The data in the tables below were collected from first year students at a community college. The variable is "number of credit cards." If the table below is a complete probability distribution, what must be the value of T?
Number of Credit Cards (x) 0 1 2 3 4 5
Number of Students (f) 122 40 28 2 2 6
Probability P(x) 0.61 T 0.14 0.01 0.01 0.03
A. 0.4
B. 0.04
C. 0.2
D. 0.02

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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Answer and Step-by-step explanation:

The Word form is:

Six hundred, seventy-two thousand, eight hundred and twenty nine.

The Expanded form is:

600,000 + 70,000 + 2,000 + 800 + 20 + 9

The Unit form is:

6 one hundred thousands, 7 ten thousands, 2 thousands, 8 hundreds, 2 tens and 9 ones.

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The value of x from the venn diagram if P(T | V) = 1/5 is 16

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

The venn diagram

From the venn diagram, we have the following probability values

P(T | V) = (x - 4)/(3x + x - 4)

Evaluate the like terms

So, we have

P(T | V) = (x - 4)/(4x - 4)

From the question, we have

P(T | V) = 1/5

This means that

(x - 4)/(4x - 4) = 1/5

When evaluated, we have

x = 16

Hence, the value of x is 16

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The calculated solution to the inequality is a < 6

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

2a - 10 < 2

Divide through the equation by 2

So, we have

a - 5 < 1

Add 5 to both sides

a < 6

Hence, the solution to the inequality is a < 6 and the graph is attached

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Answer:

The answer is C

Step-by-step explanation:

Answer:

209 different ways.

Answer:

Distance = 8

Step-by-step explanation:

The length of the line between (8,6) and (8,-2) is 8.

The distance between (8, 6) and (8, -2) is 8 units.

Distance between two points is the length of the line segment that connects two given points.

\(d = \sqrt{(x_{2}-x_{1}) ^{2} +(y_{2} -y_{1}) ^{2} }\)

According to the given question

We have two points

(8, 6) and (8, -2)

Let,

\((x_{1} ,y_{1} ) = (8,6)\)

and, \((x_{2},y_{2}) =(8,-6)\)

Therefore,

The total distance between (8, 6) and (8, -2)

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

\(=\sqrt{0+(-8)^{2} }\)

\(=\sqrt{64}\)

\(=8\) unit

Hence, the distance between (8, 6) and (8, -2) is 8 units.

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Therefore, the graph will be definitely C. Note the line should be a broken line /

Answer:

Answer is 3rd

Step-by-step explanation:

Answer is 3rd graph. y is higher than the function, so the area that is above the function is bolded. Also, as it is a strict inequation, the line will be dashed.

Given:

Let's solve using law of indices below:

Using the same method, we have:

ANSWER:

Answer:

w=-4

Step-by-step explanation:

multiply by number in front of the bracket and group like terms ,divide both side by - and the answer was -4

Answer:

5 faces

Step-by-step explanation:

The solution for x, y, and z is x = 2, y = 2, and z = 2.

To solve the equation (35)"4(23)"5(25)"7 = 2"x3"y*5"z, let's break it down step by step:

Simplify the expressions within the parentheses using the power of operator ("^").

\((35)"4 = 15^4\\(23)"5 = 6^5\\(2\times5)"7 = 10^7\)

Apply the power rule of exponents, which states that \((a^b)^c = a^{(b\times c).\)

\(15^4 \times 6^5 \times 10^7 = (15610)^{(4+5+7)\)

Simplify the expression within the parentheses.

\((15610)^{16 }= 900^{16\)

Express both sides of the equation in terms of prime factors.

\(900 = 2^2 \times 3^2 \times 5^2\)

quate the powers of the prime factors on both sides of the equation.

\(2^2 \times 3^2 \times 5^2 = 2"x \times 3"y \times 5"z\)

From this, we can conclude that x = 2, y = 2, and z = 2.

