Pythagoras is very tall for ancient Greck standards: 1.78 m. He notices that when he stands with his back to the sun, his shadow is 3.08 m in length, while the shadow cast by the lighthouse is 26 m long How tall is the lighthouse?

Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.

What is the Quadratic Equation?

A quadratic equation is a type of polynomial equation of degree 2 in one variable (x), which can be written in the form of ax² + bx + c = 0, where a, b, and c are real numbers, and a is not equal to zero. The solutions or roots of this equation can be found by using the Quadratic Formula which is z = -b ± √(b²-4ac) / 2a.

The Quadratic formula is valid for any quadratic equation in standard form (ax² + bx + c = 0), where a, b, and c are real numbers, and a is not equal to zero. The two solutions are given by the formula are the roots of the equation, and they are always real and distinct, unless the discriminant b² - 4ac is negative, in which case the roots are complex numbers.

Hence, Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.

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The complete implementation of the function 'same diff ints' is written italic below.

Below is the implementation for the function same_diff_ints in Python:

def same_diff_ints(ints):

   for i in range(1, len(ints)):

       for j in range(i, len(ints)):

           if abs(ints[j] - ints[j-i]) == i:

               return True

   return False

The function takes in a list of integers as input and iterates through the list using nested for loops. The outer for loop iterates through the list starting at index 1, and the inner for loop iterates through the list starting at the outer loop's current index.

The function compares the absolute difference between the two elements at index j and j-i with the value of i. If the absolute difference between the two elements is equal to i, the function returns True. If no such pair of elements is found, the function returns False.

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Answer:

We can start solving the problem by using algebraic equations. Let x be the total number of stickers in the box at first.

According to the problem, Wenxuan took 8 more than of the total number of stickers, so he took x + 8 stickers.

The remaining stickers after Wenxuan took his share is x - (x+8) = x - x - 8 = -8 stickers.

Charlene took 7 more than of the remaining stickers, which is -8 + 7 = -1 stickers.

So, Charlene took x - (x+8) + 7 = -1 stickers.

Siti took the last 23 stickers, so the total number of stickers remaining is -1 - 23 = -24.

Now we can use this information to set up the equation:

x + (x+8) + (x-x-8+7) + (-1-23) = x

Solving for x we get x = 32

Therefore, there were 32 stickers in the box at first.

Answer:

Let's look at each number separately. Look in the tens place to determine which way to round.

4,070 will round up since there's a 7. However, it will only round up to 4,100 so this is not the right answer.

4,617 will round down since there's a 1. However, it will only round down to 4,600 so this is not the right answer.

4,681 will round up since there's an 8. This number will round up to 4,700 so this is the correct answer.

4,797 will round up since there's a 9. However, it will only round up to 4,800 so this is not the right answer.

The correct answer is 4,681.

Step-by-step explanation:

given = y = 6x-6 .

therefore ,

=) -3(6x-6)+8x=18 - ( from given ) .

=) -18x+18+8x=18 .

=) -10x=18-18 .

=) -10x = 0 .

=) x = 0/10 = 0.

therefore ,

y=6(0)-6 .

= -6 .

therefore , x = 0 & y = -6 .

[ it takes so much time to write and solve so plzzz => ]

Answer:

30 + 4n

Step-by-step explanation:

Company X = 30 + 4n

Answer: s squared.s2.sigma i think

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x-axis is 3.93740 and y=-1 is 5.0740

We have to find the volume of given curve about x-axis

we have [tex]$\mathrm{y}=\mathrm{e}-\mathrm{x}^2,[/tex] y=0, x=-5, x=5

(a).

The volume of solid of revolution about the x-axis using disk method is evaluated as:

Volume V=[tex]\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \mathrm{dx}$[/tex]

[tex]$$\begin{aligned}& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5}\left(\mathrm{e}^{-\mathrm{x}^2}\right)^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5} \mathrm{e}^{-2 \mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}}=3.93740 .\end{aligned}$$[/tex]

V=3.93740

we use the formula

(b). The volume of solid of revolution about the y= - using washer method is:

[tex]$$\begin{aligned}& \text { volume } \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \quad 2 \mathrm{y}-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 2 \mathrm{ydx} \\& \mathrm{V}=\pi \int_{-5}^5 \mathrm{e}^{-2 \mathrm{x}^2} 2 \mathrm{e}^{-\mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}} .77245 \\& \mathrm{~V}=5.0740\end{aligned}$$[/tex]

Therefore, the The volume of solid of revolution about the y= - using washer method is 5.0740

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Answer/Step-by-step explanation:

Starting with:

8r + 5p + 7



There are three terms. 8r is a term; 5p is a term; 7 is a term. See how the terms are separated by + or -

r and p are variables. Most often the variable is a letter, that way it can stand for an unknown value. It can vary.

