find the x-values of all points where the function has any relative extrema. find the value(s) of any relative extrema. f(x)=x²-162x² 7

Answer: 12m

Step-by-step explanation:12m

Answer:

12

Step-by-step explanation:

Total weight of cheese = 1.44 lb

Weight of cheese for one sandwich = 0.08 lb

Number of sandwiches you can make from 1.44 lb

= 1.44/0.08

= 18 sandwiches

Answer:

x = 39

Step-by-step explanation:

all triangles have angle measures that add up to 180°.

This means that to find what x is, you add 102 and 39, and then subtract that from 180, so

180-(102+39) = x

180-141=x

39=x

Answer:

x° = 39°

Step-by-step explanation:

According to the angle sum property of triangles, the 3 angles in a triangle will sum up to 180°.

102° + 39° + x° = 180°

141° + x° = 180°

x° = 180° - 141°

x° = 39°

_________

Hope it helps ⚜

Answer:

Use colon method

Step-by-step explanation:

So it is more easy

The statement "The number of intervals tells you the size of the data set" is not true of histograms. Option A

The number of intervals, or bins, in a histogram is determined by the data and by the preferences of the person creating the graph. A larger number of intervals will result in a graph with more detail, but may also make it harder to see trends or patterns in the data.

The size of the data set is not determined by the number of intervals in a histogram, but by the number of data points that are being represented.

The other statements are true of histograms. An outlier can show as a gap in the data if it falls outside the range of the intervals being used.

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Based on the information, the probability will be:

P(X=7) = 0.03

P(X>=6) = 0.30

P(X=3 or 4) = 0.30

Probability is a measure that quantifies the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to happen. The probability of an event can also be expressed as a percentage between 0% and 100%.

To calculate the probability of an event, you need to know the total number of possible outcomes and the number of favorable outcomes. The probability of an event A happening, denoted as P(A), is given by:

P(A) = (Number of favorable outcomes)/(Total number of possible outcomes)

P(X=7) = 0.03

P(X>=6) = P(X=6) + P(X=7)+ P(X=8) = 0.16+0.03+0.11 = 0.30

P(X=3 or 4) = P(X=3) + P(X=4) = 0.16+0.14 = 0.30

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The integral to find the area of the region R is:

A = 2∫[9 - 12cosθ]dθ from 0 to 0.7227

To find the area of the region R inside the circle r=6cosθ and outside the curve r=9−6cosθ, we need to set up an integral that integrates with respect to θ.

First, we need to find the values of θ where the two curves intersect.

Setting the two equations equal to each other, we have:

6cosθ = 9 - 6cosθ

12cosθ = 9

cosθ = 3/4

Taking the inverse cosine of both sides, we have:

θ = ±0.7227

Since the curves are symmetric about the y-axis, we only need to consider the region in the first quadrant. Therefore, we can set up the integral as:

A = 2∫[r(θ)]dθ from 0 to 0.7227

where r(θ) is the equation of the outer curve minus the equation of the inner curve:

r(θ) = (9 - 6cosθ) - 6cosθ

r(θ) = 9 - 12cosθ

Therefore, the integral to find the area of the region R is:

A = 2∫[9 - 12cosθ]dθ from 0 to 0.7227

Note that we multiply the integral by 2 because we are only considering the first quadrant and need to account for the full area of the region R. However, we do not evaluate the integral as per the question prompt.

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The definite integral for the enclosed area can be found by determining the limits of theta where the two functions intersect. Then, set up an integral that represents the absolute value of the difference in the radii of the two curves with respect to theta.

The student is required to set up the definite integral for the area enclosed by two curves in polar coordinates. The curves are r=6cosθ and r=9−6cosθ.

Firstly, find the intersection points of these two curves which will give the limits of theta, by setting the two equations equal to each other: 6cosθ = 9 - 6cosθ. Then, construct the integral in the form of ∫∣f(θ)-g(θ)∣dθ where f(θ) and g(θ) represent the two given functions in order of their position in the given region R.

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Answer:

answer is 6 ........ 12/2=6

The average speed is:

5/3 mph

Work/explanation:

The formula for average speed is:

\(\bf{Average\:Speed=\dfrac{distance}{time} }\)

Plug in the data:

\(\begin{aligned}\bf{Average\:Speed=\dfrac{15}{6}}\\\bf{=\dfrac{5}{3} \:mph}\end{aligned}\)

Answer:

First Question: Bombinoes Pizza

Second Question: Little Squeezer's

Third Question: Little Squeezer's

Step-by-step explanation:

The first step before even solving any of the problems is to convert all the initial word problems to y = mx + b.

The questions are worded a bit differently but we will assume that all of the "b"'s are the bonuses.

