2. A small box in the shape of a cube for packaging has a volume of 216 cubic inches.
(a) For a medium box, the length, width, and height are all tripled. What is the ratio of the sides, area of the bases, and volumes of the boxes? Show your work.
(b) What is the volume of a medium box? Show your work.

Answers

Answer 1

(b) The volume of the medium box is 5832 cubic inches.

What is ratio?

In mathematics, a ratio is a comparison of two quantities or numbers. It is expressed as the quotient of one number divided by another, and is often written as "a:b" or "a/b". Ratios are used to compare the sizes of two or more quantities, and they can be used to solve problems involving proportions and percentages.

For example, if a recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, this means that for every 2 cups of flour used, 1 cup of sugar should be used as well. Similarly, if a company has a debt-to-equity ratio of 2:1, this means that for every $2 of debt, the company has $1 of equity.

(a) Let x be the length of the sides of the original box. Then the volume of the box is x^3 = 216, so x = 6.

When the length, width, and height are all tripled, the new side length of the medium box is 3x = 18.

The ratio of the sides of the medium box to the original box is 18:6, or simplified, 3:1.

The area of the base of the original box is. [tex]x^2 = 6^2 = 36[/tex]square inches.

The area of the base of the medium box is. [tex](3x)^2 = 18^2 = 324[/tex] square inches.

The ratio of the 5832 of the bases of the medium box to the original box is 324:36, or simplified, 9:1.

The volume of the medium box is. [tex](3x)^3 = 18^3 = 5832[/tex]cubic inches.

The ratio of the volumes of the medium box to the original box is 5832:216, or simplified, 27:1.

(b) The volume of the medium box is 5832 cubic inches.

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Related Questions

A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot

Answers

The distance of the object from the helicopter is 698 ft.

What is distance?

Distance is the length between two points.

To calculate how far the object is above the helicopter, we use the formula below.

Formula:

Sin∅ = O/H..................... Equation 1

Where:

∅ = AngleO = OppositeH = Hypotenus = Distance of the object from the Helicopter

From the question,

Given:

O = 250 ft∅  = 21°

Substitute these values into equation 1 and solve for H

H = 250/Sin21°H = 697.61 ftH ≈ 698 ft

Hence, the distance is 698 ft.

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Find the solution to the system of equations. Write the solution as an ordered pair. If there are no solutions, write 'no solutions'. If there are infinitely many, write 'infinitely many'.

y = −72
x + 11

7x + 2y = 20

Answers

The solution to the system of equations is (23, -72).

How to find system of equations ?

The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.

Substituting y = -72 in the second equation, we get:

7x + 2(-72) = 20

Simplifying this equation, we get:

7x - 144 = 20

Adding 144 to both sides, we get:

7x = 164

Dividing both sides by 7, we get:

x = 23.428571...

So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).

However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:

(x, y) = (23, -72)

Therefore, the solution to the system of equations is (23, -72).

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Show that cosh2x−sinh2x=1 � � � ℎ 2 � − � � � ℎ 2 � = 1 Differentiate with respect to x � e3xx2+1 � 3 � � 2 + 1 y=secx � = sec ⁡ � y=tanx2 � = tan ⁡ � 2 Differentiate with respect to x � y=ln(x+sinx) � = ln ⁡ ( � + sin ⁡ � ) y=cosxx2 � = cos ⁡ � � 2 Find dydx � � � � given siny+x2y3−cosx=2y sin ⁡ � + � 2 � 3 − cos ⁡ � = 2 � Differentiate from first principles y=cosx � = cos ⁡ � x3+2x2+3x+4 � 3 + 2 � 2 + 3 � + 4 Find d2ydx2 � 2 � � � 2 Given 3x3−6x2+2x−1 3 � 3 − 6 � 2 + 2 � − 1

Answers

We can conclude that cosh2x−sinh2x=1.

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.

Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.

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Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

We will show that [tex]\cosh^2x-sinh^2x=1[/tex].

Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]

Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]

Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]

Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]

[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]

Hence, [tex]cosh^2x-sinh^2x=1[/tex]

Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]

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The correct form of question is Show that cosh2x−sinh2x=1 .

please help!

If r=0.5 m, A = ???

(Use the r key.)

