Can someone help me with this math homework please!

The expression can be simplified as 2.09 × 10⁻⁹.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

We have to evaluate (23)⁻³ . (34)⁻³.

We have a rule of exponent that,

aⁿ . bⁿ = (a . b)ⁿ

Applying the rule,

(23)⁻³ . (34)⁻³ = (23 × 34)⁻³

                      = 782⁻³

We have another rule of exponent that,

a⁻ⁿ = 1 / aⁿ

So, 782⁻³ = 1 / 782³ = 2.09 × 10⁻⁹

Hence the simplified form is 2.09 × 10⁻⁹.

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i. cos 0 =  \(\sqrt{3}\)

ii. tan 0 = 1/ \(\sqrt{3}\)

Trigonometric functions are a set of given functions which are required in determining the value(s) of the sides or internal angle(s) of a given right angled triangle; when the value of one none right angle is given.

In the given question, we have;

sin 0 = 1/2

This implies that;

sin 0 = opposite/ hypotenuse = 1/2

So that;

opposite = 1

hypotenuse = 2

Apply the Pythagorean's theorem so as to determine its adjacent, we have;

adjacent = \(\sqrt{3}\)

Then,

cos 0 = adjacent/ hypotenuse

         =  \(\sqrt{3}\) / 1

cos 0 =  \(\sqrt{3}\)

ii. tan 0 = opposite/ adjacent

            = 1/  \(\sqrt{3}\)

tan 0 = 1/ \(\sqrt{3}\)

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Answer:

7.5

Step-by-step explanation:

annsnsjdjdndnfbbrbdbtbfbfbfbt

Answer:

X = 10 Unknown Side:  30 and 21

Step-by-step explanation:

We need to know the total earnings and total expenses for the day. Without this information, we cannot accurately determine Leo's profit. If you can provide additional details or the complete notebook entries, I would be happy to assist you in calculating the profit.

To determine Leo's profit for the first day, we need more information than what is provided in the question. The notebook shows the money earned and spent, but the given information stops at "10," without specifying whether it represents money earned or money spent. Additionally, we don't have any other earnings or expenses mentioned in the question.

To calculate the profit, we need to know the total earnings and total expenses for the day. Without this information, we cannot accurately determine Leo's profit. If you can provide additional details or the complete notebook entries, I would be happy to assist you in calculating the profit.

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Value of x for which defined function f(x) = x²e⁻ˣ² gives the relative maximum value is equal to option D. -1 or  1.

Function 'f' is defined by f(x) = x²e⁻ˣ²

To get the relative maximum value of the function f(x) =  x²e⁻ˣ² find the first derivative we have,

f(x) =  x²e⁻ˣ²

Apply product rule of derivative :

d/dx ( u × v ) = v du /dx + u dv /dx

f' ( x ) =  e⁻ˣ² d/dx (x²) + x² d/dx (e⁻ˣ²)

⇒ f' (x) = 2x  e⁻ˣ² - 2x (x² ) ( e⁻ˣ² )

⇒  f' (x) = 2x  e⁻ˣ² - 2x³ e⁻ˣ²

⇒ f' (x) = 2x  e⁻ˣ²( 1 - x² )

To get the value of x for maximum function f' (x ) = 0 we get,

2x  e⁻ˣ²( 1 - x² ) = 0

⇒ 2≠0 or x =0 or  e⁻ˣ² ≠ 0 or 1 - x² = 0

⇒ x = 0 or x = ± 1

When

x = 0 ⇒ f(x) = 0

x = 1 ⇒ f(x) = e⁻¹

x = -1 ⇒ f(x) = e⁻¹

x = -1 or 1 represents the relative maximum value of f(x).

Therefore , value of x which represents the relative maximum value of the function f(x) = x²e⁻ˣ² is equal to option D. -1 or 1.

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33

Vocabulary

Before going into an explanation, let's go over some important vocabulary.

Solving for MN

Using the postulate above we can make a new equation. First, let's set up an equation that mirrors the postulate.

Now, let's plug in the values we know.

Then, solve.

This proves that a possible value of MN is 33.

Answer:

-14

Step-by-step explanation:

1. \((-18) - (-4)\)

2. \(-18 - (-4)\)

3. \(-18 + 4\)

4. \(-14\)

Using the stars and bars method again, we have 5 bars and 8 stars, which results in equation  C(13,5) = 13! / (5! * 8!) = 1287 number of solutions.

