Natasha and Rodrigo are in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that either Natasha and Rodrigo are both selected or Natasha and Rodrigo are both not selected

Answer:

Step-by-step explanation:

28 kg + 750 g = 28*1000 + 750

                          28000 + 750

                       = 28750 g

Number of sack = Total quantity of sugar ÷ quantity of sugar in a sack

                           = 28750 ÷ 500

                           =  57 sacks

Answer:

57 sacks

Step-by-step explanation:

28750 ÷ 500 =

57 sacks

Glad to help! :)

Answer:

A

Step-by-step explanation:

m angle b equals 59 now we have to find the arc of angle b.

so use the equation arc AC = 2(59)

arcAC = 118

360 - 118

=242

121/2

= 60.5

Answer:

(0, -2)

Step-by-step explanation:

You are correct: x = 0 at the y-intercept, and the y-intercept is show with the y-coordinate of -2

A sense of 3 dimensional space on a 2 dimensional surface be created using flat shapes by Overlapping , Shadows and Volume and shading .

A sense of three-dimensional space on a two-dimensional surface can be created using flat shapes by using various techniques that give the illusion of depth and volume.

Some of the techniques are :

(i) Overlapping : This involves placing objects on top of one another to create a sense of depth and hierarchy.

(ii) Shadows : The Shadows can be used to create a sense of depth by suggesting that objects are casting a shadow on each other, which implies that they exist at different levels of the image.

(iii) Volume and shading: Adding volume to shapes by shading and adding highlights can help to create the illusion of three-dimensional space on a two-dimensional surface.

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The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

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Answer:

8 6/11 is about 8.545, 17/2 = 8.5

From least to greatest: 17/2, 8 6/11, 8.83, 8.838

Step-by-step explanation:

8 6/11 is a mixed fraction

Converting it to improper fraction

Converting it to improper fraction11*8+6=88+6

Converting it to improper fraction11*8+6=88+6=94

Converting it to improper fraction11*8+6=88+6=9417/2 =8.5

8.838 is approximately 8.84

Having simplified all the values

The values to be arranged are 94, 8.838, 8.5 and 8.83

From smallest to biggest you have:

8.83, 8.838, 8.5, 94

I hope I helped

A slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

The slope of a linear relationship represents the rate of change between two variables. In this case, a slope of b = 0.007 suggests a weak positive relationship between the variables. The positive sign indicates that as the independent variable increases, the dependent variable also tends to increase. However, the small value of 0.007 indicates that the increase in the dependent variable is relatively small for each unit increase in the independent variable.

To illustrate, let's consider an example where the independent variable represents time and the dependent variable represents the number of customers in a store. With a slope of 0.007, it means that for every unit increase in time (e.g., one hour), we can expect a small increase of 0.007 customers on average. This indicates a weak positive relationship, as the increase in customers is relatively modest for each unit increase in time.

In summary, a slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

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Answer:

I believe that Tony will have to work 16 or 17 hours to have enough money to buy the TV

Step-by-step explanation:

$276.99 - 135 = $141.99

$8.50 x 8 = $68

$8.50 x 16 = $136

$8.50 x 17 = $144.50

$8.50 x 33 = $280.50

$136 < $141.99 $144.50 > $141.99

$8.50 x 16 or $8.50 x 17

Check to see if the numbers are correct.

If they are you will have to make a choice.

I hope this helped. ☺

Solving for y in the equation -8x + y = 9 gives y = 9 + 8x

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

-8x + y = 9

To solve for y, we make it the subject of the formula

In this case, we simply add 8x to both sides of the equation

Using the above as a guide, we have the following:

8x -8x + y = 9 + 8x

Evaluate the like terms

y = 9 + 8x

Hence, teh solution is y = 9 + 8x

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Answer:

9 1/10th m/s2 :)

Step-by-step explanation:

The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...

Answer:

x+3?

Step-by-step explanation:

honestly, there is not alot of information present here. so when a hear "a number" i think variable.... which would be set up as x+3

The domain of g(x) is all real numbers except for x = 0. Similarly, the output of the function will never be 0, so the range is all real numbers except for 0.

We first need to understand what domain and range mean in the context of functions. The domain of a function is the set of all possible input values, while the range is the set of all possible output values. In other words, the domain represents the values that can be plugged into the function, while the range represents the resulting values that the function produces.
In Algebra, functions are commonly represented as equations or graphs. When analyzing a function, we can determine the domain and range by examining the equation or graph. For example, if we have the function f(x) = x^2, we can see that any real number can be plugged in for x, so the domain is all real numbers. The output of the function will always be a non-negative value, so the range is all non-negative real numbers.
In some cases, the domain or range may be restricted due to certain conditions. For instance, if we have the function g(x) = 1/x, we cannot plug in 0 for x because it would result in a division by zero error. Therefore, the domain of g(x) is all real numbers except for x = 0. Similarly, the output of the function will never be 0, so the range is all real numbers except for 0.
In conclusion, the domain and range of a function in Algebra depend on the specific equation or graph being analyzed. By examining the function, we can determine the set of all possible input and output values.

