The largest of the great pyramids in Egypt was built with a square base having edges measured 754 feet and a height of 418 feet. To the nearest cubic foot, what was the volume of the original structure

Two positive angles that have a sum of π/2 radians are complementary angles, whereas two positive angles that have a sum of π radians are supplementary angles.

Complementary angles are two angles whose measures add up to a right angle, which is equal to π/2 radians or 90 degrees. In other words, if α and β are complementary angles, then α + β = π/2.

Supplementary angles, on the other hand, are two angles whose measures add up to a straight angle, which is equal to π radians or 180 degrees. If α and β are supplementary angles, then α + β = π.

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Answer:

377 parents

Step-by-step explanation:

We start by writing an exponential equation

FV = PV(1 - r)^t

FV is future value = ?

PV is present value = 440

r is rate = 5/100 = 0.05

t = 3

Substituting these values

FV = 440(1 - 0.05)^3

FV = 377.245

This is approximately 377

Now,

The cube root of 7 = 7^1/3

= 1.912

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The product that is the factored form of the polynomial 3x⁴ - 2x² + 15x² - 10 is (x² + 5)(3x² - 2).

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

The polynomial is first correctly stated as follows

This is rearranged, grouped and solved as follows:

\(\sf 3x^4+15x^2-2x^2-10\)

\(\sf (3x^4+15x^2)-(2x^2+10)\)

\(\sf 3x^2(x^2+5)-2(x^2+5)\)

Factorizing the common factors, we have the product of the factored form of the polynomial as follows:

\(\boxed{\rightarrow\bold{(x^2 + 5)(3x^2 - 2)}}\)

Thus, the product that is the factored form of the polynomial 3x⁴ - 2x² + 15x² - 10 is (x² + 5)(3x² - 2).

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Answer:

a. 4×d=24

Step-by-step explanation:

Since it is asking for the number of dogs and each dog has 4 legs, you multiply

And dogs is (d), so a

Answer:

Answer:

800 miles

Step-by-step explanation:

Let the amount of miles = m

Company A charges a flat rate of $160 a day, and $0.60 per mile:

total = 0.60m + 160

Company B charges a flat rate of $80 a day, and $0.70 per mil:

total = 0.70m + 80

Step-by-step explanation: Rank me brain list or thanks it :) Hope it helps!

The questions that could be used to challenge each claim goes as follows.

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The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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Answer:

180

Step-by-step explanation:

The answer is 180 because 20 nickels make a dollar and you do 20x9 and that equals to 180

Answer:

$180 nickels

Step-by-step explanation:

9x 20= 180

The surface area of the cuboid is 3.286 cm²

A cuboid is a solid shape or a three-dimensional shape.

Surface area is the amount of space covering the outside of a three-dimensional shape.

The surface area of a cuboid is expressed as;

SA = 2( lb + lh + bh)

length = 1 2/5 = 7/5

breadth = 5/8

height = 3/8

lb = 7/5 × 5/8 = 7/8

bh = 5/8 × 3/8 = 15/64

lh = 7/5 × 3/8 = 21/40

surface area =2( 7/8 + 15/64+21/40)

= 2( 0.875 + 0.234 + 0.525)

= 2( 1.634)

= 3.268 cm²

The surface area of the cuboid is 3.268 cm²

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The asset's variance is approximately 0.0358, and its standard deviation is approximately 0.1891.

To calculate the variance and standard deviation of the asset's returns, we'll follow the steps mentioned earlier using the given probability distribution:

⇒ Calculate the expected return (μ):

μ = (0.27 * 0.25) + (0.18 * 0.25+) + (0.10 * 0.30) + (0.04 * 0.20+)

  = 0.0675 + 0.045 + 0.03 + 0.008

  = 0.1505

⇒ Calculate the variance (σ^2):

σ^2 = [(0.27 - μ)^2 * 0.25] + [(0.18 - μ)^2 * 0.25+] + [(0.10 - μ)^2 * 0.30] + [(0.04 - μ)^2 * 0.20+]

Substituting the values and simplifying:

σ^2 = [(0.27 - 0.1505)^2 * 0.25] + [(0.18 - 0.1505)^2 * 0.25+] + [(0.10 - 0.1505)^2 * 0.30] + [(0.04 - 0.1505)^2 * 0.20+]

    = [(0.1195)^2 * 0.25] + [(0.0295)^2 * 0.25+] + [(-0.0505)^2 * 0.30] + [(-0.1105)^2 * 0.20+]

    = 0.017972 + 0.00021617 + 0.0030309025 + 0.01459516

    = 0.0358141325

⇒ Calculate the standard deviation (σ):

σ = √(σ^2)

  = √(0.0358141325)

  ≈ 0.1891

Therefore, the asset's variance is approximately 0.0358 and the standard deviation is approximately 0.1891.

