A students tuition was $4263 a loan was obtained for 4/7 of the tution how much was the Loan?

A parabolic tunnel has the shape of a parabola in cross-section, with one axis being symmetric (the width) and the other axis being the height at the center. To find the cross-sectional area of the parabolic tunnel, we can use the formula for the area of a parabola:

Area = (1/2) x Width x Height

Given that the width of the parabolic tunnel is 20 feet and the height at the center is 12 feet, we can substitute these values into the formula:

Area = (1/2) x 20 x 12 = 120 square feet.

So the cross-sectional area of the parabolic tunnel is 120 square feet.

There are a total of 27 steps on the staircase.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Let x be the total number of steps in the staircase.

Larry climbs exactly 2/3 of the stairs.

Number of steps Larry climbed = 2x/3

She goes back exactly 1/2 of the way to the bottom.

Number of steps returned = (2x/3) (1/2) = 2x/6 = x/3

She is at x/3 steps from the bottom.

From that spot, she climbs exactly 2/3 of the way to the top.

Remaining steps to the top = x - x/3 = 2x/3

Number of steps Larry climbed = 2/3 of the way to the top = (2/3)(2x/3) = 4x/9

So we get,

x/3 + 4x/9 + 6 = x

x - x/3 - 4x/9 = 6

x - 7x/9 = 6

2x/9 = 6

2x = 54

x = 27

Hence there are 27 steps in the staircase.

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The complete question is as follows :

Lara starts at the bottom of a long staircase. She climbs exactly 2/3 of the stairs. Then, she goes back down exactly 1/2 of the way to the bottom. From that spot, she climbs exactly 2/3 of the way to the top. Finally from there, she climbs 6 stairs to reach the top. How many stairs are in the staircase?

In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.

An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)

A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).

If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.

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Complete question -

Seven times a number in algebraic expression

Answer:

D. 15

Step-by-step explanation:

4+5+6=

4+5=9..

9+6=

15.

Thus, Answer is D. 15

Answer:

Your answer is: D)15cm

Step-by-step explanation:

To find the perimeter add all of the side together.

6+4+5=15

Answer:

2. True

3. Maximum

4. [tex]2(m-9)^2[/tex]

Step-by-step explanation:

Question 2:

Yes, it is the vertex formula used to calculate the vertex of a quadratic funtion.

Question 3:

Since the first term of the equation has a negative coefficient, the parabola turns upside down, which opens down. Therefore the equation has a maximum.

Question 4:

[tex]2m^2-36m+162\\[/tex]

Find the GCF:

[tex]2(m^2-18m+81)[/tex]

Find the perfect square binomial:

[tex]81*1=81\\\\(-9*-9)\\\\-9*-9=81\\\\-9-9=-18[/tex]

Therefore this equation can be written as a perfect square binomial.

[tex]2(m-9)^2[/tex]

Answer:

There are a lot of questions the reporter could ask.

Step-by-step explanation:

There are several statistical questions that a sports reporter could ask about the data on the number of touchdowns scored each week during the football season, depending on their focus and the information they want to gather. Some examples could be:

   What is the mean number of touchdowns scored per week?

   What is the median number of touchdowns scored per week?

   What is the mode of number of touchdowns scored per week?

   What is the range of the number of touchdowns scored per week?

   What is the standard deviation of the number of touchdowns scored per week?

   Is there a trend or pattern to the number of touchdowns scored per week?

   Is there a difference in the number of touchdowns scored per week between home and away games?

   What factors are associated with the number of touchdowns scored per week?

   What is the probability of scoring a certain number of touchdowns per week?

   Are the number of touchdowns scored per week follow a normal distribution?

These are just a few examples of the questions that a sports reporter could ask about the data. The specific question will depend on the goals of the analysis and what the reporter wants to convey to their audience.

(i) 1 quintal = 100 kg

2.5 quintals = 2.5100 = 250 kg

Transportation cost of 250 kg of potatoes = 105(250/35) = Rs 750

we are asked to find the transportation cost of 2.5 quintals (250 kg) of potatoes at the same rate as 35 kg of potatoes. We know that the transportation cost for 35 kg is Rs 105.

To find the cost for 250 kg, we use the proportion of 35/105 = x/750. By cross multiplying we get x= 250*105/35= 750. So the transportation cost for 250 kg of potatoes is Rs 750.

(ii) Transportation cost of 1 quintal of potatoes = 105*(100/35) = Rs 300

Transportation cost of 1 quintal of potatoes = Rs 1500 / Rs 300 = 5 quintals.

we are asked to find how many quintals of potatoes can be transported for Rs 1,500 at the same rate as 35 kg of potatoes. We first find the transportation cost of 1 quintal of potatoes by using the proportion of 35/105 = x/300.

So x = 100, thus the transportation cost of 1 quintal of potatoes is Rs 300. So we can transport 1 quintal of potatoes for Rs 300. Dividing 1500 by 300, we get 5 quintals.

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A data set which could be represented by the boxplot shown include the following: A. {6, 6, 8, 8, 9, 12, 13, 13, 14}.