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The values of x that satisfy the equation are x = 13 and x = 1. The other two options, x = -29 and x = 42, are not solutions to the equation.

A mathematical statement proving the equality of two expressions is known as an equation. The left-hand side (LHS) and the right-hand side (RHS), which are commonly joined by the equal sign (=), make up this structure.

Many mathematical operations, such as addition, subtraction, multiplication, division, exponents, and roots, can be used in equations. Finding the variable value or variables that make an equation true is the aim when solving an equation.

Based on their degree, or the highest power of the variable in the equation, equations can be categorized. A quadratic equation, for instance, has a degree of 2, while a linear equation has a degree of 1. Moreover, the number of solutions to an equation can be used to categorize it.

Starting with the equation:

(x – 7)^2 = 36

Taking the square root of both sides, we get:

x – 7 = ±6

Solving for x in each case, we get:

x – 7 = 6, which gives x = 13

or

x – 7 = -6, which gives x = 1

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To find the amount of flour poured into the tank in the first 2.5 seconds, we need to calculate the definite integral of the given rate function F(t) over the interval [0, 2.5].

The rate at which flour is poured into the tank is given by F(t) = 36/1, in pounds per second. Integrating this function will give us the total amount of flour poured into the tank over the given time interval.

The integral of F(t) with respect to t can be calculated as follows:

∫ F(t) dt = ∫ (36/1) dt

Integrating the constant term 36 gives:

= 36t

To find the definite integral over the interval [0, 2.5], we substitute the upper and lower limits of integration:

= 36(2.5) - 36(0)

= 90 - 0

= 90 pounds

Therefore, the amount of flour poured into the tank in the first 2.5 seconds is 90 pounds. None of the provided answer choices (a, b, c, d) match this result.

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The mass of each passenger car is 550 kg and the mass of the decoration is 200 kg

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

These can be represented as

(6, 3500) and (4, 2400)

The slope of the above points represent the mass of each passenger car

This is calculated as

Slope = Difference in mass/Difference in number of cars

So, we have

Slope = (3500 - 2400)/(6 - 4)

Evaluate

Slope = 550

When there are no passenger cars in the train, we have

(0, Mass of decoration)

Using the slope formula, we have

Slope = (Mass of decoration - 3500)/(0 - 6)

So, we have

Slope = (Mass of decoration - 3500)/(-6)

This gives

(Mass of decoration - 3500)/(-6) = 550

Cross multiply

Mass of decoration - 3500 = -3300

Add 3500 to both sides

Mass of decoration = 200

Hence, the mass of decoration is 200 kg

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The correct options are (b) f(x)=-3x⁵+5x-2

                                        (d) f(x)=x³-8x²

The function are written in standard form by writing the highest degree term at first and then writting other term according to decreasing order of degree of the variable.

for example f(x)=x⁴+x³+x²+x+1

So according to the question

the function should be written in standard form

so by checking every option,

(a) f(x)=8-x⁵ here highest power is 5 but that term is present at second term. so option A is incorrect.

(b) f(x)=-3x⁵+5x-2 here highest power is 5 and that term is present at first term. then all the terms are arranged in decrreasing order of power.

(c) f(x)=2x⁵+2x+x³ here highest power is 5 and that term is present at first term. then the second highest powered term is 3 and that term is present at third position which should be present at second position.

(d) f(x)=x³-8x² here here highest power is 3 and that term is present at first term. then all the terms are arranged in decrreasing order of power.

Therefore, The correct options are

(b) f(x)=-3x⁵+5x-2

(d) f(x)=x³-8x²

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Answer: The first answers are B. and D.

The second answer is 5

Step-by-step explanation: The third answer is -3

Answer:

Step-by-step explanation:

First, find the area of the circle.

pi*r^2 is 144*pi or 452.389342117 (because long numbers are fun)

165/360 is 0.45833333333

Hence, 452*0.45 is 207.345115135 or 207.35 (5 rounds up) or 207.4

Answer: 30,000m^2

Step-by-step explanation:

The formula for the area of a circle is pi*r^2. Knowing that d = 2r, we can conclude that the radius is 100m after simple algebra, and we are given that pi = 3. This makes our equation:

A = 3*100^2

A = 30,000

This means that the area of the piece of land is roughly 20,000m^2.

Step-by-step explanation:

the option that you've chose.

it's the correct answer!

have a good day :)

Answer:

The answer is D. number 4.

The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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Answer:

QR

Step-by-step explanation:

The question is just trying to see if you can read the order of the lines.

PQ is the first 2 letters of PQR so XY has to be the first 2 letters of XYZ

Answer

YZ is the second and third letters of xyz.

