(4x6) x 3 = 4 x (3x6)

Answer:

6,7,7,8,9 both have 7 for mode and median

Step-by-step explanation:

To triple a mixed number, multiply the whole number part by 3 and triple the numerator of the fraction part. For 3 1/2, the result is 9 3/2.

To triple the mixed number 3 1/2:

Multiply the whole number by 3: 3 x 3 = 9.

For the fraction part, triple the numerator: 1 x 3 = 3. The denominator remains the same.

Therefore, tripling 3 1/2 gives 9 3/2.

For a p-type silicon in which the dopant concentration N A = 5 × 10^ 18 /cm^3 , find the hole.

For a p-type silicon in which the dopant concentration NA= 5×1018/cm^3, find the hole and electron concentrations

Corresponding sides in similar figures match up. The person's shadow in the small triangle corresponds to the shadow of the Flag Pole in the large triangle. The longest side of the large triangle corresponds to the Longest side of the small triangle.

Corresponding sides in similar figures are the sides that match up.

In the given diagram of two similar triangles, the person's shadow in the smaller triangle corresponds to the shadow of the Flag Pole in the larger triangle.

The longest side of the large triangle corresponds to the Longest side of the small triangle.

rolling a 5 is a 1/6 probability

 tossing tails is a 1/2 probability

 doing both is a 1/6 * 1/2 = 1/12 probability

The converse of the conditional statement "If you are 14 years old then you are a teenager" is true. If someone is a teenager, it implies that they are at least 14 years old.

The converse of the conditional statement "If you are 14 years old then you are a teenager" is:

If you are a teenager then you are 14 years old.

The converse statement is true because if someone is a teenager, it implies that they are at least 14 years old. However, it does not guarantee that someone who is 14 years old is necessarily a teenager, as there are other age groups within the teenage years.

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To average 80 km/hr for the entire trip, the truck must go at a speed of 80 km/hr during the second half of the trip.

To find out how fast the truck must go during the second half of the trip to average 80 km/hr for the entire trip, we can use the concept of average speed. Average speed is calculated by dividing the total distance traveled by the total time taken.

Let's assume the entire trip is made up of two equal halves. In the first half, the truck travels at a speed of 70 km/hr. So, if we consider the distance traveled in the first half to be 'd', the distance traveled in the second half will also be 'd'.

Therefore, the total distance traveled for the entire trip is 2d. Now, to average 80 km/hr for the entire trip, we can use the formula:Average speed = Total distance / Total time

80 km/hr = 2d / Total time

Since the time taken for the first half is the same as the time taken for the second half, we can represent the total time as '2t', where 't' is the time taken for each half.

Substituting the values, we have:80 km/hr = 2d / (2t)

Cancelling out the common factors, we get:80 = d / t

Since the distance traveled in the first half is 'd' and the time taken for the first half is 't', the speed during the second half must be '80' km/hr to average 80 km/hr for the entire trip.

The percentage decrease in a price is 37 percent.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, in January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year.

Cost of gas per gallon = 2.05+1.20

= $3.25

Now, Percentage decrease = (Original Price - New Price)/Original Price ×100

= (3.25-2.05)/3.25 ×100

= 1.20/3.25 ×100

= 0.3692×100

= 0.37×100

= 37%

Therefore, the percentage decrease in a price is 37 percent.

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Answer:

The diver's new depth is -42 ft.                                      

Step-by-step explanation:

Given : A scuba diver at a depth of -12 ft (12 ft below sea level), dives down to a coral reef that is 3.5 times the diver's original depth.

To find : What is the diver's new depth?

Solution :

A scuba diver at a depth of -12 ft.

Dives down to a coral reef that is 3.5 times the diver's original depth.

So, We have to multiply the original depth by 3.5.

i.e. [tex]d=-12\times 3.5[/tex]

[tex]d=-42[/tex]

Therefore, the diver's new depth is -42 ft.

The function f(g(x)) is ((x^10+1)^(9/2), the derivative f'(u) is (9/2)u^(7/2), the derivative f'(g(x)) is (9/2)(x^10+1)^(7/2), the derivative g'(x) is 10x^9, and the derivative (f ∘ g)'(x) is the product of g'(x) and f'(g(x)) which equals to 10x^9 * (9/2)(x^10+1)^(7/2).

The functions are defined as f(u)=u9/2 whereas g(x)=x10+1.

To find f(g(x)), input g(x) into the f function. Thus, f(g(x))=((x10+1)9/2.

Next, the derivative of f(u) would be: f'(u)= (9/2)u7/2.

For f'(g(x)), replace u with g(x) in f'(u): f'(g(x))=(9/2)(x10+1)7/2.

The derivative of g(x) is: g'(x)=10x9.

Lastly, to find (f ∘ g)'(x), use the chain rule which states that (f ∘ g)'(x) = g'(x) * f'(g(x) : (f ∘ g)'(x) = 10x9 * (9/2)(x10+1)7/2.

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Answer:

The value of x is 11.

Step-by-step explanation:

The given number is 0.27272727..., and it is converted to the fraction as

[tex]0.272727...=\frac{3}{x}[/tex]                 ..... (1)

Multiply both sides by 100.

