if two numbers are randomly chosen without replacement from $\{1, 2, 3, 4, 5\}$, what is the probability their sum is greater than their product? express your answer as a common fraction.

Answer:

First and last one

Step-by-step explanation:first and last one

There are 7!/3! ways for 8 people to sit around a circular table if Alice, Bob, and Eve do not want to sit next to each other.

Rotation is the process of rotating an object in two or three dimensions around an axis. This axis can be a point in space, a line, or a plane. Rotation can also refer to a continuous change of direction, such as the rotation of the Earth around its axis. Rotation can be described using terms such as clockwise, counterclockwise, and angular velocity. Rotation can also be described using mathematical equations, such as Euler's rotation theorem. Rotation can be used to create symmetry in design, or to create motion in an animation.

This is because we can pick any of the 7 people to be seated first, then any of the 6 people to be seated second, then any of the 5 people to be seated third, and so on. However, since Alice, Bob, and Eve do not want to sit next to each other, we must divide the 7! by 3! to account for the fact that the order in which Alice, Bob, and Eve are seated does not matter. The 3! accounts for the fact that we could arrange the three of them in 3! = 6 different orders. Therefore, the total number of ways for 8 people to sit around a circular table if Alice, Bob, and Eve do not want to sit next to each other is 7!/(3!) = 840 ways.

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Andrew's initial deposit will grow to about $543 in 7 months.

You can use the formula A = P * e^(rt) to calculate this, where A is the final amount, P is the initial deposit, r is the interest rate, and t is the time in years. The equation for "continual" growth (or decay) is A = Pert, where "A", is the ending amount, "P" is the beginning amount (principal, in the case of money), "r" is the growth or decay rate (expressed as a decimal), and "t" is the time (in whatever unit was used on the growth/decay rate).

A = P * e^(rt)

Plug in the given values:

A = $543

P = $500

r = 0.065 (6.5% expressed as decimal)

Solving for t:

t = ln(A/P) / r

t = ln(543/500) / 0.065

t = 0.07 ( 7 months)\

Therefore, Andrew's initial deposit will grow to about $543 in 7 months.

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It will take 5.01 years for Mantago to repay the money that he would borrow.

Assume that it will take 't' years for Mantago to repay the money that he would borrow.

Here, we use monthly cashflow formula:

[tex]C=P\times r\times \frac{(1+r)^{12t}}{(1+r)^{12t} - 1}[/tex]

where, P is loan amount

r is ARM(adjustable-rate mortgage) interest rate

C is monthly cashflow

here, R = 7.5%

So, r = 0.075

For monthly payment the interest rate would be r = 0.075/12

i.e., r = 0.00625

P = 10000

C = 200

We need to find the number of years t.

[tex]200=10000\times 0.00625\times \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t} - 1} \\\\200=62.5\times \frac{(1.00625)^{12t}}{(1.00625)^{12t} - 1}\\\\ \frac{(1.00625)^{12t}}{(1.00625)^{12t} - 1}=3.2\\\\(1.00625)^{12t}}=[(1.00625)^{12t} - 1]\times 3.2\\\\(1.00625)^{12t}-3.2(1.00625)^{12t}=-3.2\\\\-2.2(1.00625)^{12t}=-3.2\\\\(1.00625)^{12t}=1.4545[/tex]

[tex]12t=60.13\\\\t=5.01\\\\t \approx 5[/tex]

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The value of missing number in the table is, 17

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table is shows the cost of gallon of gas in dollars.

Now, From the table we get;

The equation that satisfy the given conditions is,

⇒ y = 1.05x

Where, 'x' is gallons of gas and 'y' is cost of gallon of gas.

Hence, For the cost (y) 17.85 dollars, number of gallons of gas are,

⇒ y = 1.05x

⇒ 17.85 = 1.05x

⇒ x = 17.85/1.05

⇒ x = 17

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For a quadratic function [tex]y=ax^2+bx+c[/tex], we know the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

It is easy to see that for a function of the form [tex]y=a(x-h)^2+k[/tex], the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

Therefore, the vertex of the graph of [tex]f(x)[/tex] is a maximum, and the vertex of the graph of [tex]g(x)[/tex] is a minimum.

The function f(x) = -2(x + 4)+2 is minimum point and g(x) = 2(x - 2)-2 is maximum point.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = -2(x + 4)+2 and g(x) = 2(x - 2)-2

As, the equation are in the form

y = a (x-h) + k

For 1st function: f(x) = -(x + 4)²+2

f(x) = -2(x+4) + 2

So, the vertex is (4, 2) and a = -2 < 0 which is minimum point.

