draw a box plot for (35,50,50,48,48,32,38,41,48,34,29,23,41,34,43)

Answers

Answer 1

The box plot for the given data set (35, 50, 50, 48, 48, 32, 38, 41, 48, 34, 29, 23, 41, 34, 43) is as follows:

  |                 *

  |                 *

  |           *   *   *

  |         * |      

  |         * |   *  

  |   *     * | *  

  | * |   * * | *

  |-------------

To create a box plot for the given dataset (35, 50, 50, 48, 48, 32, 38, 41, 48, 34, 29, 23, 41, 34, 43), we need to determine the five-number summary, which consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

First, let's sort the data in ascending order: 23, 29, 32, 34, 34, 35, 38, 41, 41, 43, 48, 48, 48, 50, 50.

The five-number summary is as follows:

Minimum: 23

Q1: 34

Median: 41

Q3: 48

Maximum: 50

On a number line, we mark the minimum and maximum values (23 and 50) and draw a box with Q1, Q2 (median), and Q3 (34, 41, and 48). We connect the box with horizontal lines and indicate any outliers (values outside the minimum and maximum).

The box plot represents the distribution of the given dataset, with the box indicating the interquartile range and the median, and the whiskers showing the range of the data.

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Related Questions

Shipping costs $0. 15 per cubic inch. How much will Marcia pay to ship the box?

Answers

Answer:

B. 30

Step-by-step explanation:

5 x 4 = 20

20 x 10 = 200

200 x .15 = 30

Answer:

30

Step-by-step explanation:

TEST IT: Parallel and Perpendicular Lines 10 P (-8, 6) Copyright © 2023 Apex Learning Inc. 10 (0, 2) S 10 -10 2 Q 10 R (8, -2) PointP is located at (-8,6) and point R is located at (8,-2). What is the equation of SQ?​

Answers

The equation of SQ is y = (-1/2)x + 2.

Given the coordinates of point P and point R as (-8,6) and (8,-2) respectively. Now, we need to find the equation of SQ.

Let's use the slope-intercept form of the equation of a line which is y = mx + b where m is the slope and b is the y-intercept.

Firstly, we need to find the slope of the line passing through the points P and R.

 Slope of a line through two given points (x1,y1) and (x2,y2) is given by,m = (y2 - y1) / (x2 - x1).

Hence, Slope of line PR = mPR= (-2 - 6) / (8 - (-8))= (-8) / 16= -1/2. As the line SQ is parallel to the line PR, the slope of the line SQ will be the same as the slope of line PR. The slope of line SQ = mSQ= mPR= -1/2.

Now, we need to find the equation of line SQ which passes through the point (0,2) and has slope -1/2.

Hence, using the slope-intercept form of the equation of a line, we get the equation of SQ as follows: y = mx + b 2 = (-1/2)(0) + b 2 = b.

Therefore, the equation of line SQ is y = (-1/2)x + 2, where x and y are the coordinates of the points on the line.

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What is the volume of the pyramid in the diagram? The figure shows the rectangular pyramid with the dimension of height h equal to 15cm, length equal to 20 cm, width equal to 15 cm, and slant height equal to 25 cm. A. 1,500 cm3 B. 2,500 cm3 C. 4,500 cm3 D. 7,500 cm3

Answers

The volume of the pyramid in the diagram is option C: 4,500 cm³.

To find the volume of the pyramid, we can use the formula:

Volume = (1/3) * Base Area * Height

In this case, the pyramid is rectangular, so the base area is equal to the length multiplied by the width.

Given:

Height (h) = 15 cm

Length = 20 cm

Width = 15 cm

Slant height = 25 cm

First, let's find the base area:

Base Area = Length * Width

Base Area = 20 cm * 15 cm

Base Area = 300 cm²

Now, we can calculate the volume using the formula:

Volume = (1/3) * Base Area * Height

Volume = (1/3) * 300 cm² * 15 cm

Volume = 4500 cm³

Therefore, the volume of the pyramid is 4500 cm³.

The correct answer is option C: 4,500 cm³.

To summarize, the volume of the pyramid in the diagram is 4500 cm³. It is obtained by multiplying one-third of the base area (which is the length multiplied by the width) by the height of the pyramid. The given dimensions are used to calculate the base area as 300 cm². Multiplying this by the height of 15 cm and dividing by 3, we obtain the final volume of 4500 cm³.

