Find the average rage of change of each of the following functions over the interval 1 < × < 5.
​

Answer:

Correct Work

5(x+9) - 3x +4

5x+ 45- 3x+ 4

5x-3x +45+4

2x+49

Mistake made:

Answer:

The value of the correlation coefficient would not change.

Step-by-step explanation:

If the relationship between distance of trips and fares in dollars gives a correlation coefficient value of 0.950. This can be interpreted to mean that the relationship between both variables is strong and positive such that an increase in distance leads to corresponding increase in fares of the trip and vice versa. Thus, interchanging the axis upon which the variables are plotted would still tied the same correlation Coefficient value as the correlation coefficient does not depend on the axis upon which the variables are plotted.

Step-by-step explanation:

If its change it will not be right

Out of the given options, option C is a rational function because it can be expressed as the ratio of two polynomial functions:

F(x) = (x² + 5x - 6) / 3x

A function that is the ratio of polynomials is referred to as rational. When a function of one variable, x, can be written as f (x) = p (x)/q (x), where p (x) and q (x) are polynomials with q (x) 0, the function is said to be rational.

A rational function is a function that can be expressed as the ratio of two polynomial functions, where the denominator is not equal to zero.

Out of the given options, option C is a rational function because it can be expressed as the ratio of two polynomial functions:

F(x) = (x² + 5x - 6) / 3x

The numerator of the function is a polynomial of degree 2 and the denominator is a polynomial of degree 1, so it satisfies the definition of a rational function.

Option A and B are not rational functions because they cannot be expressed as the ratio of two polynomial functions.

Option D is also not a rational function because it contains a square root function, which is not a polynomial function.

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The equity dividend rate is calculated by dividing the before-tax cash flow by the equity investment.

The ratio of a year's worth of before-tax cash flow to the equity investment in the property is known as the equity dividend rate, also known as the equity capitalization rate and cash on cash return.

An equity dividend rate, which is frequently employed by real estate investors, is a helpful indicator to ascertain an investment's yearly return in relation to the capital invested. This indicator, often known as the cash-on-cash return, focuses solely on the actual cash invested in a property rather than the purchase price. In summary, using the equity dividend rate is a great technique to estimate a real estate investment's yearly profitability. The return on the real investment is shown by the equity dividend rate.

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Answer:

Someone please help me because i have this question on my test someone please help us

Step-by-step explanation:

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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Answer:

========================

To find the measure of Angle A, we'll use the sine function from trigonometry. First, let's identify the sides of the triangle:

Now we can use the sine function to find the measure of Angle A:

Now, to find the angle A, we need to take the inverse sine (arcsin) of the ratio:

Using a calculator, we find:

So, the measure of Angle A is approximately 24.9 degrees, rounded to the nearest tenth.

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are given a right angled triangle, with AB = 19 and BC = 8 . We are interested in finding out the value of angle A .

Mathematically,

\(\longrightarrow\large\pmb{ \sin\theta =\dfrac{perpendicular}{hypotenuse}} \\\)

On substituting the respective values, we have;

\(\longrightarrow \sin A =\dfrac{8}{19} \\\)

Take sin inverse on both the sides,

\(\longrightarrow \sin^{-1}(\sin A ) = \sin^{-1}\bigg(\dfrac{8}{19}\bigg) \\\)

Simplify,

\(\longrightarrow A =\sin^{-1}\bigg(\dfrac{8}{19}\bigg) \\\)

To find the value , we would have to use a calculator,

\(\longrightarrow\large\pmb{\underline{\boxed{ A = 24.9^o}}} \\\)

Therefore the approximate value of angle A is 24.9° to the nearest tenth .

The perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the vertices of the rectangle are (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).

The length of the  rectangle is:

l = 3.5 - (-3.5)

l = 3.5 + 3.5

l = 7

The width of the rectangle is:

w = 3-(-3)

w = 3 + 3

w = 6

The perimeter of the rectangle is given by:

P = 2 (l +w)

P = 2(7 + 6)

P = 26

The area of the rectangle is:
A = l × w

A = 7 × 6

A = 42

Hence, the perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

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Answer:

the numbers are 8 and 3.

Answer:

± x . x−3=±6 x - 3 = ± 6

Step-by-step explanation:

The conditions should be met  for inference is option (D) I and III only.