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Answer:

7

Step-by-step explanation:

5+10-13+5

15-13+5

2+5

Answer:

7

Step-by-step explanation:

Order of Operations: BPEMDAS

B - Brackets

P - Parenthesis

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

Step 1: Write expression

5 + 10 - 13 + 5

Step 2: Evaluate

Add: 15 - 13 + 5

Subtract: 2 + 5

Add: 7

Answer:

Layout A needs 4.8 m more fencing

Step-by-step explanation:

Khan academy answer

The standard deviation for the random variable X, the number of wins, is approximately 0.10341.

Probability of winning a certain lottery \(= 1/51,949\)

560 times were played overall.

Let X represent the random variable that represents the number of victories out of 560 plays.

The probability of winning in one play is \(p = 1/51,949\). The probability of not winning in one play is \(q = 1 - p\)

\(q = (51,949 - 1) / 51,949\)

\(q = 51,948 / 51,949.\)

What X should actually be is:

\(E(X) = np\)

\(E(X) = 560 * (1/51,949)\)

\(E(X) = 0.010793\)

The variance of X is:

\(Var(X) = npq\)

\(Var(X) = 560 * (1/51,949) * (51,948/51,949)\)

\(Var(X) = 0.010699\)

The value of X's standard deviation is

\(SD(X) = \sqrt{Var(X)}\)

\(SD(X) = \sqrt{0.010699}\)

\(SD(X) = 0.10341\)(approx)

Therefore, the standard deviation for the random variable X, the number of wins, is approximately 0.10341.

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P(A and B) = P(A) × P(B) is the formula used to assess if two events are independent (B).

P(A) is the chance that event A will occur.

The chance that event B will occur is marked as P(B).

If the chance of both occurrences happening at the same time, P (A and B), equals the product of the individual probabilities of each event, P(A) x P(B), the events are called independent.

If, on the other hand, the chance of both occurrences occurring simultaneously is less than the product of the individual probabilities of each event, the events are deemed dependent.

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a)The initial height of the flare when it is fired is 2m.

b)The height of the flare after 1 s is 38.75m

c)The flare reaches its maximum height after 2 seconds.

d) The maximum height of the flare is 65m.

e) The flare hits the water after 8 seconds.

The given equation which is h = -5.25t² + 42t + 2, can be used to solve the following questions:

a) To get the initial height of the flare when it is fired, the value of t = 0 must be used in the given equation:

h = -5.25(0)² + 42(0) + 2h

= 0 + 0 + 2h

= 2

Therefore, the initial height of the flare when it is fired is 2m.

b) To get the height of the flare after 1 s, the value of t = 1 must be used in the given equation:

h = -5.25(1)² + 42(1) + 2h

= -5.25 + 42 + 2h

= 38.75

Therefore, the height of the flare after 1 s is 38.75m

c)The maximum height of the flare is reached when the flare is at its peak.

Therefore, the time when the flare reaches its maximum height is found by dividing -b by 2a, where the equation is in the form of y = ax² + bx + c.

The equation h = -5.25t² + 42t + 2 is in the form of y = ax² + bx + c,

where a = -5.25, b = 42, and c = 2.t = -b/2a = -42/2(-5.25)

= -2

Therefore, the flare reaches its maximum height after 2 seconds.

d) To get the maximum height of the flare, the value of t = 2 must be used in the given equation:

h = -5.25(2)² + 42(2) + 2h

= -21 + 84 + 2h

= 65

Therefore, the maximum height of the flare is 65m.

e)When the flare hits the water, the height, h, is 0.

Therefore, the time when the flare hits the water is found by setting h = 0 in the given equation and solving for t:

0 = -5.25t² + 42t + 2

Using the quadratic formula:\($$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$\)

where a = -5.25, b = 42, and c = 2.

= \(\frac{-42 \pm \sqrt{42^2 - 4(-5.25)(2)}}{2(-5.25)} $$t\)

= 8.003 or t = 1.331

Since time cannot be negative, the time when the flare hits the water is after 8 seconds. Therefore, the flare hits the water after 8 seconds.

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Answer:

65=x^3+7

Step-by-step explanation:

65=x^3+7

I am not sure if I am supposed to solve this but first you would subtract 7 from both sides and get 58=x^3 and then take the cube root of both sides which is x=3.87...

The graph of y = x^2e^(-2) has a point of inflection at the values of x where the concavity of the curve changes. In mathematical terms, a point of inflection occurs where the second derivative of the function changes sign.

To find the values of x that correspond to the points of inflection, we need to find the second derivative of the function and solve for the values of x that make the second derivative equal to zero or undefined.

First, let's find the first and second derivatives of y = x^2e^(-2):

First derivative:

dy/dx = 2xe^(-2) + x^2(-2)e^(-2) = 2xe^(-2) - 2x^2e^(-2)

Second derivative:

d^2y/dx^2 = 2e^(-2) - 4xe^(-2) = 2e^(-2)(1 - 2x)

Now, set the second derivative equal to zero and solve for x:

2e^(-2)(1 - 2x) = 0

Since e^(-2) is always positive and nonzero, we can ignore it for solving this equation. Therefore:

1 - 2x = 0

2x = 1

x = 1/2

So, the graph of y = x^2e^(-2) has a point of inflection at x = 1/2.