In Mathematics, a boxplot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box-and-whisker plot, the five-number summary for the given data set include the following:

By critically observing the box-and-whisker plots or boxplot (see attachment), we can logically deduce that it correctly represents this data set {6, 6, 8, 8, 9, 12, 13, 13, 14}.

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Answer:

21x+35y=?

Step-by-step explanation:

multiply 3 by 7

multiply 5 by 7

you can't add different variables together

According to the question, there are five terms in the expression 5yz^2-z-24y+77.

Expression is the representation of an idea or feeling in a creative way. It is the manifestation of someone's thoughts, emotions, and desires through an artistic form. Expression can take on many forms including writing, music, painting, sculpting, and dancing. Expression allows us to communicate our innermost feelings and beliefs to the outside world. It can be used to reach out to those who may be feeling isolated, to inspire and empower others, or to simply bring joy to those who experience it. Expression is a unique way of conveying our ideas and is an important part of the human experience.

The first term is 5yz^2, the second term is -z, the third term is -24y, the fourth term is +77, and the fifth term is the constant 77.

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The volume of ice in Antarctica can be calculated by first determining the area of the semicircle.

This can be done by multiplying the radius (2000 km) of the semicircle (2πr2) by half, resulting in a total area of 3,14159265 x (2 x 20002) = 628318530 km2. To calculate the volume of ice, this area must be multiplied by the average thickness of the ice cover (3000 m). This results in a total volume of 18,8547595 x 1012 cm3 of ice in Antarctica. To put this into perspective, this is the equivalent of roughly 6.5 billion Olympic swimming pools of ice.The volume of ice in Antarctica can be calculated by first determining the area of the semicircle.

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Using the normal probability distribution, it is found that P(X = 8) is equal to zero.

In a normal distribution with mean  and standard deviation, the z-score of a measure X is given by:

                                   [tex]Z = \frac{X-mean }{S.D.}[/tex]

Hence, from the last bullet point, it is found that P(X = 8) is equal to zero.

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Answer:

The correct answer is 8x³y + 5y²x + x² - 14z - 2.

Step-by-step explanation:

This is in standard form because it is a polynomial with the terms arranged in descending order of their exponents, with the coefficient of each term being positive.

The exponent of x is 3, the exponent of y is 2, the exponent of z is 1, and the constant is -2.

Answer:

Step-by-step explanation:

f(x) is basically another term for y, and you already have your x values, so you can just plot the points and draw lines through them :)

For drawing graphs we have two points (x-axis and y-axis ) to loacte exact location on the graph.

X-axis point to locate on the graph parallel distance from y-axis.

Y-axis point to locate on the graph parallel distance from x-axis.

Take the y-coordinates as the f(x) and points of x-coordinates as the value of x.

1.Write down the coordinates of x-axis and y-axis

y=-3x+1

(X-axis,Y-axis)=A(-2,7),B(-1,4),C(0,1),D(1,-2),E(2,-5)

2.Write down the coordinates of x-axis and y-axis

y=-x²+5

(X-axis,Y-axis)=A(-2,1),B(-1,4),C(0,5),D(1,4),E(2,1)

3.Write down the coordinates of x-axis and y-axis

y=[tex]2^{x}[/tex]

(X-axis,Y-axis)=A(-2,0.25),B(-1,0.5),C(0,1),D(1,2),E(2,4)

These are the graphs linke images

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Answer:

<Q = 93

Step-by-step explanation:

The sum of the angles of a triangle is 180

<Q + <P + < R = 180

<Q + 51+36 = 180

<Q+87=180

<Q = 180-87

<Q = 93

The inequality is for the given term 3y + 5 < 10 is y < 5/3.

The term "inequality" refers to a mathematical expression in which the sides are not equal to one another. In essence, an inequality compares any two values and demonstrates that one value is less than, greater than, or equal to the value on the other side of the equation.

Less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠) are the inequality symbols.

Inequalities are used to compare numbers and identify the range (or ranges) of values that satisfy the requirements of a given variable.

Given to solve the inequality

3y + 5 < 10

3y < 10 - 5

3y < 5

y < 5/3

and

y ∈ (−∞, 3/5)

Thus, the inequality is for the given term 3y + 5 < 10 is y < 5/3.

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The height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches and this can be determined by using the given data.

Given :

The distribution of heights for adult men in a certain population is approximately normal with a mean of 70 inches and a standard deviation of 4 inches.

The heights that represent the middle 80 percent of the heights are:

P(-z < Z < z) = 0.80

P(Z < z) - P(Z < -z) = 0.80

P(Z < z) - (1 - P(Z < z)) = 0.80

2P(Z < z) = 1.80

P(Z < z) = 0.90

So, the value of z is 1.282.

Now, put the values of height as follows:

x1= 64.87

x2= 75.13

Therefore, the height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches.

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Material will be required to make six bench legs each 28 1/4 inch is 169.5 inches.

What is Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

What is Decimal?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

The simple solution is to convert 28 1/4 to a decimal and be cautious about converting it back to a fraction if necessary.

28 1/4=28.25

You need Six of them.

