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A plane that passes through three edges of a cube produces a triangular cross section as shown.

In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.​

75

Step-by-step explanation:

I think this is the answer I'm not sure I hope this helps

a) Two different ways.

x = ln(32)/ln(2)

2^x = 2^5

b) Only the natural logarithm way can be used.

c) x = 3.58

We want to solve:

2^x = 32

in two ways.

The first way is trivial, apply the natural logarithm to both sides:

ln(2^x) = ln(32)

x = ln(32)/ln(2)

The second way is the next one:

2^x = 32

The right number can be written as:

4*8 = 32

Now we can factorize the left side:

4*8 = (2*2)*(2*2*2) = 2^5

Replacing that we get:

2^x = 2^5

So we know that x = 5.

b) The second way can't be used to solve:

2^x = 12

Because 12 has a factor different than 2.

c) Using the natural logarithm  way:

x = ln(12)/ln(2) = 3.58

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Step-by-step explanation:

If we use direct substitution, we will get

[tex] \frac{0}{0} [/tex]

Which is intermediate from so we must use.algebraic manipulation

Let's divide everything by x

We would get

[tex] \frac{x + 1}{1} [/tex]

So the limit as x approaches 0 is

[tex]1[/tex]

Proof using a graph:

As x gets close and closer to 0, f(x) approaches 1. Limits does not care about discontinuity, only what the function gets closer to.

The inequality which describes the problem about the pot of stew Finn made is x/6 > 2.5

Number of bowls= 6

Quantity of stew in each bowl > 2.5

Quantity of stew Finn made = x

The inequality

Quantity of stew Finn made / Number of bowls > Quantity of stew in each bowl

x/6 > 2.5

Therefore, x divided by 6 greater than 2.5 is the inequality which describes the situation.

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The value of sin(tetha/2) is ±√½(1-8/√113)

In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. If θ is an angle, then the half angle is represented by θ/2.

if tan(tetha) = 7/8

this means that 7 is the opposite and 8 is the adjacent

hyp² = opp² +adj²

hyp² = 49+64

hyp = √113

sin(tetha/2) = ±√1-cos(tetha))/2

= ±√1-(8/√113))/2

therefore the value is sin(tetha)/2

= ±√1-(8/√113))/2 or ±√½(1-8/√113)

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Total number of marbles is 5 + 7 + 29 = 41.

The given parameters are

2 gold marbles,

7 silver marbles,

and 29 black marbles

Also you win $4, if it is silver, you win $2. If it costs $1 to play

Event   P(Event)  Net Winnings   P(Event) * Net Winnings

Gold     5/41          4 - 1 = 3          15/41

Silver    7/41         2 - 1 = 1           7/41

Black    29/41        -1                   -29/41

sum     -7/41 = $0.17 loss

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The value of x is equal to 8, in the equation 14x -22.

An equation is a mathematical statement consisting of two expressions joined by an equal sign. 

Solution:

The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.

setting the displayed dimensions correspond to 90° angular dimensions.

14x -22 = 90

You can solve this two-level linear equation in the usual way.

14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x

x = 112/14 = 8 . . . Step 2, divide by the factor of x

Hence, the value of x is 8. 

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Answer: 36˚

Step-by-step explanation:

180 - 3x = 2x

180 = 5x

.: x = 36˚

Note that the Economic Order Quantity is given as approximately 4,472.13 Units.

Economic Order Quantity, also known as Economic Purchasing Quantity, is the order quantity in inventory management that minimizes overall holding costs and ordering expenses. It is one of the most ancient traditional production scheduling models.

EOQ = √[(2 * AR* OC)/CC]

Were AR = Annual Requirement = 100,000 units

OC = Ordering Cost = Rs 20 per unit

CC = Carrying Cost = 10% of Per Unit Cost
Per Unit Cost  = Rs. 2

Thus,

EOQ = √[(2 * 100,000* 20)/10% * 2]

EOQ =  √[(4000000)/0.2]

EOQ = √20000000
EOQ = 4472.135955

EOQ [tex]\approx[/tex] 4,472.13 Units.

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The pattern does not have a consistency to get the differences

The method of successive differences involves finding the difference between each consecutive term in a sequence, and then using those differences to find the next term.

Here's how the method would work for the sequence given:

7; 35; 173; 771; 2529; 6667; 15,095

Difference between terms:

28; 138; 598; 1758; 4138; 8428

Second difference between terms:

110; 460; 1160; 2380; 4290

Third difference between terms:

350; 700; 1220; 1910

Fourth difference between terms:

350; 520; 690

There is no consistency between the patterns.

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In response to the above question, we may state that in the rectangle [tex]4,241,455[/tex] gallons [tex]= 4,570,000[/tex] Cubic feet[tex]x 7.48052[/tex] Gallons/cubic foot.