Now,  g(x) = 2(x - 2)-2

So, the vertex is (-2, -2) and a = 2 > 0 which is maximum point.

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Answer:

Step-by-step explanation:

You will need to utilise algebraic expressions to create an equation to show Lori's age in relation to Shawn.

The procedure will be completely described in the sections that follow with step-by-step instructions .

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We can conclude from the given problem that there are 7975/5 - 1595 different positive numbers f(a) smaller than 1992, 1991-1595 = 396 positive integers.

Integers can be anything from zero to a positive or negative number signified by a minus sign. A lower result is its corresponding positive number's additive reciprocal. In mathematical notation, an integer group is usually denoted by a bold Z or perhaps a bold "mathbb Z." An integer, unlike a fraction, is a positively, negative, or zero number (pronounced IN-tuh-jer). Examples of integers are the integers -5, 1, 5, 8, 97, & 3,043. Examples of non-integer numbers include 1.43, 1 3/4, 3.14, and also more. A group of integers is known as an integer.

Here,

imagine a number of zeros! be

=> f(a), where f(a) = a/5, a/25, a/125, a/625, etc.

Since

f(a) a/5 + a/25 + a/125 + a/625 +...,

=> f(a) = f(a+1) = f(a+2) = f(a+3) = f(a+4). = a/4

=>f(7975) = 1991

1992 is less than 7975/5 - 1595 different positive numbers, hence 396 positive integers are present.

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The student receives 84% overall which is between 80-90% and they will receive a letter grade of "B".

To determine the student's letter grade, you need to calculate the overall percentage of the total points possible.

A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or a rate, and is typically denoted by the symbol "%". To convert a number to a percentage, you multiply it by 100 and add the "%" symbol.

The first exam is out of 100 points, so the student scored 89/100 or 0.89 * 100 = 89%.

The second exam is out of 100 points, so the student scored 81/100 or 0.81 * 100 = 81%.

The final exam is out of 200 points, so the student scored 160/200 or 0.8 * 100 = 80%.

To find the overall percentage of the total points possible, you need to add the percentage scores from each exam and divide by the number of exams.

(89 + 81 + 80) / 3 = 84

Therefore,The student receives 84% overall which is between 80-90% and they will receive a letter grade of "B"

It's important to note that each institution may have different grading scales and different criteria for assigning letter grades.

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It is not possible to construct a triangle whose sides are 5cm ,5cm and 10cm , because the sum of two sides is not greater then third side .

For any three sides to form a triangle , it should satisfy the condition that , the sum of any two sides should must be greater than the third side .

We apply this condition on the given sides ,

we get ;

the sides of the triangle are  ⇒ 5cm ,5cm and 10cm ;

the sum of sides : 5 + 5 = 10 which is not greater than the third side (10cm) ;

these sides do not satisfy the condition ,

Therefore , the condition to form the triangle is not satisfied , so the triangle cannot be constructed .

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The total interest for the loan is given as follows:

46,875.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

The interest amount is the subtraction of the balance by the principal, hence it's formula can be simplified as follows:

I(t) = Prt.

The values of the parameters for this problem are given as follows:

P = 125000, r = 0.075, t = 5.

Hence the interest amount is given as follows:

I(5) = 125000 x 0.075 x 5

I(5) = 46,875.

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Using mathematical operations, we know that Bakery B makes 209/28 more cake than Bakery A per hour.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Scalars in MATLAB can be multiplied, divided, added to, subtracted from, multiplied by, and have exponents applied to them.

These operators can be used to arrange calculations involving vectors and matrices in a straightforward manner.

So, bakery A:

4 1/4 cake in 4 hours.

16+1/4

17/4 cake in 4 hours

Bakery B:

11 5/7 cake in 3 hours:

77*5/7

82/7 cake in 3 hours

Then, Bakery A: 17/4 * 7/7 =  119/28

Bakery B: 82/7 * 4/4 =  328/28

More, cake by Bakery B:
328/28 - 119/28

209/28

Therefore, using mathematical operations, we know that Bakery B makes 209/28 more cake than Bakery A per hour.

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A graphical plot with sales on the Y axis and time on the X axis is a:

a. Scatter diagram.

