PLEASE HELP ASAP!!! I'll MARK BRAINLIEST!!
Farmer Naxvip wanted to sell some hopts and totts at the market. She planned to charge $3 per hopt and $7 per tott. She expected to make at least $84. She expected to sell at most 24 units.
Write a system of statements, in standard form, modeling the relationships between amounts of hopts (x) and amount of totts (y).

Simone will need approximately 429.4 square feet of glass to cover the entire pyramid.

Calculating the surface area of a square pyramid

The surface area of a square pyramid can be calculated by using the following formula: S = l² + 2lw

where, S = surface areal = length of one side of the bases = 10 feet

w = slant height of the pyramid

We need to find the slant height of the pyramid to calculate the surface area of the pyramid.

The slant height of the square pyramid can be calculated using the Pythagorean theorem. We can draw a triangle by joining the midpoint of one of the sides of the base and the apex of the pyramid.

This will divide the pyramid into two right triangles. Using the Pythagorean theorem, we have; l² + h² = sl²

where, h = height of the pyramid = 14 feet

l = half the length of one of the sides of the base = 5 feet

Substituting the given values into the above formula, we get;

5² + 14² = s²

25 + 196 = s²

221 = s²s = √221 ≈ 14.87 feet

Now that we have the slant height of the pyramid, we can substitute the values into the surface area formula we had earlier: S = l² + 2lw

S = 10² + 2(10)(14.87)S ≈ 429.4 square feet

Therefore, Simone will need approximately 429.4 square feet of glass to cover the entire pyramid.

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cos^2(x) - cos^4(x)

sin^2 (x) cos^2 (x) can be written as sin^2 (x) cos^2 (x) = (1-cos^2(x)) cos^2(x)Expanding (1-cos^2(x)) cos^2(x) gives - cos^4(x) + cos^2(x)Therefore, sin^2 (x) cos^2 (x) in expanded form, with no powers, parentheses or products is cos^2(x) - cos^4(x).

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Function describing following curve in which a circle of radius 6 centered at (4,3,0) that lies in the plane y = 3 is [tex]r(t) = (6 cos t +4,6 sin t +3,0)[/tex], for Osts 21. Therefore the correct answer is Option c.


A circle of radius 6 centered at (4,3,0) that lies in the plane y = 3 can be described by the following function:
[tex]r(t) = (6 cost +4,6 sint +3,0), for Osts 21[/tex]
This function describes the position of a point on the circle at any given time t.

The x and z coordinates are determined by the cosine and sine function, respectively, with a radius of 6. The y coordinate is constant at 3, since the circle lies in the plane y = 3. The center of the circle is shifted by adding 4 to the x coordinate and 3 to the y coordinate.

Therefore, the correct answer is Option c. [tex]r(t) = (6 cost +4,6 sint +3,0),[/tex] for Osts 21.

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The acceleration of a bus his speech changes from 126M/S to 3097 m/s over a period of three seconds is 990. 3 m/s^2

Acceleration is can be defined as the rate of change of the velocity of an object with respect to time.

It is also defined as the rate at which velocity changes with time, that is, in both speed and direction.

Accelerations are vector quantities because they are known to have both magnitude and direction.

The orientation of an object's acceleration is determined by the configuration of the net force acting on that object.

The formula for acceleration is given as;

Acceleration = change in velocity/time

Substitute the values

Acceleration = 3097 - 126 (m/s)/3 s

Divide the values

Acceleration = 990. 3 m/s^2

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the ordered pairs of three points that could each be the other endpoint of the line segment are (10,-7) or (-14,-7) and (-2,5) or (-2,-19)

Define Line segment

A line segment in geometry contains two different points on it that called its boundaries. A line segment is sometimes called as a section of a line that links two places.

Given

One end point=(-2,-7)

Length of the line segment=12unit

Line segment is horizontal

Ordered pair that will be other end of the line segment=(-2+12,-7) or(-2-12,-7)

=(10,-7) or (-14,-7)

Line segment is Vertical

Ordered pair that will be other end of the line segment=(-2,-7+12) or(-2,-7-12)

=(-2,5) or (-2,-19)

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The researcher is not conducting non-random sampling.

