If DEF Is equivalent to GHF, what is the value of X?

The product of the terms   [tex](d - 9)[/tex]  and  [tex](2d^{2} + 11d -4)[/tex]  will be [tex](2d^{3} - 7d^{2} - 103d + 36)[/tex].

We have to find the product of two terms.

First term = (d - 9)

Second term = [tex](2d^{2} + 11d -4)[/tex]

To find the product of these two terms, we will be using the distributive property. According to the distributive property, when we multiply the sum of two or more addends by a number, it will give the same result as when we multiply each addend individually by the number and then add the products together.

We have to find :  [tex](d - 9) (2d^2 + 11d -4)[/tex]

Using the distributive property,

[tex]d * 2d^{2} + d * 11 + d * (-4) - 9 * 2d^2 - 9 * 11d - 9 * (-4)[/tex]

After further multiplication, we get

[tex]2d^{3} + 11d^2 - 4d - 18d^{2} - 99d + 36[/tex]

Now, combine all the like terms.

[tex]2d^{3} + 11d^{2} - 18d^{2} - 4d - 99d + 36[/tex]

[tex]2d^{3} - 7d^{2} - 103d + 36[/tex]

Therefore, the product of d-9 and 2d^2 + 11d -4 is [tex]2d^{3} - 7d^{2} - 103d + 36[/tex]

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The area of the trapezoid in this problem is given as follows:

C. [tex]A = 96\sqrt{3}[/tex] mm².

The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:

A = 0.5 x h x (b1 + b2).

The bases in this problem are given as follows:

11 mm and 15 + 6 = 21 mm.

The height of the trapezoid is obtained considering the angle of 60º, for which:

We have that the tangent of 60º is given as follows:

[tex]tan{60^\circ} = \sqrt{3}[/tex]

The tangent is the division of the opposite side by the adjacent side, hence the height is obtained as follows:

[tex]\sqrt{3} = \frac{h}{6}[/tex]

[tex]h = 6\sqrt{3}[/tex]

Thus the area of the trapezoid is obtained as follows:

[tex]A = 0.5 \times 6\sqrt{3} \times (11 + 21)[/tex]

[tex]A = 96\sqrt{3}[/tex] mm².

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The radius of the circle is 4 units

A circle is simply a round shape that has no corners or line segments. The body of a circle is called the circumference and a cut out of circumference is called an arc.

The distance from the centre of a circle to any part of its circumference is called a radius. Twice of a radius is called the diameter.

In the circle, the distance between the center of the circle and it's circumference is ;

4-0 = 4 units

Therefore the radius of the circle is 4 units.

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[tex]$f(x) = q_a$[/tex] for all [tex]$x \in (a-1, a+1)$[/tex]. Since a was arbitrary, it follows that f is constant on any open interval. Since f is continuous, it follows that f is constant on [tex]$\mathbb{R}$[/tex].

Let a be any real number in R. Since f is continuous, the intermediate value theorem implies that the image of any closed interval under f is also an interval. Therefore, [tex]$f([a-1, a+1])$[/tex] is an interval in [tex]$\mathbb{Q}$[/tex]. Since the only intervals in [tex]$\mathbb{Q}$[/tex] are single points, [tex]$f([a-1, a+1]) = {q_a}$[/tex] for some rational number [tex]$q_a$[/tex].

Now let b be any real number with [tex]$b > a+1$[/tex]. By the intermediate value theorem, there exists some [tex]$x \in [a, b]$[/tex] such that [tex]$f(x) = \frac{q_a+q_b}{2}$[/tex]. But since f takes only rational values, [tex]$f(x) = q_a$[/tex]. This argument applies to all real numbers b with [tex]$b > a+1$[/tex], so [tex]$f(x) = q_a$[/tex] for all [tex]$x > a+1$[/tex]. Similarly, we can show that [tex]$f(x) = q_a$[/tex] for all [tex]$x < a-1$[/tex].