To find the number of solutions for the equation x1 + x2 + x3 + x4 + x5 + x6 = 29 with x1 ≥ 1, we can reframe the equation as (x1 - 1) + x2 + x3 + x4 + x5 + x6 = 28. Now, we can use the stars-and-bars method to determine the number of solutions. There are 5 bars and 28 stars, which gives us a total of 33 positions. We need to choose 5 positions for the bars, so the number of solutions is C(33,5) = 33! / (5! * 28!) = 23751.
For the equation with x1 ≥ 1, x2 ≥ 2, x3 ≥ 3, x4 ≥ 4, x5 ≥ 5, and x6 ≥ 6, we can rewrite it as (x1 - 1) + (x2 - 2) + (x3 - 3) + (x4 - 4) + (x5 - 5) + (x6 - 6) = 8. Using the stars-and-bars method again, we have 5 bars and 8 stars, which results in C(13,5) = 13! / (5! * 8!) = 1287.
For the equation with x1 ≥ 5, we can rewrite it as (x1 - 5) + x2 + x3 + x4 + x5 + x6 = 24. Using the stars-and-bars method, there are 5 bars and 24 stars, which gives us C(29,5) = 29! / (5! * 24!) = 118755.
Unfortunately, the given constraints for option D are not clear enough to provide a solution. Please rephrase or clarify the constraints for this scenario, and I'll be happy to help you find the number of solutions.

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The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.

The volume of cone (V) = 1/3 * πr²h

Volume of cylinder (V) = πr²h

Where, r is the radius of their bases.

The base area formula for the cone = πr²

Calculate the area of the base of the cone that has a radius (r) of 2.5 in:

Area of the base of the cone = π(2.5)² ≈ 19.6

The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5

≈ 42.5 cubic inches

Volume of cylinder (V) = πr²h = π * 2² * 4

≈ 50.3 cubic inches

The difference in volume = 50.3  - 42.5

= 7.8 ≈ 8 cubic inches

Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.

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Answer:

  False

Step-by-step explanation:

You want to know if it is true that the graph of a rational function cannot cross a horizontal asymptote.

Once a function is on its final approach to an asymptote, it will approach, but not cross, that asymptote.

The function may have a variety of behaviors prior to that point, so may cross the horizontal asymptote one or more times before its final behavior is established.

An example with the asymptote y = 0 is attached.

<95141404393>

Answer:

b

Step-by-step explanation:

A two-tailed test is a hypothesis test in which the rejection region is option (B) in both tails of the sampling distribution

The hypothesis test is defined as the statistic approach checking the results of a research study support a particular theory when we apply that result to population

A two-tailed test is a hypothesis test that defined in which the critical area of the distribution is two sided, so the sample will be greater than or less than a certain range of values

Therefore, the rejection region of a two-tailed test is a hypothesis test is in both tails of the sampling distribution.

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The Volume generated when the region between the curves is rotated around the y - axis is 1216500335.46

Volume of the curves:

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π ∫dc [f(y)]2dy.

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y).

Given,

y = x³

Here we have to find the volume along to the y axis.

With limit as y = 0 and y = 27.

When we apply the values it can be written as,

=>\(V=\pi \int\limits^0_{27} {(x^3)^2} \, dx\)

\(\implies V=\pi \int\limits^0_{27} {(x^6)} \, dx\)

Apply the limits then we get,

\(\implies V = \pi [0^6 - (27)^6]\)

=> V = π [0 - 387420489]

=> V =   π x 387420489

=> V = 1216500335.46

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Answer:

(2, 4, 3)

Step-by-step explanation:

Range = Y

Answer:

you multiply the square root of six and the square root of two

The table of values that represents exponential decay is (c)

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

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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Answer:

1,000 lightbulbs that day were tested

Step-by-step explanation:

Answer:

true for all x  or AllRealNumbers

Step-by-step explanation:

The total area of the figure is obtained as option B: 21 3/8 cm².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

To find the total area of the figure, we need to find the area of the rectangle and the area of the triangle, then add them together.

The area of the rectangle is -

Length x Breadth

= (3 1/2) cm x (4 1/2) cm

= (7/2) cm x (9/2) cm

= 63/4 cm²

The area of the triangle is -

1/2 x Base x Height

= 1/2 x (4 1/2) cm x (5/2) cm

= 45/8 cm²

To find the total area of the figure, we add the area of the rectangle and the area of the triangle -

Total area = Area of rectangle + Area of triangle

Total area = (63/4) cm² + (45/8) cm²

Total area = (126/8) cm² + (45/8) cm²

Total area = 171/8 cm²

Therefore, the total area of the figure is 21 3/8 cm² or 21.375 cm² if we want to use decimal notation.

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Answer:

Its 10:4 so its 5:2 when dividing

5:2 is the answer

The ratio of orange fish to green fish in the fish tank is given by 5 : 2

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the proportion equation be represented as A

Now , the value of A is

Let the total number of fishes in the fish tank be = 14 fishes

The number of orange fishes = 10 fishes

The number of green fishes = 5 fishes

Now , the ratio of orange fish to green fish in the fish tank is = number of orange fishes / number of green fishes

On simplifying , we get

The ratio of orange fish to green fish in the fish tank is = 10 / 4

The ratio of orange fish to green fish in the fish tank is = 5/2

Hence , the proportion is 5 : 2

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The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

We have,

To determine the increasing and decreasing behavior of the function f(x) = x / (x² - 9) on the given intervals, we can evaluate the sign of the derivative of the function.