Random sampling is a sampling technique in which every individual or element of the population of interest has an equal opportunity of being selected for the sample. Each member of the population has an equal chance of being selected for the sample. Random sampling helps to ensure that the sample is representative of the population.

Non-random sampling, on the other hand, is a sampling technique in which the individuals or elements of the population of interest are not randomly selected. In other words, not every member of the population has an equal chance of being selected. This sampling method is biased and can lead to an unrepresentative sample.

The researcher is not conducting a non-random sampling technique because she is observing every child in the population of interest. The population of interest, in this case, is the children on the playground.

The researcher is not conducting non-random sampling because random sampling is a sampling technique in which every individual or element of the population of interest has an equal opportunity of being selected for the sample.

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Answer:

x = -12 and x = 12.

Step-by-step explanation:

To solve for x, we need to take the square root of both sides of the equation:

x² = 144

√(x²) = √144

since sqaure root gives both positive and neagtive value, so

x = ±12

So the solutions for x are x = -12 and x = 12.

a) The probability that neither fire engine is available when needed is 0.0016. b) The probability that a fire engine is available when needed is 0.9984.

The probability of an event occurring is the likelihood that it will happen. In this case, we are looking at the probability of a specific fire engine being available when needed.

The probability that neither fire engine is available when needed can be found by multiplying the probabilities of each fire engine not being available. The probability of a specific fire engine not being available is [tex]1 - 0.96 = 0.04[/tex]. So the probability that neither is available is [tex]0.04 * 0.04 = 0.0016.[/tex]

The probability that a fire engine is available when needed can be found by subtracting the probability that neither is available from 1. So the probability that a fire engine is available when needed is[tex]1 - 0.0016 = 0.9984.[/tex]

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The interquartile range for the masses of adult men is 6.75 kg (1 decimal place).

The probability that an adult man, chosen at random, will have a mass greater than 77.5 kg is 0.4 (4 decimal places). The probability that an adult man, chosen at random, will have a mass between 76.6 kg and 83.5 kg is 0.2366 (4 decimal places). 62% of adult men have a mass greater than 78.45 kg (1 decimal place).

Let X be the mass of an adult man, then X ~ N(75, 5^2).

P(X > 77.5) = P(Z > (77.5 - 75) / 5) where Z is the standard normal random variable.

P(Z > 0.5) = 1 - P(Z ≤ 0.5) ≈ 0.3085

Therefore, the probability that an adult man, chosen at random, will have a mass greater than 77.5 kg is approximately 0.3085.

P(76.6 < X < 83.5) = P[(76.6 - 75) / 5 < Z < (83.5 - 75) / 5]

P(1.32 < Z < 1.7) = P(Z < 1.7) - P(Z < 1.32) ≈ 0.0932

Therefore, the probability that an adult man, chosen at random, will have a mass between 76.6 kg and 83.5 kg is approximately 0.0932.

Let p be the proportion of adult men with a mass greater than some value x, then we want to find x such that p = 0.62.

By standardizing and using the standard normal distribution table, we get:

P(Z > (x - 75) / 5) = 0.62

P(Z < (75 - x) / 5) = 0.38

Using the standard normal distribution table, we find that Z ≈ 0.2533

Therefore, (x - 75) / 5 ≈ 0.2533

x ≈ 76.267 kg (rounded to 1 decimal place)

Therefore, 62% of adult men have a mass greater than 76.3 kg.

The interquartile range (IQR) is a measure of spread and is defined as the difference between the 75th percentile and the 25th percentile of the distribution. For a normal distribution, the IQR is approximately 1.35 times the standard deviation.

IQR ≈ 1.35 * 5 ≈ 6.75 kg (rounded to 1 decimal place)

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Answer:

The missing measures in triangle STU are:

SU = 14, ST = (2/3)TU, TU = (4/3)ST, m∠S = 70 degrees, m∠T = 64 degrees, m∠U = 46 degrees.

