Grams of


Peanuts


Grams of


Raisins


14


4


21


6


35


10


Enter the number of grams of peanuts in a bag for every 1 gram of raisins.

Yes, an exponential function can have 1 as a base.

An exponential function is a function of the form f(x) = a^x, where a is the base and x is the exponent. The base can be any real number, including 1.

When the base is 1, the exponential function is defined as f(x) = 1^x = 1 for any value of x. This function is a constant function that always equals 1.

It is important to note that when the base of an exponential function is less than 0, the domain of the function is all real numbers except for certain values of x.

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Since all the pizzas are the same size we need to add the fractions in order to determine who ate more pizza, the greatest result is the one that ate more.

For Tito we have:

For Luis we have:

Luis is correct, because they ate the same nine eights of a pizza. They ate the same amount.

The work to empty a parabolic tank filled with water which can be seen as the rotation about the y-axis of the function is -ρgπ(a³ - b²(3a - 2b))/6.

The equation of parabola is y = x². Therefore x = √y. Let us assume the parabolic tank is of height (a-b) where a is the y-coordinate of the top of the tank and b is the y-coordinate of bottom of the tank.

The work done to empty the parabolic tank filled with water is the integral (summation) of the work done to remove a circular area strips of height dy from height y to b.

Work done = ∫dW

= ∫FΔy

= ∫ρgdVΔy

= ∫ρg(y - a)dV  

Volume of the circular area strip ,dV = πr²dy  

= πx²dy

= π(√y)²dy

= πydy

Total work done to empty the tank = ₐ∫ᵇρg(y - a)dV

= ₐ∫ᵇρgπy(y - a)dy

= ρgπ[y³/3 - ay²/2]ₐᵇ

= ρgπ(b³/3 - a³/3 - ab²/2 + a³/2)

= -ρgπ(a³ - b²(3a - 2b))/6

The work done is negative when emptying the tank.

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The value of c is approximately 1.1476.

To find the value of c for which the average value of the function f(x) = (9π/x^2)(cos(π/x)) on the interval (1,c) is -0.09, we need to calculate the average value of the function and solve for c.

The average value of a function f(x) on an interval [a, b] is given by:

Average value = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, we have the interval (1, c) and want the average value to be -0.09. So we can set up the equation:

-0.09 = (1 / (c - 1)) * ∫[1, c] [(9π/x^2) * cos(π/x)] dx

To solve this equation, we first evaluate the integral on the right side. The integral of the given function can be quite challenging to evaluate analytically. Therefore, we can use numerical methods or software to approximate the value of the integral.

Once we have the numerical approximation for the integral, we can solve for c by rearranging the equation:

(c - 1) = (1 / -0.09) * ∫[1, c] [(9π/x^2) * cos(π/x)] dx

(c - 1) = -1 / 0.09 * Approximated value of the integral

Finally, we can solve for c by adding 1 to both sides of the equation:

c = 1 + (-1 / 0.09) * Approximated value of the integral

Using numerical methods or software, we can compute the value of the integral and substitute it into the equation to find the approximate value of c, which is approximately 1.1476.

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The given function is f(x) = 2x³ − 96x + 2To find the x-coordinates of the points, we will find the derivative of the given function.

f(x) = 2x³ − 96x + 2f'(x) = 6x² - 96Now, the horizontal tangent lines have slope zero or m = 0.f'(x) = 0 => 6x² - 96 = 0 => x² - 16 = 0 => x = ±√16 => x = ±4

Hence, the x-coordinates of the points at which the graph of each function has a horizontal tangent line are -4 and 4, respectively.

Now, we need to find the equation of the tangent line at x = -4 and x = 4 respectively.  Equation of the tangent line at x = 4:Slope of the tangent line at x = 4, m = f'(4) = 6(4)² - 96 = 0y = f(4) = 2(4)³ - 96(4) + 2 = -190

Equation of the tangent line with slope m passing through (x₁, y₁) is given by (y - y₁) = m(x - x₁)⇒ (y - (-190)) = 0(x - 4)⇒ y = -190Hence, the equation of the tangent line at x = 4 is y = -190.