5 is the coefficient of p. Its the number right next to the p. (They are multiplied together)

7 is the constant. Constant means unchanging, right? So 7 is a plain old number, it doesn't change like a variable can. A plain number with no variable is a constant.

The value of a is 12. Therefore, the equation of the function is f(x) = 12|x|.

In algebra, an objective function function is one where the variables is inside the bars denoting absolute values. The absolute value is also referred to as the modulus function, and its most popular representation is f(x) = |x|, wherein x is a real number.

Finding x values that turn the equation inside the exact amount positive or negative into a constant is how absolute value equations are solved. Plot two for the negative and positive cases that intersect at the expression's 0 to graph exact value functions.

To find the value of a, we can use the point (1, 12) to set up the equation:

a = 12/|1| = 12

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The volume of the solid of revolution is  0

The volume of the solid of revolution obtained by rotating the region bounded by the curves x=0 and y=0 is zero since the area of the region is zero.

To calculate the volume of a solid of revolution, we use the formula V = ∫2dx, where r is the radius of the circle obtained by rotating the curve about the x-axis. Since the region bounded by the curves x=0 and y=0 has an area of 0, the radius r is also 0 and the integral becomes 0. Therefore, the volume of the solid obtained by rotating the region bounded by the curves x=0 and y=0 is 0.

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Answer: c) 130

Step-by-step explanation:

x+8+42=180

x=180-50

x=130

The 1x8 vector resulting from multiplying each entry of x by 4.x4 = [4*x1, 4*x2, 4*x3, 4*x4, 4*x5, 4*x6, 4*x7, 4*x8]

For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], x4 would be [4, 8, 12, 16, 20, 24, 28, 32]. This can be represented mathematically as x4 = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8] which is the same as 4*x = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8]. By multiplying each entry of x by 4, we can create a new vector x4 with every entry multiplied by 4.Multiplying each entry of a 1x8 vector x by 4 can be expressed as multiplying the vector by the scalar 4, resulting in a 1x8 vector x4. For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], then x4 = [4, 8, 12, 16, 20, 24, 28, 32].

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A matrix is in the row-echelon form if:

1. The first nonzero element of each nonzero row (called the leading entry) is to the right of the leading entry of the row above it.

2. Each leading entry is 1 (also called a pivot).

3. Each element above and below a pivot is 0.

A matrix is in the reduced row-echelon form if it is in row-echelon form and also:

4. Each pivot is the only nonzero element in its column.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The numbers, symbols, or expressions in a matrix are called its entries or elements. Matrices are often used in linear algebra, a branch of mathematics that deals with vector spaces and linear transformations.

They can be used to represent systems of linear equations, perform operations such as matrix addition and multiplication, and solve systems of linear equations.

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The length of the ladder used in the question is; 6.974 ft

The 3 main trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Now, since the ladder makes an angle of 35 degrees with the wall, it means the ladder will be the hypotenuse of the right angle triangle and the distance from the base of the wall to the base of the ladder will be labelled as h = 4 will be the opposite side of the triangle. Thus;

4/hypotenuse = sin 35

hypotenuse = 4/sin 35

hypotenuse = 4/0.5736

Hypotenuse = 6.974 ft

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Answer:

A, C

Step-by-step explanation:

A)

(120 ∙ 8) ∙ 5 = 120 ∙ (8 ∙ 5)

Multiply 8 and 5 first to get 40.

Then 40 × 120 = 4800

C)

(17 + 75) + 25 = 17 + (75 + 25)

Add 75 and 25 first to get 100.

then 17 + 100 = 117

The probability that the student got a a a given that the student was in the afternoon class is 25/57

In math the term probability is defined as based on the possible chances of something to happen

Here we have given that  a test to a group of students, the grades by the two different classes are summarized.

and it can be written like the following;

                                a             b               c                   Total

Morning class         4             20              8                    32

Evening Class         13              5               7                   25

Total                        17             25              15                  57

Here we know that the total number of students is obtained as

=> 57

And the number of students who have been taking the afternoon class is calculated as,

=> 25

Then the probability the student got a a a given that the student was in the afternoon class is written as,

=> 25/57

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The percent of increase from 5.5 feet to 6 feet is 9.1%

Percentage is a way to express a number as a fraction of 100.