In the geometry of the Euclidean plane, a rectangle is a quadrilateral having four right angles. You may also refer to it as an equiangular quadrilateral, meaning that all of its angles are equal. A straight angle could also be present in the parallelogram.

Rectangles with four evenly sized sides are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the shape of a rectangle.

As a result, it's also known as an equirectangular rectangle. A rectangle is also referred to as a parallelogram, since its opposite sides are parallel and equal.

Volume of rectangular solid is L × W × H

[tex]50 × 30 × 20 = 30000[/tex] cubic yards

[tex]50 × 30 × 6 = 9000[/tex]cubic yards

[tex]30000–9000 = 21000[/tex]cubic yards

This needs to be converted to gallons of water. We are given the conversion factor between a gallon of water and cubic feet, therefore even though we have cubic yards rather than cubic feet, we must first convert the [tex]21,000[/tex] Cubic yards to cubic feet.

A cubic yard has a volume of 27 cubic feet.27 cubic feet per cubic yard times [tex]21,000[/tex]cubic yards equals 567,000 cubic feet.

7.48052 gallons make up 1 cubic foot.

Therefore, 4,241,455 gallons are equal to 567000 cubic feet times 7.48052 gallons/cubic foot.

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A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.

A cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.

A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.

A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

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The percent tax you paid when you bought the bike is approximately 8.493%.

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

given ,

You paid $29.75 in tax when you bought a $350 bike

To find the percent tax, we can divide the amount of tax by the total cost (including tax) and multiply by 100 to express the result as a percentage.

tax = 29.75

total = 350

percent tax = (tax / total) * 100

So the percent tax would be

percent tax = (29.75 / 350) * 100

= 8.493%

Therefore, The percent tax you paid when you bought the bike is approximately 8.493%.

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On solving the provided question we can say that 2 decimal places =29.92 miles per hour

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the

top speed is 26 knots,

1 knot = 1.15078 miles per hour

26 knots = 26 * 1.15078

= 29.92028 miles per hour

2 decimal places

=29.92 miles per hour

boat has a  displacement of 96000 tons

1 ton = 0.907185 metric tonnes

96000 tons = 0.907185 * 96000

= 87,089.76 metric tonnes

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In a casee whereby Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00 the price per dozen is $350 per dozen

The concept that will be use here is division. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

The total  dozen = 8 dozen eggs

The total price of the 8 dozen eggs $2,800.00

The price per dozen = $2,800.00/ 8 dozen

=$350 per dozen

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Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

The probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.

What is probability ?

Probability is a metric used to determine how likely an event or result is to occur. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.

A group of potential possibilities is referred to as an event in probability theory. By dividing the number of positive possibilities by the total number of possible outcomes, the probability of an event happening is determined.

The fish in the hatchery tank are distributed in length according to a normal distribution, with a mean length of 9.7 inches and a standard deviation of 1.2 inches.

With a mean that is equal to the population mean and a standard deviation that is equal to the population standard deviation divided by the square root of the sample size, the distribution of the sample means will also follow a normal distribution.

The formula to calculate the z-score for the sample mean is:

z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] )

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we want to find the probability that the sample mean is less than 10 inches. So we need to calculate the z-score for a sample mean of 10 inches:

z = (10 - 9.7) / (1.2 /[tex]\sqrt{40}[/tex]) = 1.21

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.21 is approximately 0.8869. This means that there is an 88.69% chance of getting a sample mean less than 10 inches.

Therefore, the probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.

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Answer:

              In order from least to greatest, the numbers would be organized as such:  [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex]. So C is the correct answer.

Step-by-step explanation:

              At first glance, these numbers are not the simple whole and decimal numbers one might be used to. However, we can find their approximate values and order them correspondingly. [tex]\frac{2}{3}[/tex] is a fraction that is less than one, so on a number line it would be between 0 and 1, making it the smallest number out of the four. [tex]\sqrt{5}[/tex] and [tex]\frac{5}{2}[/tex] are both between 2 and 3, but [tex]\sqrt{5}[/tex] is approximately equal to 2.24, while [tex]\frac{5}{2}[/tex] is equal to 2.5. Therefore, we can conclude that [tex]\frac{5}{2}[/tex] is greater than [tex]\sqrt{5}[/tex]. Lastly, [tex]\pi[/tex] is a constant number that is the ratio of a circle's circumference to its diameter that equals approximately 3.14, so we can conclude that [tex]\pi[/tex] is the greatest number out of the four.

            Now that we have the four numbers in an easier and visually more clear way to find their exact values, we know that the order of these numbers from least to greatest would be choice C: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex] .

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

[tex]-13[/tex]

Step-by-step explanation:

The common difference of the arithmetic sequence is [tex]-13[/tex].