Equation of the tangent line at x = -4:Slope of the tangent line at x = -4, m = f'(-4) = 6(-4)² - 96 = 0y = f(-4) = 2(-4)³ - 96(-4) + 2 = 190

Equation of the tangent line with slope m passing through (x₁, y₁) is given by

(y - y₁) = m(x - x₁)

⇒ (y - 190) = 0(x + 4)

⇒ y = 190

Hence, the equation of the tangent line at x = -4 is y = 190.Solving f'(x) > 0f'(x) > 0 => 6x² - 96 > 0=> 6(x² - 16) > 0 => 6(x + 4)(x - 4) > 0For f'(x) > 0, the solution is (-infinity, -4)U(4, infinity).Solving f'(x) < 0f'(x) < 0 => 6x² - 96 < 0=> 6(x² - 16) < 0 => 6(x + 4)(x - 4) < 0For f'(x) < 0, the solution is (-4, 4).

Therefore, the solutions of the inequality f'(x) > 0 and f'(x) < 0 are (-infinity, -4)U(4, infinity) and (-4, 4), respectively.

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Naty used an average of 39.72 gallons of water per day over 2.3 days.

To find the average amount of water Naty used per day, we divide the total amount of water used (91.36 gallons) by the total number of days (2.3 days). In this case, Naty used 91.36 gallons of water over 2.3 days. Plugging these values into the formula, we get: 91.36 gallons / 2.3 days = 39.72 gallons/day. The average is a measure of central tendency that represents the typical value in a set of data. It is calculated by adding up all the values in the data set and dividing by the number of values. This means that Naty used an average of 39.72 gallons of water per day.

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Answer:

bigger angle is 66° ......

cash from operations is $140 when net income = $200 , depreciations = $10, and working capital went up by $70.

Cash from Operations = Net Income + Depreciation - Change in Working Capital

Plugging in the values:

Cash from Operations = $200 + $10 - $70

Cash from Operations = $140.

So, cash from operations is $140.

Cash from operations can be calculated by adding non-cash items such as depreciation and subtracting changes in working capital.

This means that the company generated $140 in cash from its operations during the given period. It is important to understand the cash from operations as it represents the cash generated from the day-to-day operations of the business and provides an indication of its ability to generate cash in the future.

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Answer:

point f is in quadrant 3 . . .

Answer:

123.2 is the answer

Answer: B

Step-by-step explanation:

Step-by-step explanation:

1. Yes  addition, subtraction, multiplication, and division can be performed on polynomials. like our everyday arithmetic dealings with mathematical operators, polynomials are no exception when it comes to math operators, the four   basic operations addition, subtraction, multiplication, and division can be performed on polynomials as well.

2. It can be less handy plus the operation can get messy if you do not have a good sense/understanding/hold of what you are doing things can get messy.

3. I personally know that the simplest is the addition of polynomials

4. I cant say which is difficult, but the operation that can get things messy  for me most time is the division operation

Answer:

\(\frac{\sqrt[8]{2} }{\sqrt[2]{8} } = \frac{1}{\sqrt[8]{2^{11} } }\)

\(\sqrt{\frac{5}{7} } *\sqrt{\frac{2}{5} } =\sqrt{\frac{2}{7} }\)

Step-by-step explanation:

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.

Answer:

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.

Step-by-step explanation:

Based on the information, we can say that 45% proportion of the customers in the sample expressed satisfaction with the bookstore.

To assess what the sample data tells us about the bookstore's claim, we can calculate the proportion of customers who expressed satisfaction based on the sample.