Using a single variable on each axis, the scatter diagram plots pairings of numerical data in an effort to identify any relationships between them. A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the more highly correlated the data is. You may also visualise the strength of any relationship. If the researcher believes there may be a correlation, a line of greatest fit can also be drawn on the graph.

Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

Thus, correct option: a

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Answer:

119 eggs

Step-by-step explanation:

To start off, we know that this number has to be of some multiple of 7. Because if the eggs are taken out 7 at a time, and no eggs are left over, then the total number of eggs can be divisible by 7. Because there is however a multiple if you take out the eggs 2-6 times, there are eggs left over. The smallest multiple of 7 we can test is simply 7. To check, we can start with dividing 7 by 6 and getting a remainder of 1 instead of 5. So we know that 7x1 doesn't work.

The next smallest multiple of 7 that isn't multiplied from 2-6 is 7x7 to get 49. from here we can check that 49/6 = 8 r1 (r meaning remainder). So we know that 7x7 can't work. From here, the next smallest number would be 7x11.

7x11 = 77. 77/6 is 12 r5. This so far looks good. Now we can try 5. 77/5 = 15 r2. This doesn't work, so we try the next largest number which is 7x13 which is 91.

91/6 = 15 r1 which doesn't work. Next we try 7x17 which is 119. 119/6 is 19 r5 (looks good), 119/5 = 23 r4 (looks good), 119/4 is 29 r3, 119/3 is 39 r2, and 119/2 is 59 r1! Which means our answer is that the least number of eggs in the basket is 119.

Plan V is a mobile phone plan that costs $10.00 per day, or $40.00 per month. The plan includes 100 texts. If the customer goes over the 100 included texts, they will be charged $0.50 for each additional text. The plan also includes 100 minutes of talk coverage, but if the customer goes over the 100 minutes, they will be charged $0.99 per additional minute. Additionally, the plan includes 100 MB of data, but if the customer goes over the 100 MB, they will be charged $2.05 per additional MB.

Answer: height is 5

Step-by-step explanation:

Area of the parallelogram is altitude x height. You divide area (35) by altitude (7) to get 5

Answer:

Step-by-step explanation:

One fraction that is smaller than 5/8 id 4/8, 3/8, 2/8, of 1/8; by decreasing the amount out of eight, you are reducing the fraction. Another way to make a fraction smaller is by increasing the denominator, increasing the denominator allows you to have tthe same amount out of a bigger total: 5/9, 5/10, 5/11, 5/12, 5/13, and so on.

Answer: 1/10

Step-by-step explanation: 5/8 = .625 > .100 = 1/10

The distance is 3.21 +/- 0.04 mm using the first three measurements, and 3.16 +/- 0.08 mm using the entire set of ten measurements.

What is deviation ?

Deviation is a measure of how much a set of values differs from a certain value, typically the mean (average) of the set. There are two types of deviation ,

The absolute deviation is the difference between each value and the mean.

The standard deviation is the square root of the average of the squared absolute deviations.

The mean distance = (3.27 + 3.23 + 3.15) / 3 = 3.21 mm

The standard deviation = sqrt(((3.27 - 3.21)^2 + (3.23 - 3.21)^2 + (3.15 - 3.21)^2) / 2) = 0.04 mm

So, using the first three measurements, we can report the distance as 3.21 +/- 0.04 mm

To report the distance and uncertainty using the entire set of ten measurements, we can calculate the mean and standard deviation of the ten measurements.

The mean distance = (3.27 + 3.23 + 3.15 + 3.16 + 3.28 + 3.14 + 3.16 + 3.12 + 3.32 + 1.46) / 10 = 3.16 mm

The standard deviation = sqrt(((3.27 - 3.16)^2 + (3.23 - 3.16)^2 + (3.15 - 3.16)^2 + (3.16 - 3.16)^2 + (3.28 - 3.16)^2 + (3.14 - 3.16)^2 + (3.16 - 3.16)^2 + (3.12 - 3.16)^2 + (3.32 - 3.16)^2 + (1.46 - 3.16)^2) / 9) = 0.08 mm.

The distance is 3.21 +/- 0.04 mm using the first three measurements, and 3.16 +/- 0.08 mm using the entire set of ten measurements.

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Answer: 1.5x + 12.3

Step-by-step explanation:

(3x + 5.3) + (7 - 1.5x)

Since this is not multiplication, try arranging the equation so like terms are together.

3x - 1.5x + 5.3 + 7 =

Combine like terms by adding or subtracting.

