Calculate the length of edge AD in the triangle-based pyramid below.
Give your answer to 2 d.p.

The proportional relationship between the grapes and nectarine she ate is represented by y = 5.25x while the constant of proportionality is 5.25 and she ate 3780 grapes as she ate 720 nectarine

a) y = 5.25x

b) k = 5.25

c) 3780 grapes

A mathematical concept called proportions contrasts the relationship between two or more quantities. They can be used to compare the size of one part to the size of the total and can be expressed as ratios, fractions, or percentages. For instance, if a pizza is divided into 10 equal slices and you consume 5 of them, the percentage of the pizza that you have consumed is 5/10, or 50%. The distribution of a categorical variable, such as the percentage of voters who supported a certain candidate in an election, is described in statistics using proportions.

In this problem, we can find the proportional relationship by calculating the constant of proportionality.

a)

24 nectarines = 126 grapes

1 nectarine = x grapes

cross multiply both sides and solve for x

1 * 126 = 24 * x

126 = 24x

x = 126 / 24

x = 5.25

Assuming the number of grapes is represented by y and nectarine by x

y = 5.25x

The proportional relationship is given as;

y = 5.25x

b)

The cross product can be used to solve proportions by setting up an equation that equates the two products. For example, if the proportion is a:b = c:d, the equation would be ad = bc. By using the cross product, the equation can be simplified and the proportion can be solved for one of the variables.

c)

To determine how many grapes she has eaten if she ate 720 nectarines

y = 5.25x

y = 5.25(720)

y = 3780

She ate 3780 grapes.

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Answer:

Below in bold.

Step-by-step explanation:

R(x) = 8x/(x + 19)

When x = -19 the denominator = zero so there is a vertical asymptote which is

x = -19.

If we divide 8x by x + 19 we get  8 remainder -152.

So horizontal asymptote is R(x) = 8.

As the degree of the numerator and denominator are the same ( both 1) there is no oblique asymptote.

The total cost of the entertainment center after six years, if Zebina must pay it off, would be $9,203.19.

When a person purchases an item using a deferred payment plan with interest, the total cost of the item will be greater than the original purchase price due to the added interest.

To calculate the total cost of the entertainment center after six years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total cost, P is the original purchase price, r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $2,798, r = 0.2195 (21.95% expressed as a decimal), n = 1 (because the interest is compounded annually), and t = 6. Plugging these values into the formula gives:

A = 2798(1 + 0.2195)^6

A = $9,203.19

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No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.

1. The ratio of the distance around a circle to the distance across a circle through its center is represented by the number pi.

2. The number pi is a decimal that does not repeat.

3. The fraction 22/7 is sometimes used as an estimate for pi.

4. 22/7 is not a repeating decimal because pi is an irrational number, meaning it does not repeat and 22/7 is not an exact representation of pi.

No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.

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The particular solution of y = f(x) to the given differential equation [tex]\frac{dy}{dx} = y (xlnx)[/tex] with the initial condition f(1) = 4 is [tex]y = 4e^{\frac{1}{2}x^{2} lnx } - \frac{1}{4} x^{2} + \frac{1}{4}[/tex].

dy/dx = y(x lnx)

1/y dy = x lnx dx      Eqn (1)

Let u =  lnx, dv = x dx

Differentiate u = lnx

du = 1/x dx

Integrate dv = x dx

v = (1/x)x²

Now, integrate equation(1), we get

∫1/y dy = ∫x lnx dx

ln y = 1/2 x² ln x - 1/4 x² + C       Eqn (2)

Now, put the value of x and y to calculate the value of C

ln 4 = 1/2 ln 1 - 1/4 + C

ln 4 + 1/4 = C

Put the value of C in equation (2), and we get

ln y = 1/2 x² ln x - 1/4 x² + ln 4 + 1/4

[tex]y = 4e^{\frac{1}{2}x^{2} lnx } - \frac{1}{4} x^{2} + \frac{1}{4}[/tex]

--The given question is incorrect, the correct question is

''Find the particular solution y = f (x) to the given differential equation [tex]\frac{dy}{dx} = y (xlnx)[/tex] with the initial condition f(1) = 4."--

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The parallelogram's surface area is 24 square units as a result.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A quadrilateral is referred to as a parallelogram in geometry.

The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.

Here points are a(−3, 0), b(−1, 5), c(7, 4), and d(5, −1).

