helppppppppppppppppppppppppppp

Answer:

To the power 3 means cube.

Whenever you cube an even number it is a multiple of 8.

Whenever an exponent is used on 4, the number is always a square.

The value of the give exponent is 64.

Given that, the base is 4 and exponent is 3.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

With the base 4 and exponent 3, we have

4³

= 4×4×4

= 64

Therefore, the value of the give exponent is 64.

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Probability of rolling a number greater than 0 but less than 7 is 1.

The probability formula is as follows:

Probability = Favourable outcomes / Total outcomes

Sample space of rolling a dice:

S = {1, 2, 3, 4, 5, 6}

Total outcomes = 6

Favourable outcomes: number greater than 0 but less than 7

Favourable outcomes: 6

Then, probability of rolling a number greater than 0 but less than 7

Probability = Favourable outcomes / Total outcomes

Probability = 6/6

Probability = 1

Thus,  probability of rolling a number greater than 0 but less than 7 is 1.

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The complete question is-

A dice is being rolled. Find the probability of rolling a number greater than 0 but less than 7

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Using the algebra we can calculate the 3 gallons of strawberry juice and 2 gallons of lemon juice to make a 5-gallon mixture of juice that contains 17% sugar.

A system of equations is a set of two or more equations with multiple variables that are solved simultaneously to find a common solution that satisfies all the equations.

Let x be the amount of strawberry juice (in gallons) and y be the amount of lemon juice (in gallons) needed for the mixture.

From the problem statement, we know that the total amount of the mixture is 5 gallons, so we have:

x + y = 5

we know that the concentration of sugar in the strawberry juice is 27%, while that of the lemon juice is 2%. Since we want a mixture with a sugar concentration of 17%, we can write the following equation:

0.27x + 0.02y = 0.17(5)

Simplifying this equation gives:

0.27x + 0.02y = 0.85

Now we have two equations with two unknown variable, which we can solve using algebra. Multiplying the first equation by 0.02, we get:

0.02x + 0.02y = 0.1

Subtracting this equation using second equation, we get:

0.25x = 0.75

Solving for x gives:

x = 3

putting x = 3 into the first equation, we get:

3 + y = 5

Solving for y gives:

y = 2

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Answer:

The correct number line that shows the solutions to x+8 > 15 is option B.

Step-by-step explanation:

The correct number line that shows the solutions to x+8 > 15 is option B.

On this number line, you can see that the values of x that make the inequality true are greater than 7. Therefore, the solution set for this inequality is x > 7.

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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Answer:

5.75

Step-by-step explanation:

Make denominator to 100 by multiplying by 25

4*25=100

3*25=75

75/100=.75

Answer:

12-4

Step-by-step explanation:

The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11

A composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.

The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.

i.e. the function g(x) = 11 always returns the value 11, regardless of the input.

Therefore, we have:

g(-3) = 11

g(5) = 11

g(a) = 11

g(a+h) = 11

So, regardless of the value of a or h, the function g(x) will always return 11.

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Objective (Profit) Function : 120 Po + 40 Co + 60 Ca

Constraint Functions : Po + Co + Ca = 100 (Land Constraint) ;                    Budget Constraint : 400 Po + 160 Co + 280 Ca = 20000

LET : Acres of land for Potato, Corn, Cabbage = Po, Co, Ca respectively.

Objective Function is the function to be minimised or maximised. Here, 'PROFIT' is to be maximised.

Constraint functions denote the other conditions to be maintained, while maximising & minimising objective profit function.

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Answer:

the correct answer would be B

( 18-3 )

Step-by-step explanation:

Answer: 2/9 x = 18; If the total amount of space is 18 inches, and each book is 2/9ths of an inch thick, you have to use x to figure out the missing value of how many books will fit

Step-by-step explanation:

The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).

Given expression is,

[15 / (x - 6)] + [7 / (x + 6)]

Cross multiplying the two fractional expressions,

= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]

= [15x + 90 + 7x - 42] / [x² - 6²]

= (22x + 48) / (x² - 36)

Hence the equivalent expression is D.

