Find the open intervals on which the function is increasing and decreasing. b. Identify the function’s local and absolute extreme values, if any, saying where they occur. f(r) = 3r^3 + 16r

The average cost of all seats in the theater is $10.71

Given:

cost per seat x    number of available seats f        x × f

$5                                         22                                 110

$10                                        14                                  140

$15                                        10                                  150

$20                                       10                                  200

.........................................................................................................

Sum                                      56                                  600

..........................................................................................................

average cost of all seats = (sum of x × f) /sum of number of available seats

average cost of all seats = 600/ 56 = $10.71

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Option d. dependent variable. In an experiment, the dependent variable is the factor that is being measured or observed.

It is the variable that is expected to change or be affected as a result of the manipulation of the independent variable. The independent variable is the factor that is being manipulated or controlled in the experiment, while the controlled variable is a factor that is kept constant or consistent throughout the experiment to prevent it from affecting the dependent variable. The dependent variable is often used to draw conclusions about the relationship between the independent variable and the outcome of the experiment.

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Answer:

The missing value is 41.

Step-by-step explanation:

If r= 3c+5 you plug in the 12, which is c, and the equation becomes r= 3x12+5. 3x12= 36, and 36+5= 41.

Answer:

41

Step-by-step explanation:

because 1=3 so 12=41

hope that helped!

Answer:

-3.6

Step-by-step explanation:

proportional means the amount on the right is amount on the left multiplied by some coefficient - proportion. The proportion is calculated by dividing one side by another. Since you need to calculate weight based on days, you need the proportion of weight/days, so divide -0.27/9 or -0.78/26, in all cases you'll receive -0.03. This means for each day in hibernation hedgehog loses 0.03 pounds. 120 days will be 120*-0.03 which gives you -3.6

The general solution for the trigonometric equation given is \(\frac{5\pi }{3} + 2\pi n\), where n is an integer.

Given a trigonometric equation.

We have to find the general solution to the trigonometric equation.

Given trigonometric equation is,

-√3 csc θ = 2

We have to find the general solution to the trigonometric function.

That is, all the values of θ for which the equation holds.

-√3 csc θ = 2

-√3 (1/ sinθ) = 2

-√3 / sinθ = 2

sinθ = -√3 / 2

θ = sin⁻¹ (-√3/2)

  = - sin⁻¹ (√3/2)  [Since sin⁻¹ (-x) = - sin⁻¹ (x)]

We know that,

sin⁻¹ (√3/2) = 60 degrees = π/3

Now, -π/3 is same as 2π - π/3 = 5π/3

And the period of sine function is 2π.

Hence the general solution is,

θ = 5π/3 + 2πn, where n is an integer.

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Answer:

true

Step-by-step explanation:

for example, when you solve an equation and you get something like 16=16, which is infinitely many solutions and is also a true statement

The angle between u and (5, -5, -2) is Acute.

To determine the angle between two vectors, we can use the dot product formula. Given vectors u and v, the dot product u · v is calculated as:

u · v = (u1 * v1) + (u2 * v2) + (u3 * v3)

If u · v > 0, the angle between u and v is acute.

If u · v = 0, the angle between u and v is right.

If u · v < 0, the angle between u and v is obtuse.

Let's calculate the dot products to determine the angles:

u · (-1, 4, 5) = (4 * -1) + (-1 * 4) + (4 * 5) = -4 - 4 + 20 = 12

Since u · (-1, 4, 5) > 0, the angle between u and (-1, 4, 5) is acute.

u · (-8, 0, 8) = (4 * -8) + (-1 * 0) + (4 * 8) = -32 + 0 + 32 = 0

Since u · (-8, 0, 8) = 0, the angle between u and (-8, 0, 8) is right.

u · (-3, 1, -3) = (4 * -3) + (-1 * 1) + (4 * -3) = -12 - 1 - 12 = -25

Since u · (-3, 1, -3) < 0, the angle between u and (-3, 1, -3) is obtuse.

u · (5, -5, -2) = (4 * 5) + (-1 * -5) + (4 * -2) = 20 + 5 - 8 = 17

Since u · (5, -5, -2) > 0, the angle between u and (5, -5, -2) is acute.

(-1, 4, 5) makes an acute angle with u.

