Which expression is equivalent to (4 7i)(3 4i)? â€""16 37i 12 â€"" 28i 16 â€"" 37i 37 16i.

Answer:

<PQR, <RQP, <Q

Step-by-step explanation:

Answer:

The value of x is 70

Step-by-step explanation:

Here, we want to find the value of x

To do this, we are going to use one of the circle tangent relationships

we have this as;

24 = (118-x)/2

2(24) = 118-x

48 = 118-x

x = 118-48

x = 70

The simplification of the given square root expression by using the rules of indices is obtained as: 9/8.

Any product of numbers is written relatively succinctly using a power or an index. Indexes is the plural of index. In this booklet, we will remind everyone of how to do this and list some laws or principles that can be applied to make indices-based expressions simpler.

The laws of indices are a set of guidelines used to regulate expressions involving indices.

The given expression is-

= \(\sqrt{(\frac{9}{8})^{2} }\)

Convert the square root into the fractional power.

= \(((\frac{9}{8} )^{2}) ^{\frac{1}{2} }\)

This, power 1/2 and 2 will get cancelled to give:

= 9/8

Thus, the simplification of the given square root expression by using the rules of indices is obtained as: 9/8.

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I think x is 33

that's your answer

Answer: Can't be answered, not enough information given

Step-by-step explanation: I think you forgot to give the answer for the circumference of the hub cap so there is no way to solve for the area of this hub cap when only given PI. (Area=PI x Radius^2). :)

The probability that the PolyU team wins the relay race can be determined by calculating the cumulative probability that their combined time is less than or equal to the "time to beat" of 120 minutes.

Let's denote the time taken by George as X and the time taken by Jean as Y. Both X and Y are normally distributed with means and standard deviations given as follows:

George: X ~ N(70, 15^2)

Jean: Y ~ N(65, 10^2)

Since the times taken by George and Jean are independent, we can use the properties of normal distributions to calculate the probability of their combined time being less than or equal to 120 minutes.

To find the probability that X + Y ≤ 120, we need to find the joint distribution of X and Y and then calculate the probability of the combined time being less than or equal to 120. Since X and Y are normally distributed, their sum X + Y will also follow a normal distribution.

The mean of the sum X + Y is given by the sum of the individual means:

Mean(X + Y) = Mean(X) + Mean(Y) = 70 + 65 = 135 minutes.

The variance of the sum X + Y is given by the sum of the individual variances:

Var(X + Y) = Var(X) + Var(Y) = 15^2 + 10^2 = 325 minutes^2.

The standard deviation of the sum X + Y is the square root of the variance:

SD(X + Y) = √(Var(X + Y)) = √325 ≈ 18.03 minutes.

Now, we can use the properties of the normal distribution to calculate the probability P(X + Y ≤ 120) by standardizing the value:

Z = (120 - 135) / 18.03 ≈ -0.8313

Using a standard normal distribution table or a calculator, we can find the cumulative probability for Z = -0.8313, which represents the probability of the combined time being less than or equal to 120 minutes. Let's assume this probability is P(Z ≤ -0.8313) = p.

Therefore, the probability that the PolyU team wins the relay race can be given as 1 - p, as the team wins when their combined time is less than or equal to 120 minutes.

In summary, to find the probability of the PolyU team winning the relay race, we need to calculate the cumulative probability P(Z ≤ -0.8313) and subtract it from 1.

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Answer:

\( \frac{39}{52} = 0.75\)

Answer:

x+10/7.......................

One disadvantage of using a large sample size in research is the c) increased expense associated with data collection, participant recruitment, incentives, and data processing.

While a large sample size is generally advantageous in statistical analysis and research, it comes with certain drawbacks. One of the main disadvantages is the increased expense involved in working with a large sample size. Collecting data from a larger sample requires more resources, such as time, money, and personnel. The costs associated with data collection, participant recruitment, incentives, and data processing can escalate significantly with larger sample sizes. This can pose a challenge for research studies or projects with limited resources or tight budgets.

