what are the answers to these questions?

What Are The Answers To These Questions?

Answers

Answer 1

a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.

b) The domain of V is [0, 3) in interval notation.

c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.

d) The maximum volume is 160/27 cm³.

(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.

Since the height of the box is x cm, the volume of the box can be expressed as

V = x(20-2x)(6-2x) cm³.

(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.

(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get

dV/dx = 4x³ - 52x² + 120x.

Setting dV/dx = 0, we get

x = 0 or x = 3 or x = 10/3.

Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.

We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get

V(0) = V(3) = 0

and

V(10/3) = 160/27.

(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.

So, the length of the box is

20-2(10/3)

= 40/3 cm,

the width of the box is

6-2(10/3)

= 2/3 cm, and

the height of the box is 10/3 cm.

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Related Questions

Each of the following people bought a watch that costs 300. Which of the following people will pay the most for their purchase

Answers

The individual that will be paying the most for their purchase is: B.edgar paid with a credit card and paid the minimum payment each month

Which individual will pay the most?

The individual that will pay the most according to the data provided is Edgar. Edgar's payment is spread out to the longest length of time. So, he will have to pay the added dues for extending his payment.

Usually, the person who pays cash pays the least amount while the person who pays in installments is charged for additional time spent in making the payment.

Complete Question:

Each of the following people bought a watch that costs $300. Which of the following people will pay the most for their purchase A.Sarah paid cash B.edgar paid with a credit card and paid the minimum payment each month C.susan paid with a credit card and paid the minimum payment plus 30 each month D. Sean paid with a credit card and paid the full balance the first of the month

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The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
7
7
22

Answers

The scale factor for this right triangles is equal to 5/4.

What is a scale factor?

In Mathematics, the scale factor of any geometric figure can be determined by dividing the dimension or side length of the new figure (image) by the dimension or side length of the original figure (pre-image):

Scale factor = Dimension of new figure (image)/Dimension of original figure (pre-image)

By substituting the given dimensions into the formula for scale factor, we have;

Scale factor = image dimension/pre-image dimension

Scale factor = 15/12 = (25/4)/5

Scale factor = 5/4.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Pls, HELP!!
Law of Cosines
Solve for c. Round your final answer to the nearest tenth

Answers

The length of c in the triangle is 4.2 units.

How to find the side of a triangle?

The side of a triangle can be found using cosine law as follows:

Hence,

c² = a² + b² - 2ab cos C

where

a, b and c are the side lengthC is angle opposite to side c

Therefore,

c² = 7² + 8² - 2(7)(8) cos 32°

c² = 49 + 64  - 112 cos 32°

c² = 113 - 112(0.84804809615)

c² = 113 - 94.9813867695

c² = 18.019

square root both sides of the equation

c = √18.019

c  = 4.24487926801

c = 4.2 units

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Plssss help me quickly

Answers

Answer:

36

Step-by-step explanation:

First you calculate the area of the rectangle. then you substract the area of the triangle.

The area of a rectangle is equal to the product of its length and breadth. In other words, if the length of a rectangle is ‘l’ and its breadth is ‘b’, then its area ‘A’ can be calculated as A = l x b= 6*8= 48

The area of a triangle can be calculated using the formula A = 0.5 x b x h where ‘b’ is the length of the base of the triangle and ‘h’ is its height. so A =0.5*8*3 = 12

Area of the figure = 48-12=36

The parent function f ( x ) = 3 √ x is transformed to g ( x ) = 2 f ( x − 3 ) Which is the graph of g ( x ) ?

Answers

The graph of the function g(x) has an equation of g(x) = 6√(x - 3)

Identifying the graph of the function g(x)?