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hope it's correct answer.....and it helps

Answer:

0.5 or 1/2

Step-by-step explanation:

\(\frac{2}{4}\) simplify by 2 on both sides \(\frac{1}{2}\)

or

see attached

Answer:

\(2x - 4 = 10 \\ 2x = 10 + 4 \\ 2x = 14 \\ x = \frac{14}{2} \\ x =7\)

Step-by-step explanation:

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2x - 4 = 10

Add 4 to both sides:

2x - 4 + 4 = 10 + 4

Combine like terms:

2x = 14

Divide both sides by 2:

2x/2 = 14/2

Simplify:

X = 7

Answer: x = 7

Answer:

-9 and -8

Step-by-step explanation:

Adding -9 to 9 would equal 0, and -9 + -8 is -17. Also if you want to check, just complete the equation just plug in those two integers :)

The equation can be written according to the problem will be –17 + 9 = –8. And the two missing integers are -8 and -9.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Aman is adding -17 + 9.

He wants to write –17 as the sum of two numbers.

So that one of the numbers, when added to 9, will equal 0.

Let the other number be x. Then

-17 + 9 + x = 0

      -8 + x = 0

             x = 8

Then the equation can be written according to the problem will be

–17 + 9 + 8 = 0

      –17 + 9 = –8

Or   –17 + 8 = –9

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Answer:

1 1/2%

Step-by-step explanation:

1 square is shaded and half the other square is shaded

Answer:

A

Step-by-step explanation:

I am positive that the answer is A) □♡ based on the pattern observed in the given sequence. The symbol □ represents the tens digit and ♡ represents the units digit, and since the previous number in the sequence had ♡ as both digits, the next number should have □ as both digits. Therefore, the next number in the sequence would be □♡, which is a two-digit number where the tens digit is one less than the units digit.

B) □□: This option cannot be the next number in the sequence because it represents a two-digit number where both digits are equal, but the previous number in the sequence had ♡ as both digits. Therefore, the next number should have □ as both digits.

C) ♡♡: This option cannot be the next number in the sequence because it represents a two-digit number where both digits are equal, but the previous number in the sequence had ♡ as both digits. Therefore, the next number should have □ as both digits.

D) ♢□: This option cannot be the next number in the sequence because it represents a two-digit number where the tens digit is greater than the units digit, but the previous numbers in the sequence had the units digit greater than the tens digit. Therefore, the next number should have the tens digit one less than the units digit.

E) ♡♢: This option cannot be the next number in the sequence because it represents a two-digit number where the tens digit is less than the units digit, but the previous numbers in the sequence had the units digit greater than the tens digit. Therefore, the next number should have the tens digit one less than the units digit.

Answer:

Step-by-step explanation:

Because the first digit changes in the first 2 numbers, we can assume that the first number is at the end of a count: like 19, 29, 39...  

So the numbers will be 19,20, 21     or 29, 30 31 etc.

But we know that the last number's second digit is the same as the first number's first first digit, therefore, the square is 1

So the numbers are 19, 20, 21

So the heart will be the first digit of the of the next number, it has to be the 3rd or 5th answer. but we know the next number is 22 so it's the double heart which is the 3rd answer.

Heart heart is answer.

The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.

Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.

Iteration 1: a = 1, b = 2

c = (a + b) / 2

= (1 + 2) / 2 is 1.5

f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375

ince f(c) has a negative value, the root lies in the interval [1.5, 2].

Iteration 2:

a = 1.5, b = 2

c = (a + b) / 2

= (1.5 + 2) / 2 is 1.75

f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844

Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].

Iteration 3: a = 1.5, b = 1.75

c = (a + b) / 2

= (1.5 + 1.75) / 2 is 1.625

f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8  is -0.2141

Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].

Iteration 4: a = 1.625, b = 1.75

c = (a + b) / 2

= (1.625 + 1.75) / 2 is 1.6875

f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.

Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].

Iteration 5: a = 1.625, b = 1.6875

c = (a + b) / 2

= (1.625 + 1.6875) / 2 is 1.65625

f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .

Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].

Iteration 6: a = 1.625, b = 1.65625

c = (a + b) / 2

= (1.625 + 1.65625) / 2 which gives 1.640625

f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.

Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].

teration 7: a = 1.640625, b = 1.65625

c = (a + b) / 2

= (1.640625 + 1.65625) / 2 results to 1.6484375

f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116

Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].

Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.

b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.

Iteration 1:

x₁ = x₀ - (f(x₀) / f'(x₀))

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.

f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.

x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.

Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.

c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.

Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))

f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375

x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826

Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.

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Given the coordinates:

A(3, -5)

B(10, -8)

C(12, -13)

D(5, -10)

Then, applying the given rule, we have:

A'(3 - 13, -5 + 21) = ( -10, 16)

B'(10 - 13, -8 + 21) = ( -3, 13)

C'(12 - 13, -13 + 21) = ( -1, 8)

D'(5 - 13, -10 + 21) = ( -8, 11)