Write the following sets of identities
a) minor- to -minor b) reciprocal
c. )CFCs d) pythgurean
*right answers only don't answer unless you 100%*



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The equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).

To find the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1), first, determine the slope of the given line. The slope is -8. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the new line will be 1/8.

Now, use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point (-4, 1). Plug in the values: y - 1 = (1/8)(x - (-4)).

Simplify the equation: y - 1 = (1/8)(x + 4). Distribute the 1/8: y - 1 = (1/8)x + (1/2). Finally, add 1 to both sides: y = (1/8)x + (1/2) + 1.

So, the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).

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The time between buses arriving at the stop follows an exponential distribution with a mean of 26 minutes.

To find the probability of waiting at least 4 minutes for the bus, we can use the cumulative distribution function (CDF) of the exponential distribution:

P(waiting at least 4 minutes) = 1 - P(waiting less than 4 minutes)

The probability of waiting less than 4 minutes can be calculated using the CDF:

P(waiting less than 4 minutes) = 1 - e^(-4/26) ≈ 0.146

Therefore, the probability of waiting at least 4 minutes for the bus is:

P(waiting at least 4 minutes) = 1 - 0.146 ≈ 0.854

So the probability of having to wait at least 4 minutes for the bus is about 85.4%.

The first step in solving the equation is to isolate the radical term, and the second step is to eliminate the radical by raising both sides to the power of 3. Solving this equation for x initially yields x = 0, x = 2, and x = -2. Checking the solutions shows that it is not a real solution.

The first step in solving the equation (4x)[tex]^{1/3}[/tex] - x = 0 is to isolate the radical term by adding x to both sides of the equation. This gives us

(4x)[tex]^{1/3}[/tex]= x.
The second step is to raise both sides of the equation to the power of 3, which eliminates the radical. This results in 4x = x³.

Solving this equation for x initially yields x = 0, x = 2, and x = -2.
Checking the solutions shows that only x = 2 is a valid solution, as plugging it back into the original equation yields (4*2)[tex]^{1/3}[/tex] - 2 = 0. However, plugging in x = 0 results in a division by zero, and plugging in x = -2 yields a negative number under the radical, which is not a real solution.

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The population of the city after 5 years is approximately 7.94 million.

Assuming that the population of the city grows exponentially, we can use the formula:

P(t) = [tex]P0 * e^(^r^t^)[/tex]

Where:

- P(t) is the population after time t

- P0 is the initial population

- r is the annual growth rate expressed as a decimal

- t is the time elapsed in years

Using the given information:

- P0 = 6.47 million

- r = 2.91% = 0.0291

Let's calculate the population after 1 year:

[tex]P(1) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^1^)[/tex]

= 6.66 million (rounded to two decimal places)

So, the population of the city after one year is approximately 6.66 million.

We can also calculate the population after 5 years:

[tex]P(5) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^5^)[/tex]

= 7.94 million (rounded to two decimal places)

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The value of the test statistic z is approximately -2.12. The Option D is correct.

To test the hypothesis that the mean wrist breadth of men is equal to 9 cm, we will use a one-sample z-test.

The null hypothesis is: H0: µ = 9 cm

The alternative hypothesis is: Ha: µ ≠ 9 cm

We are given a sample of n = 72 men with a sample mean of x = 8.91 cm and a population standard deviation = 0.36 cm.

The test statistic for a one-sample z-test is given by: z = (x - µ) / (o / sqrt(n))

Substituting the given values, we get:

= (8.91 - 9) / (0.36 / sqrt(72))

z = -2.119

At a significance level of a = 0.01, the critical values for a two-tailed test are ±2.576.

Since our test statistic (-2.119) falls outside of this range, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean wrist breadth of men is not equal to 9 cm.

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Note that the Volume of one prism = (1/16) unit³

The given volume of the cube, v₁ = 1 unit cube

The height of the unit cube, h₁ = 1 unit

The length of the unit cube, w₁ = 1 unit

The height of the unit cube, l₁ = 1 unit

The number of identical prism located along the height = 2 identical prism

The number of identical prism located along the width = 2 identical prism

The number of identical prisms located along the length = 4 identical prism

Therefore;

The height of each identical rectangular prism that make up the unit cube, h₂ = h₁/2 = 1/2 unit

Similarly, for each identical rectangular prism, we have;

The width, w₂ = w₁/2 = 1/2 unit

The length, l₂ = l₁/4 = 1/4 unit

The volume of each one of the identical rectangular prism, v₂ = h₂ × w₂ × l₂

⇒  v₂ = 1/2 unit × 1/2 unit × 1/4 unit = 1/16 unit³

So it is correct to state that the volume of one of the identical rectangular prisms = (1/16) unit³.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

The problem involves finding the radius of a cylindrical can that will minimize the cost of the metal to make the can, given that the can must hold one liter of oil.

