A science class measured the mass of an amount of sand.about how many grains of sand are there in 7 grams of sand

The maximum profit that for the equation p(x) = 2800x - 85x² - x³ - 109000 is $672500

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Given the profit function:

p(x) = 2800x - 85x² - x³ - 109000

The profit is maximum at:

p'(x) = 0

p(x) = 2800 + 170x - 3x²

2800 + 170x - 3x² = 0

x = 70

p(70) = 2800(70) - 85(70)² - (70)³ - 109000 = 672500

The maximum profit is $672500

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The sine of angle θ is given as follows:

sin(θ) = -8/17.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

The point in this problem has the coordinates given as follows:

(15/17, -8/17).

Hence the trigonometric ratios are given as follows:

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Answer:no image

Step-by-step explanation:

Step-by-step explanation:

No image is overe there please add the image

Answer:

Step 1:

Let x = number of years

Let y = Value of the laptop after x years

Step 2:

Write an equation that expresses the value of the laptop after x years y = 0.8((4700)x)

Step 3:

Set the equation equal to 1000 and solve for x

1000 = 0.8((4700)x)

1 = 0.8(4700)x

1/0.8 = 4700x

1.25 = 4700x

x = (1.25/4700)

Answer: The laptop will be worth $1000 or less after 0.0026608 years.

Answer:

1 year

Step-by-step explanation:

4700 x .8= 3760

4700 - 3760 = 940$

In 1 year the laptop will be $940

the circumference of the circle with a radius of  [tex]2.5[/tex] meters, approximated using  [tex]\pi = 3.14[/tex], is  [tex]15.7[/tex] meters. Thus, option C is correct.

The circumference of a closed curved object, such a circle or an ellipse, is the length around its perimeter.

The circumference of a circle is the distance around its perimeter. [tex]C = 2r[/tex] , where r is the radius (the distance from the centre of the circle to any point on its border), and pi is a mathematical constant roughly equal to  [tex]3.14159[/tex], is the formula for a circle's circumference.

The formula for the circumference of a circle is [tex]C = 2\pi r[/tex]  , where r is the radius of the circle.

Substituting the given value of the radius, we get:

[tex]C = 2 \times 3.14 \times 2.5 = 15.7[/tex] meters (approx.)

Therefore, the circumference of the circle with a radius of  [tex]2.5[/tex] meters, approximated using π = 3.14, is 15.7 meters.

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The area of the composite figure is equal to 75.5 square meters

The composite figure can be observed to be made up of a big rectangle, a smaller rectangle, a triangle and a smaller triangle. We calculate for the area of the four shapes and sum the results to get the total area of the composite figure as follows:

area of the big rectangle = 6 m × 4 m = 24 m²

area of the smaller rectangle = 7 m × 2 m = 14 m²

area of the big triangle = 1/2 × 10 m × 6 m = 30 m²

area of the smaller triangle = 1/2 × 5 m × 3 m = 7.5 m²

total area of the composite figure = 24 m² + 14 m² + 30 m² + 7.5 m²

total area of the composite figure = 75.5 m²

Therefore, the area of the composite figure is equal to 75.5 square meters

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The value of the function is 136

It is important that we note that functions are described as expressions that are used to explain the relationship between two variables.

From the information given, we have that;

g(x)=2x

h(x)=x^(2)+4

To determine the composite function, we would need to substitute the value of h(-8) as x in the function g(x)

Then, we have that;

h(-8) = (-8)^2 + 4

Find the values

h(-8) = 68

Now, substitute the value as x , we have that;

g(h(-8)) = 2(68)

expand the bracket and multiply

g(h(-8)) = 136

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Answer:

240 8018

Step-by-step explanation:

two hundred forty eight thousand and eighteen

Answer:

"B".  Domain is all real numbers, and the Range is all positive real numbers

Step-by-step explanation:

It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form [tex]y=a*b^x[/tex] where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.

Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).

The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.

The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.

Since "a" is positive, the Range is positive numbers only.

Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.

Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero".  There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0".  So, the Range is written as { y | y>0 }.

Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.

Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"

After Cami cut 17¹/₂ inches of a rope that was 50 inches long, the length of the remaining rope in inches, written in decimal form, is 32.5 inches.

To determine the remaining length of the rope, we apply subtraction operation.

However, since the cut rope was expressed in fractions, we can convert it to decimals before the subtraction.

The total length of the rope = 50 inches

The cut portion of the rope = 17¹/₂ inches

The remaining portion = 32¹/₂ inches or 32.5 inches (50 - 17¹/₂)

Thus, the remaining portion of the rope after Cami cut 17¹/₂ inches is 32.5 inches.

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Answer:

x^1/4 + 8x^1/4 + 12

Step-by-step explanation:

Using the FOIL method, we get x^1/4 + 8x^1/4 + 12

After 5 years, there will be $4,528.73 in Charlie's account if no withdrawals are made.

Compound interest means addition of interest to the principal sum of a loan or deposit. To get the amount, we will use the formula [tex]A=P(1+r/n)^{nt}[/tex] to get sum of money in the account.

Data:

P = 4,200, r = 1.51%, m = 4, t = 5

Plugging the values, we get:

[tex]A = 4200(1+0.0151/4)^{4*5}\\A = 4200* {1.003775}^{20}\\A = 4200*(1.07826994224)\\A = $4528.73375741\\A = $4528.73.[/tex]

Complete question "A bank offers an investment account with an annual interest rate of 1.51% compounded quarterly. Charlie invests 4200 into the account for 5 years. Answer the questions below. Assuming no withdrawals are made, how much money is in Greg's account after 5 years?"

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The height of the school building is approximately 4.38 meters (rounded to the nearest hundredth).

JX / BX = JM / BT

Substituting the known values, we get:

(d1 + d2) / h = d1 / (h - 1.75)

(d1 + d2) * (h - 1.75) = d1 * h

d1 * h + d2 * h - 1.75 * d1 - 1.75 * d2 = d1 * h

d2 * h - 1.75 * d1 - 1.75 * d2 = 0

h = (1.75 * d1 + 1.75 * d2) / d2

h = (1.75 * 8.75) / 3.5

h = 4.375

The height of the school building is approximately 4.38 meters

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There would be 35 more defective bean seeds than pumpkin seeds in the shipment.

Calculate the number of defective bean seeds:

Defective bean seeds = Total bean seeds * Defect rate for bean seeds

Defective bean seeds = 1,750 * 0.05 = 87.5

Since we can't have half a seed, we'll round it up to the nearest whole number.

Defective bean seeds = 88

Calculate the number of defective pumpkin seeds:

Defective pumpkin seeds = Total pumpkin seeds * Defect rate for pumpkin seeds

Defective pumpkin seeds = 1,750 * 0.03 = 52.5

Similarly, we'll round it up to the nearest whole number.

Defective pumpkin seeds = 53

Calculate the difference in defective seeds:

Difference in defective seeds = Defective bean seeds - Defective pumpkin seeds

Difference in defective seeds = 88 - 53 = 35

So, there would be 35 more defective bean seeds than pumpkin seeds in the shipment.

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In a shipment of 1,750 seeds of each type, with a defect rate of 5% for bean seeds and 3% for pumpkin seeds, how many more defective bean seeds would be expected than pumpkin seeds?

Answer:

A square's length & width are equal

Step-by-step explanation:

Kamal's shape is not a square, because a square is equilateral (equal length in all sides), but his square is 2:1,

The net profit margin for the boots is 42.5%.

Net profit margin is the measure of  how much profit is generated as a percentage of revenue. It is the ratio of net profits to revenues.

Revenue from selling the boots is $80.

Total expenses = cost +  operating expenses

The cost is $30, and the operating expenses is 20% of the revenue. That is:

2/100 * $80 = $16.