(-8, 0, 8) makes a right angle with u.

(-3, 1, -3) makes an obtuse angle with u.

(5, -5, -2) makes an acute angle with u

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The magnitude of proju(v) is:

|proju(v)| = √((40/33)^2 + (-10/33)^2 + (40/33)^2) ≈ 1\

Suppose u = 〈4,-1,4).

(-1,4,5) makes an acute angle with u.

To find the angle between two vectors, we can use the dot product formula:

u · v = |u| |v| cosθ

where θ is the angle between u and v.

Let v = (-1, 4, 5). Then,

u · v = (4)(-1) + (-1)(4) + (4)(5) = 16

|u| = √(4^2 + (-1)^2 + 4^2) = √33

|v| = √((-1)^2 + 4^2 + 5^2) = √42

So,

cosθ = (u · v) / (|u| |v|) = 16 / (√33 √42) ≈ 0.787

θ ≈ 38.5°

Since 0 < θ < 90°, the angle between u and v is acute.

(-8,0,8) makes a right angle with u.

To verify this, we can again use the dot product formula:

u · v = |u| |v| cosθ

Let v = (-8, 0, 8). Then,

u · v = (4)(-8) + (-1)(0) + (4)(8) = 0

|u| = √(4^2 + (-1)^2 + 4^2) = √33

|v| = √((-8)^2 + 0^2 + 8^2) = √128

So,

cosθ = (u · v) / (|u| |v|) = 0 / (√33 √128) = 0

Since cosθ = 0, θ = 90° and the angle between u and v is a right angle.

(-3,1,-3) makes an obtuse angle with u.

Using the same process as before, we have:

u · v = (4)(-3) + (-1)(1) + (4)(-3) = -28

|u| = √33

|v| = √((-3)^2 + 1^2 + (-3)^2) = √19

So,

cosθ = (u · v) / (|u| |v|) = -28 / (√33 √19) ≈ -0.723

θ ≈ 139.3°

Since θ > 90°, the angle between u and v is obtuse.

(5,-5,-2) makes 4 with u.

To find the projection of v = (5, -5, -2) onto u, we can use the projection formula:

proju(v) = ((u · v) / |u|^2) u

u · v = (4)(5) + (-1)(-5) + (4)(-2) = 10

|u|^2 = 4^2 + (-1)^2 + 4^2 = 33

So,

proju(v) = ((u · v) / |u|^2) u = (10 / 33) 〈4,-1,4) = 〈40/33,-10/33,40/33)

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Answer:

The total amount of tickets sold was 198 tickets.

Step-by-step explanation:

To get this answer, all we have to do is simply divide the amount of money total by the price of the tickets.

So we get 1584 ÷ 8

Which will equal to 198

Hope this helps:) Goodluck!

Answer:

300g for 7.49 has the best value

Step-by-step explanation:

200g for 5.69

200/5.69

35.15g for 1

300g for 7.49

300/7.49

40.05g for 1

The probability that the time between two arrivals is less than or equal to 1 minute is 0.42.

The time (in minutes) between arrivals of customers to a post office is to be modelled by the exponential distribution with mean 0.75.We are to calculate the probability that the time between two arrivals is less than or equal to 1 minute.We know that, for an exponential distribution, the probability density function is given by:f(x) = 1/μ e^(-x/μ)where μ is the mean of the distribution.In this case, μ = 0.75. Therefore, the probability density function is:f(x) = 1/0.75 e^(-x/0.75)To calculate the probability that the time between two arrivals is less than or equal to 1 minute, we need to integrate this probability density function from 0 to 1:f(x) = ∫0^1 1/0.75 e^(-x/0.75) dxf(x) = [-e^(-x/0.75)]0^1f(x) = -e^(-1/0.75) + e^(0)f(x) = 0.424Approximating this probability to two decimal places, we get:P(X ≤ 1) = 0.42 (rounded off to two decimal places).Therefore, the probability that the time between two arrivals is less than or equal to 1 minute is 0.42.

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Answer:

K=5

Step-by-step explanation:

They used black the most and red the least. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Convert the fraction number into a decimal number. Then we have

Paint color     Amount of gallon

White                  1/2 = 0.50

yellow                 1/4 = 0.25

Green                2/5 = 0.40

Blue                   7/12 = 0.5833

Red                     1/8 = 0.125

Black                 5/6 = 0.833

They used black the most and red the least. Then the correct option is D.

