The system of equations
\[\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 2, \quad \frac{yz}{y + z} = 1\]
has exactly one solution. What is $z$ in this solution?

To complete the table with tally marks and frequencies, we'll assume the range of values for the frequencies is from 1 to 5. Here's the completed table:

Subjects                              Tally Marks                                Frequency                          

Mathematics                       |                                                         1

Science                               ||                                                        2

Filipino                               |||                                                       3

English                               ||||                                                      4

Araling Panlipunan       |||||                                                     5

Now, let's assign tally marks and frequencies to each subject:

Mathematics:

For a frequency of 1, we can use a single tally mark: |

So, the tally marks for Mathematics would be: |

Science:

For a frequency of 2, we can use two tally marks: ||

So, the tally marks for Science would be: ||

Filipino:

For a frequency of 3, we can use three tally marks: |||

So, the tally marks for Filipino would be: |||

English:

For a frequency of 4, we can use four tally marks: ||||

So, the tally marks for English would be: ||||

Araling Panlipunan:

For a frequency of 5, we can use five tally marks: |||||

So, the tally marks for Araling Panlipunan would be: |||||

By filling in the tally marks and frequencies, the table is now complete.

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The set Y^X can be defined as the set of all possible mappings between the elements of X and Y.

In mathematics, the set of all functions from a set X to a set Y is denoted by Y^X, and is defined as the set of all possible mappings from X to Y. The set Y^X consists of all possible functions that can be constructed from the set X to the set Y.

Here, the function is a mapping between two sets in which each element of the first set is mapped to one and only one element of the second set.

An example of the set of all functions from X to Y is as follows: Consider the sets X = {1,2,3} and Y = {a,b,c}. Then the set of all functions from X to Y is denoted by Y^X. It is represented as follows:

Y^X = {f | f: X → Y}

Therefore, the set of all functions from X to Y is given by:

Y^X = { (1,a), (1,b), (1,c), (2,a), (2,b), (2,c), (3,a), (3,b), (3,c) }

where each element in Y^X is a function that maps each element of X to an element of Y.

The set of all functions from X to Y is an important concept in mathematics as it is widely used in many areas such as graph theory, topology, and calculus.

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The fraction 13/7 lies between the fractions 6/6 and 6/7.

We have,

Between the fractions 6/6 and 6/7, there are infinitely many fractions.

To find a fraction that lies between these two fractions, we can take their average.

The fraction 6/6 simplifies to 1, and the fraction 6/7 cannot be simplified further.

To find the average, we add the two fractions and divide the sum by 2:

(6/6 + 6/7) / 2

To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 6 and 7, which is 42.

Converting the fractions to have a common denominator:

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

Simplifying the expression:

(42/42 + 36/42) / 2

Combining the numerators:

(78/42) / 2

Dividing:

78/42 = 13/7

Thus,

The fraction 13/7 lies between the fractions 6/6 and 6/7.

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Answer: A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? Start Fraction 50 Over 3 End Fraction feet cubed Start Fraction 100 Over 3 End Fraction feet cubed 75 feet cubed 100 feet cubed

Step-by-step explanation: Because first you need to find the radius and height, Next you will have to find the volume of both, We know h= height and r=radius, so then you plug everything in.

The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.

According to the problem, two equations can be set up:

If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:

A + n = 7(B - n)

If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:

A - n = 2(B + n)

We can rearrange these equations to make them easier to solve:

8n = 7B - A

3n = A - 2B

Setting these equal to each other, since they are both equal to 24n, gives:

21B - 3A = 8A - 16B

37B = 11A

A / B = 37 / 11

= 3. 36

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The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer:

[tex]\cos G=\dfrac{2}{3}[/tex]

[tex]\csc E=\dfrac{3}{2}[/tex]

[tex]\cot G=\dfrac{2}{\sqrt{5}}[/tex]

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

[tex]\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}[/tex]

Therefore:

[tex]\hrulefill[/tex]

To find cos G, use the cosine trigonometric ratio:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

[tex]\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

[tex]\hrulefill[/tex]

To find csc E, use the cosecant trigonometric ratio:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

[tex]\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}[/tex]

[tex]\hrulefill[/tex]

To find cot G, use the cotangent trigonometric ratio:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

[tex]\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}[/tex]

The acquisition of the patent can be recorded in the books such that it takes the form of:

Date                      Account title                                Debit                Credit

April 1.                  Patents                                        $115,200

                             Cash                                                                 $115,200

To record the purchase of a patent, you would typically debit the Patents asset account and credit the Cash (or Accounts Payable if purchased on credit) account.

Here's the journal entry:

Date: [Date of purchase]

Debit: Patents [Cost of the patent]

Credit: Cash [Amount paid]

If the patent was purchased on credit instead of cash, the entry would be:

Date: [Date of purchase]

Debit: Patents [Cost of the patent]

Credit: Accounts Payable [Amount owed]

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Rest of the question :

Record the acquisition of patent. If an amount box does not require an entry, leave it blank.

Answer:

A. 6/8

Step-by-step explanation:

6/8 can be simplified to 3/4 when you divide both the numerator and the denominator by 2.

