a square pyramid has a base edge of 32 inches and an altitude of 1 foot. a square pyramid whose altitude is one-fourth of the original altitude is cut away at the apex of the original pyramid. the volume of the remaining frustum is what fractional part of the volume of the original pyramid?

The equation for the line in​ the slope-intercept form will be y = x/2 + 2.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

From the graph, the intercepts of the line will be (-4, 0) and (0, 2). Then the equation is given as,

x / (-4) + y / 2 = 1

Convert the equation into a slope-intercept form. Then we have

x / (-4) + y / 2 = 1

- x / 2 + y = 2

y = x/2 + 2

The equation for the line in​ the slope-intercept form will be y = x/2 + 2.

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A 95% confidence interval for the mean of 3243 dollars.

In statistics, the confidence interval formula is used to express the degree of uncertainty surrounding a sample estimate of a population parameter. It is used to describe the degree of uncertainty surrounding a sampling technique.

Given random sample = 55

mean = $2900

standard deviation = $1300

Confidence Interval = m ± z(SD/√n)

n = Number of terms

m = Sample average

SD = Standard Deviation

z = Value corresponding to confidence interval in z table

value of z for 95% confidence interval is 1.96,

substitute the values in formula,

Confidence Interval = m ± z(SD/√n)

Confidence Interval = 2900 ± 1.96(1300/√55)

Confidence Interval = 2900 ± 343.581

Confidence Interval =  3243.581

Confidence Interval =  3243

Hence the mean is 3243 dollars.

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Answer: We can set up an equation to represent the total cost for both florists:

Cost for Flowers Florist = 2x + 10

Cost for Fub's Roses = 1x + 19

where x is the number of roses David buys.

To find out the number of roses David would have to buy for both florists to charge him the same amount, we set the two equations equal to each other and solve for x:

2x + 10 = 1x + 19

x = 9

So David would have to buy 9 roses for both florists to charge him the same amount.

Step-by-step explanation:

On average, an underground storage tank has a remaining useful life of between 10-20 years depending on the construction, maintenance, and environment it is in. The tank's remaining useful life is also dependent on the type of material used in its construction.

Tanks constructed from steel or fiberglass have a life span of around 15-20 years, while concrete tanks have a longer life expectancy of up to 25 years.  In this case, the tank has been in place for 15 years, which puts it at the midpoint of its expected life expectancy.

Depending on the maintenance and environment that the tank has been subjected to, it is not unlikely that it could last longer than its expected life, but it is recommended to inspect the tank periodically to ensure that it is still in good condition. If the tank is not properly maintained, the remaining useful life may be significantly shorter.

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Answer:

3 3/4 * 2 1/2 = 758 = 9 38 = 9.375. Spelled result in words is seventy-five eighths (or nine and three eighths).

Think of 20% as 20/100 = 0.20

Then we multiply, not divide, this value with 600

0.20*600 = 120 is the answer.

Answer: She divided it by 2 which is incorrect, instead she should multiply 20% by 600kg to get 20% of 600

[tex]\frac{20}{100}[/tex] x 600 (the answer will be 120kg)

The number of hours it would take Miller's family to reach their destination is [tex]2\frac{2}{3}[/tex] hours. This can be solved using the concept of fractions.

A fraction is expressed as p/q, where q ≠ 0. Proper fractions, in which the numerator is less than the denominator, and improper fractions, in which the numerator is higher than the denominator, are the two sorts of fractions.

Given, The Miller family must drive 8 hours to reach their destination.

The first time they stopped after driving  hours and again for the second time they stopped after driving  hours.

Therefore the total hours they drive is,

= [tex](2\frac{2}{3}+2\frac{2}{3})[/tex] hours.

= (8/3 + 8/3) hours.

= 16/3 hours.

= [tex]5\frac{1}{3}[/tex] hours.

So, The number of hours they still need to drive is,

= (8 - 16/3) hours.

= (2⁴ - 16)/3 hours.

= 8/3 hours.

= [tex]2\frac{2}{3}[/tex] hours.

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The steps to draw the absolute value graph is explained below.

The term graph is known as  a mathematical representation of a network and it describes the relationship between lines and points

Here we have to define the steps to be performed to plot the graph for the absolute value function.

As we all know that every absolute value graph will make a “V”-shaped figure.

And the graph consists of two pieces that is one with a negative slope and one with a positive slope.

Here we have the the point of their intersection is called the vertex.

Here we also know that the absolute value graph is symmetrical, which means it can be folded in half on its line of symmetry.

in order to plot the graph for the absolute value function then we have to plot two lines for the positive and negative cases that meet at the expression's zero.