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Jug A contains 6/7 as much water as Jug B.Jug C contains 3/5 as much water as Jug A.Find the ratio of the volume of water in Jug B to the volume of water as Jug C.

Answers

The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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If f(x)=1/x, which equation describes the graphed function

Answers

y = f(x+2) +1 is the equation which describes the graphed function.

What is translation?

Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same. In mathematics, a translation is the up, down, left, or right movement of a shape.

When F crosses the x-axis when it is poitive. +1 indicates a 1 unit down translation.

So, the equation will be y = f(x+2) + 1. y = f(x+2) -1 is the equation which describes the graphed function.

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please help!!! if i don’t get this test right then i fail and i really can’t ! i’ll mark brainlyist ! pleasee
anyone

Answers

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160


Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

1.
Problem
Solve the following questions. Write your answers clearly in the spaces provided.
The rectangular face of the cuboid below has an area of 126 cm². The ratio of thelength to the height of the rectangular face is 7:2. Find its volume.

Answers

The volume of the cuboid, obtained using the specified area of the rectangular face and the square thickness surface, indicates that the possible volume of the cuboid are;

2,646 cm³ or 756 cm³, depending on the thickness of the cuboid

What is a cuboid?

A cuboid is a hexahedron consisting of six quadrilateral faces.

The area of the rectangular face of the cuboid, A = 126 cm²

The ratio of the length to the height of the rectangular face = 7 : 2

Let L represent the length of the rectangular face, and let H represent the height of the face, we get;

A = L × H = 126

L/H = 7/2

Therefore; L = (7/2) × H

Plugging in the value of L, in the equation for the area, we get;

A = (7/2) × H × H = (7/2) × H² = 126

H² = 126 × (2/7) = 36

H = √(36) = 6

The height of the rectangular face, H = 6 cm

L = (7/2) × H

Therefore, L = (7/2) × 6 = 21

The length, L, of the rectangular face, L = 21 cm

Whereby the cuboid consists of two square faces, we get;

The possible volume, V, of the cuboid are V = H×L² or V = L×H²

Therefore, the possible volume of the cuboid are;

V = 6 × 21² = 2646 cm³

V = 21 × 6² = 756 cm³

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NEED HELP PLEASEE HELP ME ASAP​

Answers

a. Gross profit rate is -5.56%

b Operating profit margin rate is -5.56%

c. Net profit margin rate is -5.56%

d ROI is -5.26%

How to calculate the value

a. Gross profit rate = (Total Revenue - Cost of Goods Sold) / Total Revenue * 100

Gross profit rate = (P180,000.00 - P190,000.00) / P180,000.00 * 100

Gross profit rate = -P10,000.00 / P180,000.00 * 100

Gross profit rate = -5.56%

b. Operating profit margin rate = Operating Profit / Total Revenue * 100

Operating profit margin rate = (-P10,000.00) / P180,000.00 * 100

Operating profit margin rate = -5.56%

c. Net profit margin rate = Net Profit / Total Revenue * 100

Net profit margin rate = (-P10,000.00) / P180,000.00 * 100

Net profit margin rate = -5.56%

d. Return on Investment (ROI) = Net Profit / Investment * 100

ROI = (-P10,000.00) / P190,000.00 * 100

ROI = -5.26%

Yes, creativity is often present in the operation of ordinary small businesses. Small business owners need to find innovative ways to attract customers, differentiate themselves from competitors, and maximize limited resources.

Yes, the daily business practices of small owners can be considered within the concept of entrepreneurship. Entrepreneurship involves the identification and exploitation of opportunities to create value, often through the establishment of new businesses or the enhancement of existing ones.

