from the exact solution.

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An expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]

We are given that the area of a rectangle is [tex]$A=x^2+x-15$[/tex], and we want to find an expression for the length of the rectangle in terms of A.

Recall that the area of a rectangle is given by the formula: [tex]$A=L\cdot W$[/tex], where L is the length and W is the width. We can use this formula to write L in terms of A and W as [tex]$L=\frac{A}{W}$[/tex].

We know that the rectangle has a length and a width, so we need to find an expression for the width W in terms of A. We can rearrange the given formula for A to solve for W:

[tex]&& \text{(substitute }L=x+5\text{)}[/tex]

[tex]W&=\frac{x^2+x-15}{x+5} && \text{(divide both sides by }x+5\text{)}[/tex]

Now that we have an expression for W in terms of A, we can substitute it into our expression for L to get:

[tex]L&=\frac{A}{W}[/tex]

[tex]&=\frac{x^2+x-15}{\frac{x^2+x-15}{x+5}} && \text{(substitute the expression we found for }W\text{)}\&=x+5[/tex]

Therefore, an expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]

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Step-by-step explanation:

it would mean that she made 53 batches of soap and 4 batches of lotion.

now, is it a solution ?

then both inequalities must be true with these values.

5×53 + 15×4 <= 325

265 + 60 <= 325

325 <= 325 correct

20×53 + 35×4 <= 1200

remember, 1 hour = 60 minutes.

1060 + 140 <= 1200

1200 <= 1200 correct

so, (53, 4) is the intersection point of both limit lines. and it is as such an extreme point and optimum.

In the following question, among the conditions given, the statement is said to be, the exact molarity of the NaOH solution is 0.0960 M.

The question is asking to calculate the exact molarity of the sodium hydroxide from Experiment 1.
KHP stands for potassium hydrogen phthalate, and one mole of sodium hydroxide (NaOH) will neutralize one mole of KHP. To solve the problem, use the mass of KHP and a stoichiometry problem.
First, calculate the number of moles of KHP:
Moles KHP = (Mass KHP (g) / Molar Mass KHP (g/mol))
Then, calculate the moles of NaOH:
Moles NaOH = (Moles KHP * Mole Ratio NaOH/KHP)
Finally, calculate the molarity of NaOH:
Molarity NaOH = (Moles NaOH / Volume NaOH (L))

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well, we know the discount is just 30 - 21 = 9, so hmm if we take 30(origin amount) to be the 100%, what's 9 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 30 & 100\\ 9& x \end{array} \implies \cfrac{30}{9}~~=~~\cfrac{100}{x} \\\\\\ 30x=900\implies x=\cfrac{900}{30}\implies x=30[/tex]

Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Option 1 is the better choice as it has a lower total cost.

Simple interest is a type of interest that is calculated on the original principal amount of a loan or investment. It is a fixed percentage of the principal amount that is paid by the borrower or earned by the lender over a specific period of time.

To compare the two options, we need to calculate the total cost of each option and compare them.

Option 1: 10% discount and pay off with 4% simple interest

The discount reduces the price of the television to $1000 x 0.9 = $900. If the customer chooses to pay it off at 4% simple interest, the total cost would be:

Total cost = $900 + ($900 x 0.04 x 3) = $972

Option 2: Full price and pay off in 3 years with no interest

The total cost of this option would be simply the full price of $1000 paid over 3 years, so:

Total cost = $1000 / 3 = $333.33 per year x 3 years = $1000

Comparing the two options, we see that Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Therefore, Option 1 is the better choice as it has a lower total cost.

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The complete question is: The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better?

Option 1 with the discount and 4% simple interest.

Option 2 with no discount and no interest.

The roots of the equation 2x² + 10x + 9 = 2x does not exist i.e no real roots

To find the roots of the given quadratic equation 2x² + 10x + 9 = 2x, we can start by rearranging the equation to the standard form of a quadratic equation

2x² + 10x + 9 - 2x = 0

Simplifying the left-hand side, we get:

2x² + 8x + 9 = 0

Now, we can use the quadratic formula to find the roots of the equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 8, and c = 9.