I. The seeds should be randomly assigned to a treatment is a necessary condition for making inference as it helps to ensure that the treatment groups are comparable, and any observed differences in germination rates are due to the treatment, not other factors.

II. The group sizes should be less than 10 percent of the population sizes is not relevant in this scenario as we don't have any information about the population size.

III. The number of successful seeds and unsuccessful seeds in each group should be at least 10 is a necessary condition for using a confidence interval to estimate the difference in proportions between the two groups.

Therefore, both I and III conditions must be met for making valid inferences about the difference in proportions between the two groups.

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The given question is incomplete, the complete question is :

A gardener wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. to investigate, the gardener will assign 50 seeds to be soaked before planting and 50 seeds to be planted without being soaked. after two weeks, the gardener will record how many seeds in each group germinated and construct a 95 percent confidence interval for the difference in proportions. which of the following conditions for inference should be met?

I. The seeds should be randomly assigned to a treatment.

II. The group sizes should be less than 10 percent of the population sizes, III. The number of successful seeds and unsuccessful seeds in each group should be at least 10.

A)I only B) II only c) III only D I and III only

The table that represents the relationship between Lemon poppy and Bran muffins is as under:

Lemon poppy Muffins                    Bran Muffins

22                                                             2

66                                                             6

88                                                             8

Given that a backery sells 22 Lemon Poppy Muffins for every 2 Bran Muffins.

We are required to find the table that represents the relationship between lemon poppy and Bran Muffins.

To find the table we need to just multiply 1,2,3,4,5,etc.

Table contain rows and columns which shows some relationship between variables.

Table which shows represents the relationship between lemon poppy and Bran Muffins is as under:

Lemon Poppy Muffins                     Bran Muffins

22                                                            2

44                                                            4

66                                                            6

88                                                            8

Hence the table that represents the relationship between Lemon poppy and Bran muffins is as under:

Lemon poppy Muffins                    Bran Muffins

22                                                             2

66                                                             6

88                                                             8

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Answer:

4

Step-by-step explanation:

(3-4)+5

-1+5

4

For this problem, we use the sine law to compute the length of the missing sides:

Recalling that the interior angles of a triangle add up 180 degrees we get:

Substituting the angles and solving for the length of the missing sides we get:

The height of the triangle with respect to the side WU is:

Finally, using the formula for the area of a triangle:

Answer: 57.2 square yards.

The 18% he gets over the goods purchased exceeds Rs. 6300.

a decrease from the gross amount or value of something: for example, a(1): a reduction from the usual or list price.

Total Purchase Value = Total discount in rs * % discount

= 1520/16 x 100 = 9500

Discount on upto 3200 = 3200 x 14% = 448

Discount on upto 3201-6300 = (6300-3200) x 14% = 496

Balance discount = 1520 - 448 - 496 = 576

Above 6300 purchase amount = 9500 - 6300 = 3200

Discount % = 576/3200 x 100 = 18%

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Complete question:

A customer gets 14% discount on purchasing goods whose value is up to Rs. 3200 and gets 16% discount whose value is between Rs. 3201- Rs. 6300 and customer gets certain % discount while purchase the goods exceeds Rs. 6300. A customer gets a total discount of Rs. 1520 is 16% of the total purchase value. find the %age he gets over the goods purchased exceeds Rs. 6300 ?

Answer:

-40

-11

-3

11

15

Step-by-step explanation:

the further your away from zero on the left on a number line the smaller the number gets and the further your away from zero on the right on a number line the greater it gets

Answer:

-40, -11, -3, 11, 15

And that us the answer

Answer:

-8

Step-by-step explanation:

Slope = (y1-y2) / ( x1-x2)

            = ( f-4) / (-8 - -6)      =  6

                  (f-4) / -2    = 6

                    f-4 = -12

                     f = - 8

Answer:

f = -8

Explanation:

Find slope:

\(\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)

Here given:

Inserting into slope formula:

\(\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6\)

\(\sf \rightarrow \dfrac{4-f}{2 } = 6\)

\(\sf \rightarrow 4-f = 12\)

\(\sf \rightarrow -f = 12-4\)

\(\sf \rightarrow -f =8\)

\(\sf \rightarrow f =-8\)

Answer:-1

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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This type of data can be analyzed using a two-way analysis of variance (ANOVA) to determine the effect of both the day of the week (weekday or weekend) and the shift (morning or evening) on chair production. The manager can use this information to make predictions about future production based on the day of the week and shift.