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Solve the equation for w.

w divided by 1.3 minus 4.9 equals 7.5

9.5
2
16.12
3.38

Answers

To solve the equation for w, we will isolate the variable on one side of the equation. Here's the step-by-step solution:

w / (1.3 - 4.9) = 7.5

First, simplify the expression inside the parentheses:

w / (-3.6) = 7.5

Next, multiply both sides of the equation by -3.6 to eliminate the fraction:

(-3.6) * (w / -3.6) = (-3.6) * 7.5

This simplifies to:

w = -3.6 * 7.5

Now, calculate the right-hand side of the equation:

w = -27

Therefore, the solution to the equation is:

w = -27

the domain, range and intercepts of a function are shown. which set of information could be characteristics of the functions inverse

Answers

Option - Range: y >= -2, is the most likely set of information that could be a characteristic of the function's inverse. Domain: x >= -1 ,  y-intercept: (0, -1) , x-intercept: (1, 0).

To determine which set of information could be characteristics of the function's inverse, we need to consider the properties of inverse functions.

The inverse of a function swaps the roles of the domain and range of the original function. It also swaps the x-intercepts and y-intercepts.

Among the given options:

Domain: x >= -1

  This information about the domain of the function does not provide any insight into the inverse function. The domain of the inverse function would depend on the range of the original function.

Range: y >= -2

  This information about the range of the function could potentially be a characteristic of the inverse function. If the original function had a range of y >= -2, then the inverse function would have a corresponding domain.

y-intercept: (0, -1)

  This information about the y-intercept of the function would not directly correspond to the x-intercept of the inverse function. The inverse function would have a y-intercept at x = -1, corresponding to the given x-intercept of the original function.

x-intercept: (1, 0)

  This information about the x-intercept of the function would not directly correspond to the y-intercept of the inverse function. The inverse function would have a y-intercept at y = 1, corresponding to the given y-intercept of the original function.

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PLEASE HELP ON QUESTION ASAP. if answer is correct i will rate you five stars a thanks and maybe even brainliest.

Alex drove for 3 hours at average speed of 60mph and for 2 hrs at 45 miles per hour. Whats his average speed for the whole journey.

also could you please show me how our working out should look like in an exam

Answers

To find the average speed for the whole journey, you need to calculate the total distance traveled and divide it by the total time taken. Here's how you can do it:

Distance traveled at 60 mph = 60 mph x 3 hrs = 180 miles

Distance traveled at 45 mph = 45 mph x 2 hrs = 90 miles

Total distance traveled = 180 miles + 90 miles = 270 miles

Total time taken = 3 hrs + 2 hrs = 5 hrs

Average speed for the whole journey = Total distance / Total time

= 270 miles / 5 hrs

= 54 mph

Therefore, Alex's average speed for the whole journey is 54 mph.

In an exam, your working out might look something like this:

60 mph x 3 hrs = 180 miles

45 mph x 2 hrs = 90 miles

Total distance traveled = 180 miles + 90 miles = 270 miles

Total time taken = 3 hrs + 2 hrs = 5 hrs

Average speed for the whole journey = Total distance / Total time

= 270 miles / 5 hrs

= 54 mph

Make sure to show your calculations clearly and label your units to avoid any confusion.

9 ft
16 ft
What is the volume of the cylinder?

Answers

Answer:The formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2.

Step-by-step explanation:

HELP PLEASEEEEE
Which expression is equivalent to the expression quantity negative 7 over 6 times t plus 4 over 9 end quantity minus expression quantity negative 5 over 12 times t plus 2 over 3 end quantity

Answers

The expression quantity negative 7 over 6 times t plus 4 over 9 end quantity minus expression quantity negative 5 over 12 times t plus 2 over 3 end quantity can be simplified as follows:

= (-7/6)t + (4/9) - (-5/12)t - (2/3)

= (-7/6 + 5/12)t + (4/9 - 2/3)

= (-21 + 10)/12t + (2 - 4)/9

= -11/12t - 2/9

= -(11/12)t - (2/9)

Therefore, the expression is equivalent to -(11/12)t - (2/9).

An equilateral triangle was rotated to create this figure. What is true about the axis of rotation?

Answers

The true statement about the axis of rotation is the option;

It is parallel to a side of the equilateral triangle, but is separate from the equilateral triangle.

What is an axis of rotation?

The axis of rotation is a straight line around which all points on a rotating body rotates.

