Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64cm^2

Answer:

Option B - 6x-6/x

Step-by-step explanation:

Given : If [tex]f(x)=\frac{x-3}{x}, g(x)=x+3,h(x)=2x+1[/tex].

To find : What is the value of  [tex](g(h(f)))(x)[/tex]

Solution :

[tex](g(h(f)))(x)=g(h(f(x)))[/tex]

i.e, substitute the value of f(x) in h(x) and then put that h(x) in g(x).

[tex]g(h(f(x)))=g(h(\frac{x-3}{x}))[/tex]

[tex]g(h(f(x)))=g(2(\frac{x-3}{x})+1)[/tex]

[tex]g(h(f(x)))=(2(\frac{x-3}{x})+1)+3[/tex]

Solving the RHS,

[tex]=(2(\frac{x-3}{x})+1)+3[/tex]

[tex]=(\frac{2x-6}{x})+1)+3[/tex]

[tex]=(\frac{2x-6+x}{x})+3[/tex]

[tex]=\frac{3x-6}{x}+3[/tex]

[tex]=\frac{3x-6+3x}{x}[/tex]

[tex]=\frac{6x-6}{x}[/tex]

Therefore, The value of [tex](g(h(f)))(x)=\frac{6x-6}{x}[/tex]

Hence, Option B is correct.

Taking into account the definition of combination, you can take 1716 different collections of 6 books.

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in which the order in which the elements are chosen is not taken into account and repetition is not possible.

The combination is calculated by:

[tex]C=\frac{m!}{n!(m-n)!}[/tex]

The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.

In this case it is possible to apply a combination, not all the elements enter, the order in which the books are chosen does not matter, and they are not repeated.

Being m= 13 and n=6, the combination is calculated by:

[tex]C=\frac{13!}{6!(13-6)!}[/tex]

Solving:

[tex]C=\frac{13!}{6!7!}[/tex]

C= 1716

Finally, you can take 1716 different collections of 6 books.

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The probability of rolling a number greater than 4 with a single fair die is 1/3 or approximately 0.33. This is calculated as the number of desired outcomes (a roll of 5 or 6) divided by the total possible outcomes (1, 2, 3, 4, 5, or 6). The actual results of a short series of rolls may vary, but over time the results should average out to this probability.

The question is asking to calculate the probability of rolling a die and getting a number greater than 4. In a fair six-sided die, the possible outcomes of a single toss are 1, 2, 3, 4, 5, or 6, making the total possible outcomes 6. The outcomes greater than 4 are 5 and 6, which gives us 2 desired outcomes.

Remember, probability is calculated as the number of desired outcomes over the number of total possible outcomes. So in this case, the probability is 2 (the number of outcomes greater than 4) divided by 6 (the total number of outcomes when rolling a die) which gives a probability of 1/3 or approximately 0.33.

This suggests that if you throw the single fair die repeatedly over time, about one third of the results would show a number greater than 4. It's essential to remember this is a theoretical probability, and actual short-term results may vary, but they should correspond to this probability in the long run per the law of large numbers.

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Since it is specifically stated that the line intersects the x-axis, then this means that y = 0. Therefore substituting y = 0 into the given equation will us the value of x.

Substituting y = 0:

3 x + 2 * 0 = 72

3 x = 72

x = 24

Therefore this means that the line intersect the x-axis at point (24, 0).

2/3 (5 × 4) ÷ 3 + 6/7 = 334/63

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem.

Let's write down the problem that is wanted to be solved:

[tex]\frac{2}{3} ( 5 \times 4 ) \div 3 + \frac{6}{7}[/tex]

[tex]\frac{2}{3} ( 20 ) \div 3 + \frac{6}{7}[/tex] → Parentheses First

[tex]\frac{40}{3} \div 3 + \frac{6}{7}[/tex] → Multiplication

[tex]\frac{40}{9} + \frac{6}{7}[/tex] → Division

[tex]\frac{280}{63} + \frac{54}{63}[/tex] → Match the denominator of the fraction

[tex]\frac{334}{63}[/tex] → Final Answer

From the results above, it can be concluded that the results of this operation 2/3 (5 × 4) ÷ 3 + 6/7 is 334/63

Grade: Middle School

Subject: Mathematics

Chapter: Order of Operations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS

The dimensions of the garden where 320 ft of the antique picket fencing are to be used to enclose the garden are 96 feet and 64 feet.

Given that:

A garden is in rectangular shape.

The length of the antique picket fencing used to enclose the garden is 320 feet.

The perimeter defines the enclosing length.

So, the perimeter is 320 feet.

Let P = 320.

Let l represent the length and w represents the width of the garden.

The width is exactly two-thirds of the length.

So, [tex]w=\frac{2}{3} l[/tex].

The perimeter of the garden is:

P = 2(l + w)

  = 2 (l + [tex]\frac{2}{3} l[/tex])

  = [tex]\frac{10}{3} l[/tex]

So, substitute P = 320.

[tex]\frac{10}{3} l=320[/tex]

Simplifying,

l = 96 feet

So, w = 64 feet

Hence, the dimensions are 96 feet and 64 feet.

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Answer:

Step-by-step explanation:

Answer: x = 12

Step-by-step explanation:

1/3 = 4/x

1x = 12

X = 12

2020 is 20 years after 2000, so put 20 where t is in the equation and evaluate.

P = 16,581e^(0.02·20) = 16,581e^0.4

P ≈ 24,736

The model predicts the population in 2020 will be about 24,736.

Answer:

Statement C, E and F are true.        

Step-by-step explanation:

We have to find the true statements about a regular polygon.

Regular Polygon  

A) False

This is not a necessity that all angles measure 90 degrees.

B) False

It may or may not be a a quadrilateral.

C) True

All regular polygons are closed figure.

D) False

All regular polygons are not hexagon but hexagon is a polynomial.

E) True

All the angles of a regular polygon are equal.

F) True

Since all the sides of a regular polygon are equal, thus, its sides are congruent line segments.

Answer:

Step-by-step explanation:

The form for finding the nth term of an arithmetic sequence is a(n) = b +(n-1)d, where a is the function of the nth term, b is the first number in the sequence, n is the nth term, and d is the common difference. Plugging in what we know we get:

a(31) = -108 + 30 x 18

multiply

a(31) = -108 + 540

add

a(31) = 432

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Final answer:

The value of P(A intersection B) is 0.20.

Explanation:

Given that events A and B are independent, the probability of their intersection can be found by multiplying their individual probabilities. So, P(A ∩ B) = P(A) * P(B). From the given information, P(A) = 0.40 and P(B) = 0.50. Therefore, P(A ∩ B) = 0.40 * 0.50 = 0.20.

The probability of achieving exactly two successful calls in eight attempts in a telephone survey using a random digit dialing machine is approximately 0.324 or 32.4%.

To calculate the probability of achieving exactly two successful calls in eight attempts in a telephone survey using a random digit dialing machine, we can use the binomial distribution formula. The formula is:

P(x) = (nCx) * (p^x) * ((1-p)^(n-x))

Where:

Plugging in the values from the question, we have:

P(2) = (8C2) * (0.15^2) * ((1-0.15)^(8-2)) = 28 * 0.0225 * 0.411771 = 0.3239965

Therefore, the probability of achieving exactly two successful calls in eight attempts is approximately 0.324 or 32.4%.

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41+0.10x = 31+0.15x

10 +0.10x=0.15x

10=0.05x

x=10/.05

x= 200 text messages

check 200*0.10 = 20 +41 =61

200*0.15 = 30+31 = 61

 they equal each other so number of texts is 200