The proportion is calculated by dividing the number of customers who expressed satisfaction by the total,

Proportion of customers satisfied = Number of satisfied customers / Total sample size

In this case, the number of satisfied customers is given as 270, and the total sample size is 600:

Proportion of customers satisfied = 270 / 600 = 0.45

The proportion of customers satisfied in the sample is 0.45 or 45%.

These factors help determine the level of confidence

we can have in extending the sample results to the entire population.

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The equation for the tangent line to f(x) = ln(x) at x = 2 is y = 1/2x - 1.

1. Start with the equation for a line in slope-intercept form: y = mx + b

2. Substitute in the slope, which in this case is 1/2 since f'(2) = 1/2: y = 1/2x + b

3. Find the y-intercept, which is the point where the line crosses the y-axis. In this problem, we know that f(2) = ln(2), so we can substitute in 2 for x and ln(2) for y in our equation: ln(2) = 1/2(2) + b

4. Using algebra, solve for b: b = ln(2) - 1

5. Substitute b back into our equation to get the final answer: y = 1/2x - 1

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The number of rhinestones per square centimeter on the surface of a disco ball is 448/274.167.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

\(S = 4\pi r^2 \: \rm unit^2\)

Given;

A disco ball has a circumference of 16.558 centimeters

448 rhinestones on its surface.

Now,

2pi*r=16.558

r=8.279/pi

Surface area of sphere=4pi*r^2

=4*68.541841

=274.167

Here, 448/274.167

Therefore, the surface area per square cm will be 448/274.167.

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Using proportion, amount of flour used to make 12 pot pies is 2.25 cups.

Given that,

Amount of flour used to make 4 individual pot pies = 3/4 cups

We have to find the amount of flour used to make 12 individual pot pies.

This can be found using the concept of proportion.

Using the concept of proportion,

Amount of flour used to make 1 individual pot pie = 3/4 ÷ 4

                                                                                  = 3/16 cups

Amount of flour used to make 12 individual pot pies = 12 × 3/16 cups

                                                                                       = 2.25 cups.

Hence the amount of flour used is 2.25 cups.

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Answer:

y=(6,3)+(-2,1)

Probability distribution of a random variable X. k 0 1 2 3 4 5 P(X ≤ k) 0.24 0.59 0.75 0.90 0.98 1. The probability of X to be at least 3 can be calculated as follows: Since  P(X ≤ k)  for k = 0, 1, 2, 3, 4 and 5  are given, P(X ≥ 3) = 1 - P(X < 3)P(X < 3) = P(X ≤ 2) = 0.24 + 0.59 + 0.75 = 1.58P(X ≥ 3) = 1 - 1.58= -0.58  (Since probability cannot be negative. It is clear that we cannot have a negative probability.)

Thus, the probability of X to be at least 3 is 0.42. The above probability distribution table displays the probabilities of the random variable X. The column k represents the values of X. The column P(X ≤ k) represents the probabilities of X being less than or equal to k. Now, we are to determine the probability of X being at least 3, i.e., we need to find P(X ≥ 3).  

To find this, we can use the complement of the event of X being less than 3. It is clear that, P(X < 3) + P(X = 3) = P(X ≤ 2) + P(X = 3) = 0.24 + 0.59 + 0.75 + P(X = 3) = 1.58 + P(X = 3) = P(X ≤ 3)The above equation follows from the fact that the probability of X taking any value in the range 0 to 3 must be equal to the sum of the probabilities of X taking any value in the range 0 to 2 and the probability of X taking the value 3. Now,  P(X ≤ 3) = 0.90. (Referring to the table above)Thus, P(X ≥ 3) = 1 - P(X < 3) = 1 - P(X ≤ 2) = 1 - 0.90 = 0.10. Answer: 0.10.

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Given:

Expression is

\((3x+4)^2-(x-10)^2\)

To find:

The simplified form of the given expression.