Substituting these values into the formula, we get:

x = (-8 ± √(8² - 4(2)(9))) / 2(2)

Simplifying the expression under the square root, we get:

x = (-8 ± √-8) / 4

The square root of -8 is not a real number

So, the equation has no real root

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Expression which Defines function h is as follows :

[tex]f(g(h(x))) = 81x^9 + 2916x^8 - 351x^7 - 81762x^6 - 13230x^5 + 705228x^4 - 127752x^3 - 348744x^2 + 12480x + 20736.[/tex]

In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable).

To find f(g(h(x))), we must first find h(x), then plug it into g(h(x)), and finally into f. (x).

[tex]h(x) = 3x^2 + 12x[/tex]

[tex]g(h(x)) = h(x) - 1 = (3x^2 + 12x) - 1 = 3x^2 + 12x - 1[/tex]

[tex]f(g(h(x))) = 3(3x^2 + 12x - 1)^3 + 9(3x^2 + 12x - 1)^2 - 12(3x^2 + 12x - 1)[/tex]

Simplifying this expression is time-consuming, but we can use the binomial theorem to expand each term and then combine like terms to get:

[tex]f(g(h(x))) = 81x^9 + 2916x^8 - 351x^7 - 81762x^6 - 13230x^5 + 705228x^4 - 127752x^3 - 348744x^2 + 12480x + 20736[/tex]

Therefore, [tex]f(g(h(x))) = 81x^9 + 2916x^8 - 351x^7 - 81762x^6 - 13230x^5 + 705228x^4 - 127752x^3 - 348744x^2 + 12480x + 20736.[/tex]

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Step-by-step explanation:

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

Analyze the proportion below and complete the instructions that follow.

2x+5/3 = x-5/4

-7

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Analyze the ratio below and complete the instructions that follow.

$30:$6

Simplify the ratio.

5:1

If 14/3 = x/y then 14/x =

3/y

Analyze the diagram below and complete the instructions that follow.

In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Analyze the diagram below and complete the instructions that follow.

If AB:BC is 3:11, solve for x.

9

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

Analyze the diagram below and complete the instructions that follow.

Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

Analyze the diagram below and complete the instructions that follow.

Given that CB/CA = DE/DF, find BA.

10.5

Analyze the proportion below and complete the instructions that follow.

2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow.

Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow.

Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow.

Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Analyze the diagram below and complete the instructions that follow.

If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

Answer:

The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.

Step-by-step explanation:

qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]

where r = |z| = magnitude of z and theta = arg(z) = argument of z.

Calculate the magnitude of z:

|r| = sqrt((3)^2 + (4)^2) = 5

And the argument of z:

theta = arctan(4/3) = 0.93 radians

Now, find the two square roots of z:

sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]

= +/- 1.58 * [cos(0.47) + i sin(0.47)]

= +/- 1.58 * [0.89 + i*0.46]

Using a calculator, simplify this expression to:

sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8

Mrs. Banks has enough fruit to make the 44 qt of jelly she wants, but she will have 4 lb of leftover fruit.

Here we have to use the arithmetic operations. First, we need to convert the total quantity of jelly to gallons since we have the amount of fruit needed per gallon. One gallon is equal to 4 quarts, so 44 quarts is equal to 11 gallons.

Next, we can calculate how much fruit is needed for 11 gallons of jelly by multiplying the amount of fruit needed per gallon by the number of gallons

11 gallons x 6 lb of fruit per gallon = 66 lb of fruit needed

Since Mrs. Banks only has 70 lb of fruit, she has enough to make the 44 qt of jelly she wants, but she will have 4 lb of leftover fruit:

70 lb of fruit - 66 lb of fruit needed = 4 lb of leftover fruit

Learn more about Arithmetic operations here

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The given question is incomplete, the complete question is:

Mrs. Banks wants to make 44 qt of jelly with 70 lb of fruit. If each gallon of jelly needs 6 lb of fruit, will

she have enough fruit? How much leftover fruit does she have, or how much extra fruit is needed?

Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest:

A = P*e^(rt)

where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).

For Sophie's account, we have:

P = $92,000

r = 6 1/8% = 0.06125 (as a decimal)

t = 14 years

A = 92000*e^(0.06125*14)

A = $219,499.70 (rounded to the nearest cent)

For Damian's account, we have:

P = $92,000

r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)

t = 14*12 = 168 months

A = 92000*(1+0.005521)^168

A = $288,947.46 (rounded to the nearest cent)

Now we can subtract Sophie's final amount from Damian's final amount to find the difference:

Difference = $288,947.46 - $219,499.70

Difference = $69,447.76

Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.