Doing so will give you respectfully:

Bombinoe's : y = 2.5x +56

Little Squeezer's: y = 3x + 48

Pizza Tent: y or S = 2.75 + 52

For the Little Squeezers, you must find the unit rate, which can be done by looking at the increases of money, since it increases by 2 pizzas per rate change you can see that it would be 6/2 which gives you a unit rate of  $3 per pizza delivered.

To answer the first question, you must plug the value of pizzas into the "x" in y = mx+ b.

Doing so will give you the following values:

Bombinoes : $81.00

Little Squeezer's: $78.00

Pizza Tent: $79.50

So Bombinoes Gives the most for 10 pizzas delivered.

The second question requires you to look at the "m" value for the equation. And you must determine the greatest one.

2.5x

3x

2.75x or 2.75p

3x would be the answer.

Lastly, the third problem requires you to do the same math as in the first question.

Doing so will give you the values:

B: $111.00

LS: $114.00

PT: $112.5

So Little Squeezer's would give you the most for delivering 22 pizzas.

The sample space for rolling a fair eight-sided die is {1, 2, 3, 4, 5, 6, 7, 8}.

We have to find the sample space for rolling a fair eight-sided die.

The sample space for rolling a fair eight-sided die consists of all the possible outcomes of a single roll of the die.

As the die has eight sides numbered from 1 to 8, the sample space can be represented as:

S = {1, 2, 3, 4, 5, 6, 7, 8}

Therefore, the sample space for rolling a fair eight-sided die is {1, 2, 3, 4, 5, 6, 7, 8}.

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Answer:

48 sq m

Step-by-step explanation:

Given quadrilateral is a parallelogram.

Here,

Base = 8 m

Height = 6 m

Area of parallelogram = Base * Height

-> Area = 8 * 6 = 48 sq m

The dimensions of each pen will maximize the total enclosed area are:  Length 81 feet; Width 81 feet.

Length = x

Width = y

Area = xy

Perimeter equation is

2(x + y) = 324

  x + y = 162

Substituting the perimeter equation

Area = x(162 - x)

Area = -x2 + 162x

If the zeros of the quadratic are 0 and 162, then the median  will be where the maximum area occurs.

162/ 2

= 81

Hence, the dimensions are

Length = 81 feet

Width = 162 - 81 = 81 feet

Therefore the dimensions of each pen will maximize the total enclosed area are:  Length 81 feet; Width 81 feet.

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Mr. Sanchez’s class sold fruit pies for $1.65 each and Mr. Kelly’s class sold bottles of fruit juice for $1.36 each. Together, the classes sold 79 items and earned $118.17 for their school.(a) Writing and solving the system of equations that model the problem: So, the correct option is A.

Let x be the number of fruit pies that Mr. Sanchez’s class sold and y be the number of bottles of fruit juice that Mr. Kelly’s class sold, we can form the following system of equations:

x + y = 79 -------(1)1.65x + 1.36y = 118.17 ----- (2)To solve the above system of equations by elimination method, we can multiply equation (1) by 1.36 on both sides and then subtract equation (2) from it. This can be shown below:1.36(x+y)= 1.36(79)1.36x + 1.36y = 107.44 (3) Subtracting equation (2) from equation (3), we get:1.65x + 1.36y = 118.17-1.36x - 1.36y = -107.44--------------------Adding, we get:0.29x = 10.73x = 37

Therefore, y = 42 Substituting the value of x and y in equation (2), we get:1.65(37) + 1.36(42) = 118.17

The classes earned the same amount of money $118.17.(b) Both the classes earned the same amount of money $118.17.(c) No class earned more money than the other. The difference in the amount of money earned is $0.

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Answer:

(x-4)² -11 where a = 4, b = 11

Step-by-step explanation:

The final form (x-a)² - b evaluates to x² - 2ax + a² -b

Matching

x² - 8x    +  5    

x² - 2ax  +  a² -b

This gives us -2ax = -8x or -2a = -8 or a = 4

and a² - b = 11 ==> 16 - b = 11 or b =5

Rewritten form is

(x-4)² -11

The two types of control charts for variables are the X-bar chart and the R-chart.

Control charts are widely used in statistical process control to monitor and analyze the variability and stability of processes over time. They are used for variables data, which are measurements or observations that can be quantified.

1. X-bar Chart: The X-bar chart is used to monitor the central tendency or average of a process. It tracks the sample means over time to detect any shifts or trends. It helps in assessing whether the process is in control or if there are any systematic variations from the target value.

2. R-chart (Range chart): The R-chart is used to monitor the variability or dispersion within a process. It tracks the ranges (the difference between the highest and lowest values) of samples over time. By analyzing the range values, it helps in understanding whether the process is stable and consistent or if there are any unusual variations or outliers.