6/2=3 and 8/2=4

6/8=3/4

To double-check, you can simply divide the numerator by the denominator to see if you get the same answer of 0.75 (in this case).

The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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The amount you need to deposit in an account now  is $4444.44

From the question, we have the following parameters that can be used in our computation:

Amount = $6000

Duration = 5 years

interest = 7%

The amount can be calculated as

Principal amount = Amount/(1 + Rate * Time)

substitute the known values in the above equation, so, we have the following representation

Principal amount = 6000/(1 + 7% * 5)

Evaluate

Principal amount = 4444.44

Hence, the amount is $4444.44

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Answer:

2

Step-by-step explanation:

mean = ( 3 + 2 + 0 + 1 + 0 + 2 + 3 + 4 + 1 + 2 + 2 + 1 ) / 12

mean = 21 / 2

mean = 1.75

mean = 2

Answer:

The middle

Answer: C

Based on the information given, one might conclude that the population mean is probably greater than 85 minutes. So, the correct answer would be C. The population mean is probably greater than 85 minutes.

Answer:

C. Has to be greater than 85

Step-by-step explanation:

The following are six measures of solvency or profitability that can be determined from the given data of Gates Inc.:Debt ratio: The debt ratio measures the proportion of total assets that are financed by the creditors. It is calculated as: Debt ratio = Total liabilities / Total assets= 3,000,000 / 7,000,000= 0.43 or 43%

Debt-to-equity ratio: The debt-to-equity ratio measures the amount of debt financing in relation to the amount of equity financing. It is calculated as: Debt-to-equity ratio = Total liabilities / Total stockholders' equity= 3,000,000 / 5,000,000= 0.6 or 60%Interest coverage ratio:

The interest coverage ratio measures the number of times the company can cover its interest expenses with its earnings before interest and taxes (EBIT). It is calculated as:Interest coverage ratio = EBIT / Interest expense= (18,900,000 - 120,000 - (1,570,000 + 930,000 - 100,000 - 400,000)) / 120,000= 174,760 / 120,000= 1.5 or 1.5 timesCash coverage ratio:

The cash coverage ratio measures the number of times the company can cover its interest expenses with its cash flow from operations. It is calculated as:Cash coverage ratio = (EBIT + Depreciation) / Interest expense= (18,900,000 - 120,000 - (1,570,000 + 930,000 - 100,000 - 400,000) + 3,200,000 / 10) / 120,000= 764,760 / 120,000= 6.4 or 6.4 times Return on assets (ROA):

The return on assets ratio measures the company's ability to generate earnings from its assets. It is calculated as:ROA = Net income / Total assets= 930,000 / [(7,000,000 + 3,000,000) / 2]= 930,000 / 5,000,000= 0.186 or 18.6%Return on equity (ROE): The return on equity ratio measures the company's ability to generate earnings from its equity financing. It is calculated as: ROE = Net income / Total stockholders' equity= 930,000 / 5,000,000= 0.186 or 18.6%

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Kevin takes to complete the remaining work alone:

3 + 1 = 4 days in total.

Let's calculate the rates at which Kevin and David can paint the house individually.

Kevin's rate of work is 1/6 of the house per day (since he can complete the house in 6 days), and David's rate is 1/9 of the house per day (since he can complete the house in 9 days).

When they work together for 3 days, their combined rate is:

(1/6 + 1/9) of the house per day = 5/18 of the house per day.

In 3 days, they complete:

3 * (5/18) = 5/6 of the house.

The remaining work is 1 - (5/6) = 1/6 of the house.

Now, since Kevin is completing the remaining work alone, his rate is 1/6 of the house per day.

To determine how many days it takes for Kevin to complete the remaining work, we divide the remaining work (1/6) by Kevin's rate (1/6):

(1/6) / (1/6) = 1 day.

Therefore, it will take Kevin 1 additional day to complete the remaining work alone.

The total number of days taken to paint the house is the initial 3 days they worked together plus the additional day Kevin takes to complete the remaining work alone:

3 + 1 = 4 days in total.

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the number of adults who bought tickets is 25.

The perimeter of the parallelogram ABCD is equal to 136

A parallelogram is a geometric shape with four sides, where opposite sides are parallel and have equal lengths. Its opposite angles are also equal in measure.

AB is equal to DC so;

5x - 18 = 2x + 12

5x - 2x = 18 + 12 {collect like terms}

3x = 30

x = 30/3 {divide through by 3}

x = 10

AB = 2(10) + 12 = 32

BC = 3(10) - 6 = 36

perimeter of parallelogram = 2(32 + 36)

perimeter of parallelogram = 2 × 68 = 136

Therefore, the perimeter of the parallelogram ABCD is equal to 136

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The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for I:

[tex]I=200000 \cdot 0.12 \cdot 6[/tex]

[tex]I=24000 \cdot 6[/tex]

[tex]I=144000[/tex]

Therefore, the return on Ayanda's investment using Option 1 is R144000.