= 1/2 [-3 (4 + 1) - 1 (- 7 - 20)]

= 1/2 [-3 (5) - 1 (-27)]

= 1/2 [-15 + 27]

= 1/2 [12]

= 6 sq units

Area of parallelogram abcd = Area of triangle abc + Area of triangle acd

= 18 + 6

= 24 sq units.

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There are two types of roots for an equation: real roots and complex roots. Real roots are the solutions of the equation where the values of the variables are real numbers, and complex roots are the solutions of the equation where the values of the variables are complex numbers.

There are two types of roots for an equation: real roots and complex roots. Real roots are the solutions of the equation where the values of the variables are real numbers. To find the real roots of an equation, one can use various methods such as graphing, factoring, completing the square, and the quadratic formula. If the equation is a linear equation, one can also use the slope-intercept form to find the real root. Complex roots are the solutions of the equation where the values of the variables are complex numbers. Complex roots are usually found using the quadratic and cubic formulas. These formulas involve complex numbers and can be used to solve equations with complex coefficients. The roots can also be found graphically by plotting the equation on a complex plane and finding the intersecting points. The real and imaginary parts of the root can then be determined.

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Answer:

No.

Step-by-step explanation:

An integer, by definition, is a whole number.

The given number, -48.29, is a decimal number, implying that it is not whole. Therefore, -48.29 is not a integer.

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Answer:

Step-by-step explanation:

maybee the 2ed one

There are six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits: 12, 24, 32, 42, 43, and 124.

1. 12: 1 and 2

2. 24: 2 and 4

3. 32: 3 and 2

4. 42: 4 and 2

5. 43: 4 and 3

6. 124: 1, 2 and 4

The six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits are 12, 24, 32, 42, 43, and 124. To find these numbers, we begin by examining all the possibilities that can be formed using the digits 1, 2, 3, and 4. We can form 12, 24, 32, 42, 43 and 124 by combining different combinations of the digits. For example, 12 is made up of the digits 1 and 2. 24 is made up of 2 and 4. 32 is made up of 3 and 2. 42 is made up of 4 and 2.

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Answer:

Greetings!!!

Converse:- MELTS IN YOUR HAND NOT IN YOUR MOUTH!

Inverse:- DOESN'T MELT IN YOUR HAND BUT MELTS IN YOUR HAND!

Contrapositive:- MELTS IN YOUR HAND NOT IN YOUR MOUTH!

Hope it helps!!!

A function P that represents the profit made from selling x bracelets is

The number of bracelets this company must sell to break even is equal to 15 bracelets.

In Mathematics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the amount of profit made from selling x bracelets can be calculated by using the following function:

Profit made = Revenue earned – Cost of production

P(x) = R(x) - C(x)

P(x) = 20x - (180 + 8x)

P(x) = 20x - 180 - 8x

P(x) = 12x - 180

In order to break even, the number of bracelets that this company must sell would be calculated by equating the profit function to zero and solving for x as follows;

P(x) = 12x - 180

0 = 12x - 180

12x = 180

x = 180/12

x = 15 bracelets.

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Answer:

In this problem, we need to add a point to this graph which creates a right triangle with the given points.

The easiest way to do this is to find a point that is perpendicular to both of the points; more simply put, it has to have the x-coordinate of one of the given points and the y-coordinate of the other given point.

For example, adding the point (50, -14) to the graph satisfies this criteria, using the x-coordinate of (50, 25) and the y-coordinate of (130, -14). However, you could also use the y-coord of the first point and the x-coord of the second to add the point (130, 25). Both points in bold satisfy the criteria.

See the attached image for a graph of these points and the right triangles they create.

The interval of increase for the given function is (-1 , 0) (0 , infinity).

The real-valued functions that tend to rise and decrease with changes in the value of the function's dependant variable are increasing and decreasing intervals of real numbers. You must ascertain the function's first derivative in order to identify intervals of rise and decline.

This is done to determine whether the function's sign is positive or negative. If the value of the function f (x) rises as the value of x rises, the function interval is said to be positive. Instead, if the value of the function f (x) drops as the value of x increases, the function interval is said to be negative.

The given function is:

C(x) = x1/5(x + 6)

Find the derivative of the given function to get calculate the interval of increase and decrease.

The interval of increase is (-1 , 0) (0 , infinity).

Th graph is concave up when derivative of, f is greater than 0. The intervals in which the function depicts this behavior will be the interval that will have a concave up curve.

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The area enclosed by the figure is 6425 square meters.

The area enclosed by the figure is made up of a square of 50m x 50m = 2500 m^2 There are four semicircles attached to each side of the square.

