Find volume of a 6mi sphere

The distance of the flag pole from the end of the shadow is 23.32 feet.

A 20 foot flag pole is casting a shadow that is 12 feet long. Therefore, the distance of the top of the flag pole to the tip of the shadow can be calculated as follows:

The situation forms a right angle triangle.

Hence, using Pythagoras's theorem, we can find the distance.

Therefore,

c² = a² + b²

where

Therefore,

20² + 12²  = c²

400 + 144 = c²

c = √544

c = 23.3238075794

Therefore,

distance of the flag pole to the end of the shadow = 23.32 feet

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The interest earned in savings is given by the equation I = $ 50

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the interest be represented as I

Now , the amount invested A = $ 5000

The number of months = 12 months = 1 year

The rate of interest = 1 %

The interest I = A - P = P ( 1 + r/n )ⁿᵇ - P

So , the compound interest I = 5000 ( 1 + 1/100 )¹ - 5000

On simplifying the equation , we get

The compound interest I = 5000 ( 1 + 0.01 ) - 5000

The compound interest I = 5000 ( 1.01 ) - 5000

The compound interest I = 5050 - 5000

The compound interest I = $ 50

Hence, the interest is $ 50

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Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.

The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. Polynomials are mathematical expressions made up of variables (also known as indeterminates) and coefficients. A mathematical expression known as a polynomial is made up of two or more algebraic terms that are added, subtracted, or multiplied (never divided!). In polynomial expressions, which often also have at least one variable, constants and positive exponents are frequently utilized. The equation x2 4x + 7 denotes a polynomial.

given

a) (a - b)(a - b) = a² - 2ab + b²

b. (a + b)(a - b) = a²-6²

c. (a+b) (a²-ab+6²) = a³ - 6³

d. (a-b) (a² + ab +6²) = a³ - 6³

e. (a + b)(a + b) = a² + 2ab + b²

Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.

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The complete question is :- Match the following polynomial by its factored form .

a. (a - b)(a - b)

b. (a + b)(a - b)

c. (a+b) (a²-ab+6²)

d. (a-b) (a² + ab +6²)

e. (a + b)(a + b)

Answer:

A, E

Step-by-step explanation:

The lower part, the cone, is shaped like a cone.

The upper part, the ice cream, is shaped like a hemisphere.

Answer: A, E

Answer: 7/10 of a mile

Step-by-step explanation:

As we can use the expression that Eric used to solve this question!

7/8 x 4/5 = 7/10 of a mile

So, on solving the question we can say that the linear equation A(t)=1500e^0.3r = A(t) = 1232

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

A(t)=1500e^0.3r

the linear equation

A(t) = 1232

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Answer:

4a^2-2a+7

Step-by-step explanation:

combine like terms

7a+-9a= -2a

8a^2 - 4a^2 =4a^2

and anything to the power of 0 is a 1

so 7x1 is 7

so the answer is 4a^2 -2a+7

Answer:

(2/11)^3/(4/22)^6

= (2/11)^3/(2/11) ^6

=1/(2/11)^3

=(11/2)^3

Answer:  Choice G  [tex]3\text{x} \le 21[/tex]

======================================================

Reason:

The inequality for choice G solves to the following shown below.

[tex]3\text{x} \le 21\\\\3\text{x}/3 \le 21/3\\\\\text{x} \le 7\\\\[/tex]

In the second step, I divided both sides by 3 to undo the multiplication going on when saying "3x".

Once we arrive at [tex]\text{x} \le 7[/tex], the graph will have a closed endpoint at 7 and shading to the left. This is to visually describe all values of x that are 7 or smaller. The endpoint is included as part of the solution set.

This shows why choice G is the answer.

---------------------

Something like choice F has the inequality [tex]\text{x}-2 \le 9[/tex] solve to [tex]\text{x} \le 11[/tex] after adding 2 to both sides. The graph of [tex]\text{x} \le 11[/tex] involves a closed endpoint at 11 and shading to the left, which doesn't match the given number line graph. This allows us to rule out choice F.

Choices H and J are ruled out for similar reasoning.

Answer:

band could rent room B for a maximum of 9.44 hours.

