An engineer determines that the angle of elevation from her position to the top of a tower is 52°. She measures the angle of elevation again from a point 47 meters farther away from the tower and
finds it to be 31°. Both positions are due east of the town. Find the height of the tower

pls help

The estimate volume of the box holding the tissue boxes is 1125 cubic inches.

Let the Volume of each tissue box be 'v'

Number of tissues be 'n'

The estimate volume of the box holding the tissue boxes be V.

As given in Question:

Volume of each tissue box v = 125 cubic inches

Number of tissues n from the attached image (given below);

                                          n = 3×3

                                          n = 9 tissue boxes

The estimate volume of the box holding the tissue boxes V;

                                         V = nv

                                         V = 9 × 125

                                         V = 1125 cubic inches.

The estimate volume of the box holding the tissue boxes is 1125 cubic inches.

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Emily can read 5 words per minute.

Minutes are often used to measure the duration of activities such as meetings, phone calls, or workouts. They are also used to express the duration of processes or events that occur over a short period of time.

To find out how many words Emily can read per minute, we need to divide the total number of words she can read by the amount of time it takes her to read them.

75 words in 15 minutes can be written as a ratio:

75 words / 15 minutes

To simplify this ratio, we can divide both the numerator and the denominator by 15:

(75 words / 15 minutes) ÷ (15 minutes / 15 minutes)

This gives us:

5 words / 1 minute

Therefore, Emily can read 5 words per minute.

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Answer: 75 inches

Step-by-step explanation:

Using Pythagorean's Theorem, a² + b² = c², let a represent the length of the bed.

a² + 40² = 85²

a² + 1600 = 7225

a² = 5625

a = 75

The length of the bed is 75 inches.

Hope this helps!

Answer: 75

Step-by-step explanation: We can think of Aubrey’s bed as a triangle, Since the area doesn't matter. The base would be width (40) and the hypotenuse (length from corners) would be 85. So, since A^2+B^2=C^2 and c is 85 and a is 40. The equation is 40^2+?^2=85^2 so if we solve the numbers whit exponents we would get this: 1600+?=7225. Then we would just subtract 1600 from 7225 which is: 5625. Now we are not done. 5625 is just the square version of 5625. So we would need to find the square root. Which is 75.

Answer:

2 + 2 + ?? = 4,000

?? = 3996

Step-by-step explanation:

You're welcome.

D. No, not similar

ΔFNY: 8<10<12 ⇔ FN<NY<FY

ΔWRY: 14 <18<21 ⇔ WR<YW<YR

[tex]\dfrac{FN}{WR} = \dfrac{8}{14} = \dfrac{4}{7}[/tex]

[tex]\dfrac{NY}{YW} = \dfrac{10}{18} = \dfrac{5}{9}[/tex]

[tex]\dfrac{FY}{YR} = \dfrac{12}{21} = \dfrac{4}{7}[/tex]

[tex]\dfrac{FN}{WR} = \dfrac{FY}{YR} \bf \neq \dfrac{NY}{YW}[/tex]

The x and y-intercept of the given point (1,1), (-5,7) is 2 and 2.

The equation of a line can be represented in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, let's find the slope.

(1,1), (-5,7)

m = 7 - 1 / -5 - 1

m = 6 / -6

m = - 1

Let's find the x and y-intercept using (1, 1)

y = -x + b

1 = -1 + b

b = 1 + 1

b = 2

Therefore,

y = - x + 2

Let's find x and y-intercept

y = -(0) + 2

y = 2

- x = y + 2

-x = 0 + 2

x = 2

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The product  is less than 35.

To analyze this problem without calculating, we can look at the factors involved in the product. The first factor is 7, and the second factor is 5(3)/(4).

The second factor, 5(3)/(4), is less than 5 because it is the product of 5 and a fraction less than 1.

When we multiply 7 by a number less than 5, the result will be less than 35.

Therefore, the product of 7 and 5(3)/(4) is less than 35.

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The Zeros of the equation would be x = -5/2.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given the equation as;

[tex]f(x)=-8x^3-20x^2[/tex]

We can factor;

4x^2 ( 2x+5)  

Using the zero product property

2x = 0

2x + 5 = 0

x = -5/2

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The other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.