Each semicircle has a radius of 25m, so the area of each semicircle is,

(1/2) * pi * 25^2

= (1/2) * 3.14 * 625 m^2.

The total area of the four semicircles is,

4 * (1/2) * 3.14 * 625 m^2

= 2 * 3.14 * 625 m^2

= 3925 m^2

To find the total area enclosed by the figure, add the area of the square to the area of the semicircles:

2500 m^2 + 2 * 3.14 * 625 m^2

= 2500 m^2 + 3950 m^2

= 6425 m^2.

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Considering margin of error only accounts for random sampling errors and not bias, the statement "The margin of error of a confidence interval is the error from biased sampling methods" is false.

A margin of error is a statistical term that takes into account the difference between the outcomes of a random survey sample and the projects outcome. To put it another way, you can determine the degree of unpredictability in data and study results by looking at the margin of error.

Margin of error calculations are based only on the error associated with random samples. It does not account for other possible sources of error such bias in the questions, prejudice owing to eliminating groups that could not be contacted, people refusing to respond or lying, and miscounts and miscalculations.

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The fundamental theorem of algebra states that you will have ‘n’ roots for an nth-degree polynomial, including multiplicity. So, your roots for f(x) = x^3 are 0 (multiplicity 3). The total number of roots is still 3 because you have to count 0 thrice.

A polynomial can be defined as an expression which consists of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division. 
·[tex]f(x)= ax^{n}+bx^{n-1}+cx^{n-2} +k[/tex]

We can also phrase it as there are going to be ‘n’ values of x for which it will make polynomial f(x)=0.

For Example: [tex]p(x)= x^{2}-6x+9[/tex]

                   ⇒   n = 2

                   ∴ Total number of roots = 2

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Therefore , the solution to the given problem of percentage comes out to be  total number of student  = 182 (approx).

In mathematics, a percentage is a number or ratios that is expressed as a portion of 100. Occasionally, the acronyms "pct.," "percent growth," & "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a quantity is a percentage by placing it next to it.

Here,

Given :  22% of x is 40

thus,

To find the value of x , where x is the total number of students in that class.

=>  22/100* x = 40

=> x = 40 * 100 /22

=> x = 4000/22

=> x =181.81

So, x = 182 (approx)

Therefore , the solution to the given problem of percentage comes out to be   total number of student  = 182 (approx).

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The scale of the scale factor for the model to actual is 1 ich = 50 feet.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The actual length of a model has a scale of Scale 1" = 50'.

So, 1 inch of the model length is equal to 50 feet of actual length.

Therefore, The length of scale for the model to actual is 1 ich = 50 feet.

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the fox population in a certain region has an annual growth rate of 8 percent per year. it is estimated that the population in the year 2000 was 7600.

(a) function model for the t year after 2000 (exponential model):

[tex]p(t) = 7600 (1.08)^t[/tex]

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

Population in 2000,

P(0) = 7600

Growth rate = 8% each year

(a) function model for the t year after 2000 (exponential model):

[tex]p(t) = 7600 (1.08)^t[/tex]

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48600 rupees is needed to exchange 450 us dollars

Percentage Decrease is the percentage change in the value when it is decreased over a period of time.

How to determine this

When 1 us dollar is exchanged at 120 rupees

And devaluated by 10%

i.e 10% of 120 rupees

= 10/100 * 120

= 1200/100

= 12 rupees devaluated

So, 120 - 12 = 108 rupees can be exchanged

How much is 450 us dollars

Let x represent the number

If 1 us dollars = 108 rupees

450 us dollars = x

x = 450 * 108/1 rupees

x = 48600 rupees

Therefore, 48600 rupees can be exchanged for 450 us dollars

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Answer:

(- 3, 2 )

Step-by-step explanation:

to find the start, do the reverse, that is move 1 unit to the right.

this means adding 1 to the x- coordinate

start = (- 4, 2 ) → (- 4 + 1, 2 ) → (- 3, 2 )

Answer:

see the picture attached

Step-by-step explanation:

To graph this, we will count to a negative five on the graph. This means that we will move to the left five spaces and plot a point at (-5,0). Now, we will create a vertical line at -5 to encapsulate all of the values found at x = -5. This is essentially an infinite line, but the picture I included shows it on a 10 x 10 plane. Hope this helps!

Answer:

What is X= -5 graphed

Step-by-step explanation:

Graph x=-5 x = −5 x = - 5 Since x = −5 x = - 5 is a vertical line, there is no y-intercept and the slope is undefined.

The greatest integer that does not exceed S/10 is 2.