Therefore, [tex]$f(x) = q_a$[/tex] for all [tex]$x \in (a-1, a+1)$[/tex]. Since a was arbitrary, it follows that f is constant on any open interval. Since f is continuous, it follows that f is constant on [tex]$\mathbb{R}$[/tex].

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The pair of points to be used is k and M.

A line of best fit is a straight line which is used to show the relations among non-linear points in a scatter plot. Thus it evenly varies the points on its two sides. This is majorly used when dealing with a cartesian coordinate, or plotted points on a graph.

Considering the given scatter plot, it can be observed that points J, L, M and K on non-linear. Thus the straight line that can be used to as line of best fit is by joining point K and M.

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The value of the function f(x) =  ( x² + 7 ) / ( x² + 4x - 21 )  for x = 5 is equal to 4/3.

The function is equal to,

f(x) =  ( x² + 7 ) / ( x² + 4x - 21 )

find the value of f(x) at x=5 by substituting x=5 into the given function we have,

⇒ f(5) = ( 5² + 7 ) / ( 5² + 4(5) - 21 )

⇒ f(5)  = ( 25 + 7 ) / ( 25 + 20 - 21 )

⇒ f(5)  = 32 / 24

Now reduce the fraction by taking out the common factor of the numerator and the denominator we get,

⇒ f(5)  = ( 8 × 4 ) / ( 8 × 3 )

⇒ f(5)  = 4/3

Therefore, the value of the function f(x) at x=5 is 4/3.

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The given question is incomplete, I answer the question in general according to my knowledge:

Find the value of the function f(x) at x = 5.

f(x) =  ( x² + 7 ) / ( x² + 4x - 21 )

The answer is

(-x-6i)(x-6i)

The optimal number of carts and pretzel price will depend on the size of the population and the competitive landscape. The park should conduct market research to determine the ideal price point and number of carts for their specific market.

To determine how many carts the amusement park should put out and what they should set their pretzel price to in order to maximize their profit for an arbitrary population p, several factors need to be considered.

Firstly, the demand for pretzels will depend on the size of the population p. If p is large, the park should put out more carts to meet the demand. However, if p is small, fewer carts would be sufficient.

Secondly, the price of the pretzels will also affect demand. If the price is too high, people may choose to buy other snacks or not purchase anything at all. On the other hand, if the price is too low, the park may not be able to cover their costs and make a profit. Therefore, the park should set the pretzel price to a level that is competitive with other snacks but still allows for a reasonable profit margin.

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At a significance level of 0.01, the conclusion would be that there is not enough evidence to support the alternative hypothesis (H1: μ > 72).

To lea

a. To calculate the p-value, we can use the standard normal distribution and the test statistic formula:

Test statistic (Z) = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Z = (75.2 - 72) / (6 / sqrt(16))

Z = 3.2 / 1.5

Z = 2.13 (rounded to two decimal places)

To find the p-value, we need to calculate the area under the standard normal curve to the right of the test statistic (Z = 2.13). Using a standard normal distribution table or a calculator, we find that the area to the right of Z = 2.13 is approximately 0.016.

Since this is a one-sided test (H1: μ > 72), the p-value is the probability of observing a test statistic as extreme or more extreme than the one obtained. Therefore, the p-value is 0.016.

b. If the test were made at a significance level of 0.01 (1%), we would compare the p-value to the significance level. In this case, the p-value (0.016) is less than the significance level (0.01). Therefore, we would reject the null hypothesis.

c. To find the critical value at a significance level of 0.01, we need to determine the z-score that corresponds to an area of 0.01 in the upper tail of the standard normal distribution.

Using a standard normal distribution table or a calculator, we find that the critical value for a significance level of 0.01 is approximately 2.33.

Comparing the critical value (2.33) with the test statistic (Z = 2.13), we see that the test statistic is less than the critical value. In hypothesis testing, if the test statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, at a significance level of 0.01, the conclusion would be that there is not enough evidence to support the alternative hypothesis (H1: μ > 72).

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