a school is organizing a weekend trip to a nature preserve. for each student, there is a $50 charge, which covers food and lodging. there is also a $25 charge per student for the bus. the school must also pay a $15 cleaning fee for the bus. if the total cost of the weekend is $3,765, how many students will be going on the trip?

Answer:

n = 10

Step-by-step explanation:

2x = y

2(n)=20

n = 20/2

n = 10

The solution for the given expression b = √ -1 -2b is b = -1.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax^2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x^2 (a not equal 0) for an equation to be a quadratic equation.

The expression is:

b = √ -1 -2b

Take square on both sides of the equation. The square negates the square root and we have the following expression:

b² = - 1 - 2b

b² + 2b + 1 = 0

The quadratic formula is given as:

x = - b ± √b² - 4ac ÷ 2a

Substituting the value of b = 2, a = 1 and c = 1:

x = -2 ± √4 - 4(1)(1) ÷ 2(1)

x = -2 ÷ 2

x = -1

Hence, the solution for the given expression b = √ -1 -2b is b = -1.

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A graph of the system of linear inequalities is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given system of linear inequalities y > -x + 5 and y ≤ 3x -4 as shown on the graph attached below. Based on the graph (see attachment), we can logically deduce that the solution to the given inequality is the shaded region, with a point of intersection at the ordered pair (2.25, 2.75) in quadrant I.

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The solution is, A. m + n, must also be even .

A number that is divisible by 2 and generates a remainder of 0 is called an even number. Examples of even numbers are 2, 4, 6, 8, 10, etc. For example, assume you have ten chocolates. These chocolates may be divided into two groups, each having five chocolates. So, ten is an even number.

here, we have,

given that,

If 3(m + n) is even

so, we get,

3(m + n) is divisible by 2.

i.e. m+n is must ne divisible by 2.

Hence, The solution is,  A. m + n, must also be even .

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The statement "generally, parametric estimating requires less information and time than analogous estimating." is False.

Parametric estimating and analogous estimating are two different methods used to estimate the cost of a project or the value of a parameter.

Parametric estimating uses statistical data and mathematical models to make predictions about the cost or value of a project. This method requires specific data and information about the project, such as historical data, vendor quotes, and cost of similar projects.

The advantage of parametric estimating is that it can be more accurate and precise than other methods, but it can also be time-consuming to gather the necessary data and perform the calculations. Analogous estimating, uses information from similar projects to make predictions about the cost or value of a project.

This method requires less data and information than parametric estimating, but it can be less accurate and precise. Analogous estimating is often used as a quick and rough estimate, or when there is not enough data available to use parametric estimating.

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Answer:

The radius can be shown in 2 different forms

Fraction Form

[tex]r=\sqrt[3]{\frac{27}{\pi}}[/tex]

Decimal Form

[tex]r=2.05[/tex]

Step-by-step explanation:

The formula for the volume of the sphere is

[tex]V=\frac{4}{3}\pi r^3[/tex]

We are given the volume and we are asked to find the radius.

We can solve for [tex]r[/tex] in the equation for volume to evaluate the radius.

[tex]\frac{4}{3}\pi r^3=V[/tex]

Move [tex]\pi[/tex] and [tex]r^3[/tex] into the numerator.

[tex]\frac{4\pi r^3}{3}=V[/tex]

Divide both sides of the equation by 3.

[tex]4\pi r^3=3V[/tex]

Divide both sides of the equation by [tex]4\pi[/tex].

[tex]r^3=\frac{3V}{4\pi }[/tex]

Take the cube root of both sides to eliminate the exponent.

[tex]r=\sqrt[3]{\frac{3V}{4\pi }}[/tex]

Numerical Evaluation

Now we have an equation to evaluate [tex]r[/tex].

Given [tex]V=36[/tex]

Insert 36 in for [tex]V[/tex].

[tex]r=\sqrt[3]{\frac{3*36}{4\pi }}[/tex]

Factor 4 out of [tex]3*36[/tex] and add parenthesis.

[tex]r=\sqrt[3]{\frac{4(3*9)}{4(\pi) }}[/tex]

Cancel the common factor of 4.

[tex]r=\sqrt[3]{\frac{3*9}{\pi}}[/tex]

Multiply [tex]3*9[/tex].

[tex]r=\sqrt[3]{\frac{27}{\pi}}[/tex]

The answer can be shown in multiple forms.

Fraction Form

[tex]r=\sqrt[3]{\frac{27}{\pi}}[/tex]

Decimal Form

[tex]r=2.05[/tex]

The standard deviation changes as the  three digits 5, 5, and 20 add up to 30 and it would decrease.