Total expenses = $30 + $16 = $46

net profit = $80 - $46 = $34

Net profit margin = (Net profit / Revenue) * 100

                            = (34 / 80) * 100

                             = 42.5%

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Approximately 19142 people were in the arena at the exact moment the event ended.

To decipher an exponential equation synchronous with the provided data, we will employ the equation of [tex]F(t) = a * b^t.[/tex]

Herein, 'F(t)' stands for the total number of attendees in the stadium at 't' minutes after the stoppage of the event, with 'a' symbolizing the initial value and 'b' being the base.

Exploiting the regression aptitudes of a graphing calculator, the exponential equation that most adequately applies to the listed information is: [tex]F(t) = a * b^t[/tex] with three decimal points specified.

F(t) = 19141.846 * 0.718^t

Using the equation:

[tex]F(23) = 19141.846 * 0.718^2^3 = 2726[/tex]

Answer: Approximately 2726 people were in the arena 23 minutes after the event ended.

How many people were in the arena 60 minutes after the event ended?

[tex]F(60) = 19141.846 * 0.718^6^0 = 123[/tex]

Answer: Around 123 people were in the arena a full hour after the occurrence concluded.

How many people were present precisely when the event wrapped up?

F(0) = 19141.846 * 0.718^0 = 19141.846 * 1 = 19141.846

Answer: Approximately 19142 people were in the arena at the exact moment the event ended.

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Answer:

The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:

y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9

Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

The work done in pushing the car along the level road from point A is found to be 8147 foot-pounds.

The work done in pushing a car along a level road can be calculated using the formula,

work = force × distance × cos(angle) where the angle between the force and the direction of motion is 0 degrees (since the force is parallel to the level road). The force is given as 103 pounds, and the distance is 79 feet. Therefore,

work = 103 × 79 × cos(0) = 8147 foot-pounds

Rounding to the nearest foot-pound, the work done in pushing the car from point A to point B is 8147 foot-pounds.

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The quadratic function in standard form is f(x) = x² - 4x - 12.

The coefficients of the quadratic function in standard form is calculated as follows;

The quadratic function is in the form of;

f(x) = ax² + bx + c

when x = -4, f(x) = -12

16a - 4b + c = -12

when x = -3, f(x) = -15

9a - 3b + c = -15

when x = -2, f(x) = -16

4a - 2b + c = -16

when x = -1, f(x) = -15

1a - 1b + c = -15

when x = 0, f(x) = -12

0a + 0b + c = -12

c = -12

Simplifying the equations, the value of a and b is calculated as;

16a - 4b + c = -12

9a - 3b + c = -15

4a - 2b + c = -16

a - b + c = -15

16a - 4b = 0

9a - 3b = -3

4a - 2b = -4

a - b = -3

16a = 4b

a = b/4

Substituting this expression for a into the last equation, we get:

b/4 - b = -3

b - 4b = -12

-3b = -12

b = 4

a = b/4

a = 4/4

a = 1

Therefore, the quadratic function in standard form is:

f(x) = x² - 4x - 12

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a. To build the airport at the same distance from the center of each town, they should locate the intersection of the perpendicular bisectors of the segments connecting each pair of towns.

b. To build the airport equidistant from each road, locate the intersection of the angle bisectors at each town

The precise location of the airport will be the point where these perpendicular bisectors intersect. This point will be equidistant from the center of each town.

b. To build the airport equidistant from each road, locate the intersection of the angle bisectors at each town. This point is the precise airport location. Equidistant from all connecting roads.

They could find the intersection of the medians of the triangle formed by the three towns. The airport is located at the centroid of a triangle, equidistant from 3 towns at the intersection of medians.

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The measure of angle IHE is 23°.