Therefore, the solution for x, y, and z is x = 2, y = 2, and z = 2.

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Answer:

2

Step-by-step explanation:

Cómo resolver este problema matemático

El problema matemático es

−

3

+

+

3

x-3+x+3

x−3+x+3

Simplifica

1

Suma los números

−

3

+

+

3

+

2

Combina los términos semejantes

+

2

The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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Answer:

72 i think

Step-by-step explanation:

dhdhdhhdhdhdhxurhsgysydgdghdhdhdhhdhsusiisiisisii

Answer:

oooh k nvm

Step-by-step explanation:

Answer: -2 < x < 1

Step-by-step explanation:

move all terms not containing x from the center section of the inequality

1 < x + 3 < 4

subtract 3 from both terms outside the center

1 - 3 = -2

4 - 3 = 1

therefore our answer is:

-2 < x < 1

The total centimeters that the plants grew in all was 200 centimeters or 2.00 centimeters when written as a decimal.

Centimetres (cm) is a unit of length in the metric system, equal to one-hundredth of a metre. It is commonly used in everyday life, for example when measuring the height of a person or the size of a room. Centimetres are also used in scientific and engineering measurements, such as the size of an object or the distance between two points. Centimetres are divided into millimetres, which are one-thousandth of a metre.

This can be written as a decimal as 2.00 centimeters.

To determine the total centimeters, we simply add the individual centimeter measurements of the two plants.

Daysha's plant grew 100 centimeters and India's plant grew 100 centimeters.

Therefore, the total centimeters that the plants grew in all was 200 centimeters, or 2.00 centimeters when written as a decimal.

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Answer:

the number of downloads of the standard version is 260

Step-by-step explanation:

Let us assume the downloads of the standard version be x

And, the download of the high-quality version be y

Now as per the question

2.5x + 4.4y = 4522 .........(1)

x + y = 1140

y = 1140 - x .......................(2)

Now put the value of equation 2 in the equation 1

So,

2.5x + 4.4 (1140 - x) = 4522

2.5x + 5016 - 4.4x = 4522

-1.9x = -494

x = 260

Hence, the number of downloads of the standard version is 260

Answer:

y = -3/2x + 4

Step-by-step explanation:

y = -3/2x + b

-5 = -3/2(6) + b

-5 = -9 + b

4 = b

Answer:

4/5 times 40 = 32

1/6 times 48= 8

5/8 times 64= 40

Step-by-step explanation:

Hope this helps chu! Credit to the person below as well!

Answer:

\(Hypotenuse^2 = 5^2 + 2^2 = 25 + 4 = 29\\\\Hypotenuse= \sqrt{29}\\\\diagonal^2 = (\sqrt{29})^2 + 2^2\\\\diagonal^2 = 29 + 4 = 33\\\\diagonal = \sqrt{33} = 5.7445 = 5.8\)

The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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The composition of two isometries is an isometry.

Proof:

Let T1 and T2 be isometries. T1(A) = A' and T1(B) = B'. Therefore by isometry T1, AB = A'B'

T2(A) = A'' and T2(B) = B''. Therefore by isometry T2, AB = A''B''

T2 º T1 = T2(T1(A)) = T2(A') = A'''. T2 º T1 = T2(T1(A)) = T2(B') = B'''. Therefore under composition AB = A'''B''' and distance is preserved.

The inverse of an isometry is an isometry.

Proof:

Given T and isometry. This means T(A) = A' and T(B) = B' with AB = A'B'

The inverse of T, T⁻¹maps A' to A and B' to B, so A'B' maps to AB.

But A'B' = AB and so the inverse is an isometry

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Answer:

7.2 million dollars

Step-by-step explanation:

The domain of the function the complete set of possible values of the independent variable. In this case the domain includes all real numbers except 189.

From;

T(p) = 0.50 (p - 189)

When p = 203.4 million dollars

T(p) = 0.50 (203.4 - 189)

T(p) = 7.2 million dollars

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.