The expenses incurred when working with a large sample size can include various aspects. For example, reaching out to and recruiting a larger number of participants can require additional efforts and costs for advertising, communication, and coordination. Providing incentives or compensation to a larger sample size can also be more expensive. Additionally, data processing and analysis become more time-consuming and resource-intensive with larger datasets, potentially requiring more advanced software, hardware, or computational resources. All these factors contribute to the increased expense associated with using a large sample size in research. Therefore, it is essential for researchers and organizations to carefully consider the financial implications and resource availability before deciding on the sample size for a study or project.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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7/8 cups of sauce are needed to make 1 pizza.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Domino's can make 4 pizzas using 3 1/2 cups of sauce.

Now, for 1 pizza he needed

= (3 1/2) /4

= (7/2)/ 4

= 7/2 x 1/4

= 7/8 cups of sauce.

Hence, 7/8 cups of sauce needed.

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Answer:

3

Step-by-step explanation:

\((\sqrt{5} - \sqrt{2})(\sqrt{2} + \sqrt{5})\\\sqrt{5} (\sqrt{2} + \sqrt{5}) - \sqrt{2} (\sqrt{2} + \sqrt{5})\\\sqrt{5} * \sqrt{2} + \sqrt{5} * \sqrt{5} - \sqrt{2} * \sqrt{2} +\sqrt{2} * \sqrt{5}\\ \sqrt{5*2} + \sqrt{5*5} - \sqrt{2*2} - \sqrt{2*5}\\\sqrt{10} + \sqrt{25} - \sqrt{4} - \sqrt{10}\)

plus root 10 and minus root 10 gets cancel . So,

\(\sqrt{25} - \sqrt{4} \\\sqrt{5^{2} } - \sqrt{2^{2} }\)

square and root gets cancel

5 - 2

3

The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).

In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).

The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.

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Answer:

8

Step-by-step explanation:

Given:

13 - 0.75w + 8x

where,

w = 12

x = 1/2

13 - 0.75w + 8x

Substitute the value of w and x into the equation

= 13 - 0.75(12) + 8(1/2)

= 13 - 9 + 8/2

= 13 - 9 + 4

= 8

Therefore,

13 - 0.75w + 8x = 8

Answer:

x=60+70=130(exterior angle of a triangle is equal to the sum of two opposite interior angle)

Prove parallelogram criteria

what additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria? question 3 options: a) ≅ b) || c) || d) ≅

Answer

To determine if a quadrilateral is a parallelogram, we typically look for certain properties. However, the options you provided (a) ≅, b) ||, c) ||, d) ≅) seem to be symbols rather than additional information.

For the minimum criteria to prove a quadrilateral is a parallelogram, we typically require one of the following:

Opposite sides are parallel: If you can provide information indicating that the opposite sides of the quadrilateral are parallel, such as stating that AB || CD and AD || BC, it would help establish the quadrilateral as a parallelogram.

Opposite sides are congruent: If you can provide information indicating that the opposite sides of the quadrilateral are congruent, such as stating that AB ≅ CD and AD ≅ BC, it would also support the claim that the quadrilateral is a parallelogram.

Diagonals bisect each other: Another property of parallelograms is that their diagonals bisect each other. If you can provide information showing that the diagonals of the quadrilateral bisect each other, it would serve as evidence for the parallelogram.

Please provide any specific measurements, angles, or relationships among the sides or diagonals of the quadrilateral to further analyze and determine if it meets the minimum criteria for a parallelogram.

Slope-Intercept Form: The slope-intercept form of a linear equation is given by y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept (the point where the line intersects the y-axis).

This form is convenient for quickly identifying the slope and y-intercept of a line by inspecting the equation.

Point-Slope Form: The point-slope form of a linear equation is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line and 'm' represents the slope.

This form is useful when we have a specific point on the line and its slope, allowing us to write the equation directly without needing to determine the y-intercept.