Since DF and GI are parallel, we know that angle HJF is congruent to angle GHJ. Therefore, we have:

mHJF = mGHJ = 134°

We can now use this information to find the measure of angle IHE. To do this, we need to use the fact that the sum of the angles in a straight line is 180°. Since H, J, F, and I lie on a straight line, we have:

mHJF + mFJI + mIHE = 180°

Substituting the values we know, we get:

134° + mFJI + mIHE = 180°

Simplifying the equation, we get:

mFJI + mIHE = 46°

We still need to find the measure of angle FJI. To do this, we can use the fact that the angles in a triangle add up to 180°. Triangle GHJ is a straight line, so its angles add up to 180°. Therefore, we have:

mGHJ + mHJF + mFJI = 180°

Substituting the values we know, we get:

134° + mFJI + mFJI = 180°

Simplifying the equation, we get:

2mFJI = 46°

Dividing both sides by 2, we get:

mFJI = 23°

Finally, we can substitute this value back into our earlier equation to find the measure of angle IHE:

mFJI + mIHE = 46°

23° + mIHE = 46°

Subtracting 23° from both sides, we get:

mIHE = 23°

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Complete Question:

If DF and GI are parallel lines and mGHJ = 134°, what is mIHE?

The trigonometric ratio cosA = [tex]\frac{3}{5}[/tex] which is in the lowest form.

Trigonometric ratios are the ratios of the sides of a right triangle. The sine, cosine, and tangent are three popular trigonometric ratios. (tan).

The given triangle is a right angle,

To find the cos angle we need to take the ratio of the length of the side which is next to the angle, it is also called an adjacent side to the length of the longest side of the triangle called the hypotenuse.

[tex]cosA = \frac{Length of the side next to the angle}{length of the longest side of the triangle} \\cosA = \frac{Adjacent side}{Hypotenuse} \\cosA = \frac{6}{10}\\ cosA = \frac{3}{5}[/tex]

Therefore [tex]cosA= \frac{3}{5}[/tex]

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Answer:

First, you distribute the 3 into the brackets,

3(x - 2) + 5x

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

=3x - 6 + 5x

Adding the like terms, 3x and 5x, gives you

=8x - 6

Step-by-step explanation:

A function whose graph is the graph of y = √x, but is shifted to the left 9 units is [tex]y=\sqrt{x+9}[/tex].

In Mathematics and Geometry, the translation of a geometric figure or graph to the left means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Conversely, the translation a geometric figure upward means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, the transformed function should be written as follows:

y = √x

g(x) = (√x + 9)

[tex]y=\sqrt{x+9}[/tex]

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The graph of the function "g", which is defined for all "real-numbers" is shown below.

The function "g" which is defined for all "real-numbers" is represented as :

g(x) = {2 if x<0,

         {-1 if x=0

         {-3 if x>0

this function means that, for every input-value, which is less than 0, the output will be always 2,

For the input-value "0", the output-value will be = -1;

For all the input-value which are greater than "1", the out will be always "-3",

So, from the above information, the graph is plotted below,

The red-line represents "2 if x<0", the green line represents "-3 if x>0".

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The "Expression" which is considered equivalent to this expression "(3x-1)-2(x+2)' is (c) x-5.

In mathematics, an algebraic expression is a combination of numbers, variables, which are joined by arithmetic operations (such as addition, subtraction, multiplication, and division).

We have to find the equivalent-expression for (3x-1)-2(x+2);

⇒ (3x-1)-2(x+2),

⇒ (3x - 1) - 2x - 4,

Combing the like-terms together in the above expression,

We get,

⇒ 3x - 2x -1 - 4,

⇒ x - 5,

Therefore, the correct equivalent expression is Option (c).

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The given question is incomplete, the complete question is

Which of the following expression is equivalent to (3x-1)-2(x+2)?

(a) x+3

(b) x+1

(c) x-5

(d) x-3

The savings amount balance in the account is $ 467.39

Given data ,

You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years.

Using the formula FV = PV * (1 + i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of periods, we can calculate the future value of the savings account after 15 years.

PV = $300 (the initial deposit)

i = 0.03 (the interest rate per period)

n = 15 years (the number of periods)

FV = $300 (1 + 0.03)^15

FV = $300 ( 1.5579 )

FV = $467.39

Hence , after 15 years, the savings account will have a balance of $ 467.39

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