Given that,

The three digits 5, 5, and 20 add up to 30 and have a mean of 10 as a result. To calculate the standard deviation, use software. utilize the sample standard deviation function. Give a two-decimal place precision to your response. Assume the data set now included a fourth value, 10, which is equal to the mean.

To find : How would the standard deviation change?

S = √∑(Xi - X)²/n-1

= √ (5-10)² + (5-10)² +(20-10)² / 2

= √ 25+25+ 100 / 2

= √ 75

= 8.66

S = √∑(Xi - X)²/n-1

= √ (5-10)² + (5-10)² +(20-10)² + (10-10)² / 3

= 7.07

So, The standard deviation would drop when the three digits 5, 5, and 20 added up to 30.

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Answer:

Hi Saba!

Yes, it is possible that the ACT Math Test includes questions on the graph of polar coordinates. It is always a good idea to be familiar with all the topics covered on the ACT Math Test, so studying polar coordinates might be beneficial. However, the best way to determine what you need to study for the test is to look at the official ACT test prep materials and practice tests, which will give you a good idea of what types of questions are asked.

The probability that the pitcher will throw fewer than 4 pitches to a batter is 0.35

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favourable outcomes / total number of outcomes

This probability distribution is shown below:

Pitch                   1            2        3          4         5

Frequency         15         20      40        15        10

Probability         0.15     0.2      0.4      0.15      0.1

Thus the probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 4)

X  is the number of pitches thrown.

Therefore:

P(X < 4) = P(X = 1) or P(X = 2)

The additive rule of the probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.

P(X < 4) = P(X = 1) or

P(X = 2) = P(X = 1) + P(X = 2)

= 0.15 + 0.2

= 0.35

Hence, The probability that the pitcher will throw fewer than 4 pitches to a batter is 0.35

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The probability that less than four colours will be chosen when the spinner is spun once would be = 0.5. That is option D.

Probability is defined as the expression that show the possible outcome of an event which is likely or unlikely to occur.

The coloured spinner is divided into = 8 colour sections

The number of blue section = 3

The number of red = 1

The number of purple section = 2

The number yellow section = 2

Therefore the probability to select 4 colour when spun once = 4/8 = 1/2 = 0.5

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If it is assumed that all 52 5 poker hands are equally likely, the probability of being dealt a flush is 0.001981

Flush means all 5 cards are of the same suit.

Now, we need to select one suit out of 4 which can be done in ⁴C₁ ways.

Now, when the suit is selected, we have to select 5 cards from that specific suit. This can be done in ¹³C₅ ways

In the game of poker, there are ⁵²C₅ possible hands.

So, the probability of a flush is given by:

              P = (⁴C₁ × ¹³C₅)/⁵²C₅

              P = (4 × 1287)/2598960

              P = 5148/2598960

              P = 0.001981 or 1.981 × 10⁻³ or 0.1981 %

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Check the picture below.

The trigonometric form of the complex number is,  

-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.

here, we have,

the complex number which we get from the given graph is,

-6+ i (-6)

so, a = -6

    b = -6

i.e. z = √a^2+b^2

        =6√2

so, we know,

The trigonometric form of a complex number:

z = |z| (cosα +i sinα)

now, cosα = a/|z|

                 = -1/√2

and, sinα = b/|z|

              = -1/√2

so, solving we get,

α = 5pi/4

i.e. -6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

Hence, The trigonometric form of the complex number is,  

-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

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The inequality of the statement is x > 16

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

a city received more than 16 in of snow

In inequality, more than mean >

So, we have the following representation

Snow > 16

Represent the snow with x

So, we have the following representation

x > 16

Hence, the inequality is x > 16

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The student that has the half piece of paper with the greater area is blake.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Given;

Tyler and Blake have rectangular pieces of paper with the same length and same width

Tyler cuts his paper horizontally through the middle

Blake cuts his paper along a diagonal

Now,

Let the length and breadth be y

Tylers half area= y*y/2=y^2/2

Blakes half area=1/2* [tex]\sqrt{3}[/tex]y*[tex]\sqrt{3}[/tex]y/2

=3y^2/4

Therefore, blakes piece of paper has more area.

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An outlier in a data set can significantly affect the value of the mean but not the median because the mean is calculated by adding up all the values and dividing by the total number of values, while the median is the middle value of a set of data when it is arranged in numerical order. Outliers can greatly influence the mean because they can greatly increase or decrease the sum of all the values, which changes the average. However, outliers do not significantly affect the median because the median only depends on the middle value of the data set, and not the total sum of all the values.

Answer: 14 cupcakes

Step-by-step explanation:

42 divided by 3

The x-intercepts or roots of the parabola are the locations where a parabola contacts the x-axis. These are the solutions to the parabola equation where the y-value is equal to zero.