Taking the derivative of f(x) with respect to x and simplifying, we have:

\(f'(x) = (-x^2 + 9 - x(2x)) / (x^2 - 9)^2\\= (-x^2 + 9 - 2x^2) / (x^2 - 9)^2\\= (-3x^2 + 9) / (x^2 - 9)^2\)

To identify the increasing and decreasing behavior, we need to examine the sign of f'(x) on each interval.

For the interval (-∞, -3):

Plugging in a value less than -3, such as -4, into f'(x) yields a positive result.

Plugging in a value between -3 and 0, such as -2, into f'(x) gives a negative result.

Therefore, f'(x) is positive for x < -3 and negative for -3 < x < 0, indicating that f(x) is increasing on the interval (-∞, -3) and decreasing on the interval (-3, 0).

For the interval (-3, 3):

Plugging in a value between -3 and 0, such as -2, into f'(x) yields a negative result.

Plugging in a value between 0 and 3, such as 1, into f'(x) gives a positive result.

Therefore, f'(x) is negative for -3 < x < 0 and positive for 0 < x < 3, indicating that f(x) is decreasing on the interval (-3, 0) and increasing on the interval (0, 3).

For the interval (3, ∞):

Plugging in a value between 3 and 4, such as 3.5, into f'(x) yields a positive result.

Plugging in a value greater than 4, such as 5, into f'(x) gives a negative result.

Therefore, f'(x) is positive for 3 < x < 4 and negative for x > 4, indicating that f(x) is increasing on the interval (3, 4) and decreasing on the interval (4, ∞).

Thus,

The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

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The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

In the given probability case we have;

What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?

Let,

P = 15% = 0.15

n = 500

By considering the binomial distribution case the formula is given by

P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

                 = ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ

                 = 0.031

                 ≅ 0.03

Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

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Answer: We can start by using the information given to find the total bill amount.

If the water/sewer/garbage portion of the bill is 72% of the total bill, then the remaining 28% of the bill must be for other utilities. We can use a proportion to set up the equation:

72/100 = 94.41/x

where x is the total bill amount.

We can cross-multiply and solve for x:

72x = 100 * 94.41

x = (100 * 94.41) / 72

x = 123.84

To the nearest cent, the total amount of the utility bill was $123.84.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

4 out of 10 is 4/10 = 0.4

0.4 of 45 = 0.4 * 45 = 18

Answer: 18

As per the gaussian distributed random variables , the joint probability density function of the given variable is E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]

Gaussian distribution:

In statistics, the Gaussian distribution refers the normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

Given,

Here we need to find the the joint probability density function of the variables x and y be independent gaussian distributed random variables each with zero mean and unity variance.

Here we know that every weighted sum of the samples of the Gaussian process Z(t) is Gaussian, Z(t1), Z(t2) are jointly Gaussian random variables. Hence we need to find mean, variance and correlation co-efficient to evaluate the joint Gaussian PDF.

Then the equation is written as,

=> E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]

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Answer:

40

Step-by-step explanation:

The area of the second triangle is 200 square unit.

Given:

the area of the first triangle, A = 8 square unit

let the base of the first triangle = b

let the height of the first triangle = h

then, base of the second triangle = 5b

height of the second triangle = 5h

To find:

the area of the second triangle

The area of the first triangle is given as;

\(A = \frac{bh}{2} \\\\2A = bh\\\\2(8) = bh\\\\16 = bh ---- (1)\)

The area of the second triangle is calculated as;

\(A = \frac{5b \times 5h}{2} \\\\A = \frac{25bh}{2} \\\\recall, bh = 16\\\\A = \frac{25 \times 16}{2} \\\\A = 200 \ unit^2\)

Thus, the area of the second triangle is 200 square unit.

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The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.

Given;

Location of the tree = The other side of the river from the surveyor

Length of the line measured along the river, L = 125 feet

Angle to the tree from the start of the line = 65°10'

1° = 60'

10' = ((1/60)×10)° = (1/6)°

65°10' = (65 + 10/60)° = (65 + 1/6)°

Angle measured at the end of the line, E = 60°10'

Similarly;

E = 60°10' = (60 + 1/6)°

The interior angle, S, of the triangle formed by the tree and the line, at the start of the line is therefore;

Angle S = 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)

S = (114+5/6)°

From the angle sum property of a triangle, angle formed at the tree, T, is therefore;

T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°

According to the rule of sines, we have;

l/(sin T) = b/(sin E)

Where;

b = The length of the bridge

Which gives;

124/(sin 5°) = b/(sin (60 + 1/6)°)

b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2

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