Step-by-step explanation:

To represent the time (in hours) the band could rent room A, we need to consider both the cleaning fee and the hourly rate. The total cost of renting room A for t hours is given by the expression "50 + 24t". Since the band has $250 to spend, we can write an inequality to represent the maximum time they could rent the room:

50 + 24t <= 250

We can solve this inequality for t by subtracting 50 from both sides:

24t <= 200

Then, by dividing both sides by 24, we get:

t <= (200/24) hours

t <= 8.33 hours

So, the band could rent room A for a maximum of 8.33 hours.

b. To represent the time (in hours) the band could rent room B, we can use a similar approach as above. The total cost of renting room B for t hours is given by the expression "80 + 18t". Using the same budget of $250, we can write the following inequality:

80 + 18t <= 250

We can solve this inequality for t by subtracting 80 from both sides:

18t <= 170

Then, by dividing both sides by 18, we get:

t <= (170/18) hours

t <= 9.44 hours

So, the band could rent room B for a maximum of 9.44 hours.

c. From the above results, we can see that the band could rent room B for a slightly longer period of time compared to room A. However, the hourly rate for room B is cheaper than that of room A. So even though the band will get to use room B for a longer period of time, they will pay less overall to rent it. Additionally, the cleaning fee is cheaper in room B. Based on this information, the band should rent room B. They can stay in the room longer, pay less per hour, and pay less in cleaning fees.

The number of candy bars that the student can buy is given by the inequality c < 6 which means less than 6.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The inequality represents the amount of money a student can spend on c candy bars.

2c - 3 < 9

2c < 9 + 3

2c < 12

c < 6

This means,

c is less than 6.

Thus,

The number of candy bars that the student can buy is less than 6.

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The slope y is 3x - 10.When the line to be examined's slope is known, and the provided point also serves as the y intercept.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.

According to question:-

In the equation of a line's slope-intercept form, y = mx + b, we get y = 3x + 2, m1 = m2 gives us y = 3x +2, and m = 3 gives us the point (2 -4) where x = 2 and y = -4.

4 6 + b deducts 6 from both sides.

-10 = b, b = -10

After all, y = 3x - 10.

The complete question is,

y=3x+2 via (2,-4) parallel to

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The answer in  the system of linear equations represented in the graph have is b) One solution at (0, -1)

The system of linear equations represented in the graph has one solution, which is the point of intersection of the line with the coordinate plane.

This line can be represented by the equation y = mx + b where m is the slope and b is the y-intercept.

To find the slope, we can use the point slope formula which is m = (y2 - y1) / (x2 - x1)

We have the points (0,-1) and (1,-3)

So m = (-3 - (-1)) / (1 - 0) = -2/1 = -2

y = -2x + b is the equation of the line where x and y are the coordinates and b is the y-intercept.

b can be found by substituting the point (0,-1) in the equation.

-1 = -2(0) + b

b = -1

So the equation of the line is y = -2x - 1

therefore the solution is the point of intersection of the line with the coordinate plane which is (0, -1)

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The area of rectangle with length 3x + 2 and width 3x - 4 is 9x² - 6x - 8.

Once the length and width of a rectangle are known, the area is calculated. The area of a rectangle can be calculated by multiplying its length and width.

Here given that,

The rectangle's length is (3x + 2) units.

The width of the rectangle is (3x - 4).

We must determine the area of a rectangle.

Now,

Since the area of a rectangle equals length x width .

As a result, the area of a rectangle equals,

A = (3x + 2)  (3x - 4)

By simplifying the expression we get,

= (3x)(3x) + (3x)(-4) + 2(3x) + 2(-4)

= 9x² - 12x + 6x - 8

= 9x² - 6x - 8

Therefore the area of rectangle will be 9x² - 6x - 8.

The complete question:

"The length of a rectangle is 3x + 2 and the width is 3x – 4. What is the area of the rectangle in terms of x?"

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The time when the two submarines will be at the same depth is 25 minutes.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, Submarine A is 1200 feet underwater and has descended at a constant rate of 12 feet per minute. Submarine B is 1100 feet underwater but descends at a constant rate of 16 feet per minute

The equation will be:

1200 - 12m = 1100 - 16m

Collect the like terms

16m - 12m = 1200 - 1100

4m = 100

Divide

m = 100 / 4

= 25 minutes

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Answer:

x=2.28

Step-by-step explanation:

7x +y=11 we substitute y by ( -5)

7x +(-5)=11 (+)×(-)= --

7x-5=11

7x=11+5 when we move -5 to the opposite it become +5

7x =16

x=16 ÷7

x=2.28

Answer:

15,625

Step-by-step explanation:

5 to the 6 power = 5 × 5 × 5 × 5 × 5 × 5 = 15,625

Linear inequality represented by the graph is y > x/3

along with linear equations: y = x/3 and y = (x/3) - 2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The first line passes through

(0, 0) and (3, 1)

The slope of line is m = 1-0/3-0 = 1/3

y intercept = 0

So the equation of line is y = x/3

As the shading is outside so y > x/3

Now let us find for second line

(-3, -3) and (3, -1)

slope m' = -1 - -3/3 - - 3 = 2/6 = 1/3

Now y intercept

-2 = m(0) + c

c = - 2

So equation is y = x/3 - 2

Hence, linear inequality y > x/3 and linear equations: y = x/3, y = x/3 - 2  represent the graph.