Answers

The area of a circle of radius of 0.5 meters is 0.785 square meters.

How to find the area of the circle?

Remember that for a circle of radius r, the area is:

A = pi*r²

Where pi = 3.14

Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.

A = 3.14*(0.5m)²

A = 3.14*0.25 m²

A = 0.785  m²

That is the area of the circle.

Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?

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A=P(1+r/n)^nt Find how long it takes for $1400 to double if it is invested at 7% interest compounded monthly. Use the formula A = P to solve the compound interest problem. TE The money will double in value in approximately years. (Do not round until the final answer. Then round to the nearest tenth as needed.)​

Answers

It will take 10 years to double the amount.

Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,

[tex]A = P(1+r/n)^{nt}[/tex]

[tex]2800 = 1400(1+0.0058)^{12t}[/tex]

[tex]2= (1.0058)^{12t[/tex]

㏒ 2 = 12t ㏒ (1.0058)

0.03 = 12t (0.0025)

12t = 120

t = 10

Hence, it will take 10 years to double the amount.

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Peter needs to borrow $10,000 to repair his roof. He will take out a 317-loan on April 15th at 4% interest from the bank. He will make a payment of $3,500 on October 12th and a payment of $2,500 on January 11th.

a) What is the due date of the loan?

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th pa payment.

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

Please only serious answers ​

Answers

Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.

1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters ​

Answers

Answer:

The figure is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

Let h be the height of the flagpole.

[tex] \tan(18) = \frac{h}{80} [/tex]

[tex]h = 80 \tan(18) = 25.994[/tex]

The height of the flagpole is approximately 26.0 meters. #3 is correct.

A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. Which of these best describes the volume of this rectangular prism? (5 points)


1 unit cube and 15 smaller cubes of volume fraction 1/125 cubic inch each

1 unit cube and 75 smaller cubes of volume fraction 1/125 cubic inch each

7 unit cubes and 25 smaller cubes of volume fraction 1/125 cubic inch each

7 unit cubes and 125 smaller cubes of volume fraction 1/125 cubic inch each

Answers

The volume of the rectangular prism is 1.6 cubic inches.

Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have

L = 1/5 × x

W = 1/5 × y

H = 1/5 × z

where x, y, and z are integers.

Since the rectangular prism is completely packed with 200 cubes, we have

x × y × z = 200

We want to find the volume of the rectangular prism, which is given by

V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z

Substituting x × y × z = 200, we get

V = 1/125 × 200 = 8/5 = 1.6 cubic inches

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The given question is incomplete, the complete question is:

A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the  volume of this rectangular prism

Which statement about subnetting is correct?
A. Subnetting applies only to IPv4 networks, unless you are using classless interdomain routing.
B. Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage.
C. Subnetting in IPv4 involves the CIDR protocol, which runs at Layer 3; in IPv6, this protocol, and hence subnetting, is not used.
D. Because the subnet mask field is so much larger in IPv6, it is easier to subnet in this newer protocol stack than in IPv4.

Answers

The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.

Hence, the correct option is B.

In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.

IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.

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fuel efficiency of manual and automatic cars, part i. each year the us environmental protection agency (epa)releases fuel economy data on cars manufactured in that year. below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions. do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? assume that conditions for inference are satisfied.

Answers

Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

What is the explanation for the above response?


To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.

The t-test statistic is calculated as follows:

t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values from the given statistics, we get:

t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))

t = -3.31

Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.

Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.

Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

The volume of a cylinder is given by the formula v - pi^h, where r is the radius of the cylinder and h is the height.
Which expression represents the volume of this cylinder?

Answers

The expression that represents the volume of the cylinder is:

V = π[tex]r^{2}[/tex]h

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases. The cylinder can be thought of as a tube or a can. The lateral surface of the cylinder is formed by "unrolling" a rectangular shape along the circumference of the base.

There appears to be a typographical error in the given formula for the volume of a cylinder. The correct formula is:

V = π[tex]r^{2}[/tex]h

where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.

Using this formula, the expression that represents the volume of the cylinder is:

V = π[tex]r^{2}[/tex]h

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in an integer overflow attack, an attacker changes the value of a variable to something outside the range that the programmer had intended by using an integer overflow.T/F

Answers

True. An integer overflow attack occurs when an attacker manipulates a variable in a way that causes it to exceed its maximum value or minimum value, leading to unexpected and potentially harmful behavior.