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

f(x) = 3√x

The transformed function g(x) is given as

g(x) = 2f (x − 3)

In f(x) = 3√x , we have

f(x - 3) = 3√(x - 3)

Multiply both sides by 2

So, we have

2f(x - 3) = 2 * 3√(x - 3)

Evaluate the products

2f(x - 3) = 6√(x - 3)

Recall that

g(x) = 2f (x − 3)

So, we have

g(x) = 6√(x - 3)

This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)

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Find the slope and y-intercept of the line: 10 + 5y = 2x.

Answers

Slope: 2/5
Y-intercept: -2

Slope intercept form: y=mx+b.
Your m is your slope, and your b is your y-intercept.

MO is parallel to PR. Angle RQN=115. What is MNQ?

Answers

Since MO is parallel to PR, then angle MNQ and angle RQN are alternate interior angles and are congruent. Therefore, angle MNQ = angle RQN = 115 degrees.

What are alternate interior angles

When a line that intersects two parallel lines, also known as a transversal, creates an intersection with a pair of other lines, it forms what is referred to as alternate interior angles.

From the diagram we can see that RQN and MQN are similar angles from the diagram

Hence we have that RQN=115 = MNQ

Therefore MNQ = 115 degrees

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Express 1:0.2:0.75 in their simple form

Answers

Answer:

20 : 4 : 15

Step-by-step explanation:

1 : 0.2 : 0.75

1 : 2/10 : 75/100

1 : 20/100 : 75/100

(×100)

100 : 20 : 75

(÷5)

20 : 4 : 15

Evaluate the following expression.
If x=12,y=8, and z=6.
X2y-2z over 4

Answers

The value of the expression "(x²y - 2z)/4", when x = 12 , y = 8 and z = 6, is (c) 285.

An "Expression" is defined as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, which are written using mathematical symbols and follow certain rules.

We have to evaluate the expression : (x²y - 2z)/4, if x = 12 , y = 8 and z = 6,

To evaluate , we substitute x = 12 , y = 8 and z = 6, in the expression,

So, We have,

⇒ (12² × 8 - 2×6)/4,

⇒ (144 × 8 - 12)/4,

⇒ (144 × 8 - 12)/4,

⇒ (1152 - 12)/4,

⇒ 1140/4,

⇒ 285,

Therefore, the value of the given expression, when x=12, y=8, and z=6, is 285, the correct option is (c).

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Describe the following function

Answers

The transformation in the function y = -1/3f(x + 4) - 5 is described below

Describing the transformation in the function

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

y = f(x)

The transformed function g(x) is given as

y = -1/3f(x + 4) - 5

The sequence of transformation on the transformed function is as follows

Horizontal shift to the left by 4 unitsVertical stretch by a factor of 1/3Reflection across the x-axisLastly, vertical shift down by 5 units

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A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 15 square feet use 3.14 for pi

Answers

The distance from which the sprinkler can spread water is  4.37 feet

How to determine the value

To determine the value, we need to know the area of the circle.

The formula for the area of a circle is expressed as;

A = πr²

Given that the parameters are;

A is the area of the circler is the radius of the circle

Substitute the values, we have;

15 = 3.14r²

Divide both sides by the coefficient, we get;

r² = 4. 77

find the square root of both sides, we get;

r = 2. 19 feet

But note that the formula for diameter is given as;

Diameter = 2radius

Diameter = 2(2.19)

multiply the values

Diameter = 4.37 feet

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i need help as soon as possible!

Answers

Answer:

2600This is a probability conversion problem.

PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT

Answers

p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

What is an arithmetic series?

According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.

To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:

(141-5) = 22 + (n - 1)3

136 = 22 + 3n - 3

117 = 3n

n = 39

Therefore, there are 39 terms in the arithmetic series.

To find the sum of the first n terms of an arithmetic series, we can use the formula:

Sn = n/2(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:

S39 = 39/2(22 + (141-5))

S39 = 19(136)

S39 = 2584

Therefore, the sum of the first 39 terms of the series is 2584.

Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.

