Find the areas of the sectors formed round your answer to the nearst hundredth of a square meter

If

\(f(x) = \dfrac{2ax+b}{x-1}\)

Note that

\(f(2) = \dfrac{4a+b}{2-1} = 4a+b\)

From the given information we have

\(\displaystyle \lim_{x\to0} f(x) = \lim_{x\to0} \frac{2ax+b}{x-1} = \frac{0+b}{0-1} = -b = -3 \\\\ ~~~~ \implies b=3\)

and

\(\displaystyle \lim_{x\to\infty} f(x) = \lim_{x\to\infty} \frac{2ax+b}{x-1} = \lim_{x\to\infty} \frac{2a+\frac bx}{1-\frac1x} = \frac{2a+0}{1-0} = 2a = 4 \\\\ ~~~~ \implies a=2\)

It follows that

\(f(2) = 4\cdot2+3 = 11\)

as required.

\( \frac{1}{ {3}^{3} } \)

Answer:

The answer is A.

Step-by-step explanation:

The simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)

The expression is given as:

\(\frac{x^{3}-8x^{2}}{x^2-64}\)

Factor the numerator

\(\frac{x^{2}(x-8)}{x^2-64}\)

Express the denominator as a difference of two squares

\(\frac{x^{2}(x-8)}{(x-8)(x + 8)}\)

Cancel out the common factor

\(\frac{x^2}{x + 8}\)

Hence, the simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)

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Answer:

B this is the smallest number

The algebraic representation of the expression is (m + n)

sum of m and the number after it

= m + n

Therefore, the algebraic representation of the expression is (m + n)

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\(y = -x^2+10x\implies y = -x^2+10x+0 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 10}{2(-1)}~~~~ ,~~~~ 0-\cfrac{ (10)^2}{4(-1)}\right)\implies \left( \cfrac{10}{2}~~,~~\cfrac{100}{4} \right)\implies (5~~,~~25)\)

Answer:

3

Step-by-step explanation:

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer: The perimeter triples.

Step-by-step explanation:

Since there is a direct variation, if the side length triples, so does the perimeter.

9514 1404 393

Answer:

Step-by-step explanation:

The price increase will be ...

  4.9% × $41,000 = $2,009

__

The new price will be ...

  $41,000 +2,009 = $43,009

Answer:

11x +4

Step-by-step explanation:

Answer: -3x⁵y²

its simplified :)

Therefore, a sample size of 68 is required to estimate the population mean with 90% confidence and a margin of error of 1, based on the given information.

The population is the total number of people who reside in a specific area. By assessing the population, we can determine the number of organisms and the appropriate course of action. For instance, if we are aware of a city's exact population, we may estimate how many resources are required there.

To calculate the sample size required to estimate a population mean with a certain level of confidence and margin of error, we can use the following formula:

n = [(z*σ)/E]^2

Where:

n = sample size

z = the z-score associated with the desired level of confidence (90% confidence corresponds to z = 1.645)

σ = the population standard deviation

E = the desired margin of error (in this case, E = 1)

Substituting the given values into the formula, we get:

n = [(1.645*5)/1]^2 = 67.65

Rounding up to the nearest whole number, we get a sample size of n = 68.

Therefore, a sample size of 68 is required to estimate the population mean with 90% confidence and a margin of error of 1, based on the given information.

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Therefore, a sample size of 68 is required to estimate the population mean with 90% confidence and a margin of error of 1, based on the given information.

The population is the total number of people who reside in a certain area. We can figure out how many organisms there are and what the best course of action is by looking at the population. For example, if we are aware of a city's exact population, we may calculate the amount of resources needed there.

To calculate the sample size required to estimate a population mean with a certain level of confidence and margin of error, we can use the following formula:

n = [(z*σ)/E]²

Where:

n = sample size

z = the z-score associated with the desired level of confidence (90% confidence corresponds to z = 1.645)

σ = the population standard deviation

E = the desired margin of error (in this case, E = 1)

Substituting the given values into the formula, we get:

n = [(1.645*5)/1]² = 67.65

Rounding up to the nearest whole number, we get a sample size of n = 68.

Therefore, a sample size of 68 is required to estimate the population mean with 90% confidence and a margin of error of 1, based on the given information.

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Answer:  48 square inches

Step-by-step explanation:

To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.

area of triangle L x W = 6x4=24

area of rectangle LxW =6x4=24

24+24=48

Answer:

f (x) = (x - 2)² + 3

Step-by-step explanation:

Adding 2 to the constant k would shift the entire equation upwards by 2.

Answer:

1040

Step-by-step explanation:

Answer:

18, 14, 20

Step-by-step explanation:

Answer:

I got A 18,14, and 20

Step-by-step explanation:

PLZ CORRECT ME IF I AM WRONG PLZ AND THANK YOU

Answer:

13

Step-by-step explanation:

cos 13 x 2 = 26

13 is a factor that is more than 4 and less then 26

The factor of the number 26 that is between 4 and 26 is 13. Factors are the numbers that can divide into a number without leaving a remainder. In this case, the factors of 26 are 1, 2, 13, and 26.

In mathematics, a factor of a number is a number that divides into another number without leaving a remainder. In the case of the number 26, its factors include 1, 2, 13, and 26. The factor of 26 that is between 4 and 26 is 13.

To find this, you can go through the factors of 26 one by one. The factors are found by dividing 26 by all the numbers up to 26, and the numbers that give a remainder of 0 are the factors. In this case, 1, 2, 13, and 26 divide evenly into 26, and so are the factors of 26. Of these, only 13 lies between 4 and 26.