The manager can start by creating a table to show the average number of chairs produced on each day of the week and shift. Then, a two-way ANOVA can be performed to determine if there is a significant difference in the mean number of chairs produced between weekdays and weekends, and between morning and evening shifts.

If the results of the ANOVA show that there is a significant effect of the day of the week and/or the shift on chair production, the manager can use this information to make more accurate predictions about future chair production. For example, if the results show that chair production is higher on weekdays compared to weekends, the manager can make predictions based on this information and allocate resources accordingly.

It is important to note that other factors such as the availability of materials, number of workers, and machine downtime can also impact chair production and should be considered when making predictions.

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Answer:

First option

Step-by-step explanation:

Hi there!

The "constant additive rate of change" means a constant slope.

The slope is \(\displaystyle\frac{change \hspace{4} in \hspace{4} y}{change \hspace{4} in \hspace{4} x}\).

First of all, if the slope is constant, then we know immediately that it must be a linear function, a line. The change in y is forever the same according to the change in x. Knowing this, the second option is for-sure wrong (it's not a straight line).

Now, let's look at the first option. It is a linear function, which means it has a constant slope. However, we're given that the slope is \(-\displaystyle \frac{1}{4}\). This means that for a line, whenever it travels 4 units to the right, it travels 1 unit down (it travels down whenever the slope is negative and up whenever the slope is positive).

This is the exact case for the first option. Look at the point (-2,2) on the line. When we move 4 units to the right of that point, The line would have moved 1 unit down. We would reach the point (2,1).

Therefore, the correct answer would be the first option.

I hope this helps!

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

\(y = 4(x - 4)^2 - 2\)

or

\(y=4x^2 -32x + 62\)

Step-by-step explanation:

Given

\(V = (4,-2)\) --- vertex

\(P = (2,14)\) --- point

Required

The equation of the parabola

The equation of the parabola is of the form

\(y = a(x - h)^2 + k\)

Where

\(V (4,-2) = (h,k)\) ---- the vertex

So, we have:

\(y = a(x - h)^2 + k\)

\(y = a(x - 4)^2 - 2\)

In \(P = (2,14)\), we have:

\((x,y) = (2,14)\)

Substitute \((x,y) = (2,14)\) in \(y = a(x - 4)^2 - 2\)

\(14 = a(2 - 4)^2 - 2\)

\(14 = a(- 2)^2 - 2\)

\(14 = a*4 - 2\)

\(14 = 4a - 2\)

Collect like terms

\(4a = 14 +2\)

\(4a = 16\)

Divide both sides by 4

\(a= 4\)

So:

\(y = a(x - 4)^2 - 2\) becomes

\(y = 4(x - 4)^2 - 2\)

Open bracket to express the equation in standard form

\(y=4(x^2 -8x + 16) - 2\)

\(y=4x^2 -32x + 64 - 2\)

\(y=4x^2 -32x + 62\)

Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.

To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.

By simplifying the equation, we can see that the equation becomes:

6x - 5x = 17 - 2

Simplifying further, we have:

x = 15

Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.

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Answer:

Step-by-step explanation:

the distance between the two points are 11.

the slope is m=0

Answer:

11 units

Step-by-step explanation:

\(Solution,\\\\Let,\\\\(x_1,y_1)=(-7,-6)\\\\(x_2,y_2)=(4,-6)\\\\Now,\\\\Using\:distance\:formula,\\\\\hookrightarrow d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} } \\\\\hookrightarrow d=\sqrt{(4-(-7))^{2} +(-6-(-6))^{2} } \\\\\hookrightarrow d=\sqrt{(11)^{2} +(0)^{2} }\\\\\hookrightarrow d=\sqrt{121} \\\\\hookrightarrow d=11\: units\)

Answer:

7 mark above answer brilliant

Answer:

MP = 19

Step-by-step explanation:

17+3y=5y+9

or, 17-9 = 5y-3y

or, 8=2y

so, y = 2

Now,

MP = 5y+9

or, MP = 5×2+9

or, MP = 10+9

so, MP = 19

A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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Answer:

\(\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}\)

Step-by-step explanation:

To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:

\(\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}\)

Set each factor equal to zero and solve for x using the unit circle.

\(\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}\)

\(\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}\)

Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:

\(\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}\)