This can happen if a programmer fails to properly check and validate the input values that are being used in their code, allowing an attacker to inject a value that triggers an overflow.

As a result, the variable may be assigned a value that is outside the intended range, leading to unpredictable behavior and potentially causing the program to crash or execute unintended code. It is important for programmers to take steps to prevent integer overflow attacks, such as validating input values and using data types with sufficient capacity to hold the expected range of values.


This occurs when an arithmetic operation results in a value that is too large to be stored in the allocated memory, causing the value to wrap around and become smaller, or even negative. This can lead to unintended consequences in a program's behavior, which an attacker can exploit to gain unauthorized access or cause other security issues.

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armer abe has a budget of $300 to build a rectangular pen to protect his rambunctious sheep. he decides that three sides of the pen will be constructed with chain-link fence, which costs only $1 per foot. farmer abe decides that the fourth side of the pen will be made with sturdier fence, which costs $5 per foot. find the dimensions of the largest area the pen can enclose.

Answers

Let x be the length of the pen and y be the width of the pen.

The total cost of the pen is given by:

Cost = 3x + 5y = 300

3x + 5y = 300

3x = 300 - 5y

x = (300 - 5y)/3

The area of the pen is given by:

Area = xy = (300 - 5y)/3 * y

52 no one can win more than one prize? multiple choice 16,129,423 16,497,400 15,281,283 16,300,400

Answers

The closest choice to the actual number of ways to choose 52 different winners out of 52 contestants is 16,497,400,

To solve this problem, we can use the formula for permutations, which is:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, 52), and r is the number of objects we are choosing (in this case, the number of prizes, which is also 52).

Since no one can win more than one prize, we need to choose 52 different winners for the prizes. Therefore, the number of ways to do this is:

52P52 = 52! / (52 - 52)! = 52!

Using a calculator or computer program, we can find that 52! is approximately equal to 8.0658 × 10^67.

Therefore, the answer is 16,497,400, which is the closest choice to the actual number of ways to choose 52 different winners out of 52 contestants.

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a doctor can complete 3 examinations in 2 hours. how many examinations can the doctor complete in 4 hours? hint: use the proportion 3 exams : 2 hours :: x exams : 4 hours. 5 exams 5 exams 6 exams 6 exams 7 exams 7 exams 8 exams

Answers

Answer:

6 examinations

Step-by-step explanation:

We Know

A doctor can complete 3 examinations in 2 hours.

How many examinations can the doctor complete in 4 hours?

We see

4 hours is 2 hours times 2

We take

3 x 2 = 6 examinations

So, the doctor can complete 6 exams in 4 hours.

Find the value of ‘x’
x =

Answers

The value of x, in the image given is calculated by applying the intersecting chords theorem, which is: x = 16.

What is the Intersecting Chords Theorem?

The Intersecting Chords Theorem, also known as the Ptolemy's Theorem, states that in a circle, if two chords intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

In mathematical terms, if two chords, AB and CD, intersect at point E inside a circle, then:

AE × EB = CE × ED

Applying the theorem, we have:

5(x) = (x - 6)8

5x = 8x - 48

5x - 8x = -48

-3x = -48

x = 16

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brainliest+100 points

Answers

1a.

2x + 2y = 4xy is wrong

2x + 2y = 2(x+y) is correct

b.

3x+4= 7x wrong

c

4x²+5x = 9x² wrong

2

3x²+3x²+4x = 6x² + 4x = 2x(3x + 2)

3

sorry I don't understand this one.....

4

-4(3x-5) = -12x + 20

5

120 12 10 4 3 5 2

6

Answer:

120

12 10

4 2 5 2

2 2

find the value of 3√1 over 16​

Answers

Answer:3/16

Step-by-step explanation:

√1 is the same thing as 1

so (3*1)/16

3/16

14. An airplane flew 2,800 miles from Los Angeles to New York. The airplane flies at approximately 500
mi/hr. How many hours did it take the plane to reach New York?