It is often used to express a proportion or rate in a convenient and understandable way.

To calculate percentage, you can use the formula: (part/whole) x 100.

For example, if you scored 80 out of 100 on a test, your percentage score would be 80%.

Percentage is often used in many fields such as finance, statistics, and education.

It can be used to express the increase or decrease between two values or to compare the parts of a whole.

You can use the following calculation to determine the percentage increase from 5.5 feet to 6 feet:

Old Value * 100 / (New Value - Old Value) = Percent Increase

In this case:

(6 - 5.5) / 5.5 * 100 = 9.090909090909091%

You can round this to the nearest tenth, which would be 9.1%.

Therefore, the percent of increase from 5.5 feet to 6 feet is 9.1%.

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The price of the ABC bond on the previous day is $104 3/4

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

Rate = $10 per day

Current price = $114 3/4

Using the above as a guide, we have the following:

Previous price = Current price - Rate

Substitute the known values in the above equation, so, we have the following representation

Previous price = $114 3/4 = $10

Evaluate the difference

Previous price = $104 3/4

Hence, the previous price is $104 3/4

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Complete question

ABC bond increase by $10 everyday. If the price on a given is $114 3/4, what was the price of the ABC bond on the previous day?

The given pair of linear equations is consistent.

What are Linear Equations?

An equation is said to be linear if the maximum power of the variable is consistent. Another name for it is a one-degree equation.

Equations are declarations of equality between two mathematical expressions containing one or more variables. A linear equation is one in which the maximum power of the variable is one. a real number equation of the form ax+by+c = 0, with real numbers a, b, and c with the highest power one variable x and y.

In our question, we can see:

a1 = -3 and a2 = 4

b1 = 3 and b2 = 4

c1 = 21 and c2 = 60

a1/a2 = -¾

b1/b2 = ¾

c1/c2 = 7/20

Since a1/a2 is not equal to b1/b2, therefore our pair of liner equation is consistent.

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Answer:

75,000

Step-by-step explanation:

We have to round up to nearest thousand ,so we need to check hundred place ...

If hundred place is equal or greater than 5 ,we need to add +1 to the number which is in thousand place , If it is less than 5 we don't need to do so ....

A set S spans R^2 if any element of R^2 can be written as linear combination of elements of S the set S spans R2.

(a) Given that S={ (1,-1),(2,1) }

Let (x,y) be the any element in R^2.

(x,y) = C1(1,-1)+C2(2,1)

(x,y) = (c1+2c2,-c1+c2)

x  =  c1+2c2

y  = -c1+c2

x+y = 3c2

c2= {x+y}/{3}

c1 = c2-y

= {x+y}/{3}-y

={x-2y}/{3}

So for any element (x,y) in R^{2} we have the constants c_1,c_2 so that (x,y) can be written as,

(x,y)= {(x-2y)}/{3}(1,-1) + {(x+y)}/{3}(2,1)

So S= { (1,-1),(2,1) } spans R^2.

(b) Given that S = { (1,1) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(1,1)

(x,y)=(c_1,c_1)

x=c_1,y=c_1

If x,y are distinct then do not get a value of c_1 so that (x,y) = c_1(1,1).

So set S= { (1,1) } does not span R^2.

(c) Given that S= { (0,2),(1,4) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(0,2)+c_2(1,4)

(x,y)=(c_2,2c_1+4c_2)

x=c_2

y=2c_1+4c_2

c_1={y-4c_2} / {2}

={y-4x} / {2}

So (x,y)= {(y-4x)}/{2}(0,2)+x(1,4)

So any element of R^2 can be written as written as linear combination of elements of Set S.

Hence set S={ (0,2),(1,4) } spans R^2.