A parabola is an open curve formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements. This is known as the standard form of a quadratic function. A parabola is the graph of a quadratic function that is a U-shaped curve. A parabola is the graph of the equation y=x2 illustrated below. Parabolas are classified into three categories. There are three types of forms: vertex form, standard form, and intercept form. Each type offers a unique important characteristic for the graph. The three major forms from which we graph parabolas are known as standard form, intercept form, and vertex form. Each form will provide you with somewhat different information as well as its own set of pros and downsides.

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The decimal system is a positional notation system, which means that the value of a digit in a number depends on its position in the number.

In the decimal system, each digit can take on one of ten possible values (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9), and the value of a number is determined by multiplying each digit by its corresponding power of ten and then summing up the products.

For example, the number 123 can be written as [tex]1 x 10^2 + 2 x 10^1 + 3 x 10^0[/tex], where the exponent on the 10 indicates the position of the digit in the number. The left-most digit (1) is in the hundreds place, the next digit (2) is in the tens place, and the right-most digit (3) is in the ones place.

This positional notation system allows us to easily compare numbers by starting at the left-most non-zero place, because the value of each digit is determined by its position relative to the other digits in the number. The left-most digit represents the largest power of 10, and thus has the greatest impact on the overall value of the number. By comparing the left-most non-zero digits of two numbers, we can quickly determine which number is larger. If the left-most non-zero digits are the same, we can move on to the next digit to the right and continue the comparison until we find a difference.

This is why we use the left-to-right ordering of digits to compare numbers in the decimal system. It allows us to quickly determine the relative size of numbers, even when dealing with large or complex numbers.

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The points will  meet x when it is folded are C or E

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given that,

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet C or E

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Answer:

Below

Step-by-step explanation:

7/4 = 14/8 hr

14/8  + 27/8  = (14+27) / 8 = 41/8 = 5  1/8   hr

Rounding to four decimal places, the standard divisor is 3.4792.

The standard divisor can be calculated as follows:

Standard Divisor = Total number of schools / Total number of upgrades

Total number of schools = 104 + 33 + 26 + 4 = 167

Total number of upgrades = 48

Standard Divisor = 167 / 48 = 3.4792

Rounding to four decimal places, the standard divisor is 3.4792.

The standard divisor is a term used in resource allocation or distribution problems, where a set number of resources (e.g., funding, personnel, supplies, etc.) has to be divided among a number of recipient entities (e.g., schools, departments, regions, etc.).

The standard divisor is a number that represents the average allocation of resources per recipient entity, calculated as the total amount of resources divided by the number of recipient entities.

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Answer: A teapot.

Step-by-step explanation:

After 15 hours there will be 1.875 grams of the radioactive tellurium.

We know that the half-life of a radioactive kind of tellurium is 3 hours.

This means that for any quantity A of that radioinuclei, after 3 hours we will have half of that amount.

Then we can write the exponential equation:

M(x) = A*(1/2)^(x/3h)

Here we start with A= 60 grams, and after 15 hours we will have:

M(15h) = 60g*(1/2)^(15h/3h)

M(15h) = 60g*(1/2)^(5) = 1.875 g

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There are 120 possible ways for two tables and 90 ways for 3 tables.

If we split the six people into 4/1/1, there will be (6 4) ways to select the 4 people sitting together, and 3! ways to arrange them at their table, so this gives (6 4)(3!)=15(6)=90 possibilities.

If we split the six people into 3/2/1, we will get (6 3) ways to select the 3 people sitting together, 2! ways to arrange them at their table, and (3 2) ways to select the 2 people sitting together, so this gives (6 3)⋅2⋅(3 2)=20(2)(3)=120 possibilities.

Finally, there are 120 possible ways for two tables and 90 ways for 3 tables.

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Answers:

#6: (6,32)

#7: total cost for kites R fun   Total cost for windy kites

                    4                                              42

                     7                                               62

                     10                                             82

Answer:

Step-by-step explanation:

well then the anwser is 1.99 because the one time fee is only for downloading one movie the first, but 1.99 is the money you have to pay everytime you download a movie.

Answer:  Elasticity

Elasticity is a measure of how responsive one variable is to a change in another variable.

Option A is a correct representation of the graph of the function,

g(x) = -1/3f(x).

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given the graph of the function,

f(x) is the shape of a parabola so the graph is of a quadratic function.

and given g(x) = -1/3f(x)

graph of f(x) is on coordinates (0, 0), (1, 1), and (-1, 1)

so the function is f(x) = x²

so g(x) should lie in coordinates (0, 0), (1/3, -1/3), and (-1/3, -1/3)

the shape of g(x) will be the same as f(x), but due to the negative sign, the shape will be in opposite quadrants.

and g(x) is 1/3 time f(x) so the shape will evolve more as compared to g(x),

so the graph of Option A only follows the required condition.

Hence option A is correct.

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