[tex]0.272727...\times 100=\frac{3}{x}\times 100[/tex]

[tex]27.272727=\frac{300}{x}[/tex]            .... (2)

Subtract equation (1) from equation (2),

[tex]27.272727-0.272727...=\frac{300}{x}-\frac{3}{x}[/tex]

[tex]27=\frac{300-3}{x}[/tex]

Multiply both sides by x.

[tex]27x=297[/tex]

Divide both sides by 27.

[tex]x=\frac{297}{27}[/tex]

[tex]x=11[/tex]

Therefore the value of x is 11.

The value of the variable "x" in the fraction 0.27... = 3/x is x = 11.

To find the value of "x" in the fraction 0.27... = 3/x, we use algebraic techniques to solve for x,

Let us represent the repeating decimal 0.27... as a variable, say y,

y = 0.27...

To eliminate the repeating decimal, we multiply both sides of equation by a power of 10. In this case, we multiply by 100 to shift decimal point two places to right,

100y = 27.27...

Now, we subtract original equation from this new equation to eliminate the repeating part:

100y - y = (27.27...) - (0.27...),

Simplifying the equation:

99y = 27

y = 27/99

The fraction 27/99 is simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 9,

y = 3/11

Therefore, the required value of "x" is 11.

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Answer:

D They must have common denominators.

Step-by-step explanation:

Rational expressions are fractions formed by two polynomials, one in the numerator and other in the denominator.

The numerator is the polynomial that is at the top of the fraction and denominator is the polynomial that is at the bottom of the fraction.

To add any fractions it is necessary that they have the same denominator, this applies to rational expressions, to add them it is required that they have the same polynomial in the denominator.

Academic integrity is essential for a fair and genuine educational experience, emphasizing honesty and accountability in all academic endeavors. It is crucial for building trust, equity, and facilitating real learning outcomes, necessitating a collective effort from the academic community to maintain these values. The widespread issue of academic dishonesty further highlights the need for strict adherence to integrity principles.

Academic integrity is the cornerstone of a meaningful educational experience, emphasizing the value of honesty and fairness within the academic community. It involves the commitment to avoid cheating, plagiarism, and any form of deception or fraud in academic work, ensuring that all academic activities, from research to examination, are conducted in a manner that is fair, respectful, and accountable. The importance of academic integrity lies not only in the cultivation of a fair and trustworthy academic environment but also in fostering genuine learning and understanding, thereby empowering students to achieve authentic success that extends well beyond their academic careers.

Despite the challenges posed by technological advancements and digital resources, which have made cheating more accessible and harder to detect, maintaining academic integrity is crucial. It builds trust, understanding, equity, and facilitates real, meaningful learning outcomes. Faculty, administrators, and students alike bear the responsibility of upholding these principles to ensure that the academic community remains a space where fairness prevails and genuine knowledge acquisition is celebrated.

According to the International Center for Academic Integrity, a significant number of students have admitted to engaging in dishonest behaviors, which underscores the ongoing battle against academic dishonesty. Highlighting the importance of maintaining integrity, these statistics serve as a reminder of the collective effort needed to nurture an academic culture that values honesty above all.

Answer:

total tax is = 14685 pound

Step-by-step explanation:

Given data:

For first year -  

earning is 11000 pound

for second year

income is = 43000 - 11000 = 32000 pound

tax rate = 20%

for third year

income is = 150000 - 43000 = 107000 pound

tax rate = 40%

for fourth year

income is = 158900 - 150000 = 8900 pound

tax rate = 45%

As it is given there is no tax on first year

Tax in 2nd year  = 0.20 × 32000 = 6400 pound

Tax in 3rd year  = 0.40 × 107000 = 42800 pound

Tax in 4th year  = 0.45 × 8900 = 4005 pound

The inequality 834 + 14s > 978 - 10s can represent a situation involving saving and spending money over time. To solve it, you perform a series of operations to isolate variable 's', which in this case results in s > 6, indicating more than six weeks required for savings to exceed spending.

A real world situation that can be modelled by this inequality 834 + 14s > 978 - 10s could be a scenario involving saving and spending money. Say you start with $834 and each week you save $14 (s represents the number of weeks). On the other hand, you have $978 and you spend $10 each week. You want to figure out how many weeks it will take for the amount you have from saving to be more than the amount left from spending.

Now, to solve the inequality: subtract 834 from both sides which gives 14s > 144 - 10s, then combine like terms to get 24s > 144. Finally, divide both sides by 24 to solve for s: s > 6. Therefore, it will take more than six weeks for the money you save to exceed what remains from your starting amount of $978 after spending $10 each week.

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Answer: [tex]y=500(1.05)^x[/tex]

Step-by-step explanation:

We know that the general exponential equation to find the value after x years is written as :-

[tex]y=Ab^x[/tex], where A is the initial value and b is the multiplicative rate of change and x is the time period.

Given : The initial amount of a product = $500

After 2 years, the item is worth $551.25.

Substitute A = 500, x=2 and y= 551.25 in the above equation we get

[tex]551.25=500b^2\\\\\Rightarrow\ b^2=\dfrac{551.25}{500}\\\\\Rightarrow\ b^2=1.1025\\\\\Rightarrow\ b=\sqrt{1.1025}=1.05[/tex]

Now, substitute b= 1.05, A = 500 in the general exponential equation, we get the equation represents y, the value of the item after x years as :-

[tex]y=500(1.05)^x[/tex]

Slope formula: y2-y1/x2-x1

= -3-1/6-0

= -4/6

= -2/3

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