Given that x = -9 is a root of |(x,3,7)(2,x,2)(7,6,x)| = 0, we can use the determinant of the matrix to find the other roots. The determinant of the matrix is given by:

| (x,3,7)(2,x,2)(7,6,x) | = x(x*x - 2*6) - 3(2*x - 7*2) + 7(2*6 - 7*x)

= x^3 - 12x - 3(2x - 14) + 7(12 - 7x)

= x^3 - 12x - 6x + 42 + 84 - 49x

= x^3 - 67x + 126 = 0

Since x = -9 is a root, we can divide the polynomial by (x + 9) to get:

(x^3 - 67x + 126) / (x + 9) = x^2 - 9x - 14

Now we can use the quadratic formula to find the other two roots:

x = (-(-9) ± √((-9)^2 - 4(1)(-14))) / (2(1))

x = (9 ± √(81 + 56)) / 2

x = (9 ± √137) / 2

Therefore, the other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.

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Step-by-step explanation:

[tex] \frac{1}{2} \times 5.4 \times 6.4 \\ = 17.28 \\ \frac{1}{2} \times 6.6 \times 6.4 \\ = 21.12 \\ 17.28 + 21.12 = 38.4 {in\\ }^{2} [/tex]

In the triangle ABC, the value of AC is obtained as 5 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 10 units.

The measure of KB is given as 2 units.

The measure of KM is given as 1 unit.

According to the indirect measurement -

AB / AC = KB / KM

Substitute the values in the equation -

10 / AC = 2 / 1

2 AC = 10

AC = 5  

Therefore, the value of AC is obtained as 5 units.

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The smaller solution for the equation is - 1 and the larger solution is 2/14.

The values of the unknown variable x that fulfil the quadratic equation are the solutions to the problem. Quadratic equations' roots or zeros are known as these solutions. The answers to the given problem are the roots of any polynomial.

The given equation is:

14x² + 12x - 2 = 0

Splitting the middle term:

14x² + 14x - 2x - 2 = 0

14x (x + 1) - 2(x + 1) = 0

(14x - 2) (x + 1) = 0

x = 2/14 and x = -1

Hence, the smaller solution for the equation is - 1 and the larger solution is 2/14.

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Answer:

Proof:

Using the given information, we know that PQ is approximately equal to QS and QS is exactly equal to ST.

Since a value that is approximately equal to another value can be treated as equal in many cases, we can say that PQ is roughly equal to ST.

To prove that PQ is exactly equal to ST, we must use the transitive property of equality.

Transitive Property of Equality: If a = b and b = c, then a = c.

Using the transitive property, we can say:

PQ ≈ QS and QS = ST → PQ ≈ ST

Since PQ is approximately equal to ST and they have the same units of measurement, we can round the values to the same number of decimal places and say:

PQ ≈ ST ≈ rounded value

Therefore, PQ is exactly equal to ST because they have the same rounded value.

Answer:

= 42m²

Step-by-step explanation:

The ratio of two similar hexagons is 3:7

where the smaller correspond to 3

And

the bigger correspond to 7

where the area of the smaller haxagon is 18

so if 3 = 18m²

then 7 = ?

therefore

[tex] \frac{7}{3} \times 18 \\ = 42 {m}^{2} [/tex]

therefore the area of the bigger hexagon is 42m²

The normalized orthogonal distance between the robot and the reference trajectory line is approximately 4.16.

The normalized orthogonal distance is the distance between the robot and the reference trajectory line. We can use the following formula to calculate the normalized orthogonal distance:

normalized orthogonal distance = |(y2 - y1)x0 - (x2 - x1)y0 + x2y1 - y2x1| / √((y2 - y1)^2 + (x2 - x1)^2)

Where (x0, y0) is the position of the robot, and (x1, y1) and (x2, y2) are the positions of the two points on the reference trajectory line.

Plugging in the values given in the question, we get:

normalized orthogonal distance = |(7 - 3)5 - (8 - 2)0 + 8*3 - 7*2| / √((7 - 3)^2 + (8 - 2)^2)

Simplifying the equation, we get:

normalized orthogonal distance = |20 - 0 + 24 - 14| / √(16 + 36)

normalized orthogonal distance = |30| / √(52)

normalized orthogonal distance = 30 / √(52)

normalized orthogonal distance ≈ 4.16

Therefore, the normalized orthogonal distance between the robot and the reference trajectory line is approximately 4.16.