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Answer: Our arc length calculator can calculate the length of an arc of a circle

Step-by-step explanation:

Multiply the radius by the central angle to get the arc length.

The natural logarithm function gradually increases as x rises to positive infinity and gradually decreases as x approaches zero. Only for x>0 is the natural logarithm function ln(x) defined. Therefore, it is unknown what a negative number's natural logarithm is.

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459. 

After that, the definition of the natural logarithm can be expanded to include logarithm values for all non-zero complex numbers as well as negative numbers, albeit this results in a multi-valued function.

When seen as a real-valued function of a positive real variable, the natural logarithm function is the exponential function's inverse. Not just e, but any positive base other than 1, logarithms can be defined.

However, compared to the natural logarithm, logarithms in other bases only differ by a fixed multiplier.

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Answer:

Question 1
₹ [tex]42000[/tex]

Question 2
First table: ₹ [tex]1920[/tex]

Second table ₹ [tex]1200[/tex]

Step-by-step explanation:

Question 1

I will use R and V to denote Ravish and Vineet respectively

Question 2

So one table cost ₹1920 and the second table cost ₹1200  ANSWER

The statement describes that the survey of high school teenagers reporting that 96% of those sampled are interested in pursuing a college education to be descriptive statistics.

A given data collection, which may be a sample of a population or a representation of the complete population, can be summarised using descriptive statistics, which are concise informational coefficients. Measurements of variability and measures of central tendency make up descriptive statistics (spread). Data are summarised using descriptive statistics.

The statements made by descriptive statistics only apply to the data set from which they were derived; they never extend beyond the data you have. To characterise the fundamental characteristics of the data in a study, descriptive statistics are used. They offer concise summaries of the sample and the measurements. They serve as the foundation for almost all quantitative data analyses, along with straightforward graphical analysis.

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The perimeter of Equilateral Triangle is 14.547 m.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

The altitude of an equilateral triangle is 4.2 meters long.

let x is the measure of the side of the equilateral.

Using Pythagoras theorem

x = √(4.2)(4.2) + (x/2)(x/2) )

x = √( 4.2)² + (x²/4) )

x² = 17.64 + x²/4

3x²/4 = 17.64

x² = 17.64 (4)/3

x² = 23.52

x= 4.849

So, the perimeter of Equilateral Triangle

= 3 x side

= 3 (4.849)

=  14.547 m

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A hole occurs when there is a duplicate factor on the numerator or denominator. This is not the case here, so there are no gaps.

The denominator of f(x) cannot be zero because f(x) would become undefined. The values that x cannot be are obtained by equating the denominator to zero and solving.

To solve 5x² + 2x + 1 = 0

This does not factor, so verify the discriminant.

Here, a = 5, b = 2, and c = 1.

b² - 4ac = 4 - 20

= -16

Because the discriminant is 0, there are no real roots, and thus no vertical asymptotes.

Horizontal asymptotes can be found as

[tex]\lim_{x \to \infty}[/tex] , f(x) -> c

Divide the terms on the numerator/denominator by the highest power of x, x².

f(x) = (3x² /x² )/((5x²/x² )+(2x/x²) +(1/x²))

     = 3/ 5 + 2/x + 1/x²

Since x -> ±∞. f(x) -> 3/5 + 0 + 0

= y = 3/5

When there is a duplicate factor on the numerator/denominator, a hole occurs. This is not the case in this case, so there are no holes.

(3x2)/(5x2+2x+1) [-10, 10, -5, 5] graph

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The line equation for Carmen's donation plan is y + 2x ≤ 460.

Please refer to the attached graph below for the corresponding region.

From the case, we know that:

City youth fund = x

Educational growth foundation = y

Educational growth foundation = 2 city youth fund

Total budget = $460

Based on the case, we know that:

y = 2x --> the slope of the line constraint should be 2

Then, the line equation for this condition should be:

y + 2x ≤ $460

To construct the graph, we need to find the point constraint first.

(y= 0)

(0) + 2x = 460

x = 230 --> (230, 0)

(x = 0)

y + 2(0) = 460

y = 460 --> (0, 460)

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The triangle ΔABR and ΔRCA are congruent with each other. Then Line A R bisects Angle ∠BAC.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Line segment AB is-congruent-to line segment BC Line segment B C is congruent to line segment AC.

AB = BC = AC

In triangles  ΔABR and ΔRCA, we have

AB = AC               (Given)

∠RBA = ∠RCA     (Opposite sides have equal angle)

AR = AR               (Common sides)

The triangle ΔABR and ΔRCA are congruent with each other. Then Line A R bisects Angle ∠BAC.