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Answer:

about a 9.5 percent chance of both being a milky way

Step-by-step explanation:

Probability that both candy bars were milky way is \(\frac{2}{21}\)

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur

Given,

Number of snickers bars = 5

Number of Milky way bars =9

Number of crunch bars = 2

Number of Twix bars = 12

Total number of Candy bars = 5+9+2+12 =28

If Jack randomly selects a candy bar, eats it, then randomly selects another

Probability = Number of favorable outcome / Number of total outcome

Probability of taking Milky way bar in first pick = \(\frac{9}{28}\)

So Total number of candy bars and number of Milky way bar are decreased by 1.

Probability of taking Milky way bar in second pick = \(\frac{8}{27}\)

Probability that both candy bars were milky way = \((\frac{9}{28}).(\frac{8}{27})=\frac{2}{21}\)

Hence, Probability that both candy bars were milky way is \(\frac{2}{21}\)

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Answer:

7 > x

Step-by-step explanation:

8-6(x-3) > -4x+12

Multiply 6 with the ones in the paranthesis:

8-6x+18 > -4x+12

Simplify numbers:

26-6x > -4x+12

Do the balance method:

12-26 > -6x+4x

-14 > -2x

Simplify to x:

-14/-2 > -2x/-2

7 > x

Answer:

Step-by-step explanation:

Here you go mate

Step 1

8-6(x-3) >-4x+12  Equation/Question

Step 2

8-6(x-3) >-4x+12  Simplify

-2x+26>12

Step 3

-2x+26>12  Subtract

-2x>-14

Step 4

-2x>-14  Divide

answer

x<7

The value of the functions are;

a. x = 5/6

b. x> 5/6

c. x = 1

d. x ≤ 1

Note that functions are defined as laws or rules showing the relationship between two variables

From the information given, we have that;

f(x) = 6x - 5

g(x) = -5x + 6

To determine the functions, we have;

f(x) = 0

6x - 5 = 0

collect like terms

6x = 5

x = 5/6

f(x) > 0

6x - 5> 0

6x > 5

x> 5/6

f(x) = g(x)

6x - 5 = -5x + 6

collect like terms

11x = 11

x = 1

f(x) ≤ g(x)

6x - 5 ≤ - 5x + 6

collect like terms

11x ≤ 11

x ≤ 1

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Answer:

No

Step-by-step explanation:

To get if values can create a right angled triangle use the pythogras theory a squared plus b squared equals c squared

So in this case 4 squared plus 6 squared don't equal to 7 squared

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

The plot of the graph  y = –1.5(4)^x is shown below of which its domain and range exist on all real values

The standard exponential function is expressed as y = ab^x

where

The exponential function shows an increase along the y-axis and towards the x-axis

According to the equation, we are to plot the graph  y = –1.5(4)^x of which its domain and range exist on all real values

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Answer:

50 degrees

Step-by-step explanation:

Triangle = 180

180 - 90 = 90

? = 50 degrees

Answer:

A) 12 inches by 20 inches

Step-by-step explanation:

Dilation of a scale factor means to increase by a factor of 4.
That basically mean multiply the object by 4.

Therefore 3 inches x 4 = 12 inches

And 5 inches x 4 = 20

a. The random variable X represents the number of people over 50 who ran and died in the same eight-year period.

b. The appropriate distribution for this problem is the binomial distribution, which describes the number of successes.

c. The 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0206, 0.1149).

d. The true population proportion lies within this interval, nor does it mean that the observed proportion (0.0677) has a 97% chance of being correct.

a. The random variable X represents the number of people over 50 who ran and died in the same eight-year period. The population proportion of over-50s who ran and passed away within the same eight-year period is represented by the random variable P'.

b. The appropriate distribution for this problem is the binomial distribution, which describes the number of successes (in this case, people who ran and died) in a fixed number of independent trials (in this case, the population of people over 50 during the eight-year period), where the probability of success is constant for each trial.

c. To construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period, we can use the following formula:

\(\hat{p} \pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\)

where \hat{p} is the sample proportion, n is the sample size, and \(z_{\alpha/2}\) is the z-score associated with the desired level of confidence (97%, in this case).

Given that 1.5% of the 451 members of the 50-Plus Fitness Association died during the eight-year period, we can estimate the sample proportion as:

\(\hat{p} = \frac{X}{n} = \frac{0.015 \times 451}{1} = 6.765 \approx 0.0677\)

where X = \(0.015 \times 451 \approx 7\) is the observed number of people over 50 who ran and died in the same eight-year period.

Substituting the given values into the formula, we have:

\(0.0677 \pm 2.17\sqrt{\frac{0.0677(1-0.0677)}{451}} \approx (0.0206, 0.1149)\)

Therefore, the 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0206, 0.1149).

ii. The graph of the confidence interval would be a horizontal line segment between the two endpoints (0.0206, 0.1149) on the y-axis, with a vertical line at the midpoint (0.0677) on the x-axis.

iii. The error bound is:

\(z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \approx 0.0471\)

d. A "97% confidence interval" means that if we were to repeat this study many times, using different samples of the same size from the same population, we would expect the true population proportion of people over 50 who ran and died in the same eight-year period to be captured by the confidence interval in 97% of those repetitions. In other words, we are 97% confident that the true population proportion falls within the interval (0.0206, 0.1149). It does not mean that there is a 97% chance that the true population proportion lies within this interval, nor does it mean that the observed proportion (0.0677) has a 97% chance of being correct.

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