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The complete question is given below.

Answer:

x = 6.75, y = 15

Step-by-step explanation:

By Pythagoras Theorem,

12^2 + 9^2 = (y+5)^2

y = 15

By AA Similarity Test, Triangle BCA is similar to BED

x/9 = 15 (found y) / (15+5)

x = 6.75

Answer:

\(5\sqrt{2} +\sqrt{10}\)

Step-by-step explanation:

\(\sqrt{5} (\sqrt{10} +\sqrt{2} ) < --Given\)

\(\sqrt{5} \sqrt{10} +\sqrt{5} \sqrt{2} < -- Distribute\)

An equation is in its simpliest form when you eliminate as many square roots as possible. Here are some rules:

1.) You cannot combine numbers through addition or subtraction if they are under square roots. However, you can combine numbers through multiplication or division if they are under square roots.

2.) You cannot take the square root of a number if the answer is not a whole number (unless the problem says you can). However, you can solve the square root if the number can be simplfied into a "rootable?" number. In other words, the number under a square root can be divided into a number that can have its square root taken.

The first part...

\(\sqrt{5} \sqrt{10} = \sqrt{5} * \sqrt{10} < --Multiply\)

\(\sqrt{5} * \sqrt{10} =\sqrt{50}\)    

\(\sqrt{50} = \sqrt{25} *\sqrt{2} < --Separate\)

\(\sqrt{25} = 5 < --Solve\)

\(\sqrt{50} = 5 *\sqrt{2} < -- Substitute\)

\(5*\sqrt{2} =5\sqrt{2} < --Rewrite\)

The second part...

\(\sqrt{5} \sqrt{2} =\sqrt{5} * \sqrt{2} < -- Multiply\)

\(\sqrt{5} *\sqrt{2} = \sqrt{10}\)

Combine both parts...

\(5\sqrt{2} +\sqrt{10}\)

Answer:

option a.

abc(a+b+c).

.............

Answer: The person above his right good job

Step-by-step explanation:

False. In a Two-Way 2 x 2 Between Subjects ANOVA, there are typically two independent variables, each with two levels, resulting in a total of four groups.

A Two-Way 2 x 2 Between Subjects ANOVA involves the analysis of variance with two independent variables, each having two levels. The independent variables can be thought of as factors, and their combinations create different groups for comparison.

In this design, there are two factors, each with two levels. When you multiply the number of levels for each factor (2 x 2), you get four possible combinations or groups. Each group represents a specific combination of the two levels of the independent variables.

For example, if the first independent variable is "A" with levels A1 and A2, and the second independent variable is "B" with levels B1 and B2, the four groups in the ANOVA would be: A1B1, A1B2, A2B1, and A2B2.

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Answer:

= 32.440

Step-by-step explanation:

Change the divisor 12.5 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

4055 ÷ 125 = 32.440

and therefore:

405.5 ÷ 12.5 = 32.440

Both calculated to 3 decimal places.

The equation for circle is 28g + 16f =260

and the equation of tangent to this circle is y = \(\frac{6}{12}\) x +29

a) the main equation of circle is ax + by +2gx+ 2fy +c =0     --------- (1)

Now,

putting the points (0,0) , (0,8) and (6,12) one by one, we get,

 For the point (0,0), we get:

                c =o            ----------------------------- (2)

For the point (6,12), we get:

   6x +12y + c = (6)² + (12)²

⇒ 6x +12y +c = 36 +144

⇒ 6x +12y +c = 180          --------------------------- (3)

For the point (0,8), we get,

8y + c = 64                      ----------------------------- (4)

putting c=0,

     8y +0 = 64

⇒ y =64/8

⇒ y = 8

Putting c=0 and y =8, we get,

    6x + 12×8 +0 = 180

⇒ 6x + 96 =180

⇒ 6x = 84

⇒ x = 14

Putting all the values in equation (1), we get:

    (14)² + (8)² +28g +16g + 0 = 0

⇒ 196 + 64 + 28g +16f =0

⇒ 28g + 16f = 260

b) As we know the tangent from the circle:

       y = mx + c

⇒ 8 = -12/6 × 14 +c

⇒ c = 29

Therefore, the equation of the tangent is y = \(\frac{6}{12}\)x + 29

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The quartiles of any normal distribution lie 0.6745 standard deviations above and below the mean. The standard normal distribution can be represented by Z values.