The diagram shows a figure with a hollow cylindrical cross section and triangular cross section on the left and right, which indicates that the figure is created by the rotation of the equilateral triangle about height of the cylinder, such that the axis of rotation is a vertical line through the center of the hollow cylinder. Therefore, the axis of rotation is parallel to the height of the cylinder, and therefore, it is parallel to the base of the equilateral triangle, but it it seperate from walls of the cylinder, and therefore, separate from the equilateral triangle

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She needs to create three colours: pink, brown and turquoise which me
in stock.
To make pink paint, she must mix red and white in the ratio 3:7.
If she uses 4.5 litres of red paint, how much white paint should she use?

Answers

She should use 10.5 liters of white paint to create the desired shade of pink when using 4.5 liters of red paint.

To create pink paint, the required ratio of red to white paint is 3:7. If she uses 4.5 litres of red paint, we can calculate the amount of white paint needed by setting up a proportion.

Let's assume x represents the amount of white paint needed in liters.

According to the given ratio, we have:

3/7 = 4.5/x

To solve for x, we can cross-multiply and then divide:

3x = 4.5 * 7

3x = 31.5

x = 31.5 / 3

x = 10.5

She should therefore mix 4.5 litres of red paint with 10.5 litres of white paint to get the correct shade of pink.

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The length of a rectangle exceeds its width by 5
inches, and the area is 14 square inches. What
are the length and width of the rectangle?
Separate the answers with a comma.

Answers

Answer:

2 in and 7 in

-------------------------------

Let the length be l and width be w.

We are given that:

1) l = w + 52) lw = 14 (area is the product of length and width)

Substitute w + 5 for l into second equation:

w(w + 5) = 14w² + 5w = 14w² + 5w - 14 = 0w² + 7w - 2w - 14 = 0w(w + 7) - 2(w + 7) = 0(w + 7)(w - 2) = 0w = - 7 or w = 2

The first root is discarded as negative.

So the width is 2 in, then the length is:

l = 2 + 5l = 7 in

Answer:

length = 7 inch

width = 2 inch

Step-by-step explanation:

Let the width be "w".

Given:

Length = W + 5

Area = 14 in²

We know that the formula for the area of a rectangle:

Area = width × length

Substituting the given information into the formula, we have:

(W + 5) × W = 14

Expand the equation

W² + 5W = 14

Rearrange the equation

W² + 5W - 14 = 0

Now, we can solve this quadratic equation directly.

Factoring or using the quadratic formula, we find:

W = 2 or W = -7

Since the width cannot be negative, we take Width = 2 as the valid solution.

Plugging this value back into the equation for the length:

Length = W+ 5 = 2 + 5 = 7

Therefore, the length and width of the rectangle are 7 inches and 2 inches, respectively.

answer ASAP I will brainlist

Answers

The system has exactly one solution. The solution is (13, 8)

All three countries had the same population of 8,000 in 2023

How to calculate the solution to the system of equations

From the question, we have the following parameters that can be used in our computation:

Country A: -x + 20y = 147

Country B: -x + 10y = 67

Country C: y = 8

So, we have

-x + 20y = 147

-x + 10y = 67

y = 8

Substitute 8 for y in the first and second equations

So, we have

-x + 20 * 8 = 147

-x + 10 * 8 = 67

Evaluate the products

-x + 160 = 147

-x + 80 = 67

So, we have

x = 160 - 147

x = 80 - 67

Evaluate

x = 13

x = 13

Hence, the solution to the system of equations is (13, 8)

The interpretation is that all three countries have the same population in a particular year

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To evaluate whether customers enjoy the barista’s new smoothie, a restaurant manager surveys every other customer who orders the new smoothie. The manager determines that customers enjoy the new smoothie. Select all the statements that are true about the sampling method.

Answers

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Corrine is purchasing beads to make a new necklace and bracelet set. The two pieces of jewelry each need silver and green beads. The necklace requires 25 silver beads and 15 green beads. The bracelet requires 10 silver beads and 5 green beads. Corrine paid $27.50 for the necklace beads and $10 for the bracelet beads. How much does each silver bead cost? How much does each green bead cost? Be sure to show your work and explain your answer.

Answers

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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​Claim: A minority of adults would erase all of their personal information online if they could. A software firm survey of 473 randomly selected adults showed that ​42% of them would erase all of their personal information online if they could. Complete parts​ (a) and​ (b) below.

a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.

b. Identify the null and alternative hypotheses.

