true or false? two proofs are required to establish the provable equivalence of two sentences of tfl.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Or

Step-by-step explanation:

[tex]\bf 18a=56[/tex]

Divide both sides by 18:-

[tex]\bf \cfrac{18a}{18}=\cfrac{56}{18}[/tex]

Simplify:-

[tex]\bf a=\cfrac{28}{9}[/tex]

Or

[tex]\bf a=3.111....[/tex]

________________________

Hope this helps!

Evaluating cos20°.cos40°+cos250°.cos310°  is   (cos10° + 1) / 2.

We can use the identity cos(A + B) = cosAcosB - sinAsinB to simplify the expression.

cos20°cos40° + cos250°cos310°

= cos(40° - 20°) + cos(310° - 250°) (using the identity)

= cos20° + cos60°

= cos20° + 1/2

Now we need to evaluate cos20°. We can use the identity cos2A = 2cos^2A - 1 and let A = 10°:

cos20° = 2cos^210° - 1

cos10° = 2cos^210° - 1 + 1

cos10° = 2cos^210°

cos^210° = cos10° / 2

Now we substitute this back into our original expression:

cos20°cos40° + cos250°cos310°

= cos20° + 1/2

= cos^210° + 1/2

= (cos10° / 2) + 1/2

= (cos10° + 1) / 2

Therefore, cos20°cos40° + cos250°cos310° = (cos10° + 1) / 2.

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If there are total 160 girl students in the total number of students in the college and ratio of boys to girls is 8: 5. Then total number of students in college is equals to the 416.

In a college, the ratio of the number of boys to girls = 8 : 5, so, total ratio is 13.

Number of girl students in the total number of students in the college = 160

We have a goal here to determine the total number of students in the college.

First of all, assume x be any number such that the number of girls and boys are

Number of girls= 5x

Number of boys = 8x

Total number of students in college= 13x

But total girls in college = 160 , so 5x= 160

solve the above expression (dividing by 5)=> x = 160/5 = 32

So, total boys students in college = 8x

= 8 × 32

= 256

Total number of students in college = 13x = 13× 32

= 416

Hence, required value is 416.

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The given problem states that the number of rushing yards in game 16 is an outlier in the x-direction. Hence, we can say that game 16 has a significant effect on the equation of the least-squares regression line.

We need to find out the effects that this game has on the correlation and on the equation of the least-squares regression line. We also need to calculate the correlation and equation of the least-squares regression line with and without this game to confirm our answers.

Effect on Correlation:

An outlier in the x-direction has no effect on the correlation coefficient(r). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is not influenced by the presence of an outlier in the independent variable. So, the correlation coefficient with or without this game will remain the same.

Effect on Equation of the Least-Squares Regression Line:

An outlier in the x-direction has a significant effect on the equation of the least-squares regression line. The least-squares regression line is a straight line that summarizes the relationship between the independent and dependent variables. This line is constructed by minimizing the sum of squared deviations between the observed and predicted values. If an outlier is present, it will pull the regression line closer to it. So, the equation of the least-squares regression line will be different with or without this game.

Calculation of Correlation and Equation of Least-Squares Regression Line:

Without game 16,

the correlation coefficient and equation of the least-squares regression line are:

Correlation Coefficient(r) = 0.94

The equation of the least-squares regression line:

y = 2.25x + 10.5 With game 16,

the correlation coefficient and equation of the least-squares regression line are:

Correlation Coefficient(r) = 0.93

The equation of the least-squares regression line:

y = 1.92x + 22.8

From the above calculations, we can see that the correlation coefficient has a negligible change with or without game 16. However, the equation of the least-squares regression line is quite different with and without game 16.

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The inequality that describes the problem when coach Yamada is organizing community volleyball teams is x ≤ 9.

Why is x ≤ 9 the correct inequality that describes the problem when coach Yamada is organizing community volleyball teams? Here is why: We know that coach Yamada wants each team to have 8 players but he can't make as many full teams as he wanted to because fewer than 80 people signed up.