1 leg measures28.25 inches.

6 legs = x

Cross multiply 1/6 = 28.25 / x

x = 6* 28.25

x equals 169.5 inches

How many feet is that exactly? To calculate the amount of feet, divide by 169.5 /6=28.25 feet.

2 by 4s are typically 6 feet long. Unfortunately, you will need two of these for two more for 6 feet.

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a) limit→[infinity]N(t) = limit→[infinity](200 + 80t)/(2 + 0.05t) = 200.

What is a limit in plain English?

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

This means that as the number of years (t) approaches infinity, the number of fish in the pond (N(t)) approaches a limit of 200. In other words, as t gets larger and larger, the number of fish in the pond will get closer and closer to 200, but will never exceed 200. In the context of the problem, this means that the pond has a carrying capacity of 200 fish and that the population of fish in the pond will eventually stabilize at this level, regardless of the initial population.

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Answer:56

Step-by-step explanation:

The formula for calculating the future value of an investment compounded annually is:

FV = P(1 + r)^t

where:

FV = future value of the investment

P = principal or initial investment

r = annual interest rate as a decimal

t = number of years the investment is held

In this problem, the principal is given as $4700, the annual interest rate is given as 5.25%, and the time is measured in years since 2007.

So we can write the function as:

y = 4700(1 + 0.0525)^t

In this function, y represents the future value of the investment (in dollars) and t represents the number of years since 2007.

The above function can be written in the form A or A B , where A and B are constants or variable expressions that have no variables in common.

A = 4700

B = 1 + 0.0525

y = A*B^t

So the exponential function for the problem is:

y = 4700*(1+0.0525)^t

The probability of the ferry carrying x cars and y buses is given by the joint probability distribution for x and y. The expected toll for this trip is 3x + 10y.

The probability of the ferry carrying x cars and y buses can be found using the joint probability distribution for x and y. This joint probability distribution is the product of the individual probability distributions for the number of cars and buses. The expected toll for this trip is 3x + 10y, which indicates that each car carries a toll of $3 and each bus carries a toll of $10. The joint probability distribution for x and y can be used to calculate the probability of the ferry carrying x cars and y buses. For example, if the probability of the ferry carrying 3 cars and 2 buses is 0.2 then the expected toll for this trip would be

3x + 10y = 3(3) + 10(2) = $36.

Thus, the joint probability distribution for x and y can be used to calculate the probability of the ferry carrying a given number of cars and buses, as well as the expected toll for this trip.

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The set of all x-values at a distance of 15 or less from the number 6 can be represented in interval notation as (-9, 21).

Interval notation is a way of expressing a set of numbers in a concise and easily readable format. In this case, we are looking for all the x-values that are a distance of 15 or less from the number 6. To find these values, we need to consider the range of numbers that are 15 units away from 6 in both the positive and negative directions.

So, in interval notation, the set of all x-values at a distance of 15 or less from 6 is written as (-9, 21) which means all the values between -9 and 21 (not including -9 and 21)

Key points:

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The molar entropy of mixing is given by the equation S_mix = R(x1lnx1+x2lnx2).

To maximize the molar entropy of mixing, we need to find the value of x1 and x2 that will produce the maximum value of S_mix. Differentiating S_mix with respect to x1 and x2 and setting the derivatives equal to 0 will yield the critical points. The critical points can then be tested to see which one produces the maximum value of S_mix. After differentiating, we get x1 = x2 = 1/2. This implies that the molar entropy of mixing is maximized when the mole fraction of each component is 0.5. The corresponding maximized change in molar entropy upon mixing is Rln2 which is equal to 2.30258509299405 j/mol-k.

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For a randomly selected group of 4 adult workers, the probability that no more than 3 drink coffee at least occasionally while on the job is 37.5%.

Probability refers to the chance, odds, or likelihood that an expected outcome is obtained when there are many possible events.

Probability may be 100% certain, depicted as 1, or 100% uncertain, expressed as zero.

Other values of probability lie between one and zero as fractional values that can be depicted as percentages, decimals, or fractions.

The estimated percentage of adults who at least occasionally drink coffee = 50%

Random sample = 4

The number of adult workers from 4 who occasionally drink coffee on the job = 3

The probability of 3 out of 4 workers drinking coffee on the job = 37.5% (3/4 x 50%)

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To find the number of years it takes for an investment to grow to a certain value at a certain interest rate, you can use the formula:

n = (future value - principal) / (principal * interest rate)

Where:

n = number of years

future value = the final value of the investment

principal = the initial amount invested

interest rate = the annual interest rate as a decimal

Plugging in the given values:

n = (21150 - 5000) / (5000 * 0.17)

n = 16.65

Rounding to the nearest whole number, it would take approximately 17 years for the investment to be worth $21,150.00.

The equation describes the relationship between the rate of change of with respect to time and the rate of change of with respect to time is dx/dt -2 dy/dt              

Well   x + 2y = k                   (constant)

differentiate through wrt t

dx/dt  +  2 dy/dt = 0

so dx/dt -2 dy/dt               (so B)

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