We know that the common difference is 3, so we can write the nth term as:

an = a1 + (n - 1)d

an = 22 + (n - 1)3

an = 3n + 19

Substituting this into the formula for the sum of the first n terms, we get:

Sn = n/2(a1 + an)

Sn = n/2(22 + 3n + 19)

Sn = n/2(3n + 41)

[tex]Sn = 3/2 n^2 + 41/2 n[/tex]

Therefore, p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

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Average Weekly Earnings in Canada
Occupation 2010 2008
Forestry, logging and support $971 $812
Manufacturing $977 $943
Transportation and warehousing $900 $873
Construction $1071 $1023
Retail trade $501 $486

1. Calculate the mean (average) weekly earnings of workers in the occupations
listed for 2010.

Answers

Answer: To calculate the mean weekly earnings for each occupation in 2010, we need to add up the weekly earnings for each occupation and divide by the number of occupations.

For Forestry, logging and support:

Mean weekly earnings = (971) / (1) = $971

For Manufacturing:

Mean weekly earnings = (977) / (1) = $977

For Transportation and warehousing:

Mean weekly earnings = (900) / (1) = $900

For Construction:

Mean weekly earnings = (1071) / (1) = $1071

For Retail trade:

Mean weekly earnings = (501) / (1) = $501

Therefore, the mean weekly earnings for workers in the listed occupations in 2010 are:

Forestry, logging and support: $971

Manufacturing: $977

Transportation and warehousing: $900

Construction: $1071

Retail trade: $501

Step-by-step explanation:

multiply 9/11 x 44/81

Answers

Answer:

Step-by-step explanation:

decimal: 0.44444444444

fraction: 4/9

one two 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Answers

Answer:

31

Step-by-step explanation:

the next number is 31 in this series

Which statement concerning the equation x² - 1 = x is true?

1. Its discriminant is 0, so it has no solution.

2. Its discriminant is 5, so it has two real solutions.

3. Its discriminant is 0, so it has one real solution.

4. Its discriminant is -3, so it has two complex solutions.

Answers

The statement "Its discriminant is 5, so it has two real solutions" is not true for the equation x² - 1 = x.

The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, the equation can be rewritten as x² - x - 1 = 0, so a = 1, b = -1, and c = -1. Therefore, the discriminant is (-1)² - 4(1)(-1) = 5.

Since the discriminant is positive, the equation has two real solutions. However, this statement does not apply to the given equation because it is not in standard quadratic form.

To solve the equation x² - 1 = x, we can rearrange it as x² - x - 1 = 0 and then use the quadratic formula to find its solutions. The quadratic formula is x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values a = 1, b = -1, and c = -1, we get x = (1 ± sqrt(5)) / 2. Therefore, the equation has two real solutions, which are x = (1 + sqrt(5)) / 2 and x = (1 - sqrt(5)) / 2.

Answer:

The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -1, and c = -1. So:

x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)

x = (1 ± sqrt(5)) / 2

Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.

Please find the equation of the circle! (Thx)

Answers

Answer:

[tex] {(x - 1)}^{2} + {(y - 2)}^{2} = 5 [/tex]

Find sin (ñ/4). Round to 3 decimal places.

Answers

Answer:To find sin(π/4), we can use the fact that sin(π/4) = sin(45°). We also know that sin(45°) = 1/√2 or approximately 0.707 (rounded to 3 decimal places). Therefore, sin(π/4) is approximately equal to 0.707.

Step-by-step explanation:

HELP THIS IS ALL!!!HELPPP

Answers

Answer:

247

Step-by-step explanation:

Question 2 (2 points)
In the circle below, D is the center and segment AC is the diameter.

What is the measure of ZADC?Blank 1:
Blank 2
What is the measure of ZABC?

Answers

The measure of ∠ADC is equal to 180 degrees.

The measure of ∠ABC is equal to 90 degrees.

What is a circle?

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.

In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.