Let x represent the number of full teams coach Yamada can make. We know that 1 team can have 8 players. Therefore, the number of players needed for x full teams = 8xWe also know that fewer than 80 people signed up. So, 8x < 80, if more than 80 people signed up then coach Yamada would be able to make more than x full teams.

Since coach Yamada can't make a fraction of a team so x should be an integer. Therefore, the solution for 8x < 80 is x ≤ 9.Therefore, x ≤ 9 is the inequality that describes the problem when coach Yamada is organizing community volleyball teams.

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Answer:

The answer i got was (x - 5)2

Answer:

y+7

Step-by-step explanation:

will we use the way of long divide which will help

[tex]y-8\sqrt{y^{2}-y-56 }[/tex]

because y need another y to  became y square that mean we need y

since we have y square we could minus y-8y which is1

so 56divide (-8)=7

so it is y+7

brain please

thanks

Answer:

[tex] {x}^{2} + 8x + 16 = 18[/tex]

[tex] {(x + 4)}^{2} = 18[/tex]

x + 4 = +3√2, so x = -4 + 3√2

As there are 100 centavos in one Philippine Peso, there are 12,575 centavos in P 125.75.

An arrangement of things in a particular order is known as a permutation in mathematics. A permutation of a group of things is a particular technique to arrange them in a particular sequence, where each object is used exactly once. Consider the trio of letters A, B, and C as an example. This set can be permuted in six different ways: ABC, ACB,BAC, BCA, CAB, and CBA

These combinations each show a different way to arrange the letters in the set.

given

The Philippine Peso, represented by the letter "P," is the official unit of money in the Philippines.

One Philippine Peso is equal to 100 centavos.

We must multiply P 125.75 by 100 to convert it to centavos:

P = 12,575 centavos (125.75 x 100).

As there are 100 centavos in one Philippine Peso, there are 12,575 centavos in P 125.75.

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To represent 7 ÷ 2 on a number line, we can start by drawing a line with the numbers 0 to 7 marked on it. Then, we can divide the line into two equal parts, since we are dividing 7 by 2. The midpoint of the line will represent the result of the division, which is 3.5.

Here is a rough sketch of what the number line could look like:

0------1------2------3------4------5------6------7

|_______________|

3.5

Alternatively, we can also represent the division using a fraction model. We can draw a rectangle and divide it into two equal parts. Then, we shade in 7 of the 12 equal parts, since 7 ÷ 2 can be written as the fraction 7/2 or 7 ÷ 2 = 3 1/2.

Here is a rough sketch of what the fraction model could look like:

+----+----+----+----+----+----+

| | | | | | |

+----+----+----+----+----+----+

| | | | | | |

+----+----+----+----+----+----+

In this model, each of the 12 parts represents 1/12 of the whole. We shade in 7 of the 12 parts to represent 7/12 of the whole, which is equivalent to 7 ÷ 2.

Using the volume formula:

1. 904.32m³.

2. 226.08in³.

3. 392.50cm³.

4. 4186.66in³.

5. 395.64ft³

6. 235.50cm³.

A three-dimensional solid shape's volume is the area it takes up in space. Though it is challenging to picture in any shape, it can be contrasted with others. A compass box, for example, has a bigger volume than one that has an eraser inside of it.

The area of every two-dimensional form is calculated by dividing it into equal square units. We will do something similar to calculate the volume of solid things by dividing it into equal cubical units.

In the given question,

Volume of the sphere is: 4/3πr³.

Radius, r is = 6m.

Volume = (4× 3.14 × 6³)/3

= 904.32m³.

Volume of the cylinder is: πr²h.

Radius, r = 3in.

Height, h = 8in.

Volume = 3.14 × 3² × 8

= 226.08in³.

Volume of cone = 1/3 πr²h

Radius, r = 5cm.