Answers

This means that the majority of adults, as represented by the 42% in the survey, would erase all of their personal information online if given the opportunity.


The null hypothesis (H0) states that there is no significant difference or relationship between the variables being tested. In this case, the null hypothesis would be: A minority of adults would not erase all of their personal information online if they could.
The alternative hypothesis (H1) states that there is a significant difference or relationship between the variables being tested. In this case, the alternative hypothesis would be: A minority of adults would erase all of their personal information online if they could.
To summarize:
Null Hypothesis (H0): A minority of adults would not erase all of their personal information online if they could.
Alternative Hypothesis (H1): A minority of adults would erase all of their personal information online if they could.
In this survey, 42% of the randomly selected adults indicated that they would erase all of their personal information online if they could. If the null hypothesis were true, we would expect the percentage to be significantly lower than 42%. Therefore, based on the survey results, we reject the null hypothesis and accept the alternative hypothesis

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Sandra’s Purse Boutique has the following transactions related to its top-selling Gucci purse for the month of October. Sandra's Purse Boutique uses a periodic inventory system.

Date Transactions Units Unit Cost Total Cost
October 1 Beginning inventory 6 $ 820 $ 4,920
October 4 Sale 4
October 10 Purchase 5 830 4,150
October 13 Sale 3
October 20 Purchase 4 840 3,360
October 28 Sale 7
October 30 Purchase 8 850 6,800
$ 19,230
2. Using FIFO, calculate ending inventory and cost of goods sold at October 31.

Answers

Using the FIFO method, the ending inventory is $0, and the cost of goods sold (COGS) at October 31 is $8,240.

To calculate the ending inventory and cost of goods sold (COGS) using the First-In-First-Out (FIFO) method, we need to analyze the transactions and determine the order in which the units were purchased.

Let's break down the calculations step by step:

Beginning Inventory:

Beginning inventory units: 6

Unit cost: $820

Total cost: $4,920

Purchases:

October 10 purchase: 5 units at $830 per unit, totaling $4,150

October 20 purchase: 4 units at $840 per unit, totaling $3,360

October 30 purchase: 8 units at $850 per unit, totaling $6,800

Sales:

October 4 sale: 4 units

October 13 sale: 3 units

October 28 sale: 7 units

Now, let's calculate the ending inventory and COGS using the FIFO method:

Identify the units sold and their corresponding costs:

For the October 4 sale, we assume the units come from the beginning inventory (oldest units). Thus, we use the cost of the beginning inventory units:

4 units * $820/unit = $3,280 (COGS)

For the October 13 sale, we assume the units come from the remaining beginning inventory units:

2 units (6 units - 4 units sold) * $820/unit = $1,640 (COGS)

For the October 28 sale, we assume the units come from the October 10 purchase:

4 units * $830/unit = $3,320 (COGS)

Calculate the ending inventory:

Remaining units after sales:

Beginning inventory units - Units sold = 6 units - (4 units + 3 units + 7 units) = -8 units

Since we cannot have a negative inventory, we assume a zero ending inventory.

Calculate the COGS:

COGS = Sum of the costs of the units sold

COGS = $3,280 + $1,640 + $3,320 = $8,240

Therefore, using the FIFO method, the ending inventory is $0, and the cost of goods sold (COGS) at October 31 is $8,240.

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a. Find the open intervals on which the function is increasing and those on which it is decreasing.
b. Identify the​ function's local extreme​ values, if​ any, saying where they occur.

Answers

The function is increasing on the open intervals (-∞, -1.5) and (1.5, ∞), and it is decreasing on the open interval (-1.5, 1.55).

b. The function has local extreme values at x = -1.5 and x = 1.5.

How to analyze the function

To determine the open intervals on which the function f(x) = [tex]x^{1/5}[/tex] (x²-25) is increasing or decreasing, we need to find the intervals where the derivative of the function is positive (increasing) or negative (decreasing).

Or we plot the graph of the function and read the graph

From the graph the critical points are x = -5, x = 0 and x = 5. and the inflexion points are x = -1.5 and  = 1.5

analysis the intervals

For x < -1.5, the function is increasing on the interval (-∞, -5).

For -1.5 < x < 1.5, the function is decreasing on the interval (-5, 5).