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Answer:

\(6i\sqrt{2}\)

Step-by-step explanation:

Given expression:

\(\sqrt{-72}\)

Rewrite -72 as the product of 6 · -1 · 2:

\(\implies \sqrt{36 \cdot -1 \cdot 2}\)

Apply the radical rule  \(\sqrt{ab}=\sqrt{a}\sqrt{b}:\)

\(\implies \sqrt{36} \sqrt{-1} \sqrt{2}\)

Carry out the square root of 36:

\(\implies 6\sqrt{-1}\sqrt{2}\)

Apply the imaginary number rule \(\sqrt{-1}=i\) :

\(\implies 6i\sqrt{2}\)

Answer:

The answer is 11/8.

Step-by-step explanation:

The value of sece is ±√11/8 when the function tan²e= 3/8

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that  tan²e= 3/8

We have to find the value of sine.

We have trigonometric identity

sec²e-tan²e=1

Plug in the value of tan²e

sec²e=1+3/8

sec²e=11/8

Take square root on both sides

sece=±√11/8

Hence, the value of sece is ±√11/8 when the function tan²e= 3/8

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Answer:

\(e^{2n}x + C\) (since n is assumed to be a constant when integrating with respect to x)

Step-by-step explanation:

You are integrating with respect to x, but \(e^{2n}\) has no x-terms. Thus, it is considered a constant. The integral of any constant is equal to the constant multiplied by x.

Example: the integral of 2 is 2x, since the derivative of 2x is 2.

\(\int {e^{2n}} \, dx = e^{2n}x + C\)

If you were integrating \(e^{2x}\) with respect to x, it would look like this:

Since...

\(\frac{d}{dx} (e^{ax}) = ae^{ax}\)

The integral of \(e^{ax}\) is:

\(\int{e^{ax}} \, dx = \frac{e^{ax}}{a} + C\)

\(\int {e^{2x}} \, dx = \frac{e^{2x}}{2} + C\)

Note: C is a constant. It can be any number.

Answer: \(e^{2n}x + C\) (since n is assumed to be a constant)

Given the equation:

the given equation is for logarithm function with a base of 4

The domain will be all real numbers of x

So,

We will find the value of f(2)

So, substitute with x = 2 and solve

so,

So, the answer will be:

Answer:

The price elasticity of demand measures how responsive the quantity demanded is to a change in price. It can be calculated using the midpoint method, which is (change in quantity demanded / average quantity demanded) / (change in price / average price).

Using the midpoint method to calculate the price elasticity of demand for business travelers and vacationers, you would need more information such as the change in quantity demanded and the average quantity demanded for each group at different prices.

It is not possible to say if the demand is elastic or not for either group based on the information provided.

Answer:

t = 8588 years

Step-by-step explanation:

From the given information:

Using the formula:

\(k = \dfrac{In (2)}{t_{1/2}}\)

Given that:

\(t_{1/2}\) = 5730 years

Then:

\(k = \dfrac{In (2)}{5730}\)

\(k = \dfrac{0.6931472}{5730}\)

k = 1.20968 × 10⁻⁴

However; the expression to find the value of x is:

\(x= x_oe^{-kt}\)

\(4.6 \times 10^{-13} = 1.3 \times 10^{-12} \times e^{(-1.20968\times 10^{-4} \times t)}\)

\(\dfrac{4.6 \times 10^{-13} }{1.3 \times 10^{-12}}= e^{(-1.20968\times 10^{-4} \times t)}\)

\(0.353846= e^{(-1.20968\times 10^{-4} \times t)}\)

(-1.20968 × 10⁻⁴ × t) = In(0.353846)

(-1.20968 × 10⁻⁴ × t) = -1.03889

\(t = \dfrac{-1.03889}{-1.20968 \times 10^{-4}}\)

t = 8588 years

Answer:

Step-by-step explanation:

The question is incomplete. Find the complete question in the attached file.

a) Given the expression 9x^2 - y^2 = 1

Differentiating implicitly will give;

\(18x-2y\frac{dy}{dx} = 0\\\)

We can then make dy/dx the subject of the formula as shown;

\(18x = 2y\frac{dy}{dx}\\\frac{dy}{dx} = \frac{18x}{2y} \\\frac{dy}{dx} = \frac{9x}{y} \\y' = \frac{9x}{y}\)

b) In order to solve the question explicitly, we will first have to make x the subject of the formula before differentiating.