Height, h = 15cm.

Volume = (1 × 3.14 × 5² × 15)/3

= 392.50cm³.

Again, we have a sphere, with d = 20in.

R = d/2

= 20/2

=10in

Volume = 4/3πr³.

= (4 × 3.14 × 10³)/3

= 4186.66in³.

Again, we have a cylinder with r = 3ft and h = 14ft.

Volume =  πr²h.

= 3.14 × 3² × 14

= 395.64ft³

Lastly, we have another cone of r = 5cm and h = 9cm.

Volume = 1/3 πr²h

= (1 × 3.14 × 5² × 9)/3

= 235.50cm³.

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The solution of the system of linear equations determines if the system has no solution, one solution, or an infinite number of solutions

2·x - 3·y = 3 and -4·x + 6·y = 6

3·x - 2·y = 3 and x + 2·y = 5

-8·x + 12·y = -12 and 2·x - 3·y = 3

y = -x + 2 and y = 3·x - 2

A system of equations is a set of two or more equations that are formed by the same variable.

Each of the equations are solved as follows to determine whether it has no solution, one solution, or an infinite number of solutions

1. 2·x - 3·y = 3 and -4·x + 6·y = 6

Multiplying the first equation by 2, we get; 4·x - 6·y = 6.

Adding the above equation to the second equation,we get;

4·x - 6·y + (-4·x + 6·y) = 6 + 6 = 12

0 = 12 (False)

Therefore, the system has no solution

2. 3·x - 2·y = 3 and x + 2·y = 5

Adding the two equations, we get;

3·x - 2·y + (x + 2·y) = 3 + 5 = 8

4·x = 8

x = 8/4 = 2

Substituting x = 2 into the second equation, we get;

x + 2·y = 5

2 + 2·y = 5

2·y = 5 - 2 = 3

y = 3/2 = 1.5

y = 1.5

Therefore, the system has one solution

3. -8·x + 12·y = -12 and 2·x - 3·y = 3

Multiplying the second equation by 4, we get; 8·x - 12·y = 12

Adding the product of the second equation and 4 to the first equation we get;

8·x - 12·y + (-8·x + 12·y) = 12 + (-12) = 0

0 = 0

Therefore, the system has infinite number of solutions

4. y = -x + 2 and y = 3·x - 2

Substituting y = -x + 2 into the second equation, we get;

-x + 2 = 3·x - 2

3·x - 2 = -x + 2

3·x + x = 2 + 2 = 4

4·x = 4

x = 4/4 = 1

x = 1

y = -x + 2

y = -1 + 2 = 1

y = 1

Therefore, the system has one solution.

Therefore, the first system has no solution, the second system has one solution, the third system has an infinite number of solutions, and the fourth system has one solution.

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Answer:

It would be 37 mnths

Step-by-step explanation:

They will have the same amount of money in their bank accounts after 26 months.

Algebra is the branch of mathematics that uses letters and variables to represent the missing information in a given mathematical expression, to find the solution.

Here,

Amount of money added by Neil in January = £32

Amount of money added by Amber in January = £240

Amount of money added by Neil at the end of every month = £50

Amount of money added by Amber at the end of every month = £42

According to the given data, after a number of months, the amount of money in their bank accounts must become same.

Let n be the number of months,

(£32 + n£50) = (£240 + n£42)

n£50 - n£42 = £240 - £32

n£8 = £208

So, n = 208/8

n = 26

Hence,

They will have the same amount of money in their bank accounts after 26 months.

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Therefore, the temperature will be 17°C in the months of [tex]x = 4 + 48k[/tex] or    [tex]x = 20 + 48k,[/tex] where k is an integer.

Temperature is a measure of the average kinetic energy of the particles in a substance. In simpler terms, it is a measure of how hot or cold something is. The temperature is usually measured using a thermometer, which can be a simple device such as a mercury or alcohol thermometer, or a more complex electronic device such as a thermocouple or infrared thermometer. The standard unit of measurement for temperature is the degree Celsius (°C) or Fahrenheit (°F), although the Kelvin (K) scale is also commonly used in scientific contexts.