Step-by-step explanation:

Since triangles PQR and STU are similar, their corresponding sides are in proportion, and their corresponding angles are congruent. We can use this information to find the missing measures in triangle STU:

Since side PQ corresponds to side ST, we have:

ST/PQ = TU/PR

Substituting the given values, we get:

ST/14 = TU/21

Cross-multiplying, we get:

ST × 21 = 14 × TU

ST = (14/21)TU

Simplifying, we get:

ST = (2/3)TU

Since side QR corresponds to side TU, we have:

TU/QR = ST/RP

Substituting the given values, we get:

TU/28 = ST/21

Cross-multiplying, we get:

TU × 21 = 28 × ST

TU = (28/21)ST

Simplifying, we get:

TU = (4/3)ST

Since angle P corresponds to angle S, we have:

m∠S = m∠P = 70 degrees

Since angle R corresponds to angle U, we have:

m∠U = m∠R = 46 degrees

To find m∠T, we can use the fact that the angles in a triangle add up to 180 degrees:

m∠S + m∠T + m∠U = 180

Substituting the given values, we get:

70 + m∠T + 46 = 180

Simplifying, we get:

m∠T = 64 degrees

To find SU, we can use the fact that the corresponding sides are in proportion:

SU/PR = ST/PQ

Substituting the given values, we get:

SU/21 = (2/3)

Cross-multiplying, we get:

SU = 14

Therefore, the missing measures in triangle STU are:

SU = 14

ST = (2/3)TU

TU = (4/3)ST

m∠S = 70 degrees

m∠T = 64 degrees

m∠U = 46 degrees.

Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]

The solution to the equation √(-2x - 5) - 4 = x are x = -7 and x = -3

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

√(-2x - 5) - 4 = x

So, we have

-2x - 5 = x + 4

Take the square of both sides

so, we have the following representation

x² + 8x + 16 = -2x - 5

Evalyate the like terms

x² + 10x + 21 = 0

When factorized, we have

(x + 7)(x + 3) = 0

This means that

x = -7 and x = -3

Hence, the solutions are x = -7 and x = -3

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domain of the function is (-∞, ∞)

When answering questions on the Brainly platform, it is important to always be factually accurate, professional, and friendly. In addition, you should be concise and provide a step-by-step explanation in your answer. Irrelevant parts of the question should be ignored, and the following terms should be used in your answer.To solve the inequality 72 - 72 > 1 X-1 X, we need to simplify the inequality as shown below:72 - 72 > 1 X-1 X0 > X - 1Since we want to get X alone on one side of the inequality, we need to add 1 to both sides:0 + 1 > X - 1 + 1X > 0Thus, the solution to the inequality 72 - 72 > 1 X-1 X is (0, ∞).To find all values of x for which the graph of f(x) = x² flies above the graph of g(x) = 2x + 48, we need to solve the inequality:f(x) > g(x)x² > 2x + 48We can rearrange this inequality as follows:x² - 2x > 48Now, we need to factor the left-hand side of the inequality:x(x - 2) > 48The inequality will be satisfied if x > 0 and x - 2 > 0 (i.e. x > 2), so the solution to the inequality is x > 2.The domain of the given function f(x) = 72 + x - x² is all real numbers, since there are no restrictions on the input value x. Therefore, the domain of the function is (-∞, ∞).

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Option (a) [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.

A linear function in mathematics is one that has either one or two variables but no exponents. It is a function with a straight line as its graph.

A straight line on the coordinate plane is described by a linear function.

Option (a) [tex]y=\frac{3x}{2} -5[/tex] satisfy with all point as below,

If we take, x = 0, we get y = -5

If we take, x = 2, we get y = -2

If we take, x = 4, we get y = 1

If we take, x = 6, we get y = 4

If we take, x = 8, we get y = 7

So, here we see all the value are match according to the graph.

Therefore, [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.