Answers

Answer:

Speed= 500ml/hr

total distance= 2800 m

total time = d/t

2800/500= 5.6hrs

Step-by-step explanation:

What are the cross-products of the proportion 6/40 = 9/60? Is the proportion TRUE?

54 and 2,400; the proportion is false.

54 and 540; the proportion is true.

360 and 360; the proportion is true.

Answers

Therefore, the answer is: 360 and 360; the proportion is true.

54 and 540; the proportion is true.

360 and 360; the proportion is true.

To find the cross-products of the proportion 6/40 = 9/60, we multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

So we have:

6 × 60 = 360

9 × 40 = 360

The cross-products are 360 and 360.

To check if the proportion is true, we compare the cross-products. If they are equal, then the proportion is true; otherwise, it is false.

Since the cross-products are equal, the proportion is true.

Therefore, the answer is:

360 and 360; the proportion is true.

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Keyana puts beads at the ends of her braids. On a single braid, she places 7 beads that are
each 1.03 centimeters long. Then she adds a final bead that is 0.9 centimeter long. The
expression below can be used to find the total length of the beads on one of Keyana's braids.
7 x 1.03 +0.9
What is the total length of the beads on one braid?
A 7.3 centimeters
B.8.11 centimeters
C.9.19 centimeters
D: 10.0 centimeters

Answers

The total length of the beads on one braid is 8.11 centimeters

What is the length?

Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.

To find the total length of the beads on one braid, we need to evaluate the expression:

7 x 1.03 + 0.9

Multiplying 7 by 1.03 gives us:

7 x 1.03 = 7.21

Then, adding 0.9 gives us:

7.21 + 0.9 = 8.11

Therefore, the total length of the beads on one braid is 8.11 centimeters.

So, the correct answer is B.8.11 centimeters.

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your friend is binging half of a crate of popsicles to the picnic. of you put what is left in the crate evenly into 6 ice buckets, what fraction of the crate will go into each of ice bucket​

Answers

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

Explain about the fraction:

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.

Given data:

fraction of crate brought by friend = 1/2

Total number of ice buckets = 6

Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets

Fraction of crate in each bucket = (1/2) / 6

Fraction of crate in each bucket =  1 / (2*6)

Fraction of crate in each bucket = 1/12

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

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the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 5.3. the probability there are 8 occurrences in 10 minutes is . a. .0771 b. .0241 c. .1126 d. .9107

Answers

The probability of having 8 occurrences in 10 minutes is approximately 0.0241, which means the answer is (b).

The number of occurrences of an event in 10 minutes as a Poisson distribution with mean lambda = 5.3.

The probability of having 8 occurrences in 10 minutes is:

[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8![/tex]

where X is the random variable representing the number of occurrences of the event in 10 minutes.

Using a calculator, we can evaluate this expression:

[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8! ≈ 0.0241[/tex]

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identify the following equations as increasing linear, decreasing linear, positive quadratic, negative quadratic, exponential growth, or exponential decay.
(please help )

Answers

The types of equations in the question based on the values of the base, the slope and leading coefficients of the equations are;

11. Exponential growth

12. Exponential growth

13. Decreasing linear

14. Positive quadratic

15. Increasing linear

16. Exponential growth

17. Exponential decay

18. Exponential decay'

19. Positive quadratic

20. Linear increasing

21. Exponential growth

22. Negative quadratic

23. Negative quadratic

24. Exponential decay

What is an equation?

An equation is a statement that indicates that of two expressions are equivalent, by joining them with an '=' sign.

11. The exponential equation is; y = (5/2)ˣ

The growth or decay factor, which is the base is; (5/2) > 1, therefore, the equation is an exponential growth equation

12. The exponential equation is; y = (1/4) × 3ˣ

3 > 1, therefore the equation is an exponential growth function

13. The equation y = -2·x -10 is a linear equation with a negative slope of -2, indicating that the value of y is decreasing as x increases, therefore, the equation is decreasing linear

14. The equation, y = 2·x² + 5·x - 7, which is a quadratic equation

The leading coefficient, 2, is positive, therefore, the equation is a positive quadratic equation