For x > 1.5,  the function is increasing on the interval (5, ∞).

Regarding the local extreme values, we can observe that the function has a local maximum at (-1.5, 24.7) and local minima at (1.5, -24.7)

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please help me! Angles A and B are complementary. If mA is 48", what is the measure of ZB?
OA. 48°
OB. 42°
OC. 132°
OD. 312°

Answers

Answer:

42 degrees

Step-by-step explanation:

Complementary angles add up to 90 degrees

90-48=42

Answer:

B) 42°

Step-by-step explanation:

"complementary" means the angles add up to 90°

48° + 42° = 90°

Angle B must be 42°.

The graph of the function f(x) = (x-4)(x + 1) is shown
below.
Which statement about the function is true?

Answers

The correct statement about the function in this problem is given as follows:

The function is decreasing for all real values of x where x < 1.5.

When a function is increasing and when it is decreasing, looking at it's graph?

Looking at the graph of the function, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented  by y also increases.Looking at the graph of the function, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.

Hence the intervals of this problem are given as follows:

Decreasing for x < 1.5.Increasing for x > 1.5.

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OB.
6
5
O C. square
O D. parallelogram
4
0 1 2 3 4 5
-1
-2
The vertices of a quadrilateral on the coordinate plane are (2, 4). (-4, -2). (-2, 4), and (4, -2). What type of quadrilateral has these vertices?
O A. rectangle
trapezoid
X

Answers

The opposite sides of the quadrilateral are parallel and equal in length, we can conclude that it is a parallelogram. Otion D. parallelogram

The quadrilateral with the vertices (2, 4), (-4, -2), (-2, 4), and (4, -2) is a parallelogram.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.

Therefore, if we can show that the opposite sides of this quadrilateral are parallel and equal in length, then we can conclude that it is a parallelogram.

In order to show that the opposite sides of the quadrilateral are parallel and equal in length, we need to find the slope of each side. Recall that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

[tex]$$m = \frac{y_2 - y_1}{x_2 - x_1}$$[/tex]

Let's begin by finding the slope of the line passing through (2, 4) and (-4, -2):

[tex]$$m = \frac{-2 - 4}{-4 - 2} = \frac{-6}{-6} = 1$$Next,[/tex]

Let's find the slope of the line passing through (-2, 4) and (4, -2):

[tex]$$m = \frac{-2 - 4}{4 - (-2)} = \frac{-6}{6} = -1$$[/tex]

Since the slopes of these two lines are equal in magnitude but opposite in sign, we know that they are parallel. Therefore, opposite sides of the quadrilateral are parallel. To show that opposite sides are equal in length, we can use the distance formula:

[tex]$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$[/tex]

The distance between (2, 4) and (-4, -2) is:

[tex]$$d = \sqrt{(-4 - 2)^2 + (-2 - 4)^2}

= \sqrt{36 + 36}

= \sqrt{72}$$[/tex]

The distance between (-2, 4) and (4, -2) is:

[tex]$$d = \sqrt{(4 - (-2))^2 + (-2 - 4)^2}

= \sqrt{36 + 36}

= \sqrt{72}$$[/tex]

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The diameters of apples from a certain farm follow normal distribution with mean 4 inches and standard deviation 0.4 inch.
Apples can be size-sorted by being made to roll over mesh screens. First the apples are rolled over a screen with mesh size
3.5 inches. This separates out all the apples with diameters less than 3.5 inches. Second, the remaining apples are rolled
over a screen with mesh size 4.3 inches. Find the proportion of apples with diameters greater than 4.3 inches.
• Round your answer to four decimal places.

Answers

The proportion of apples with diameters greater than 4.3 inches is given as follows:

0.2266.

How to obtain the proportion?

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 4, \sigma = 0.4[/tex]

The z-score of a measure X is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion is one subtracted by the p-value of Z when X = 4.3, hence it is given as follows:

Z = (4.3 - 4)/0.4

Z = 0.75

Z = 0.75 has a p-value of 0.7734.

1 - 0.7734 = 0.2266.

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(a) Copy and complete the table of values for y= 2x²-x-4 for-3 ≤x≤3.
X
y
-3
17
-2 -1
0
(c) Use the graph to find the:
-4
1
2 3
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis,
draw the graph of y=2x²-x-4 for -3 ≤x≤3.
(i) roots of the equation 2x2-x-4 = 0;
(ii) values of x for which y increases as x increases,
(iii) minimum point of y.