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Answer:

Perimeter, in feet, of quadrilateral A'BAC = 2(a + b) feet

Last Option

Step-by-step explanation:

Reflecting a figure does not change its dimensions, only its orientation

Therefore when ΔABC is reflected across the line BC, the reflected image is another triangle ABC with the same dimensions and BC as the common side, B and C points are unchanged and A is reflected to A'

Therefore the quadrilateral ABCA' will have sides a and b

Perimeter of a quadrilateral = 2 x (sum of sides)

= 2(a + b)

This is the last answer choice

See figure  for an understanding

We can see here that the an expression for the perimeter, in feet,

of quadrilateral A'BAC will be: E. 2(a + b).

Perimeter is the total length of the boundary of a two-dimensional geometric shape, such as a polygon or a circle. It is the distance around the shape and is measured in units such as centimeters, meters, feet, or yards.

We see here that the above option is correct. It should be noted that as the image is reflected across side BC, the dimensions didn't change. Thus, the reflected image alongside the triangle gives a quadrilateral.

The perimeter of a quadrilateral = sum of all the sides of a quadrilateral.

Thus, for  quadrilateral A'BAC, the perimeter = a + a + b + b = 2a + 2b = 2(a + b).

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The answers are:

35. f(x)⋅g(x) = 9x2 - 0.25

36. (f(x))2 = 9x2 + 3x + 0.25

37. (g(x))2 = 9x2 - 3x + 0.25

To MULTIPLYING FUNCTIONS, we simply multiply the corresponding terms of each function together. Let's use the given functions f(x)=3x+0.5 and g(x)=3x−0.5 and perform the indicated operations.

35. f(x)⋅g(x) = (3x+0.5)(3x−0.5) = 9x2 - 0.25

36. (f(x))2 = (3x+0.5)2 = 9x2 + 3x + 0.25

37. (g(x))2 = (3x-0.5)2 = 9x2 - 3x + 0.25

So, the answers are:

35. f(x)⋅g(x) = 9x2 - 0.25

36. (f(x))2 = 9x2 + 3x + 0.25

37. (g(x))2 = 9x2 - 3x + 0.25

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Answer:

48 servings

Step-by-step explanation:

since there are 16 cups in a gallon and 2 cups makes 6 servings, then to find the number of servings a gallon makes we divide the amount of cups in a gallon (16) by how many you need to make the recipe (2), and 16/2=8 so now we multiply how many times we can make the recipe with a gallon (8) by how many servings the recipe makes (6) to get 8x6=48 servings

(-3x + 2y + z = 0 )

The equation of the plane passing through the origin and containing the vectors \( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \) and \( \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] \) can be found by taking the cross product of the two vectors and using the resulting vector as the normal vector of the plane. The cross product of the two vectors is given by:

\( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \times \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] = \left[\begin{array}{c}(-1)(3) - (1)(0) \\ (1)(3) - (1)(1) \\ (1)(0) - (1)(-1)\end{array}\right] = \left[\begin{array}{c}-3 \\ 2 \\ 1\end{array}\right] \)

Therefore, the equation of the plane is given by:

\( -3x + 2y + z = 0 \)

This is the equation of the plane passing through the origin and containing the two given vectors.

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The median is 138.

What is the median?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.

Here, we have

Given: data set:

135, 149, 156, 112, 134, 141, 154, 116, 134, 156.

To get the box plot we begin by arranging the data in ascending order:

135, 149, 156, 112, 134, 141, 154, 116, 134, 156

rearranging the data set we get:

112,116, 134, 134, 135, 141, 149, 154, 156, 156

then:

Lower value = 112

Q1 = 134

Median = (135+141)/2 = 138

Q3 = 154

Largest value =156

Hence, the median is 138.

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Answer:

please your question is incomplete

Step-by-step explanation:

if....... of a number

The simplified expression is a^(-(3)/(8)).

To simplify the expression (a^(-(1)/(2)))/(a^(-(1)/(8))), we need to use the properties of exponents. Specifically, we will use the property that states that when dividing two expressions with the same base, we can subtract the exponents.

So, in this case, we have:

(a^(-(1)/(2)))/(a^(-(1)/(8))) = a^(-(1)/(2) - (-(1)/(8)))

Simplifying the exponent:

= a^(-(4)/(8) + (1)/(8))

= a^(-(3)/(8))

In conclusion, the simplified expression of (a^(-(1)/(2)))/(a^(-(1)/(8))) is a^(-(3)/(8)).