To find in which months the temperature will be 17°C, we need to solve the equation:

[tex]f(x) = 17[/tex]

Substituting the given equation of f(x), we get:

[tex]5 cos(x/12) + 14.5 = 17[/tex]

Simplifying this equation, we get:

[tex]cos(x/12) = 0.5[/tex]

[tex]cos(x/12) = cos(π/3 + 2kπ) or cos(x/12) = cos(5π/3 + 2kπ)[/tex]

cos(5π/3) = -0.5. Also, cos(x) has a period of 2π. Therefore, we can write:

[tex]cos(x/12) = cos(π/3 + 2kπ) or cos(x/12) = cos(5π/3 + 2kπ)[/tex]

where k is an integer.

Solving for x, we get:

[tex]x/12 = π/3 + 2kπ or x/12 = 5π/3 + 2kπ[/tex]

[tex]x = 4π + 24kπ or x = 20π + 24kπ[/tex]

Multiplying both sides by 12, we get:

[tex]x = 4π12 + 24kπ12 or x = 20π12 + 24kπ12\\x = 4π + 288kπ or x = 20π + 288kπ[/tex]

or in terms of 2π:

[tex]x = 4 + 48k or x = 20 + 48k[/tex]

where k is an integer. [tex]π[/tex]= pi

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As a result, if one curve has a higher standard deviation, it will have a function lower height, and vice versa, to ensure that the area under the curve is equal to one.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

False.

If two normal curves have different standard deviations, the curve with the greater standard deviation has a broader spread but is not always taller. The greatest point of a normal density curve, which is positioned at its mean, determines its height. The standard deviation influences the contour of the curve and the dispersion of the values, but it does not directly effect the height of the curve. The height of the curve is defined by the normal distribution formula, which includes the reciprocal of the standard deviation. As a result, if one curve has a higher standard deviation, it will have a lower height, and vice versa, to ensure that the area under the curve is equal to one.

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Answer:

y = 2x+3

Step-by-step explanation:

first we must find the slope, which is change in y / change in x.

so, if we have 2 points on the line, (0, 3) and (1, 5), the slope is 2/1 = 2.

next, find the y-intercept. this is clearly (0, 3).

so, the equation is y = mx + b with m = slope and b = y-int.

plugging in the values, the equation is y = 2x+3

Rewrite the expression for y when x>5 without absolute values: y = 2x + 4

Rewrite the expression for y when -2<x<5 without absolute values: y = 2x - 6

Given the absolute values given:

If we rewrite without the absolute value for the condition, then there would be different values for y as shown above which is:

y = (x-3) + (x+2) - (x-5)

y = 2x + 4

Rewrite the expression for y when -2<x<5 without absolute values:

y = (x-3) + (x+2) - (5-x)

y = 2x - 6

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a. The marginal density function for Y2 is fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.

b. For y2 ≤ y1 ≤ 10 of y2 is the conditional density f(y1|y2) is defined

(a) To find the marginal density function for Y2, we integrate the joint pdf over all possible values of Y1:

fY2(y2) = ∫fY1,Y2(y1,y2) dy1, where the integral is taken over the range where 0 ≤ y2 ≤ y1 ≤ 10, otherwise 0.

fY2(y2) = ∫₀¹⁰3y1 dy1 = 1.5y² |₀y2 = 1.5y2², where 0 ≤ y2 ≤ 10.

So the marginal density function for Y2 is:

fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.

(b) The conditional density f(y1|y2) is defined as:

f(y1|y2) = fY1,Y2(y1,y2) / fY2(y2), where fY2(y2) > 0.

So the conditional density is defined for all y1 such that 0 ≤ y2 ≤ y1 ≤ 10 and 0 ≤ y2 ≤ 10, i.e.,

y2 ≤ y1 ≤ 10.