Answers

The minimum point of y is (0, -4).

X | y

-3 | 17

-2 | -4

-1 | -7

0 | -4

1 | -1

2 | 4

3 | 11

Using these values, we can proceed with the requested tasks:

(b) To draw the graph of y = 2x² - x - 4, we will use a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis. Here's how the graph looks:

   |   |   |   |   |   |   |

   |   |   |   |   |   |   |

   |   |   |   |   |   |   |

   |   |   |   |   |   |   |

   |   |   |   |   |   |   |

----+---+---+---+---+---+---+--

  -3  -2  -1   0   1   2   3

The graph will have a parabolic shape, opening upward.

(i) To find the roots of the equation 2x² - x - 4 = 0, we need to find the x-values where the graph intersects the x-axis. From the graph, we can see that the roots are approximately x = -2 and x = 1. These are the values where the graph crosses the x-axis.

(ii) To find the values of x for which y increases as x increases, we need to identify the intervals on the x-axis where the graph is moving upwards. From the graph, we can see that as x increases from -3 to -2, and from 1 to 3, y is increasing. Therefore, the values of x for which y increases as x increases are x ∈ (-3, -2) and x ∈ (1, 3).

(iii) To find the minimum point of y, we need to locate the vertex of the parabolic graph. From the graph, we can see that the vertex is approximately at x = 0, y = -4. Therefore, the minimum point of y is (0, -4).

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Need Help Please ASAP

Answers

A. The conditional probability that a dog owner also owns a cat is approximately 0.344.

B. The conditional probability that a cat owner also owns a dog is approximately 0.346.

How to calculate the value

A. P(D) = 0.61 (61% own a dog)

P(C) = 0.29 (29% own a cat)

P(D ∩ C) = 0.21 (21% own both a cat and a dog)

The conditional probability P(C|D) represents the probability of owning a cat given that you own a dog. We can calculate it using the formula:

P(C|D) = P(D ∩ C) / P(D)

Plugging in the values we have:

P(C|D) = 0.21 / 0.61

≈ 0.344 (approximately)

B. To find the conditional probability that a cat owner also owns a dog, we use a similar approach. Let's denote D as the event of owning a dog and C as the event of owning a cat. We are given the following information:

P(D) = 0.43 (43% own a dog)

P(C) = 0.26 (26% own a cat)

P(D ∩ C) = 0.09 (9% own both a cat and a dog)

The conditional probability P(D|C) represents the probability of owning a dog given that you own a cat. We can calculate it using the formula:

P(D|C) = P(D ∩ C) / P(C)

Plugging in the values we have:

P(D|C) = 0.09 / 0.26

= 0.346

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Find the product
3(z+4)(x-5)

Answers

Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Suppose Tom has 19 coins totaling $2.95. If he has only quarters and nickels, how many of each type does he have?

Number of quarters =
Number of nickels =

Answers

Suppose Tom has 19 coins totaling $2.95. If he has only quarters and nickels, he has 10 quarters and 9 nickels.

Number of quarters = 10

Number of nickels = 9

Let's solve the problem step by step:

Let's assume the number of quarters as q and the number of nickels as n.

The value of each quarter is $0.25, so the total value of quarters is 0.25q.

The value of each nickel is $0.05, so the total value of nickels is 0.05n.

According to the problem, we have the following two equations:

q + n = 19 (since Tom has a total of 19 coins)

0.25q + 0.05n = 2.95 (since the total value of the coins is $2.95)

Now, we can solve this system of equations to find the values of q and n.

Multiplying equation 1 by 0.05, we get:

0.05q + 0.05n = 0.95

Subtracting this equation from equation 2, we have:

0.25q + 0.05n - (0.05q + 0.05n) = 2.95 - 0.95

Simplifying:

0.2q = 2

Dividing both sides by 0.2:

q = 10

Substituting the value of q into equation 1:

10 + n = 19

Subtracting 10 from both sides:

n = 9

Therefore, Tom has 10 quarters and 9 nickels.

Number of quarters = 10

Number of nickels = 9

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