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the length of the actual kitchen wall is 144 inches.

The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.

Given, On a scale drawing, a kitchen wall is 6 inches long. The scale factor is 1/24

If the scale factor is 1/24, it means that every 1 inch on the drawing represents 24 inches in real life.

Let's set up a proportion:

1 inch on the drawing : 24 inches in real life = 6 inches on the drawing : x inches in real life

where x is the length of the actual wall.

To solve for x, we can cross-multiply:

1 inch on the drawing * x inches in real life = 6 inches on the drawing * 24 inches in real life

x = 6 inches on the drawing * 24 inches in real life / 1 inch on the drawing

x = 144 inches in real life

Therefore, the length of the actual kitchen wall is 144 inches.

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The value of perimeter of CAR is  12 + 6√2 + 6√3. (C)

The value of the perimeter of triangle CAR can be found by adding the lengths of all three sides of the triangle.

In this case, the perimeter would be the sum of side CA, side AR, and side CR.

To find the perimeter, we can use the formula P = CA + AR + CR.

If we plug in the given values for each side, we can solve for the perimeter:

P = 6 + 6√2 + 6√3

P = 12 + 6√2 + 6√3

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The volume of Sphere T is 216 times greater than the volume of Sphere S.

The volume of a sphere is given by the formula:

V = (4/3)πr³

where V is the volume and r is the radius of the sphere.

The volume of Sphere S is:

V_s = (4/3)πr³

The volume of Sphere T is:

V_t = (4/3)π(6r)³

Divide the volumes

V_t / V_s = (4/3)π(6r)³/ (4/3)πr³

So, we have

V_t / V_s = 216

Hence, the number of times is 216

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Answer:

If 2 is a rational root of the equation x^3 - 5x^2 - 4x + 20 = 0, then (x - 2) is a factor of the polynomial. This is because of the rational root theorem, which states that any rational root of a polynomial with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is 20 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±4, ±5, ±10, and ±20.

Since 2 is a root, we can use long division or synthetic division to divide x^3 - 5x^2 - 4x + 20 by (x - 2). We get:

code

2 | 1 -5 -4 20 | 2 -6 -20 |------------ | 1 -3 -10 0

Therefore, we have:

x^3 - 5x^2 - 4x + 20 = (x - 2)(x^2 - 3x - 10)

Now, we need to solve the quadratic equation x^2 - 3x - 10 = 0. We can use the quadratic formula:

x = (3 ± sqrt(3^2 - 4(1)(-10))) / 2 x = (3 ± sqrt(49)) / 2 x = (3 ± 7) / 2

So the solutions to the equation x^3 - 5x^2 - 4x + 20 = 0 are:

x = 2, x = (3 + 7)/2 = 5, x = (3 - 7)/2 = -2

Therefore, the solution set is {2, 5, -2}.

Step-by-step explanation:

Step 1: Use the Rational Root Theorem to find possible rational roots The Rational Root Theorem states that any rational root of a polynomial with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is 20 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±4, ±5, ±10, and ±20. Since we are given that 2 is a root, we can conclude that (x - 2) is a factor of the polynomial.

Step 2: Use long division or synthetic division to divide the polynomial by (x - 2) We can use long division or synthetic division to divide the polynomial x^3 - 5x^2 - 4x + 20 by (x - 2). Both methods will give the same result, but I'll show the synthetic division method here:

code

2 | 1 -5 -4 20 | 2 -6 -20 |------------ | 1 -3 -10 0

The first row of the division represents the coefficients of the polynomial x^3 - 5x^2 - 4x + 20, starting with the highest degree term. We divide the first coefficient by the divisor, which gives us 1/1 = 1. Then we multiply the divisor (2) by the quotient (1), which gives us 2. We write 2 below the next coefficient (-5), and subtract to get (-5) - 2 = -7. We bring down the next coefficient (-4) to get -7 - (-4) = -3. We repeat the process with -3 as the new dividend, and so on, until we get a remainder of 0 in the last row.

The second row shows the partial quotients (in this case, just one quotient of 1), and the third row shows the coefficients of the quotient polynomial x^2 - 3x - 10. The last row shows the remainder, which is 0 in this case.