1000 can be factored as 1000 = 2^3 * 5^3. The positive divisors of 1000 are the numbers of form 2^i * 5^j, where i and j are non-negative integers and i <= 3, j <= 3.

The sum of all numbers of the form a/b, where a and b are relatively prime positive divisors of 1000, is the sum of all numbers of the form 2^i * 5^j / (2^k * 5^l), where i, j, k, and l are non-negative integers and i, j, k, l are non-negative integers and i <= 3, j <= 3 and (i,j) is not equal to (k,l).

There are total 24 such terms in the sum.

We can evaluate the sum as:

(1/1 + 1/2 + 1/4 + 1/5 + 1/8 + 1/10 + 1/20 + 1/25 + 1/40 + 1/50 + 1/80 + 1/100 + 1/125 + 1/200 + 1/250 + 1/400 + 1/500 + 1/625 + 1/1000 + 2/5 + 4/25 + 8/125 + 16/625)

S = (1 + 0.5 + 0.25 + 0.2 + 0.125 + 0.1 + 0.05 + 0.04 + 0.025 + 0.02 + 0.0125 + 0.01 + 0.008 + 0.005 + 0.004 + 0.0025 + 0.002 + 0.0016 + 0.001 + 0.0004 + 0.0008 + 0.00016 + 0.000064)

S = (2.93120)

Therefore, the greatest integer that does not exceed S/10 is 2.

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The equations of the two circles are (x-0)^2 + (y-0)^2 = 2^2 or x^2 + y^2 = 4 and (x-1)^2 + (y-1)^2 = 1^2 or (x-1)^2 + (y-1)^2 = 1.

The equation of a circle with centre (a,b) and radius r is given by (x-a)^2 + (y-b)^2 = r^2.

C1 has centre (0,0) and radius 2, so its equation is (x-0)^2 + (y-0)^2 = 2^2 or x^2 + y^2 = 4.

C2 touches the x and y axes each in one point, so it must have a centre on the line y=x and a radius equal to the distance from the centre to either of those points of tangency. Since the centre of C2 is on the line y=x and it is in the first quadrant, the coordinates of the centre are (1,1). The distance from the centre to the point of tangency on the x-axis is 1, so the radius is 1. The equation of C2 is (x-1)^2 + (y-1)^2 = 1^2 or (x-1)^2 + (y-1)^2 = 1.

Therefore, The equations of the two circles are (x-0)^2 + (y-0)^2 = 2^2 or x^2 + y^2 = 4 and (x-1)^2 + (y-1)^2 = 1^2 or (x-1)^2 + (y-1)^2 = 1.

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the height intercept would be 0 given the pool has no water at the beginning.

Which is the vertical intercept?

The vertical intercept (y-intercept) is found by evaluating the function when the input variable, x, is 0 and is always the same as the constant b. It can be thought of as the original value of the function. The horizontal intercept (x-intercept) is the value of the variable x when the function value is 0.

according to the constant dividend growth model

price = d1 / (r - g)

d1 = next dividend to be paid

r = cost of equity

g = growth rate

$2.5 / (0.1 - 0) = $25

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a. The value of h'(3) is 45.

b. The value of H'(1) is 36.

The complete table is in the attachment. h' and H are derivates from function h(x) and H(x). Using the Chain Rules to derivate the function.

Calculate the h'(x) function

h(x) = f(g(x))

h'(x) = d/dx {f(g(x))}

h'(x) = f' (g(x)) × g'(x)

h'(3) = f' (g(3)) × g'(3)

h'(3) = f'(2) × 9

h'(3) = 5 × 9

h'(3) = 45

Calculate the H'(x) function

H(x) = g(f(x))

H'(x) = d/dx {g(f(x))}

H'(x) = g' (f(x)) × f'(x)

H'(1) = g' (f(1)) × f'(1)

H'(1) = g'(3) × 4

H'(1) = 9 × 4

H'(1) = 36

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The jncenter is the center of the inscribed circle of a triangle.

The given equation system has the following solution: (10, 11).

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the system of equations below:

2x+3y=53

3x-y=19

From equation 2, y = 3x - 19 .......... 3

Substitute equation 3 into 1 to have;

2x+3y=53

2x + 3(3x - 19) = 53

2x + 9x - 57 = 53

11x = 110

x = 10

Substitute x = 10 into equation 3 to have:

y = 3x - 19

y = 3(10) - 19

y = 30 - 19

y = 11

Hence the solution to the given system of equation is (10, 11).

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