QR are the 2nd and 3rd letters of PQR

1. To calculate the APR (Annual Percentage Rate) for the terms of trade 2/15 net 60, we need to determine the effective interest rate per period. Here, the terms offer a 2% cash discount if payment is made within 15 days; otherwise, the full amount is due within 60 days. Assuming a year has 360 days, the APR can be calculated as follows:

APR = (Discount % / (1 - Discount %)) x (360 / (Term - Discount Period))

   = (0.02 / (1 - 0.02)) x (360 / (60 - 15))

   = (0.02 / 0.98) x (360 / 45)

   = 0.0204 x 8

   = 0.1632 or 16.32%

Therefore, the APR for the terms 2/15 net 60 is approximately 16.32%.

To find the effective rate of forgoing the cash discount, subtract the discount rate from 1 and multiply by the reciprocal of the difference in discount and credit periods:

Effective Rate = (1 - Discount %) / (1 - (Discount % x Credit Period))

             = (1 - 0.02) / (1 - (0.02 x 60))

             = 0.98 / 0.88

             = 1.1136 or 111.36%

Therefore, forgoing the cash discount has an effective rate of approximately 111.36%.

2. For the terms of sale 1/7, net 21, the APR and effective rate can be calculated similarly. The discount rate is 1%, and the credit period is 21 days.

APR = (0.01 / (1 - 0.01)) x (360 / (21 - 7))

   = (0.01 / 0.99) x (360 / 14)

   = 0.0101 x 25.71

   = 0.2598 or 25.98%

The APR for the terms 1/7 net 21 is approximately 25.98%.

Effective Rate = (1 - Discount %) / (1 - (Discount % x Credit Period))

             = (1 - 0.01) / (1 - (0.01 x 21))

             = 0.99 / 0.79

             = 1.2532 or 125.32%

Forgoing the cash discount has an effective rate of approximately 125.32%.

3. To find the average collection period, we need to determine the average number of days it takes for customers to pay their invoices. The terms are 1/7 net 30, indicating a 1% cash discount if paid within 7 days, with the full amount due within 30 days. Assuming the 40% discount is taken, the average collection period can be calculated as follows:

Average Collection Period = (Credit Period x (1 - Discount %)) + (Discount Period x Discount %)

                        = (30 x (1 - 0.01)) + (7 x 0.01)

                        = 29.7 + 0.07

                        = 29.77 days

Therefore, the average collection period is approximately 29.77 days.

The Accounts Receivable Turnover can be calculated by dividing the annual sales by the average accounts receivable. Given that 3,500 units are sold annually at $275 per unit, and 40% of customers take the discount, the calculation is as follows:

Accounts Receivable Turnover = Annual Sales / (Accounts Receivable / (1 - Discount %))  = (3,500 x $275) / (Accounts Receivable / 0.6)   = $962,500 / (Accounts Receivable / 0.6)

To find the amount of accounts receivable, we rearrange the formula:

Accounts Receivable = $962,500 / (Accounts Receivable Turnover / 0.6)

Please provide the Accounts Receivable Turnover value to calculate the specific amount of accounts receivable.

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Answer:

The inverse is 1/2x -1/2

Step-by-step explanation:

f(x) = 2x+1

y = 2x+1

Exchange x and y

x = 2y+1

Solve for y

Subtract 1

x-1 = 2y+1-1

x-1 =2y

Divide by 2

x/2 -1/2 = 2y/2

1/2x -1/2 = y

The inverse is 1/2x -1/2

7.

From the diagram, we can conclude:

Therefore:

Add like terms:

Solve for x:

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

8-9

From the diagram we can conclude:

So:

Therefore:

The equation for the nth term of the given geometric sequence is Tₙ = \(8 * 9^{(n-1)\)

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. Let's denote the first term as "a" and the common ratio as "r."

Given the geometric sequence 8, 72, 648..., we can observe that each term is obtained by multiplying the previous term by 9. Therefore, the common ratio (r) is 9.

To find the nth term (Tₙ) of a geometric sequence, we can use the following formula:

Tₙ = \(a * r^{(n-1)\)

where "n" is the term number.

In this case, the first term (a) is 8, and the common ratio (r) is 9. Plugging these values into the formula, we get:

Tₙ = \(8 * 9^{(n-1)\)

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Since the other Hexagon has a side length of 6 and a perimeter of 36, when you divide 36 by 6, you get 6. That's also how many sides there are. So then you also multiply the side length of 3 by 6 (sides) and the perimeter you get is 18.

Answer:

\(The \ equation \ in \ point \ and \ slope \ form \ is; \ y - 3 = -\dfrac{1}{2} \cdot (x - 1)\)

Step-by-step explanation:

The coordinates of the points through which the line passes are (1, 3) and (5, 1)

The slope, m, of a line given the coordinates of two known points on the line, (x₁, y₁), (x₂, y₂) can be found as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

The slope of the given line is therefore \(m =\dfrac{1-3}{5-1} = \dfrac{-2}{4} = -\dfrac{1}{2}\)

The equation of the line in point and slope form is therefore, y - y₁ = m·(x - x₁) or y - y₂ = m·(x - x₂)

Therefore, by substituting the known values, we have the equation in point and slope form as follows;

\(y - 3 = -\dfrac{1}{2} \cdot (x - 1)\)