Specifically, we need to find the radius of the can that will minimize the surface area, and hence the cost, of the metal required to make the can.

To solve the problem, we need to first write an expression for the surface area of the can in terms of its radius, and then differentiate this expression with respect to the radius to find the critical point. We then need to check that the critical point corresponds to a minimum value of the surface area, which will give us the optimal radius for the can. Optimization problems like this one are used in many fields, including engineering, economics, and physics, to find the best course of action given certain constraints and objectives.

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A set of data points could be modeled by a decreasing linear function include the following: C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}.

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the set of data points, we can reasonably infer and logically deduce that it set C is decreasing as follows 50, 42, 33, 25, 16.

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The value of sin(θ) = √15/4

The value of csc(θ) = [tex]\sqrt[4]{\frac{15}{15} }[/tex]

The value of sec(θ) = 4

The value tan(θ) = ±√15

The value of cot(θ) = ±√15/15

We can use the identity sec²(theta) - 1 = tan²(theta) to find the value of tan(theta).

Given sec(θ) = 4, we have:

sec²(θ) = 4² = 16

Then, using the identity:

tan²(θ) = sec²(θ) - 1 = 16 - 1 = 15

Taking the square root of both sides, we get:

tan(θ) = ±√(15)

Since sec(θ) is positive, we know that cos(theta), which is the reciprocal of sec(θ), is also positive. This tells us that θ is in the first or fourth quadrant, where sin(θ) is also positive.

Therefore:

sin(θ) = √(1 - cos²θ))

= √(1 - (1/16))

= √15/16)

= √(15))/4

Using the reciprocal identities, we can find the values of csc(θ) and cot(θ):

csc(θ) = 1/sin(θ)

= 4√(15)

[tex]\sqrt[4]{\frac{15}{15} }[/tex]

cot(θ)

= 1/tan(θ)

= ±√(15)/15

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The probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.

i) To find the probability that the word starts with M, we need to consider the total number of possible arrangements of the letters and the number of arrangements that start with M. The word "MOBILE" has 6 letters, so there are 6! = 720 possible arrangements of the letters. To find the number of arrangements that start with M, we can fix the M in the first position and arrange the remaining 5 letters in the remaining positions, which gives us 5! = 120 arrangements. Therefore, the probability that the word starts with M is:

P(starts with M) = number of arrangements that start with M / total number of arrangements

= 120 / 720

= 1/6

ii) To find the probability that the word starts with M and ends with E, we can fix the M in the first position and the E in the last position, and then arrange the remaining 4 letters in the remaining positions. This gives us 4! = 24 arrangements. Therefore, the probability that the word starts with M and ends with E is:

P(starts with M and ends with E) = number of arrangements that start with M and end with E / total number of arrangements

= 24 / 720

= 1/30

Thus, the probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.

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The point guard has to decide whether to shoot a three-point attempt or pass the ball to another player for a two-point shot. The point guard has a 30% success rate for three-point shots, while the teammate has a 48% success rate for two-point shots.

To determine the best option, we can compare the expected values for each decision. Here's a step-by-step explanation:

1. Calculate the expected value of the point guard's three-point attempt:
  - Success rate: 30% (0.3)
  - Point value: 3
  - Expected value: 0.3 (3 )= 0.9

2. Calculate the expected value of the teammate's two-point shot:
  - Success rate: 48% (0.48)
  - Point value: 2
  - Expected value: 0.48 (2) = 0.96

3. Compare the expected values:
  - Three-point attempt: 0.9
  - Two-point shot: 0.96

Since the expected value of the teammate's two-point shot (0.96) is higher than the point guard's three-point attempt (0.9), it would be a better decision for the point guard to pass the ball to the teammate for a two-point shot.

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The given integral is ∫₁₀ (10/(x-2)) dx.

The given integral is divergent and the answer is "oo".