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James would pay R77,410.46 in taxes on his R364,321 annual taxable income for the tax year that ends on February 28, 2022.

James's tax bracket, deductions, and credits, among other things, would all affect how much tax he pays. The various income ranges that are subject to various rates of taxation are referred to as tax brackets.

Income up to R216 200: 18% of taxable income

Income from R216 201 to R337 800: R38 916 plus 26% of taxable income above R216 200

Income from R337 801 to R467 500: R70 742 plus 31% of taxable income above R337 800

Income from R467 501 to R613 600: R110 739 plus 36% of taxable income above R467 500

Income from R613 601 to R782 200: R163 335 plus 39% of taxable income above R613 600

Income from R782 201 to R1 656 600: R229 089 plus 41% of taxable income above R782 200

Income above R1 656 601: R587 593 plus 45% of taxable income above R1 656 600

Based on James' annual taxable income of R364,321.

The first R216,200 of James' income would be taxed at 18%, which equals R38,916.

The remaining R148,121 of James' income would be taxed at 26%, which equals R38,494.46.

Therefore, James' total tax liability would be R77,410.46.

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James,67 year old, has an annual taxable income of R364321 per year, What amount of tax he pays?

 Dylan  initial investment was £1200

Interest are of two types :- 1. Simple interest

                                             2.Compound interest

Here Dylan has invested on yearly terms therefore , We need to need to calculate the simple interest here

Given ,

          Principal = ?

           Interest= £72

           Time = 2 years

            rate = 3%

Formulae  for simple interest is=( Principal * (Rate/100) *Time)

Therefore

                 72 = (Principal *(3/100) *2)

                  72 = ( Principal* 0.06)

                  Principal= 72/0.06

                  Principal= £1200

Therefore the initial investment was £1200 by dylan

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Therefore, Dylan's initial investment was £1200.

Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested that is added to the principal at regular intervals, usually monthly, quarterly or annually. The interest rate remains constant throughout the loan or investment term, and the interest earned or paid is calculated solely on the initial principal amount. Simple interest is commonly used for short-term loans or investments, and the formula for calculating it is straightforward:

by the question.

we can start by using the formula for simple interest:

Simple interest = Principal x Rate x Time

Where the Principal is the initial investment, the Rate is the annual interest rate, and the Time is the number of years.

We know that the Rate is 3% per annum and the Time is 2 years, so we can write:

Simple interest = Principal x 0.03 x 2

Since we are given that the value of the investment increased by £72 at the end of the 2-year period, we can set up an equation:

Value of investment - Initial investment = Simple interest

£72 = Principal x 0.03 x 2

£72 = Principal x 0.06

Principal = £72 / 0.06

Principal = £1200

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Answer:

[tex]x=20[/tex]

Step-by-step explanation:

Answer:

Let percentage that has been to both be x

60+80 –2x = 100

=> 140 –2x = 100

2x = 140 – 100

2x = 40

=> x = 20

Step-by-step explanation:

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Tthe Fourier series may converge to a value that is different from the left and right limits of f at the point of discontinuity, or it may not converge at all (known as Gibbs phenomenon).

To determine the specific value to which the Fourier series converges at a point of discontinuity, we would need to analyze the specific function f and its Fourier series.

This typically involves calculating the Fourier coefficients, examining the convergence properties of the series, and potentially using techniques such as Cesàro summation to obtain a more accurate estimate of the limit.

Without further information about the specific function and point of discontinuity, we cannot provide a more specific answer.

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The discount on the retailer's price is 27.08%. To calculate the discount percentage, we can use the following formula: Discount % = (MSRP - Retailer's price) / MSRP * 100%

The question asks to find the percentage discount between the manufacturer's suggested retail price (MSRP) and the retailer's price. To do this, we use the formula for calculating percentage discount. We subtract the retailer's price from the MSRP, divide that by the MSRP, and multiply by 100 to get the percentage. Plugging in the given values, we find that the discount percentage is 27.08%, which means that the retailer is selling the product at a 27.08% lower price than the MSRP.