Standard Form: The standard form of a linear equation is given by Ax + By = C, where 'A', 'B', and 'C' are constants, and 'A' and 'B' are not both zero.

This form represents a linear equation in a standard, generalized format.

It allows for easy comparison and manipulation of linear equations, and it is commonly used when solving systems of linear equations or when dealing with equations involving multiple variables.

These three forms provide different ways of representing a linear equation, each with its own advantages and applications. It is important to be familiar with all three forms to effectively work with linear equations in various contexts.

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The probable question may be:
Write the three forms of a linear equation for the following.

Slope-Intercept Form:

Point-Slope Form:

Standard Form:

The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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Answer:

Length L = 51.88 feet

Step-by-step explanation:

From the given information,

The length of the pendulum can be determined by using the Formula for the period T which  is the time of one full oscillation of a simple pendulum.

\(T = 2 \pi \sqrt {\dfrac{L}{g}}\)

where;

T = period of the time of one full oscillation = 8 seconds

L = length in feet

g = acceleration due to gravity in  feet = 32 ft/s²

π = 22/7

\(8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}\)

\(8 = 6.2857 \times \sqrt {\dfrac{L}{32}}\)

\(\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}\)

\(1.273=\sqrt {\dfrac{L}{32}}\)

\(1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}\)

\(1.273 \times { \sqrt {32}}}= {\sqrt L}\)

\(7.2012= {\sqrt L}\)

L = 7.2012²

L = 51.88 feet

Answer:

2a & 5a

Step-by-step explanation:

I don't know I guessed dont input the answers i said

Answer:

A. 0.25 inches

B. 0.125 inches

Step-by-step explanation:

A.

The smallest increment is represented by 1/4. Converting this into decimal form would make this 0.25.

Work:

1/4 = x/100

1 × 100 = 4 × x

100 = 4x

25 = x

25/100

0.25

B.

The uncertainty is what is not labeled on the ruler. We know 0.25 (1/4), 0.50 (2/4), and 0.75 (3/4) are labeled on the ruler. Out of all the options, 0.125 is not labeled. Therefore, 0.125 is the uncertainty.

Answer:

In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.Step-by-step explanation:

hope this help

9514 1404 393

Answer:

  follow directions. h represents a horizontal shift, + shifts to the right. k represents a vertical shift, + shifts up.

Step-by-step explanation:

Modern math instruction often tends toward giving you a task that is intended to help you discover for yourself particular mathematical relationships. This is one such task.

Here, you're intended to follow the instructions: using the technology provided (a graphing tool at the link) to discover the effect of changing the values of h and k in the function.

__

The first attachment shows plots from my graphing tool for different values of h. The red curve shows h=-2, the blue curve shows h=0, and the green curve shows h=1. If you look for the marked upward zero crossing, you see that it is unshifted for h=0, shifted left 2 units for h=-2, and shifted right 1 unit for h=1.

You are intended to conclude that the value of h represents the amount by which the function is shifted to the right.

__

The second attachment shows plots from my graphing tool for different values of k. As before, the red curve shows k=-2, the blue curve shows k=0, and the green curve shows k=1. Again, the upward zero crossing has been marked to show the effect. For k=-2, the curve is shifted down 2 units; for k=1, it is shifted up 1 unit. There is no shift when k=0.

You are intended to conclude that the value of k represents the amount by which the function is shifted upward.

__

If you do what the problem tells you to do, you can see these effects in real time, watching changes as they occur. You are expected to describe them. Only you know what the "vocabulary from 9/21-922" is.

_____

Additional comment

Math instruction builds on previously seen concepts. This is not a subject in which you can be successful adopting the strategy of "test and forget." You're better off with a strategy of "learn it thoroughly and remember," working as many problems as necessary to keep it fresh in your mind.

Applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees

Based on the linear angles theorem, we have the following equation which we will use to find the value of y:

3y + 11 + 10y = 180

Add like terms

13y + 11 = 180

Subtract 11 from both sides

13y + 11 - 11 = 180 - 11

13y = 169

13y/13 = 169/13

y = 13

Plug in the value of y

3y + 11 = 3(13) + 11 = 50 degrees

10y = 10(13) = 130 degrees.

Therefore, applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees.

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a) \(Calculation of 5 point DFT of x(n) is: X(k) = [28, -2 - 16j, -8, -2 + 16j, -2]\)On squaring the values of X(k),\(we getY(k) = X(k)²= [784, 68 - 80j, 64, 68 + 80j, 4]\)

Now we need to compute the inverse DFT of Y(k) which is given below:

\(Let us calculate the 5-point IFFT by using the circular convolution approach as: Y(k) = X(k)²[784, 68 - 80j, 64, 68 + 80j, 4] = x²(k)By using 5-point IFFT\),

\(we can obtain the values of y(n) as below:y(n) = [1960, -360 + 168j, 256, -360 - 168j, 16]b) Given x(n) = ejwon, 0≤n≤N - 1\)and zero otherwise.

We need to find the Fourier Transform X(w) of x(n) and N-point DFT X(k) of x(n).

\(The Fourier Transform X(w) of x(n) is:X(w) = Σx(n)ejwn = Σejwon ejwn = N∑(k=0) ej2πkn/N\)

The above expression is a Geometric series.

\(When the common ratio is |r|<1, the sum of the geometric series becomes:S = a(1 - r^n)/(1 - r)\)

\(Substituting r = ej2π/N and a=1, we get:S = 1(1 - ej2πn/N)/(1 - ej2π/N)\)

\(Hence, the Fourier Transform X(w) of x(n) is:X(w) = N(1 - ej2πn/N)/(1 - ej2π/N)\)

The N-point DFT of the finite length sequence x(n) is given by:\(X(k) = Σx(n)ej2πkn/N  , for 0 ≤ k ≤ N - 1\)

\(Here, the given sequence x(n) is:x(n) = ejwon, 0≤n≤N - 1\) and zero otherwise.

\(Substituting the given sequence in the above equation, we get:X(k) = Σej2πkn/Nfor 0 ≤ k ≤ N - 1 = Σcos(2πkn/N) + jsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

\(Here, let us separate the real and imaginary parts as below:X(k) = Σcos(2πkn/N) + jsin(2πkn/N) for 0 ≤ k ≤ N - 1= Σcos(2πkn/N) + Σjsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

\(On substituting the values of cos and sin in the above equation, we get: X(k) = Re(X(k)) + jIm(X(k)), for 0 ≤ k ≤ N - 1where, Re(X(k)) = Σcos(2πkn/N) for 0 ≤ k ≤ N - 1Im(X(k)) = Σsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

Therefore, we can calculate the N-point DFT X(k) of x(n) by using the above expression.

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Given :

Some points on two line j and k on the graph.

To Find :

The solution of the system.

Solution :

We know, solution of system is given by the points that satisfy all the equation given in the system.

From the given tables we can see that point ( 3, 18 ) satisfy both the equation j and k.

Therefore, the solution of the system is ( 3, 18 ).

Answer:

$660

Step-by-step explanation: 5% per year

5x2= 10%

percent is always out of 100

100+10=110      110 divided by 100= 1.10

600x1.10= $660

Answer:

9,40,41

Step-by-step explanation:

Answer:

C. 9,40,41

Step-by-step explanation:

The last number in any answer is always the hypotenuse and that is what u will use, because according to the formula:

hypotenuse² = opposite²+adjacent² so;

41²=40²+9²

1,681 = 1600 + 81

1,681 = 1,681

so it is balanced and that means the answer is ✅

Answer:

EXPLANATION BELOW

Step-by-step explanation:

7 | 0, 4, 8

8 | 0, 8, 9

9 | 5

10 | 1, 9

11 | 6, 7

hope this helps!! you basically just divide the number into two-