Together, the X-bar chart and the R-chart provide valuable insights into process performance and allow for early detection of any deviations or abnormalities, helping organizations maintain quality standards and take appropriate corrective actions when necessary.

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With convolution theorem the equation is proved.

According to the statement

we have given that the equation and we have to evaluate with the convolution theorem.

Then for this purpose, we know that the

A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.

And the given equation is solved with this given integral.

So, According to this theorem the equation becomes the

\(\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).\)

Then after solving, it become and with theorem it says that the

\(\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .\)

Hence by this way the given equation with convolution theorem is proved.

So, With convolution theorem the equation is proved.

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Answer:

10 days

Step-by-step explanation:

Answer:

AC, AB, BC

Step-by-step explanation:

3x-13+2x-20+x+15=180

6x-18=180

6x=198

x=33

<a 86

<b 46

<c48

All of these fractions are equivalent to a number greater than 26, none of them is not equivalent to 26

To determine which fraction is not equivalent to 26, convert each fraction to a decimal or mixed number and compare it to 26.

131/3 = 43.666

123612/36 = 3433

4124/12 = 343.666

696/9 = 77.333

Since all of these fractions are equivalent to a number greater than or equal to 26, none of them is not equivalent to 26. Therefore, the answer is "none of the above".

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The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².

To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:

Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.

So, the integral for the area of the region is given by:

A = ∫a b [x₂(y) - x₁(y)] dy

Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10

So,

A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy

=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy

=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2

=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]

=> A = 174/3

Hence, the area of the region enclosed by the curves is 174/3 units².

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Answer: 14 Units

Step-by-step explanation: Subtract (10-2) and (11-5)

Based on the given frequency table, out of the 1000 trials, the confidence interval of (-0.151, 0.551) occurred 360 times, and the confidence interval of (-0.029, 0.829) occurred 309 times.

These two intervals have their upper and lower endpoints on either side of the population proportion of 0.3. Therefore, they do not capture the population proportion of 0.3, To determine the proportion of confidence intervals that capture the population proportion of 0.3, we need to look for the intervals that contain the value 0.3.

We can see from the frequency table that the confidence interval of (0.171, 1.029) occurred 133 times. This interval contains the population proportion of 0.3. Therefore, out of the 1000 trials, the proportion of confidence intervals that capture the population proportion of 0.3 is 133/1000 = 0.133 or approximately 13.3%.

Step 1: Identify the confidence intervals that capture the population proportion of 0.3.
We do this by checking if 0.3 lies between the lower and upper endpoints of each confidence interval.

0.0 to 0.0: No
-0.151 to 0.551: Yes
-0.029 to 0.829: Yes
0.171 to 1.029: Yes
0.449 to 1.151: No
1.0 to 1.0: No

Step 2: Count the number of confidence intervals that capture the population proportion of 0.3.
There are 3 confidence intervals that capture 0.3.

Step 3: Determine the proportion of the confidence intervals that capture the population proportion of 0.3.
To calculate the proportion, divide the number of confidence intervals that capture 0.3 by the total number of intervals, which is 6.

Proportion = 3 / 6 = 0.5

So, 50% of the 95% confidence intervals capture the population proportion of 0.3.

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Answer: Option d.  0.26

Step-by-step explanation:

Since the addition of complementary angles = 90°

75° + x = 90°

x = 90° - 75 °

x = 15°  ( the complementary angle )

sine 15° = 0.25882

             = 0.26 correct to two decimal places

The perimeter of the rectangle with vertices (-3,2), (-3,3),(3,3), and (3,-2) is 19.21 units.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

\(\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We have:

Vertices of the rectangle:

(-3,2), (-3,3), (3,3), and (3,-2)

The distance between (-3, 2) and (-3, 3):

= 1

The distance between (-3, 3) and (3, 3):

= 6

The distance between (3, 3) and  (3, -2):

= 5

The distance between (3, -2) and (-3, 2):

= 7.21

Perimeter of the rectangle = 1 + 6 + 5 + 7.21 = 19.21 units

Thus, the perimeter of the rectangle with vertices (-3,2), (-3,3), (3,3), and (3,-2) is 19.21 units.

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Answer:

x=7

Step-by-step explanation:

In order for this figure to be a rhombus, the interior sides have to  add up to 180, and the angle not given by an expression has to be 90.

90+8x+7+3x+6=180

Combine like terms

90+11x+13=180

103+11x=180

Subtract 103 from both sides

11x=77

Divide both sides by 11

x=7

These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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Answer:12x+2

Step-by-step explanation: the first step is to put g of x in f of x like this

3(4x)+2

Answer:

Step-by-step explanation:

If the graph of the parent function is shifted 7 units up and is steeper than the parent function, which of these could represent the function? answer choices.