To see why the integral is divergent, we can use the following limit comparison test:

∫₁₀ (10/(x-2)) dx ~ ∫₁₀ (1/x) dx, as x → 2.

The symbol "~" means "is asymptotic to". We can use this comparison because as x approaches 2 from the right, the function 10/(x-2) approaches positive infinity.

Now, we know that the integral ∫₁₀ (1/x) dx diverges because the improper integral of 1/x from 1 to infinity diverges. Therefore, by the limit comparison test, the original integral is also divergent.

Hence, the given integral ∫₁₀ (10/(x-2)) dx is divergent, and the answer is "oo".

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False because the statement "a 95 percent confidence interval estimate will have a margin of error.

A 95% confidence interval (CI) estimate is a range of values that is likely to contain the true population mean with 95% confidence. The margin of error for a confidence interval depends on the sample size, the variability of the data, and the desired level of confidence.

The general formula for the margin of error of a 95% confidence interval for the population mean is:

Margin of error = (z-value) x (standard deviation /√n)

where z-value is the number of standard deviations corresponding to the desired level of confidence (for a 95% CI, this value is 1.96), standard deviation is the standard deviation of the sample data, and n is the sample size.

The margin of error is usually expressed as a percentage of the sample mean, not the population mean. Moreover, the percentage of the margin of error is not fixed, but it varies depending on the data and the sample size.

Therefore, the statement "a 95 percent confidence interval estimate will have a margin of error that is approximately + or - 47.5 percent of the size of the population mean" is not correct.

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Answer:

x = 4

Step-by-step explanation:

5x = 20  Divide both sides by 5

[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]

x = 4

Helping in the name of Jesus.

The original height of the candle was approximately 26 inches. Rounded to the nearest inch, it will be 27 inches.

Formula for the surface area of a cylinder:

S = 2πrh + 2πr^2

where S is the surface area, r is the radius, and h is the height.

The radius is 2 inches and that the surface area after burning half the candle is 176 square inches. Substitute this values in the equation for surface area:

176 = 2π(2)(h/2) + 2π(2)^2

Simplifying:

176 = 2πh + 8π

168 = 2πh

h = 168/(2π)

h ≈ 26.75

So the original height of the candle was approximately 26 inches. Rounded to the nearest inch, the original height is 27 inches.

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An author can show indirect characterization through a character's thoughts, feelings, actions, and the setting of the story, as well as through their effect on others and their role in the rising action of the plot.

All of these elements can provide insights into a character's personality, motivations, and values, without the author explicitly stating them.

By carefully observing the character's interactions with others, their reactions to events, and the situations in which they find themselves, readers can draw conclusions about who the character is and what drives them.

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An equation that models the situation, where p represents the number of pineapples Chad can purchase and w represents the number of watermelons he can purchase will be; 2.15p + 3.75w = 25.20.

Let's use the given information to create an equation to model this situation. We know that Chad spends a total of $29.68 on the fruit salad, so we can start with;

2.15p + 3.75w + 4.48 = 29.68

This equation represents the total cost of the fruit salad, which includes the cost of the pineapples (2.15p), the cost of the watermelons (3.75w), and the cost of the bag of grapes (4.48).

To make this equation more specific to the problem of finding the number of pineapples and watermelons Chad can purchase, we need to use the variables p and w to represent those quantities. We can set up a second equation based on the information given about the total number of fruits;

p + w + 1 = T

Here, T represents the total number of fruits in the salad, and we add 1 to account for the bag of grapes.

Now we can use substitution to eliminate the variable T. Solving for T in terms of p and w;

T = p + w + 1

Substitute this expression for T into first equation;

2.15p + 3.75w + 4.48 = 29.68

Simplify;

2.15p + 3.75w = 25.20

Therefore, the model of this situation is; 2.15p + 3.75w = 25.20

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Answer:

x ~= 61.0°

Step-by-step explanation:

This is a trig question. The marked angle is unknown so we will use an inverse trig function to find a missing angle. On your calculator you may need to use the 2nd button or shift to get not just "cos" but the inverse cos. It might look like cos with a -1 exponent or "arccos" or "acos"

So the triangle is a right triangle. The angle is next to one of the given sides. "Next to" is called "adjacent" these mean the same thing. One side is adjacent to the angle. The other given side is the hypotenuse.