[tex]\hrulefill[/tex]

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for I:

[tex]I=200000(1+0.095)^6-200000[/tex]

[tex]I=200000(1.095)^6-200000[/tex]

[tex]I=200000(1.72379142...)-200000[/tex]

[tex]I=344758.28426...-200000[/tex]

[tex]I=144758.28426...[/tex]

[tex]I=144758.28[/tex]

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

[tex]\hrulefill[/tex]

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

20[tex]c^{6}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × [tex]c^{(3+3)}[/tex]

= 20[tex]c^{6}[/tex]

Based on the image attached, the solution for GE  is approximately 22.72.

To  be able to solve the equation √129 + √129 = GE, one need to simplify the  expression and then isolate GE.

Step 1: One can add the square roots:

Note that the equation:

√129 + √129 = GE.

Step 2:  Do put together the square root terms:

2√129 = GE.

Step 3:  Then Divide by 2:

√129 = GE/2.

Step 4: The Square both sides:

129 = (GE²)/4.

Step 5: So, Multiply by 4:

516 = GE².

Lastly, Take the square root:

√516 = √(GE²)

√516 = GE

GE = 22.72. approx.

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See text below



Step 26

Solve the equation for GE:

√129+√129 = GE

GE=2/129

Show steps

The length of AC is [tex]4\sqrt(2)[/tex].

Create a diagram using the information provided.

As per the diagram, give the points and circles names.

Find the lengths of AD, AE, and EC using the provided information.

Use the Pythagorean Theorem to calculate the length of AC.

The following diagram displays the details:

Diagram illustrating the points at which two circles with radii of 10 and 6 cross.

A common tangent, which connects the two circles, runs through the larger circle at point D and the smaller circle at point E.

Stretched to point C, where it intersects the larger circle, is the line segment DE.

The following equations can be used to determine the lengths of AD, AE, and EC:

AD = 10 - 6 = 4

AE = 6 - 6 = 0 EC = 10 - 6 = 4

[tex]AC = \sqrt(32) = 4\sqrt(2)[/tex]

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Note: The complete question is- A larger circle with radius 10 and a smaller circle with radius 6 intersect each other at two points. A common tangent of the two circles is drawn, which intersects the larger circle at point D and the smaller circle at point E. The line segment DE is extended to intersect the larger circle at point C. Find the length of AC.

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

Answer:

how do you find the measure of an angle? Using a Protractor The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.

Step-by-step explanation:

Answer: all are 8

Mean:8
Median:8

Mode: 8

Step-by-step explanation:

Mean is the average: add all them up and divide by how many numbers there are

Median: is basically the middle number: put the line in number order and find the number in the middle

Mode: most frequent number

Answer:

Mean = 8

Median = 8

Mode = 8

Step-by-step explanation:

Finding the mean:

The mean is the sum of all the data points divided by the total number of data points.  Since there are 8 data points in total, we can find the sum and divide it by 8 to find the mean:

Mean = (2 + 12 + 8 + 15 + 8 + 7 + 3 + 9) / 8

Mean = (64) / 8

Mean = 8

Thus, the mean of the given data is 8.

Finding the median:  

The median is the value that lies in the middle of the data.  First, we must arrange the data in ascending numerical order:

2, 3, 7, 8, 8, 9, 12, 15.

Because there are 8 data points, we have two numbers in the middle, namely 8 and 8.  In order to find the mean, we find the average of these two numbers:

Median = (8 + 8) / 2

Median = 16 / 2

Median = 8

Thus, the median of the given data is 8.

Finding the mode:

The mode is the most frequently occurring value in a data set.  8 occurs most frequently so the mode of the given data is 8.

Answer:

T1=-12

T2=-19

T3=-26

Step-by-step explanation:

Determine which term will have a value of -6998

-7n-5=-6998

-7n=-6998+5

-7n=-6993

-7n/-7=-6993/-7

n=999

The values of the missing values in the triangle given are :

A.)

Using Trigonometry, the marked angle B can be related in the following ways:

Hypotenus = 9.43

Opposite = 5

Adjacent = 8

SinB = opposite / hypotenus = 5/9.43

CosB = Adjacent / Hypotenus = 8/9.43

TanB = opposite / Adjacent = 5/8

B.)

Angle A can be obtained using the relation :

CosA = Adjacent / Hypotenus

CosA = 47/61 = 0.770

A =

[tex] {cos}^{ - 1} (0.770)[/tex]

A = 39.6°

Hence, A = 39.6° to the nearest degree.

C.)

Using Trigonometry, the length of side x :

Tan D = opposite / Adjacent

Tan28 = 21/x

0.5317 = 21/x

x = 21/0.5317

x = 39.5 mm

Therefore, the value of x is 39.5mm

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Answer:

the answer is,

[tex]p(x) = \sqrt[3]{2-x} \\[/tex]

Step-by-step explanation:

The expression that represents the side length of the triangle in this problem is given as follows:

10x + 3.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter for this problem is given as follows:

30x + 9.

The triangle is an equilateral triangle, meaning that all side lengths are the same, hence the side length is given as follows:

(30x + 9)/3 = 30x/3 + 9/3 = 10x + 3.

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