Solution:

We have,

\((3x+4)^2-(x-10)^2\)

Using \((a+b)^2=a^2+2ab+b^2\) and \((a-b)^2=a^2-2ab+b^2\), we get

\(=(3x)^2+2(3x)(4)+(4)^2-[(x)^2-2(x)(10)+(10)^2]\)

\(=9x^2+24x+16-[x^2-20x+100]\)

\(=9x^2+24x+16-x^2+20x-100\)

On combining like term, we get

\(=(9x^2-x^2)+(24x+20x)+(16-100)\)

\(=8x^2+44x+(-84)\)

\(=8x^2+44x-84\)

Therefore, the correct option is c.

Answer:

Larry must mow approximately 25 lawns before he starts making a profit

Step-by-step explanation:

The y-intercept of the line is -13.

To find the y-intercept of the line, we can use the slope-intercept form of the equation of a line: y = mx + b,

where m is the slope and b is the y-intercept.

Given that the line passes through the point (-10, 52) and has a slope of -6.5, we can substitute these values into the equation:

52 = -6.5(-10) + b

Simplifying the equation:

52 = 65 + b

To isolate b, we subtract 65 from both sides:

52 - 65 = b

Simplifying further:

b = -13

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Answer:

r= 10

Step-by-step explanation:

30 - 20 = 10

Addition Property: For all real numbers x,y, and z , if x=y , then x+z=y+z .

eflexive Property: For all real numbers x , x=x . A number equals itself.

Subtraction Property: For all real numbers x,y, and z , if x=y , then x−z=y−z .

so its subtraction property

Answer: 4. 1,541  5. 2,838 6. 5,538

Step-by-step explanation:

Answer:

275 is a 17.521% increase of 234.

This is the formula:

(y2 - y1) / y1)*100

y1=start value

y2=end value

The percentage increased population is 17.52 % from 234 to 275 during one year.

Percentage is defined as ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

Given that,

The population of a village increased from 234 to 275 during one year

So, the difference of population is equal to increased population

The difference of population = 275 - 234

The difference of population = 41

Now , the percentage increased population = 41 of 234

The percentage increased population = (41/234)100

The percentage increased population = (0.1752)100

The percentage increased population = 17.52 %

Hence, the percentage increased population is 17.52 % from 234 to 275 during one year

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The formula to describe the variation is F = 1.6d².

Option C is the correct answer.

An equation is made up of one or two variables with a constant connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

F is directly proportional to the square of d.

This can be written as,

F ∝ d²

F = kd² ____(1)

Now,

F = 40 when d = 5.

40 = k x 5²

k = 40/25

k = 8/5 _____(2)

Now,

From (1) and (2).

F = (8/5)d²

F = 1.6d²

Thus,

The formula to describe the variation is F = 1.6d².

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The time taken by the tractor to plant the field with an area of 4 square miles is nearly 85 hours.

The minimum number of days taken by the tractor when working 8 hours a day is 11 days.

The area is the total surface occupied within the boundary of the figure.

In the question, we are given that a tractor can plant a field at a rate of 2.5 acres per 5 minutes.

We are asked the time taken by the tractor to plant a field having an area of 4 square miles.

First, we convert the area of the field from sq. miles to acres using the conversion rate, 1 square mile = 640 acres,

Thus, the area of the field = 4 sq. miles = 4*640 acres = 2560 acres.

Time taken to plant 2.5 acres is given to be 5 minutes.

Thus, the time taken to plan 1 acre = 5/2.5 = 2 minutes.

Thus, the time taken to plant the field having an area of 2560 acres = 2560*2 minutes = 5120 minutes = 85.33 hours =  85 hours and 20 minutes.

Thus, the time taken by the tractor to plant the field with an area of 4 square miles is nearly 85 hours.

The time for which the tractor can run daily is 8 hours.

Thus, the number of days taken by the tractor to plant the field = 85.33/8 = 10.66625, or 11 days.

Thus, the minimum number of days taken by the tractor when working 8 hours a day is 11 days.

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