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The probability of 50% shows that the  mean cholesterol level of the sample will be no more than 210 for the given mean and standard deviation.

As given in the question,

Area average represents the mean ' μ ' = 210 mg /dL

Standard deviation 'σ ' = 30 mg /dL

Sample 'n' =  48

Normal distribution 's' = σ /√n

                                     = 30 /√48

                                     = 4.35

Probability so that mean of the given sample not more than 210

By using central limit theorem we have,

Z = ( X - μ ) /s  

  = ( 210 - 210 )/ 4.35

  = 0

When Z = 0 it has p-value equals to 0.5.

0.5 = 50%

Therefore, the probability of 50% shows that the  mean cholesterol level of the sample will be no more than 210.

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The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)

The points that are on the line are given below.

(-9, -10), (-3, -1), and (3, 8)

The inequality of the line is given as,

(y - 8) ≥ [(8 + 1) / (3 + 3)] (x - 3)

y - 8 ≥ (3/2)(x - 3)

2y - 16 ≥ 3x - 9

2y - 3x ≥ 7

The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

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Answer: c

Step-by-step explanation:

The solution set to the given system of equation is -

x = 4 & y = 1.5.

Given is the system of linear equations as -.

- 5x + 6y = - 11

6y = x + 5

In mathematics, a system of linear equations is a collection of one or more linear equations involving the same variables.

The types of systems of linear equations are as follows:

The system of linear equations is -

- 5x + 6y = - 11

6y = x + 5

We can write -

6y = x + 5

x = 6y - 5

Now, we can write -

- 5(6y - 5) + 6y = - 11

- 30y + 25 + 6y = - 11

- 24y = - 11 - 25

- 24y = - 36

y = 36/24

y = 9/6

y = 3/2

y = 1.5

Then, we can write -

x = 6 x 3/2 - 5

x = 9 - 5

x = 4

Therefore, the solution set to the given system of equation is -

x = 4 & y = 1.5.

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The domain of f(x) = 3x - 2 is (-∞, +∞) or the set of all real numbers.

The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). For f(x) = 3x - 2, the domain is all real numbers.

In other words, for any value of x, whether it is a whole number, a fraction, a decimal or a negative number, we can substitute it into the function and find the corresponding output. Therefore, the domain of f(x) = 3x - 2 is (-∞, +∞) or the set of all real numbers.

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I'm sorry that you don't understand this question but sadly I am unable to help since I don't understand this question and what is going on.

The domain of the function y = √(x - 5) is x >= 5, that is [5, ∞).

The domain of the function y = sqrt(x - 5) is the set of all input values (x-values) for which the function is defined.

In this case, the square root function is defined for all non-negative values of x - 5. If x-5 is negative, it would result in an imaginary number, which is not defined. However, since x - 5 cannot be negative, x must be greater than or equal to 5. Therefore, the domain of the function y = √(x - 5) is x >= 5.

--The question is incomplete, answering to the question below--

"What is the domain of the function y = sqrt(x - 5)?"

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Answer:

1.  a = -14 and b = -10

2. c = 12 and d = 1

Step-by-step explanation:

See the attached worksheet.  Consolidate like terms, where possible and compare to the rigfht side of the equation,.  Assign values to the variables to make both sides equal.

Answer: 30

Step-by-step explanation: 6 + 4 + 4 + 9.5 + 6 + 6.5 = 30

If the recipe needs 1/4 cup of brown sugar, that would be one batch.

2/4 = 2 batches

3/4 = 3 batches

So if there is one cup that would equal 4 bathes of yummy cookies.

The combination of entrees and desserts that the restaurant serve will be:

A. The restaurant could serve 40 entrees and 25 deserts.

E. The restaurant could serve 64 entrees and 40 deserts.

The word problem in mathematics refers to a question that is written as a sentence which requires an individual to use his or her mathematics knowledge.

In this case, the local restaurant serves 8 entrees for every 5 desserts.

In this case it should be noted that:

40 / 25 = 8 / 5

64 / 40 = 8 / 5

The correct options are A and E.

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A collection of vectors v 1, v 2, …, v r from R n is linearly independent if the only scalars that satisfy are k 1 = k 2 = ⃛ = k r = 0.

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Now that we additionally know the point (3, -1) through which the new line should pass, we may express a line using the point-slope form: y = - 5 / 3 x + 4.

5x + 3y = 6

3y = -5x + 6

y = -5/3x + 6 / 3

y = - 5 / 3x + 2

y - y0 = m(x - x0)

y - (-1) = -5 / 3 (x - 3)

y + 1 = -5 / 3 x + 5

y = - 5 / 3 + 4.

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