\(9x^{2} -y^{2} = 1\\9x^{2} = 1+ y^{2}\\y^{2} =9x^{2}- 1\\y^{2} = 9x^{2} - 1\\y = \sqrt{9x^{2}- 1 } \\\)

Using chain rule to solve the equation;

let;

\(u = 9x^{2} -1\\ y = u^{1/2}\)  

du/dx = 18x

dy/du = \(1/2u^{-1/2}\)

dy/dx = dy/du * du/dx

dy/dx = \(1/2u^{-1/2} * 18x\)

\(\frac{dy}{dx} = \frac{1}{2}({9x^{2}-1 } )^{-1/2} * 18x\\\frac{dy}{dx} = 9x({9x^{2} -1 } )^{-1/2} \\\frac{dy}{dx} = 9 x(\sqrt{{\frac{1}{9x^{2} -1} } }) \\\frac{dy}{dx} = \frac{9x}{\sqrt{9x^{2}-1 } }\)

c) In order to confrim that solutions to part (a) and (b) are consistent, we will substitute \(y = \sqrt{9x^{2} - 1 } \\\) into the answer in (a) as shown;

From (a) \(\frac{dy}{dx} = \frac{9x}{y} \\\)

\(y' = \frac{9x}{ \sqrt{9x^{2} - 1 } \\} } \\}\)

This shows that they are consistent

Answer:

10 gallons per hour

Step-by-step explanation:

1/4x4=1. 2 1/2x4=10. Hope it helps!

We are given

Proportion (p)

Level of significance = 99%

margin of error = 1.5% = 0.015

We want to find n

Solution

Note: The margin of error formula is given as

The image of the formula to use is

In the question, we have

Substituting the parameters

Therefore, the sample size is as large as

Probability of getting a 1 on the blue die, P(E) = 1/6

Given,

Two fair dice, one being blue and the other red.

E is the event of getting a 1 on the blue die.

F is the event of all the numbers being equal.

To find,

Probability of event E occurring, that is, the probability of getting a 1 on the blue die, P(E)

Probability (Event) = (Number of favourable outcomes) / (Total possible outcomes)

No of favourable outcomes = 6C1 = 6!/(5! x 1!) = 6

No of total possible outcomes = 36

Probability of event E occurring, that is, the probability of getting a 1 on the blue die, P(E) = 6/36 = 1/6

Therefore, by using two fair dice, one blue and one red, the probability of getting a 1 on the blue die is 1/6.

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The rate of interest compounded continuously is 16.7%

What does the math term "rate of interest" mean?

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.

Formula: \(A=Pe^{rt}\)

Where A = final amount

P = initial amount

e =mathematical constant approximated as 2.7183

r = rate of interest

t = time

Initially (t=0) in 1945 a famous painting was sold for $21,210

\(21210 = Pe^{0} \\P = 21210\)

In 1987 (t=42) the painting was sold for $33.3 million

\(33.3 * 10^{6} = 21210 e^{42r} \\e^{42r} = \frac{33.3 * 10^{6}}{21210 } \\\\e^{42r} = 1570.014\\42r = ln( 1570.014)\\r = \frac{1}{42} ln( 1570.014)\\r = \frac{1}{42} 7.36\\r = 0.167\\r = 16.7%\)

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9514 1404 393

Answer:

  354,998

Step-by-step explanation:

If the number is less than 350,000, it will not round to 400,000.

If the number is 355,000 or more, it will not round to 350,000.

The number (n) must satisfy ...

  350,000 ≤ n < 355,000

__

If we're restricted to integers, the number could be any between 350,000 and 354,999, inclusive. One possibility is 354,998.

Answer:

10¢

Step-by-step explanation:

First, to be able to differentiate between the B&W and Color copies, use x in place of the B&W copies and y in place of the Color copies.

Then, write a system of equations to solve (the system of equations input was not working, so there is no brace):

 8x + 2y = $1.20

 10x + 10y = $3.00

Then, solve the system of equations:

   8x +  2y = $1.20

 10x + 10y = $3.00

Isolate x to be able to substitute:

8x + 2y = $1.20

8x = -2y + 1.2

x = -2/8y + 1.2/8

x = -0.25y + 0.15

Substitute:

10x + 10y = $3.00

10 (-0.25y + 0.15) + 10y = 3

-2.5y + 1.5 + 10y = 3

7.5y + 1.5 = 3

7.5y = 1.5

y = $0.20

Now that you have the cost of the Colored copies, you can plug it in to find the B&W copies:

8x + 2y = $1.20

8x + 2(0.2) = 1.2

8x + 0.4 = 1.2

8x = 0.8

x = $0.10

Rearrange terms

5 +