The trig function that puts together Adjacent and Hypotenuse is cosine.

cos (angle) = adj/hyp

We know the two sides. Fill them in.

cos (angle) = 31/64

We are looking for the angle.

cos x = 31/64

Use the inverse cos to find the angle.

cos^-1 (31/64) = x

This is a calculator activity. Unless your teacher has given you tables of values (this is how it was done before calculators) you have to use a calculator.

x = 61.0284677763

round to the nearest tenth.

x ~= 61.0

If x-2 and x+2 are the factors of the polynomial p(x) = x³− 4mx²− 2nx + 1 = 0, then  the values of m and n are 5/4 and 1/2, respectively.

Given that the factors of the polynomial p(x) = x³  - 4mx²  - 2nx + 1 are x - 2 and x + 2, we can write:

p(x) = (x-2)(x+2)(x-a)

where a is the remaining root of p(x).

Expanding this equation, we get:

p(x) = (x²-4)(x-a) = x³ - (4+a)x² + 4ax - 4a

Comparing the coefficients of this expression with the coefficients of the original polynomial, we get the following system of equations:

4+a = 4m

4a = -2n

-4a = 1

Solving these equations, we get:

a = -1/4, m = 5/4, n = -2a = 1/2

Therefore, the values of m and n are 5/4 and 1/2, respectively.

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The test that should be run on the claim by Proctor & Gamble should be B. z-test of a proportion.

The alternative hypothesis indicates a c. left-tailed test.

The p - value is 0.2665. Unilever does not have sufficient evidence to reject Proctor & Gamble's claim, so A. no.

Conducting a z-test of a proportion is necessary in light of the proportion-based nature (at least half of the bars being 99.44% pure) of the inquiry, instead of means. Proctor & Gamble had asserted that over fifty percent of their bars exhibit 99.44% purity or better; Unilever wishes to investigate this assertion's accuracy.

Consequently, we run our test under null-hypothesis framework that considers fifty percent of bars possessing sufficient purity level and alternative hypothesis positing <50% do. The resultant course of action entails carrying out a left-tailed test.

The p - value. Find the test statistic:

z = ( 0. 4795 - 0.5) / √ ( ( 0.5 x (1 - 0.5) ) / 146)

z = - 0. 6236

z- table shows the p - value is 0. 2665 as a result.

With the p - value being higher than the normal significant level of 0. 05, Unilever should not reject Proctor & Gamble's claim.

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Answer:

48 adult tickets were sold.

Step-by-step explanation:

Let's use algebra to solve this problem:

Let's define:

From the problem statement, we know:

We can use the first equation to solve for x in terms of y:

x = 320 - y

Substituting this expression for x into the second equation, we get:

3(320 - y) + 8y = 1200

Expanding the left side, we get:

960 - 3y + 8y = 1200

Simplifying, we get:

5y = 240

Solving for y, we get:

y = 48

Therefore, 48 adult tickets were sold.

Additional:

To find the number of student tickets sold, we can substitute y=48 into the first equation:

x + 48 = 320

x = 272

Therefore, 272 student tickets were sold.

To rewrite a given expression with lower index 0, which involves changing the subscript of any variable or quantity to 0.

To rewrite a given expression with lower index 0. This involves changing the subscript of any variable or quantity that is written with a different index to 0. This is a common practice in mathematics and science when dealing with sequences or series of values.

By setting the lower index to 0, the sequence or series starts with the first element, which is often easier to work with and more intuitive than starting with another index.

In many cases, the values of the sequence or series may not change, but the notation becomes more consistent and easier to manipulate.

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Answer:

here sorry I'm late

Step-by-step explanation:

The perimeter of the fence for the pasture is 10W + 6.

To find the perimeter of the fence, we need to add up the lengths of all four sides. Let's start by using the given information to find the length and width of the pasture.

Let's say the width of the pasture is W. Then, according to the problem, the length of the pasture is 3 more than 4 times the width, which can be expressed as:

Length = 4W + 3

Now that we have the length and width, we can find the perimeter by adding up all four sides:

Perimeter = 2(Length + Width)

Perimeter = 2(4W + 3 + W)

Perimeter = 2(5W + 3)

Perimeter = 10W + 6

Therefore, the perimeter of the fence is 10W + 6.

Note: The question is incomplete. The complete question probably is: You are building a fence for your pasture. The length is three more than four times the width. What is the perimeter of the fence.