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Answer:

Part A

The volume of solution A is represented as a fraction, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (the top number in the fraction) as the dividend and the denominator (the bottom number in the fraction) as the divisor. So the dividend is 1, and the divisor is the volume of solution A.

Part B

No, we cannot divide 2 by 9 evenly because they are not divisible without a remainder.

Part C

Since we cannot divide 2 by 9 evenly, the first digit of the quotient will be 0.

Part D

We set up the long division problem as follows:

 0.2 7 7 7 7 ...

-------------

9 | 1.0000

- 0.9

-----

1 0 0

9 0

---

1 0 0 0

9 0

-----

1 0 0 0

9 0

-----

1 0 0 0 0

9 0

-----

1 0 0 0 0

The decimal equivalent of 2/9 is 0.27777... (repeating). We can see that the division process continues indefinitely with the same repeating pattern, so we use an ellipsis to indicate that the pattern continues infinitely.

Part E

If we keep repeating the long division process for 2/9, we will continue to get the same repeating decimal pattern of 0.27777..., with no end in sight.

Part F

The volume of solution B is represented as the fraction 3/8, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (3) as the dividend and the denominator (8) as the divisor.

Part G

No, we cannot divide 3 by 8 evenly because they are not divisible without a remainder.

Part H

Since we cannot divide 3 by 8 evenly, the first digit of the quotient will be 0.

Part I

We set up the long division problem as follows:

 0.3 7 5

---------

8 | 3.0000

- 2.4

----

6 0

5 6

---

4 0 0

3 2

---

7 0 0

6 4

---

3 6 0

3 2

---

2 8 0

2 4

---

4 0

The decimal equivalent of 3/8 is 0.375. We can see that the division process terminates after a finite number of decimal places.

Part J

If we keep repeating the division process for 0.375, we will always get the same decimal number because the process terminates and doesn't involve any repeating pattern.

Part K

The volume of solution C is represented as the fraction 1/5, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (1) as the dividend and the denominator (5) as the divisor.

Part L

No, we cannot divide 1 by 5 evenly because they are not divisible without a remainder.

Part M

Since we cannot divide 1 by 5 evenly, the first digit of the quotient will be 0.

Part N

We set

Answer:

65%

Step-by-step explanation:

Given data

Cost price= £4000

Selling price=  £1400

% loss= cost price-selling price/cost*100

% loss= 4000-1400/4000*100

% loss= 2600/4000*100

% loss= 0.65*100

% loss= 65%

Hence the %loss is 65%

There can be 78,364,164,096 different license plates created if there are 7 numbers or letters on the plate, determined using the product rule.

We can use the product rule to determine the number of different license plates that can be created if there are 7 numbers or letters on the plate.

Assuming that each position on the license plate can be filled with any number or letter, we can use the multiplication principle to find the total number of possibilities. For each position, there are 26 letters and 10 digits to choose from (assuming the use of the English alphabet), so there are 36 choices for each position.

Therefore, the total number of different license plates that can be created is:

36 x 36 x 36 x 36 x 36 x 36 x 36 = 36^7

This simplifies to:

78,364,164,096

So there are 78,364,164,096 different license plates that can be created if there are 7 numbers or letters on the plate.

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--The given question is incomplete, the complete question is given

" which of these numbers of different license plates can be determined if there are 7 numbers or letters on the plate? using only the product rule (without the use of the sum rule or some other rule)?

Permutations and combinations might sound like synonyms. However, in probability theory, they have distinct definitions. Combinations: The order of outcomes does not matter. Permutations: The order of outcomes does matter. For example, on a pizza, you might have a combination of three toppings: pepperoni, ham, and mushroom.

Hope this is the answer you are looking for.