Therefore, to calculate the position of the quartiles in terms of standard deviations from the mean, the Z-score formula is used.

Where Q₁, Q₂ and Q₃ are the first, second, and third quartiles, respectively, and Z₁, Z₂ and Z₃ are the Z-scores corresponding to the three quartiles.

From the empirical rule, it is known that the first quartile is located at -0.6745 standard deviations below the mean,

the second quartile (or median) is located at 0 standard deviations from the mean, and the third quartile is located at +0.6745 standard deviations above the mean.

Therefore, by plugging in these values into the Z-score formula, the Z-scores corresponding to the three quartiles can be calculated.

Z₁ = -0.6745Z2

= 0Z₃

= 0.6745.

Therefore, the quartiles of any normal distribution lie 0.6745 standard deviations above and below the mean.

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Answer:

0.2 units

Step-by-step explanation:

It is given that,

Cody has 1/ 2 of a cup of powdered sugar. He sprinkles 2/ 5 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies.

We need to find the sugar content on the brownies.

ATQ,

\(B=\dfrac{1}{2}\times \dfrac{2}{5}\\\\B=\dfrac{1}{5}\\\\B=0.2\ \text{units}\)

So, Cody sprinkles 0.2 units of sugar on the brownies.

x = 12.

Perpendicular lines are lines that intersect at a 90-degree angle. So, for example, line ST is perpendicular to line CD. So line ST is perpendicular to line CD.

Perpendicular lines always intersect each other, however, all intersecting lines are not always perpendicular to each other. The two main properties of perpendicular lines are: Perpendicular lines always meet or intersect each other. The angle between any two perpendicular lines is always equal to 90.

Given that

line m and n are perpendiculars

then angle ∠a = ∠b

then

5x + 20 = 7x -4

7x -5x = 20 + 4

2x = 24

x = 24/ 2

x = 12.

Hence the value of x = 12

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The inequality when rewritten with first with zero on one side and secondly with one rational expression on the other side gives;

1) Option A; add -3 to both sides

2) Option C; multiply both sides by (x-2)

The inequality we want to rewrite is;

[3/(x + 2)] + 4 ≥ 3

Now, when working with fractions of equations, when we want to simplify it, we do so by multiplying each term by the LCM of the denominators.

However, in this case, we want to first make the inequality to have zero on one side. Thus, to do that, we have to get rid of the 3 on the right by adding 3 to both sides of the inequality.

Now, if we want to make one rational expression to be on one side, then we need to multiply both sides by the LCM of the denominator which is (x + 2).

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Answer:

add -3 to both sides

Step-by-step explanation:

edge

Answer:

x = 0

Step-by-step explanation:

Calculate the product

Any expression multiplied by 0 equales 0

Solution

X = 0

Hope this helps!

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

The option that follows is c .

The between-group estimate for calculating the degrees of freedom in ANOVA is calculated using the formula k - 1, where k represents the number of groups or treatments being compared.

This estimate represents the variability between the group means and is used in the F-ratio calculation to determine if the differences between the groups are significant.

When conducting ANOVA, the between-group estimate is an important factor in determining the degrees of freedom. This estimate represents the variability between the group means and is used to calculate the F-ratio, which determines if the differences between the groups are significant. The between-group estimate is calculated using the formula k - 1, where k represents the number of groups being compared. This formula is used because the estimate is based on the number of independent sources of variation between the groups. By accurately calculating the degrees of freedom, researchers can determine if the differences between the groups are statistically significant.

The between-group estimate for calculating the degrees of freedom in ANOVA is crucial for determining the statistical significance of differences between groups. It is calculated using the formula k - 1, where k represents the number of groups being compared. This estimate represents the variability between the group means and is used in the F-ratio calculation. Accurately calculating the degrees of freedom is essential in conducting valid ANOVA analyses.

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Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.

The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.

So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:

(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)

= (1/4) × 8x − (1/3) × 12y

= 2x − 3y

Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.

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