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The measure of each labeled angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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

The rhombus

By corresponding angles, we have

∠3 = 49°

∠1 = 49°

The diagonals of a rhombus bisect each other at right angles

So, we have

∠2 = 90°

Ths sum fo angles in a triangle is 180

So, we have

∠4 = 180 - 90 - 49°

Evaluate

∠4 = 41°

Hence, the measure of the angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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Answer:

11.325 %

Step-by-step explanation:

44.50 . . ... .. 100%

0.445. . . . . . . . .1 %

49.54 . . . . . . . .?%

49.54 : 0.445=111.325 %

111.325-100 = 11.325%

Answer:

Step-by-step explanation:

As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).

A function in mathematics is a relationship between a set of potential outputs and a number of potential inputs, with the feature that each input is associated to only one possible output. It is a principle or set of guidelines that allots a different output value towards each input value. Equations, graphs, and tables are frequently used to depict functions in order to explain how the output changes as the input does. They are employed to express relationships between various quantities, such as the length of time it takes for an automobile to drive a certain distance or the height of an object in relation to its weight. The concept of a function is crucial to many departments of science and math, and it is widely applied in areas like engineering,

given

We can use trigonometry to determine the angle that Luis's backpack creates with the ground.

Consider the backpack's handle to represent the hypotenuse of a right triangle, with the vertical leg being Luis's hand's distance from the ground (3 feet) and the horizontal leg being the backpack's height (3.5 feet).

The angle can be determined using the inverse tangent function (tan-1):

53.13 degrees at tan-1(3.5/3)

As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).

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Answer:

Querido/a [Pen pal's name],

¡Hola! Espero que estés bien. Quería escribirte sobre mis gustos musicales. Me encanta la música de todo tipo, pero mis géneros favoritos son el pop y el rock. Me gusta escuchar artistas como Taylor Swift, Ed Sheeran, Coldplay y Queen. También disfruto escuchar música latina como el reggaetón y la salsa.

Además de escuchar música, también me gusta tocar algunos instrumentos. Toco la guitarra y el piano desde hace algunos años y me encanta aprender nuevas canciones y melodías en ambos instrumentos.

Creo que la música es una forma maravillosa de expresión y me encanta poder hacer música yo mismo.

¿Y tú? ¿Qué tipo de música te gusta? ¿Tocas algún instrumento? Me encantaría saber más sobre tus gustos musicales y si tienes algún hobby musical.

Espero tu respuesta pronto. ¡Cuídate mucho!

Saludos cordiales,

[Your name]

x = 4.56

y = 8.24

z = 12.99

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The main difference is that Sierra needs to create two equal arcs, while Keaton needs to create six equal arcs to form the vertices of their respective shapes.

For Sierra's inscribed square:
1. Draw a circle with a compass.
2. Mark a point on the circle as one vertex of the square.
3. Draw a diameter passing through the marked point.
4. Use the compass to create two equal arcs, one on each end of the diameter, intersecting the circle.
5. Connect the intersection points to create the square.

For Keaton's inscribed regular hexagon:
1. Draw a circle with a compass.
2. Mark a point on the circle as one vertex of the hexagon.
3. Use the compass to create six equal arcs around the circle, each arc intersecting the end of the previous arc.
4. Connect the intersection points to create the hexagon.

The main difference is that Sierra needs to create two equal arcs, while Keaton needs to create six equal arcs to form the vertices of their respective shapes.

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The number of people who liked both milk and curd is 500.

Here's how you can calculate it:

- The number of people who liked only milk is 720.

- The number of people who liked only curd is 880.

- The number of people who did not like either milk or curd is 400.

- Let x be the number of people who liked both milk and curd.

- We can use the formula: Total = Group 1 + Group 2 - Both + Neither.

- Substituting the values, we get: 2500 = 720 + 880 - x + 400.

- Solving for x, we get: x = 500.

- Therefore, 500 people liked both milk and curd.

The number of people who liked at least one of the drinks is 2100.

Here's how you can calculate it:

- The number of people who liked only milk is 720.

- The number of people who liked only curd is 880.

- The number of people who liked both milk and curd is 500.

- Therefore, the total number of people who liked at least one of the drink is: 720 + 880 + 500 = 2100.

Answer:

liked both milks: 900

liked at least 1: 2100

Step-by-step explanation:

there are 2500 people

ONLY LIKE 1 type- 1600 people

400 don't like milk

2500-1600=900

2500-400=2100