A cylinder with a radius of 8 inches is cut from the prisim. What is the volume of the new object

Answer:

2nd answer option : 6^(13/4)

Step-by-step explanation:

what are we doing, when 2 equal base terms with exponents are multiplied ? we add the exponents !

this is like 3⁴×3³ = 3⁷

because

3×3×3×3 × 3×3×3 = 3×3×3×3×3×3×3 = 3⁷

it is that simple.

and that concept is also valid for any kind of number as exponent. even for fractions and so on.

so,

6^3 × 6^(1/4) = 6^(3 + 1/4) = 6^(12/4 + 1/4) = 6^(13/4)

To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

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

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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the width of the box is 1.21 ft

length of the box = 2 times the width

let the width = w

length = 2(w) = 2w

height = 6ft more than its width

height = 6ft + w = 6 + w

Volume of the rectangular box = length × width × height

Volume of the rectangular box = 2w × w × (6 + w)

Volume of the box is given as = 21ft³

21 = 2w × w × (6 + w)

21 = 2w²(6 + w)

21 = 12w² + 2w³

But since we can't have width as a negative number, w will be the positive number

w = 1.207206

To two decimal place, w = 1.21

Hence, the width of the box is 1.21 ft

To find the percentage decrease;

Decrease = 11 000 - 10 500 = 500

%decrease = 500 / 11000 x100%

=4.55%

You can identify that the expression is a polynomial and its degree is 2.

As you can see in the exercise, it has the following form:

You know two terms of the expression:

By definition, a Perfect square expression is an expression that can be factored in the form of the product of two Binomials:

Therefore, knowing the two terms of the expression given, you can set up that:

Then:

The answer is:

For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.

f(x) = 7/8x² - 14

Substitute f(x) with 0 -

0 = 7/8x² - 14

Add 14 to both sides -

7/8x² = 14

Multiply both sides by 8/7 -

x² = 16

Take the square root of both sides -

x = ±4

Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.

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Answer: exponential

Step-by-step explanation: the x in the equation is an exponent

Answer:

Exponential.

Step-by-step explanation:

The function shown is h(x) = 8(1/3)^x.

Essentially this is showing powers of 1/3 multiplied by 8.

This would not make a line, as it involves an exponent.

As a result, this function is exponential, because of the exponent involved.

Answer:

14

Step-by-step explanation:

We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.

There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.

To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.

Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):

Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.

Therefore, the probability that a randomly selected student scored A or B

in Biostatistics is:

Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.

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Answer:

4.

-building

-artisting

-selling

-making good

-trading

-farming

5. "Being settled meant being tied to land and possessions; being nomadic meant having a mobile community with a mobile food supply. This allowed nomads to attack and plunder resources. They could gain access to agricultural products without having to farm or trade."

6. " They were also trained in riding and archery, as they sometimes had to defend their communities from outsiders. Women’s graves sometimes contained weapons, suggesting they had a role in military life as well."

Step-by-step explanation:

Answer:

I am implying that the correct answer would be A, The Pacific plate.

Step-by-step explanation:

The Australian, Nazca and Pacific plates move up to four times faster than the smaller African, Eurasian and Juan de Fuca plates.

The 3 fastest plates:

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

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There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Answer:

- 7

Step-by-step explanation:

Step 1:

- 2 ( x - 3 ) + 4x = - ( - x + 1 )        Equation

Step 2:

- 2x + 6 + 4x = x - 1         Multiply/Open Parenthises

Step 3:

2x + 6 = x - 1       Combine Like Terms

Step 4:

x + 6 = - 1     Subtract x on both sides

Answer:

x = - 7        Subtract 6 on both sides

Hope This Helps :)

Answer:

21 km²

Step-by-step explanation:

A = ᵃ ⁺ ᵇ/2 (h)

A = 5 + 9/2 (3)

A = 14/2 (3)

A = 7 x 3

A = 21 km²

Answer:

122 miles

Step-by-step explanation:

Let n = number of miles driven

Given:

⇒ 14.95 + 0.95n = 130.85

Subtract 14.95 from both sides:

⇒ 0.95n = 115.90

Divide both sides by 0.95

⇒ n = 122

Therefore, he drove 122 miles.

Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

Let's write this verbal phrase as an inequality.

First of all, let the number be n.

"three times n" can be written like so:-

\(\pmb{3n}\)

Now, 18 is greater than 3n:-

\(\pmb{18 > 3n}\)

Which means 3n is less than 18:-

\(\bigstar{\boxed{\pmb{3n < 18}}}\)

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, THEN the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

Step-by-step explanation:

The Euclidean postulate in geometry is represented as:

If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, THEN the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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The number of pork sliders sold is given as follows:

24 pork sliders.

The number of pork sliders sold is obtained applying the proportions in the context of the problem.

The total number of pork sliders is given as follows:

120 pork sliders.

The percentage of pork sliders sold is given as follows:

20%. (proportion of 0.2).

Hence the amount sold is given as follows:

0.2 x 120 = 24 pork sliders.

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Answer:6

Step-by-step explanation:

The original number that was multiply by 5 instead of 3 is 6.

The equation that can be used to represent the informatioin in the question is:

5x - 3x = 12

Where x is the original number

In order to determine the value of x, take the following steps

Combine similar terms: 2x = 12

Divide both sides by 2

x = 6

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Answer:

10 times

Step-by-step explanation:

Subtract the price of food per day from the daily cost and divide the season pass price by the daily cost without food.

120+(6•x) x=days 120+(6•x)=18•x

Answer:

41.2

miles

Explanation:

To solve the question, first find the number of miles Rachel power walked.

She walked

2

3

5

or

2.6

miles a day for seven days. Multiply seven days by

2.6

to find the total number of miles Rachel power walked that week.

2.6

⋅

7

=

18.2

Next, find the number of miles Rachel jogged.

She jogged

5.75

miles a day for four days. Multiply

4

by

5.75

to find the number of miles Rachel jogged that week.

5.75

⋅

4

=

23

Rachel power walked 18.2 miles and jogged 23 miles. Add the two values up to find the total number of miles that she power walked and jogged.

18.2

+

23

=

41.2

Answer: False.

Step-by-step explanation:

The statement is:

"The sum of two irrational numbers is always an irrational number."

We know that √2 is an irrational number.

Then the opposite number, (-1)*√2 is also an irrational number.

Then we can sum two irrational numbers like:

√2 + (-√2) = 0

and 0 is a rational number.

Then we have found a counter-example, which means that the statement is false.