Answer: undefined

Step-by-step explanation: can’t raise a negative number to a integer exponent

a) The function that represents this situation is,

⇒ y = 35 (1 - 12.9%)ⁿ

Where, 'n' is number of years and 'y' is mass of element.

b) For 4 years, the mass of the element is, 19.95 milligrams

c) No, the mass of the radioactive element will never be 0 milligrams.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The function that represents this situation is,

⇒ y = 35 (1 - 12.9%)ⁿ

Where, 'n' is number of years and 'y' is mass of element.

Now, For 4 years, the mass of the element is,

⇒ y = 35 (1 - 12.9%)ⁿ

⇒ y = 35 (1 - 12.9%)⁴

⇒ y = 35 (1 - 0.129)⁴

⇒ y = 35 (0.87)⁴

⇒ y = 35 × 0.57

⇒ y = 19.95 milligrams

No, the mass of the radioactive element will never be 0 milligrams.

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Answer:

Step-by-step explanation: Here's a step-by-step guide on how to graph the equation -3y + 6x = 6:

Isolate y: To isolate y, first subtract 6x from both sides of the equation: -3y + 6x = 6 => -3y = -6x + 6.

Divide both sides of the equation by -3: Dividing both sides of the equation by -3, we get: -3y / -3 = (-6x + 6) / -3.

Simplify the equation: On simplifying the equation, we get: y = 2x - 2.

Plot the y-intercept: The y-intercept of the equation is when x = 0. So, when x = 0, y = 2 * 0 - 2 = -2. This point is (0, -2). Plot this point on the graph.

Plot a second point: Pick a value of x and plug it into the equation to find the corresponding y value. For example, let's take x = 1. Plugging x = 1 into the equation, we get y = 2 * 1 - 2 = 0. This point is (1, 0). Plot this point on the graph.

Draw the line: Connect the two points plotted on the graph. This line represents the solution set of the equation.

That's it! You have successfully graphed the equation -3y + 6x = 6.

Answer:



Step-by-step explanation:

The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.

The system of equations that represents the question is:

f + s = 168 equation 1

2.41f + 1.57s = (1.66 x 168)

2.41f + 1.57s = 278.88 equation 2

Where:

The elimination method would be used to determine the required values

Multiply equation 1 by 2.41

2.41f + 2.41s = 404.88 equation 3

Subtract equation 2 from equation 3

126 = 0.84s

s = 126 / 0.84

s = 150

Substitute for s in equation 1

f + 150 = 168

f = 168 - 150

f - 118 gallons

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Answer:

If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.

Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:

V = Bh

3/8 = (1/4)h

Multiplying both sides by 4, we get:

3 = h

So the height of the prism is 3 inches.

Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.

The linear function for the amount of store credit he will have left after purchasing x video games is given as follows:

f(x) = 299 - 60x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

f(x) = 299 - 60x.

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Answer:

BEF

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.

There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).

Looking at the following answers provided, we can see that BEF is a proper angle, because it is made up of two rays in the proper order.

KGH on the other hand, is not. KGH would be a proper angle if it was in the correct order (GHK or KHG), but because it is not in the right order, it is not a proper angle. LEA is not a proper angle either. We know that an angle is made up of two rays, but LEA isn't, and it's the same with ADE.

Answer:

BEF and ADE

Step-by-step explanation:

These points when connected make and angle. The others do not as they sinply dont make sense or have the points in a way that makes the whole statement false.

The number of guests that shared one platter is 10.

A. Since 3 people bring a total of 4 platters each, there are a total of 3 x 4 = 12 platters.

If the 120 guests share the platters equally, then each platter is shared by 120/12 = 10 guests. Therefore, 10 guests share 1 platter.

B. Landon's reasoning is incorrect.

While it is true that 3 people bring 4 platters each, the total number of platters is 3 x 4 = 12, not 7.

Therefore, 7 guests cannot be the correct answer. The correct answer is 10 guests share 1 platter, as explained in part A.

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Three people each bring 4 platters of food to a family reunion. The 120 guests all share the platters equally. A. How many guests share 1 platter? Explain your answer. 3.AR.1.2 B. Landon thinks that the answer is 7 guests. He says, " 3+4=7, and 7 rounds to 10 . Then 10×12=120." Do you agree with his reasoning

Answer:

162π - 324 (exact) or 184.938

Step-by-step explanation:

You probably don't even need help on this one anymore, its just the same as the previous one I helped you with.

Diameter = a^2 + b^2 = c^2 = 18^2 + 18^2 = c^2

√648 = c (this is exact) so radius is √648/2

Area of square = lw = 324

Area of circle = (√648/2)^2π = (648/4)π = 162π

Area of shaded region = 162π - 324 (exact) or 184.938

Answer:

1.02n or 51/50n

Step-by-step explanation:

n + 2% raise = 1.02n and 50/51n