15. The equation y = 4·x - 3 has a positive slope, of 4, therefore, it is an increasing linear equation

16. The exponential equation (2/5)·9ˣ, with 9 > 1, is an exponential growth equation

17. The equation  3·(1/4)ˣ, with (1/4) < 1, is an exponential decay equation

18. The equation 2·(0.1)ˣ, with 0.1 < 1, is an exponential decay equation

19. The equation y = (x + 2)² is a quadratic equation

(x + 2)² = x² + 4·x + 4

The leading coefficient is 1, therefore, the equation is a positive quadratic equation

20. The linear equation 4·x + y = 7 with a positive slope of +4 indicates that the y-value of the function is increasing as the x-value of the equation is increasing, therefore, the function is an increasing linear equation

21. The exponential equation, y = 2·5ˣ, with 5 > 1, and 2 > 0, is an exponential growth equation.

22. The equation y = -(x - 3)² is a quadratic equation. The minus sign in front of the expression (x - 3) indicates that the leading coefficient, obtained by expansion, is negative

y = -(x - 3)² = -(x² - 6·x + 9) = -x² + 6·x - 9

The leading coefficient is -1, therefore the equation negative quadratic

23. The equation, y = -6·x² -5·x + 4, with a leading coefficient of -6 is a negative quadratic equation

24. The exponential equation, y = (1/7)·(3/8)ˣ, with (1/7) > 0 and (3/8) < 1 is an exponential decay equation

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6) Practice: Using Visual Cues Label each part of the diagram. Then use your labels to complete the sentences. Square Root Notation √6 1. The expression √ means "the of b". 2. The exponent 1 symbol (√) stands for the 3. The number or expression under the radical symbol is called the​

Answers

1. The expression √b means "the square root of b".

2. The radical symbol (√) stands for the exponent 1/2.

3. The number or expression under the radical symbol is called the radicand.

What is radicand?

A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.

The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.

The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.

The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.

The exponent of the radical symbol is 1/2, which implies that the expression is a square root.

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What is the argument of z = StartFraction 1 Over 16 EndFraction minus StartFraction StartRoot 3 EndRoot Over 16 EndFraction i?

Answers

To find the argument of the complex number z = 1/16 - (sqrt(3)/16)i, we need to find the angle that the complex number forms with the positive real axis in the complex plane.

We can start by finding the magnitude of z, which is the distance between the origin and the point representing z in the complex plane:

|z| = sqrt( (1/16)^2 + (sqrt(3)/16)^2 )

= sqrt(1/256 + 3/256)

= sqrt(4/256)

= 1/4

Next, we can find the argument of z using the formula:

arg(z) = tan^(-1)(Im(z)/Re(z))

where Im(z) is the imaginary part of z, and Re(z) is the real part of z.

In this case, we have:

Re(z) = 1/16

Im(z) = -(sqrt(3)/16)

Therefore, we get:

arg(z) = tan^(-1)(Im(z)/Re(z))

= tan^(-1)(-(sqrt(3)/16)/(1/16))

= tan^(-1)(-sqrt(3))

= -60° (in degrees)

So, the argument of z is -60 degrees (or -π/3 radians).

Answer:

A

Step-by-step explanation:

a kite flying in the air has a 94- string attached to it, and the string is pulled taut. the angle of elevation of the kite is . find the height of the kite. round your answer to the nearest tenth.

Answers

The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

Solve for x please

Choices are...
10
5
25
90

Answers

Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10

In the graph below, line k with equation y = -k makes a 45° angle with the x- and y- axes.

Rx: (2, 5)

1. (-2, 5)
2. (-2, -5)
3. (2, -5)

Answers

In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).

What is a graph?

The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.

The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)

Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).

Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).

The point (2,5) will change to if it is reflected across the line y=x (5,2).

Therefore, the correct option is 1. (-2, 5).

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Monique claims the surface area of the cylinder is about 1001.66 square feet explain Monique's error find the correct surface area.

Answers

Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.

To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.

However, we can use Monique's estimate to estimate the values of r and h.

1001.66 = 2πr^2 + 2πrh

Dividing both sides by 2π, we get:

500.83 = r^2 + rh

We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.

For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:

500.83 = 5^2 + 5h

495.83 = 5h

h = 99.166

So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:

S = 2π(5^2) + 2π(5)(99.166)

S = 1570.8 square feet

This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.

Step-by-step explanation:

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