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Answer:

x= -3/5+4y/5

x= -3/5 or -0.6 in decimal form

Step-by-step explanation:

I hope this helps :)

The given polynomial is x⁵ + (1/5)x³ - x⁵ - x + 5 + x³, Combining the like terms, we get: 2x⁵ + (6/5)x³ - x + 5 This is the polynomial in standard form.

To rewrite the given polynomial in standard form, we first need to combine the like terms. The polynomial can be simplified by adding the coefficients of the same degree terms. After combining like terms, we get -2x⁵ + (6/5)x³ - x + 5. This is the standard form of the polynomial, where the terms are arranged in descending order of degree, and each term has a coefficient multiplied by a power of x. In this case, the highest degree term is -2x⁵, followed by (6/5)x³, -x, and finally, the constant term 5.

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Complete Question

Rewrite the following polynomial in standard form. -x⁵ + (1/5)x³ - x⁵ - x + 5 + x³

The correct situation which can be modeled with a periodic function is,

⇒ The height of a pebble stuck in the tread of a tire.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, The situations that can be modeled with a periodic function is that,

The height of a pebble stuck in the tread of a tire.

And, A function is said to be periodic if it gives same value after a same period. And functions which are not periodic are called aperiodic.

Thus, The correct situation which can be modeled with a periodic function is,

⇒ The height of a pebble stuck in the tread of a tire.

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The equatiοn οf the circle is [tex](x + 5)^2 + (y + 6)^2 = 25[/tex].

The standard fοrm equatiοn οf a circle with radius "r" and center (a, b) is:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

In this case, the center is (-5, -6) and the radius is 5. Sο, we can substitute these values intο the standard fοrm equatiοn and get:

[tex](x - (-5))^2 + (y - (-6))^2 = 5^2[/tex]

Simplifying the equatiοn, we get:

[tex](x + 5)^2 + (y + 6)^2 = 25[/tex]

Therefοre, the equatiοn οf the circle is [tex](x + 5)^2 + (y + 6)^2 = 25.[/tex]

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Since opposite angles of a parallelogram are equal, angle A = angle C and angle B = angle D where x is 35.

What is parallelogram?

A parallelogram is a four-sided flat shape in which opposite sides are parallel and have the same length. It is a type of quadrilateral, which means it has four sides.

The opposite angles of a parallelogram are also equal, which means that if angle A is equal to angle C, then angle B is equal to angle D. Moreover, the adjacent angles of a parallelogram are supplementary, which means that if angle A and angle B are adjacent angles, then angle A + angle B = 180 degrees.

According to the question:
Since AB = CD and angle A is 60 degrees, it means that opposite sides AB and CD are parallel and have the same length. Therefore, the figure ABCD is a parallelogram.

To determine the value of angle B, we can use the fact that the opposite angles in a parallelogram are equal. That is, angle B = angle D.

Since angle A + angle B + angle C + angle D = 360 degrees for any quadrilateral, we can write:

angle A + angle B + angle C + angle D = 60 + (3x+15) + angle C + angle D = 360

Simplifying this equation, we get:

4x + 75 + angle C + angle D = 360

angle C + angle D = 360 - 4x - 75 = 285 - 4x

Since angle B = angle D, we have:

angle B + angle D = 2 angle D = (3x+15)

Therefore, we can solve for angle D:

2 angle D = (3x+15)

angle D = (3x+15)/2

Now, we can substitute this into the equation for angle C + angle D:

angle C + (3x+15)/2 = 285 - 4x

Multiplying both sides by 2, we get:

2 angle C + 3x + 15 = 570 - 8x

Simplifying and solving for angle C, we get:

2 angle C = 555 - 11x

angle C = (555 - 11x)/2

Therefore, the angles of the parallelogram ABCD are:

angle A = 60 degrees

angle B = (3x+15) degrees

angle C = (555 - 11x)/2 degrees

angle D = (3x+15)/2 degrees

Note that since opposite angles of a parallelogram are equal, angle A = angle C and angle B = angle D.


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Q. Determine the figure given below which has Angle A= 60 and Angle B=(3x+15)

Answer:

Assuming you're referring to a product of two numbers, if one number is decreased by a factor of two and the other is decreased by a factor of eight, the overall effect on the product will depend on the relative values of the two numbers.