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pleaseeee help me!!


mathematics the pic below

Answers

Answer:

15, 18, 21, 24, 27, 30 ( +3)

7, 14, 28, 56, 112, 224, 448 ( x 2)

77, 70, 63, 56, 49, 42, 35 ( - 7)

20, 31, 42, 53, 64, 75, 86, 97 (+11)

22, 35, 48, 61, 74, 87 (+13)

Which equation can be used to solve for x

Answers

Answer:

  (a)  7(x +3.5x) = 56

Step-by-step explanation:

You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.

Daily run

The morning run is given as x.

The evening run is 3.5 times as long, so is 3.5x

The total mileage each day is (x +3.5x).

Weekly total

In 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:

  7(x +3.5x) = 56

PLS HELP ASAP
I AM SO CONFUSED WID THIS!
The numbers 1-20 are written on pieces of paper and put in a box. Two pieces of paper are randomly selected and not replaced.

a) Are the events dependent or independent? _________

b) What is the probability of selecting a number less than 6 both times? ________

Answers

the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

how to find probability ?

a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.

b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.

The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.

Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.

To find the probability of both events occurring, we multiply the probabilities:

P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)

P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19

Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

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Anna saved $20 in a jar each month for 2 3/4 years. she spent 75% of her savings on a computer. how much money did anna have left in the jar

Answers

Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.

So, total months = 9 + 12 + 12 = 33

Now, using the multiplication operation, we get

⇒ Total money saved = 33 * 20

⇒ Total money saved = $660

It is given that she spent 75% of her savings on computer.

So, using the subtraction operation, we get

⇒ Amount left = 660 - 75%

⇒ Amount left = $165

Hence, Anna has $165 left in the jar.

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What is 0 + 0? Please help I wont pass kinder garden :(

Answers

Answer:

Step-by-step explanation: 0+0=0

Answer:

0

Step-by-step explanation:

0+0= nothing that why.

What is 10500-8395______

Answers

Answer:

2105, plug it into calculator

help please PLEASE !!!!!

Answers

Answer:

Positive Association

Complementary Angles

Negative Association

Clusters in Data

Supplementary Angle

Non-linear Association

Step-by-step explanation:

Match the boxes on the left to the answers:

Positive Association

Complementary Angles

Negative Association

Clusters in Data

Supplementary Angle

Non-linear Association

A biomedical manufacturing process has only 12.5% chance of producing a commercially successful result. The mean number of processes to be performed before a commercially successful one is?

Answers

The mean number of processes to be performed before a commercially successful one is 8.

The probability of success in each attempt is 0.125, so the parameter of the geometric distribution is p=0.125.

The mean of a geometric distribution with parameter p is equal to 1/p, so:

Mean = 1/p = 1/0.125 = 8

Therefore, the mean number of processes to be performed before a commercially successful one is 8.

In probability and statistics, the mean (or average) is a measure of the central tendency of a set of numbers. It is calculated by adding up all the numbers in a set and then dividing the sum by the total number of values in the set. The mean is a commonly used measure of the central tendency because it takes into account all the values in the set and provides a single value that represents the "typical" value.

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Input Signals: P = 0 and Q = 1.

Answers

The output of the OR gate will be 1.

What is a NOT Gate?

An important component for electronics and computing, the NOT gate or inverter is a basic digital logic gate. It is designed with one input and output that conduct logical negation.

Essentially, this means it turns the input signal to its opposite. When given an input binary value at "1," the method generates "0" as the output and vice versa.

Two input signals, P=0 and Q=1, are subjected to the following process. The message carried by Q is inverted via a NOT gate using its negation feature, returning Q' = 0 at its output.

The resultant value of Q' (evaluated as zero), is then processed using an OR logic operation along with input P into another gate. Outputs from an OR port may only produce "1" if any of the input signal(s) carry a 1. As one of the inputs from this specific procedure provides "0", the result will inevitably be "1".

Consequently, a final analysis reveals that regardless of what the initial value for P was, the result obtained formulating the two signals through a NOT and OR devices matches an outcome of "1".

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