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Answer:(a) To find the net cost equivalent, we can use the formula:

Net Cost Equivalent = Original Cost / (1 - (Discount Rate / 100))

Using this formula, the net cost equivalent for a series discount of 5/10/12 is:

Net Cost Equivalent = Original Cost / (1 - (5/100)) / (1 - (10/100)) / (1 - (12/100))

(b) To find the single discount equivalent for a series discount of 5/10/12, we can use the formula:

Single Discount Equivalent = (1 - (1 - (Discount Rate1 / 100)) x (1 - (Discount Rate2 / 100)) x ... x (1 - (Discount RateN / 100))) x 100

Using this formula, the single discount equivalent for a series discount of 5/10/12 is:

Single Discount Equivalent = (1 - (1 - (5/100)) x (1 - (10/100)) x (1 - (12/100))) x 100

Answer:

150 students in total

Step-by-step explanation:

30 students is 20%

20% x 5 = 100%

30 x 5 = 150 students

This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] diverges.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given a series, [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] we need to see if the series converges or not.

the ratio test will fail if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | =1[/tex]. Otherwise, the series converges absolutely if  [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | < 1[/tex] and diverges if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | > 1[/tex]

Testing for the series  [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}\\[/tex],

=> [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right |[/tex]

=>  [tex]\displaystyle \lim_{n\to \infty} \left |\frac{(n+1)!}{n!} \right | \\[/tex]

=> [tex]\lim_{n \to \infty} (n + 1)[/tex]

This value will always be greater than 1 for any positive value of n.

Therefore, This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] does not converge.

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The domain and the range of y = 12x - 36 are the set of all real numbers

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

y = 12x - 36

There is no restriction on the input values, x

So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).

The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).

This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.

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Complete question

What is the Domain of y = 12x - 36

x > 3 ,

-3 ≤ x ≤ 3,

all real numbers

Also, determine the range

Step-by-Step Explanation:

3rd term (a3) = -6

12th term (a12) = -3

We know, nth term of an AP = a1 + (n - 1)d, where d = common difference

a3 = a + (3-1)d = a + 2d = -6...(I)

a12 = a + (12-1)d = a + 11d = -3..(II)

Subtracting (II) from (I), we have

2d - 11d = -6 + 3

=> -9d = -3

=> d = 1/3

Therefore, a + 2×1/3 = -6

=> a + 2/3 = -6

=> a = -6-2/3 = -20/3

Therefore, 18th term

= a + (18-1)d

= -20/3 + 17/3

= -3/3

= -1

Answer:

-1

Hope it helps.

If you have any query, feel free to ask.

The number of cans to be added to 18 gallon tank is given by equation

A = 2.25 cans

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of cans for 18 gallon tank be A

Now , the equation will be

The number of cans per 8 gallons = 1 can

So , the number of cans for 1 gallon = number of cans per 8 gallons / 8

On simplifying the equation , we get

The number of cans for 1 gallon = 1/8

The number of cans for 1 gallon = 0.125 can

And ,

The number of cans for 18 gallons A = 18 x number of cans for 1 gallon

Substituting the values in the equation , we get

The number of cans for 18 gallons A = 18 x 0.125

The number of cans for 18 gallons A = 2.25 cans

Hence , the number of cans is 2.25 cans

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As per the given confidence interval, the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal is 336 ± 0.197

The term confidence interval is defined as the statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall.

Here we have given that the random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council.

Here we have also know that the percent of confidence interval is 95%.

Here we also identified the following values,

Total population = 1,018

Very supportive population = 336

Somewhat supportive population = 387

Not supportive population= 295

Then the value of confidence interval is calculated as,

Proportion of positive results = P = x/N = 0.3301

Lower bound = 0.3012

Upper bound = 0.3599

Therefore, it can be written as,

=> 336 ± 0.197

Complete Question:

A random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council. Based on the responses, which of the following is a 95% confidence interval for the proportion of all city residents who would respond very supportive of somewhat supportive of the proposal?

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In a parallelogram, opposite sides are equal in length, which can be used to calculate the length of AE. AB is equal to 26 and BD is equal to 20, so AE is equal to 6.

In contrast to a parallelogram, which has equal sides on both sides and diagonals that bisect each other, a rhombus has equal sides on all four sides and diagonals that cross at 90 degrees.

The length of each side is the same. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half.

In a parallelogram, opposite sides are equal in length. Therefore, we can use this fact to calculate the length of AE in the given parallelogram.

Since AB is equal to 26 and BD is equal to 20, we can set up the equation:

26 = AE + 20

Subtract 20 from both sides of the equation to solve for the length of AE:

26 - 20 = AE

6 = AE

Therefore, AE is equal to 6.

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