Step 3: Factor the quotient polynomial We now have x^3 - 5x^2 - 4x + 20 = (x - 2)(x^2 - 3x - 10), since (x - 2) is a factor of the polynomial. We can factor the quadratic polynomial x^2 - 3x - 10 by finding two numbers that multiply to -10 and add to -3. These numbers are -5 and 2, so we can write:

x^2 - 3x - 10 = (x - 5)(x + 2)

Step 4: Find the solutions to the equation We now have:

x^3 - 5x^2 - 4x + 20 = (x - 2)(x^2 - 3x - 10) = (x - 2)(x - 5)(x + 2)

The solutions to the equation are the values of x that make the polynomial equal to 0. These values are the roots of the equation. We have:

x - 2 = 0, so x = 2 is a root x - 5 = 0, so x = 5 is a root x + 2 = 0, so x = -2 is a root

Therefore, the solution set is {2, 5, -2}.

The solution set of the equation x^(3)-5x^(2)-4x+20=0 is found to be {2, 5, -2}.

One rational root of the given equation is 2. We can use synthetic division to find the other roots.

Set up the synthetic division table by placing the root (2) in the leftmost column and the coefficients of the equation (1, -5, -4, 20) in the top row.

2|1-5-420|2-6-201-3-100

Multiply the root (2) by each of the numbers in the bottom row and place the result in the row below. Then add the numbers in the top and bottom rows to get the numbers in the final row.

The final row represents the coefficients of the reduced equation: x^(2)-3x-10=0. We can use the quadratic formula to find the remaining roots:

x = (-(-3) ± √((-3)^(2) - 4(1)(-10))) / (2(1))

x = (3 ± √(9 + 40)) / 2

x = (3 ± √49) / 2

x = (3 ± 7) / 2

x = 5 or x = -2

So the solution set of the equation is {2, 5, -2}.

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The remainder when f(x) is divided by x-1 is 0.

Remainder Theorem states that given a polynomial function and a value for x, the remainder when the polynomial is divided by (x-a) is equal to the value of the polynomial when x=a. This theorem can be used to quickly and accurately find the remainder of a division problem, making it a very useful tool.

The remainder theorem states that if a polynomial f(x) is divided by x-a, then the remainder is f(a). In this case, we want to find the remainder when f(x) is divided by x-1. Therefore, we need to find f(1).

f(1) = 2(1)^(3) + 3(1)^(2) - 12(1) + 7
f(1) = 2 + 3 - 12 + 7
f(1) = 0

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The value of x will be 6° according to the remaining angles values in the diagram.

What is a Triangle?

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

How are the sum of triangles calculated in a triangle?

In a triangle, the total interior angles are supplementary. In other words, the sum of a triangle's inner angle measurements is 180°. Hence, we can write the triangle sum theorem's formula as A + B + C = 180° for the triangle ABC.

Now according to the question

                          => 40+110+8x-18=180 (Theorem)

                          => 150+8x-18=180

                          => 8x=180-150+18

                          => 8x=48

                          => x=6°

The  value of x will be : 6°

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The point where the two lines come together (1,1). Hence, x = 1 and y = 1 are the answers to the system of equations.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

The technique of solving a system of equations involves calculating the unknown variables while maintaining the equations balanced on both sides. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true.

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The maximum number of sports drinks that can be purchased for $80 is 90 when they are priced at $0.70 per drink. (option B)

Let's start by finding the number of sports drinks that can be purchased for $80 when they are priced at $0.80 per drink.

The price of each drink is $0.80, and the shipping and handling cost is $10.

Let x be the number of sports drinks that can be purchased for $80:

0.80x + 10 = 80

Subtracting 10 from both sides:

0.80x = 70

Dividing both sides by 0.80:

x = 87.5

Since we cannot purchase a fraction of a sports drink, we must round down to the nearest whole number, which is 87.

Now let's check if we can purchase more sports drinks for $80 when they are priced at $0.70 per drink.

The price of each drink is $0.70, and the shipping and handling cost is $17.

Let y be the number of sports drinks that can be purchased for $80:

0.70y + 17 = 80

Subtracting 17 from both sides:

0.70y = 63

Dividing both sides by 0.70:

y = 90

Since we cannot purchase a fraction of a sports drink, we must round down to the nearest whole number, which is 90.

Therefore, the maximum number of sports drinks that can be purchased for $80 is 90 when they are priced at $0.70 per drink.

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