Let's say the product is given by P = a * b, where a and b are the two numbers. If we decrease one number by a factor of two, we can write it as 0.5a. Similarly, if we decrease the other number by a factor of eight, we can write it as 0.125b. So the new product, P', can be written as:

P' = (0.5a) * (0.125b)

= 0.0625ab

So the new product will be 1/16th (0.0625) of the original product. This means that the product will be decreased by a factor of 16.

In other words, if you decrease one number by a factor of two and the other by a factor of eight, the resulting product will be 16 times smaller than the original product.

The 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.

What is statistics ?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to gather, describe, and draw inferences from data, which can be used to make decisions, predictions, or conclusions about a population or a phenomenon.

To find the 5 number summary, we need to find the minimum, maximum, and the three quartiles of the given dataset:

The minimum value is 40.

To find the quartiles, we first need to sort the data in ascending order:

40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69

The median (quartile 2) is the middle value of the dataset, which is 55.

Quartile 1 (Q1) is the median of the lower half of the dataset, which includes the values 40, 42, 46, 48, and 51. The median of this lower half is (46+48)/2 = 47.

Quartile 3 (Q3) is the median of the upper half of the dataset, which includes the values 58, 66, 67, 68, and 69. The median of this upper half is (66+67)/2 = 66.5.

The maximum value is 69.

Therefore, the 5 number summary for the given dataset is:

Minimum: 40

Q1: 47

Median (Q2): 55

Q3: 66.5

Maximum: 69

Therefore, the 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.

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The average cost of a letter was 7.11.

The average cost of a letter can be calculated using the following formula:

Average cost per letter = Total Cost / Number of Letters

In this instance, the average cost of a letter is 7.11 (rounded to the nearest cent):

Average cost per letter = 3,455 / 485

Average cost per letter = 7.11

To calculate the average cost of a letter, we used a simple formula. The total cost was divided by the total number of letters to get the average cost per letter. This amount was then rounded to the nearest cent to get the final answer of 7.11.

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Hence, in answering the stated question, we may say that We may now trigonometry compare the two sides and observe that they are equal, demonstrating the provided identity.

Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. Owing to the application of geometry in astronomical research, the topic originally originated in the Hellenistic era, beginning in the third century BC. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.

The first stage in Rita's evidence would be determined by the method she uses to verify her identity. Nonetheless, one alternative method to begin the proof is to use the trigonometric identities:

sin(-θ) = -sin(θ) and cos(-θ) = cos(θ)

Applying these identities, we can rewrite the given equation's left side as:

sin(-) cos(-) = cos() (-sin())

After that, we may employ the following identity:

tan( ) = sin( )/cos( )

to rewrite the following equation's right side as:

-1 tan() = -sin()/cos()

We may now compare the two sides and observe that they are equal, demonstrating the provided identity.

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When 25 percent of doctors make less than $180k and 25% make more than $320k, a. Approximately 13.14% of physicians earn less than $200,000. and b. Approximately 7.75% of physicians earn between $280,000 and $320,000.

a. The fraction of physicians who earn less than $200,000 can be estimated using the given information as follows:

Let's denote the mean salary of physicians in this specialty by μ and the standard deviation by σ. Since the salaries are approximately normally distributed, we can use the properties of the standard normal distribution to solve this problem.

We know that 25% of the physicians earn less than $180,000, which means that their z-score (number of standard deviations from the mean) is: z = (180,000 - μ) / σ

Using a calculator, we can find the z-score corresponding to the 25th percentile, which is approximately -0.674. Therefore: -0.674 = (180,000 - μ) / σ

Similarly, we know that 75% of the physicians earn more than $180,000, which means that their z-score is: z = (320,000 - μ) / σ

Using the calculator, we can find the z-score corresponding to the 75th percentile, which is approximately 0.674. Therefore: 0.674 = (320,000 - μ) / σ

Solving these two equations simultaneously, we can find μ and σ:

μ = $250,000

σ = $53,333

Now, to find the fraction of physicians who earn less than $200,000, we need to calculate the z-score corresponding to this salary: z = (200,000 - μ) / σ = -1.125

Using the calculator, we can find that the fraction of physicians who earn less than $200,000 is approximately 0.1314.

b. The fraction of physicians who earn between $280,000 and $320,000 can be estimated using the same method as above. We need to calculate the z-scores corresponding to these salaries:

z1 = (280,000 - μ) / σ = 0.596

z2 = (320,000 - μ) / σ = 0.674

Using the calculator, we can find the area between these two z-scores, which represents the fraction of physicians who earn between $280,000 and $320,000. This area is approximately 0.0775.

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Answer:

total cost equation = ( 9+x) times 4 = 724. Total,price of a ticket is 162$

Step-by-step explanation:

Since insurance for each ticket costs 19$ and the family bought four and the ticket itself costs x, the costs of the four tickets is (19+x) times 4. If thr total cost is 724 then we can take 19 times4 and subtract that from it because 19times 4 + x times 4 is the same as (19+x) times 4. From this we fet 648. Now we have x4 or x times 4 = 648 leftover, so divided 648 by 4 to get one x out of it since it is made up of four x. You get 162 from this, so the price of a ticket without insurance is 162$

In terms of i the imaginary root of √−13 is √13i as we know that √(-1) is represented by 'i'.

In mathematics, an imaginary root (also known as a complex root) is a root of a polynomial equation that involves the imaginary unit 'i'. The imaginary unit is defined as the square root of -1, and it is represented by the letter 'i'. A polynomial equation can have either real roots, imaginary roots, or both.

To write √(-13) in terms of 'i', we can start by expressing it as:

√(-1) x √(13) x √(1)

We know that √(-1) is represented by 'i', so we can substitute it in the expression:

'i' x √(13) x √(1)

Since √(1) is equal to 1, we can remove it from the expression:

'i' x √(13)

Therefore, the answer for √(-13) in terms of 'i' is 'i'√(13), which is the simplified form.

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The question is -

Write in terms of i. Simplify your answer as much as possible √−13.

There are 286 different ways to select 3 players from a 13-player baseball team to visit schools to support a summer reading program.

This is a combination problem, where we want to select 3 players from a team of 13 players, without regard to order.

The number of ways to select r items from a set of n distinct items is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items and r is the number of items to be selected.

In this case, we want to select 3 players from a team of 13 players, so we can use the combination formula:

C(13, 3) = 13! / (3!(13-3)!) = (13 x 12 x 11) / (3 x 2 x 1) = 286

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The side of the right triangle can be found as follows:

b = 4√2 units

d = 7√3 / 2 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's use trigonometric ratios to find the side of the right triangle as follows;

Let's find b as follows:

sin 45 = opposite / hypotenuse

sin 45° = b / 8

cross multiply

b = 8 sin 45

b = 8 × √2 / 2

b = 8√2 / 2

b = 4√2 units

Let's find d as follows:

sin 60° = d / 7

cross multiply

d = 7 sin 60

d = 7 × √3 / 2

d = 7√3 / 2 units

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If a restaurant makes smoothies in batches of 6.4 litres. the maximum number of batches of smoothie that can be made from 42 litres of lime juice is 50.

If the ratio of ice cream to mixed fruit juice is 5:3, then,

Fraction of the smoothie that is ice cream =5/(5+3) = 5/8

Fraction that is mixed fruit juice =  3/(5+3) = 3/8

If 35% of the mixed fruit juice is lime juice, then,

Fraction of the mixed fruit juice that is lime juice=  35/100 = 7/20

Fraction of the smoothie that is lime juice = (3/8) x (7/20) = 21/160

To make one batch of smoothie, we need 6.4 litres of mixed fruit juice, of which (21/160) x 6.4 = 0.84 litres is lime juice.

To make 42 litres of lime juice, we nee:

42/0.84 = 50 batches of smoothie.

Therefore, the maximum number of batches of smoothie that can be made from 42 litres of lime juice is 50.

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