3x - 1.5x + 5.3 + 7 = 1.5x + 12.3

Step-by-Step Explanation:

[tex]x + \frac{2}{5} = \frac{1}{3} \\ = > x = \frac{1}{3} - \frac{2}{5} \\ = > x = \frac{5 - 6}{15} \\ = > x = \frac{ - 1}{15} [/tex]

Answer:

A) x = -1/15

Answer:

Two like terms in the expression 4x + 5 + 11x are 4x and 11x. Both terms have the variable x, and the coefficients (4 and 11) are just numbers and do not affect the variable. Like terms can be combined by adding or subtracting the coefficients and leaving the variable the same.

Answer:It is 4x and 11x!

Step-by-step explanation: Since they have same variables, they are like terms.

Answer: To find the probability of Janice making her next free throw, you can use the proportion of successful free throw shots out of the total number of free throw shots attempted so far.

First, we need to find the number of free throws made by Janice so far:

80% success rate * 15 free throws attempted = 12 free throws made

Then we add the number of free throws made today:

12 + 3 = 15

Then we add the number of free throws attempted today:

15 + 5 = 20

So the probability of Janice making her next free throw is:

15 free throws made / 20 free throws attempted = 75%

So, the probability that Janice will make her next free throw is 75%.

It's worth noting that this answer is based on the assumption that her success rate will remain the same and doesn't take into account any other variable or change in her performance.

Step-by-step explanation:

After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times

1. To calculate the number of members after one year, multiply the initial number of members (101010) by the factor of 1.21.21:

101010 x 1.21.21 = 12312

2. To calculate the number of members after two years, multiply the initial number of members (101010) by the factor of 1.21.21 twice:

101010 x 1.21.21 x 1.21.21 = 149149

3. To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times:

101010 x 1.21.21 x 1.21.21 x 1.21.21 = 180180

After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.

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Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.

A mathematical equation resembles a formula connecting two assertions when the equals letter (=) is employed to denote equality. An equation in algebra is a statement of fact that demonstrates the equality of numerous mathematical variables. For example, the equation obd + 6 = 12 has an equal sign separating the numbers doc d + 6 and 12. You can mathematically expression how many syllables correspond per each side of every letter. Often, a symbol's message is its exact opposite.

Here,

Given :

Equation : y =57x for the distance travelled by  alisha.

Thus,

To find the equation is correct or not.

By comparing it with distance/time = speed equation we get to know

that the equation represented by alisha is wrong.

The correct equation can be => y/x =57 .

Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.

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Answer:

The answer would be B) x = -3.

Step-by-step explanation:

Answer:

53000 and 42400

Step-by-step explanation:

100*530and 80*530

The setup cost for printing the math workbooks, given the printed cost of the books, is $ 1, 800

The setup cost for printing the math workbooks is a fixed cost which means that it will not change regardless of the number of books that are printed.

Since we know that 1, 000 books are printed to be $ 14, 300 and that 5, 000 books cost $ 64, 300, we can find the cost of the books without the setup cost to be :

= Difference in cost of books / ( Difference in number of books )

= ( 64, 300 - 14, 300 ) / ( 5, 000 - 1, 000 )

= 50, 000 / 4, 000

= $ 12. 50

The setup cost is therefore :

= Cost of printing -  (Number of books x cost per book )

= 14, 300 - ( 1, 000 x 12 .5)

= $ 1, 800

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Answer:

Here is a picture of it graphed

Step-by-step explanation:

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} -›}[/tex]

Step-by-step explanation:

The outcome of the integral, in accordance with the stated statement, is (ln x)^31/31 + c.

Integration is the process's polar opposite of differentiation. The integration process involves determining a function's anti derivative. Integration is the process of combining smaller, discrete data sets that cannot be represented in a numerical value and cannot be contributed individually. Calculus (Unification) is used in electrical engineering to calculate the precise length of power line needed to connect two transmission system that are miles apart from one another.

For the predicament,

[tex]\Rightarrow \int \frac{(\ln x)^{30}}{x} d x[/tex]

Consider y = lnx, differentiate with respect to x

dy = 1/xdx

Substitute these values on the integral,

[tex]\begin{aligned}& \Rightarrow \int y^{30} d y \\& \Rightarrow \frac{y^{31}}{31}+c \\& \Rightarrow \frac{(\ln x)^{31}}{31}+c\end{aligned}[/tex]

Therefore, we may say that the integral's value is (ln x)^31/31 + C.

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