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Answer:

8 × sin(35)

Step-by-step explanation:

remember the trigonometric norm circle and the triangle inside describing with its sides the trigonometric function values of the angle at the center of the circle.

sine is the vertical side, cosine is the horizontal side.

and the longest side really creating that angle at the center is the radius (going all the way from the center to the circle arc).

do not forget, the trigonometric functions sine, cosine, ... deliver values for the norm circle only (radius = 1).

for any circle larger or smaller these function values need to be multiplied by the actual radius to get the actual side lengths of the triangle.

now, we are allowed to rotate or twist/turn a given right-angled triangle to be oriented like the basic trigonometric triangle.

in our case we can simply flip things upside-down.

and we see, BC is simply sine of 35° (multiplied by the radius 8).

it does not matter that it is originally pointing down. it is for the angle 35°, and sine of angles 0° <= angle <= 180° must be positive.

The standard normal random variable P(z > 2.11) = 1(1/2(1+erf(1.45))

A standard normal random variable Z has a mean of 0 and a standard deviation of 1.

P(Z > 2.11) can be found using the cumulative distribution function (CDF) of the standard normal distribution.

The CDF of the standard normal distribution is provided by:

F(z) = P(Z 2.11) we can use the complement rule:

P(Z > 2.11) = 1 - P(Z 2.11)

               = 1 - F(2.11)

               = 1 - (1/2) * (1 + erf(2.11/sqrt(2)))

               = 1 - (1/2) * (1 + erf(1.45))

Where erf is the error function.

This value can be calculated using a calculator or a standard normal table by looking up the value of erf(1.45) and subtracting it from 1/2.

Therefore, the resulting value is the probability that a standard normal random variable is greater than 2.11

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The only solution that satisfies the inequality is the point (0,0)

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Answer:51

Step-by-step explanation:

7*7=49，10*10=100 100-49=51

The mathematical expression which correctly uses exponents to write "6 factors of 2" include the following: B. 2⁶

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as bⁿ.

In Mathematics, factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors simply refers to numbers which can be multiplied together to get another number.

Next, we would translate the word statement into an algebraic expression as follows;

6 factors of 2 = 2 × 2 × 2 × 2 × 2 × 2

6 factors of 2 = 2⁽¹ ⁺ ¹ ⁺ ¹ ⁺ ¹ ⁺ ¹ ⁺ ¹⁾

6 factors of 2 = 2⁶

In this context, we can reasonably infer and logically deduce that "6 factors of 2" can be correctly written by using an exponent as 2⁶.

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Complete Question:

Which of the following correctly uses exponents to write "6 factors of 2"? A. 6² B.2⁶ C. 6 ∙ 2 D. 12

Answer:

mario

Step-by-step explanation:

If triangle ABC has the following measurements, than the measure of side c is 25.08

What is triangle ?

A triangle in which it contains three sides and three angles and the sum of three angles be 180 degrees.
Given ,

a = 17

b = 23

C = 76 degrees.

So,

we know that,

c = [tex]\sqrt{a^{2}+b^{2}-2abcosc }[/tex]

c = [tex]\sqrt{17^{2} + 23^{2} - 2*17*23*cos76 }[/tex]

c = [tex]\sqrt{289 + 529 - 884*cos76}[/tex]

c = [tex]\sqrt{818-189}[/tex]

c = [tex]\sqrt{629}[/tex]

c = 25.08

hence , If triangle ABC has the following measurements, than the measure of side c is 25.08

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The equation of the parallel line will be y = (2/3)x - 8/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y - 4 = 2/3 (x - 3)

The equation of the line that is parallel to the given line will be written as,

y = (2/3)x + c

The equation of the line that passes through (1, -2), then we have

- 2= (2/3)(1) + c

- 2 = 2 /3 + c

c = - 8 / 3

Then the equation of the parallel line will be y = (2/3)x - 8/3.

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The resulting expression would be 8b + 4v + 13.

What is an Expression?

An expression consists of one or more numbers or variables along with one more operation.

If we combine like terms in 4b - 2v + 4b + 6v + 13 the resulting expression would be, 8b + 4v + 13.

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The resulting expression would be 8b + 4v + 13.

An expression is created by combining one or more variables or numbers with another operation. A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

If we combine like terms in 4b - 2v + 4b + 6v + 13 the resulting expression would be, 8b + 4v + 13.

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The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

transformation of functions

f(x) - f(x) -2

translate 2 units down

f(x) - f(x - 2)

translate 2 units right

f(x) - f(x) + 2

translate 2 units up

The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.

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The value for expression 2/3xy² when x = -1/3 and y = 1/2 is 8.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is 2/3xy².

The value of x is given as x = -1/3.

The value of y is given as y = 1/2.

To find the value of the expression, substitute the value of x and y in the expression -

= 2/3xy²

Expand using the power rule -

= [2/(3 × (-1/3) × (1/2)²)]

Use the arithmetic operation of multiplication -

= [2/(3 × (-1/3) × (1/4)]

= [-2/(-3/12)]

= -2/(-1/4)

The denominator will reciprocate -

= -2 × -4

= 8

Therefore, the final value is obtained as 8.

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The formula for Rn for the given function is[tex]\int\limits^5_{-1} {9x^2} \, dx =\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)[/tex]. And the area is 378 units².

The approximate area under the graph of a function f(x) throughout the range [a, b] can be calculated using a Riemann sum. Then, the formula to determine the length of each subinterval is given by [tex]\Delta x=\frac{b-a}{n}[/tex].

Substituting the given interval in the above formula, we get,

[tex]\begin{aligned}\Delta x &=\frac{5+1}{n}\\&=\frac{6}{n}\end{aligned}[/tex]

Now, the sample point [tex]x_i[/tex] is given as

[tex]\begin{aligned}x_i&=a+i\Delta x\\&=-1+i\left(\frac{6}{n}\right)\\&=\frac{6i}{n}-1\end{aligned}[/tex]

The formula for Rₙ is calculated as follows,

[tex]\begin{aligned}R_n&=\sum_{i=1}^{n}f(x_i)\Delta x\\&=\sum_{i=1}^{n}9\left(-1+\frac{6i}{n}\right)^2\frac{6}{n}\\&=\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)\end{aligned}[/tex]

Then, the area under the curve is computed as follows,

[tex]\begin{aligned}\int\limits^{5}_{-1} {9x^2} \, dx&= \lim_{n \to \infty} \sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)\\&=\lim_{n \to \infty}\left( \sum_{i=1}^{n}\frac{54}{n}-\sum_{i=1}^{n}\frac{648i}{n^2}+\sum_{i=1}^{n}\frac{1944i^2}{n^3}\right)\\&=\lim_{n \to \infty}\left(\frac{54}{n}\sum_{i=1}^{n}(1)-\frac{648}{n^2}\sum_{i=1}^{n}(i)+\frac{1944}{n^3}\sum_{i=1}^{n}(i^2)\right)\end{aligned}[/tex]

Solving this we get,

[tex]\begin{aligned}\int\limits^5_{-1} {9x^2} \, dx &=\lim_{n \to \infty}\left(\frac{54}{n}(n)-\frac{648}{n^2}\left(\frac{n(n+1)}{2}\right)+\frac{1944}{n^3}\left(\frac{n(n+1)(2n+1)}{6}\right)\right)\\&=\lim_{n \to \infty}\left(54-\frac{324(n+1)}{n}+\frac{324(n+1)(2n+1)}{n^2}\right)\\&=\lim_{n \to \infty}\left(54-324\left(1+\frac{1}{n}\right)+324\left(2+\frac{1}{n}+\frac{2}{n}+\frac{1}{n^2}\right)\right)\end{aligned}[/tex]

As the value of n tends to ∞, then 1/n is zero. Substituting these n values, we get,

[tex]\begin{aligned}\int\limits^5_{-1} {9x^2} \, dx&=54 -324+324(2+0)\\&=\mathrm{378\;units^2} \end{aligned}[/tex]

The required answers are [tex]\int\limits^5_{-1} {9x^2} \, dx =\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)[/tex] and 378 units².

The complete question is -

Find a formula for Rₙ for the function f (x) = (3x)² on [− 1, 5] in terms of n. Compute the area under the graph as a limit.

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