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.

Answer:

  x = (1 +i√83)/6  or  x = (1 -i√83)/6

Step-by-step explanation:

You want the solutions to the quadratic equation 3x² -x +7 = 0.

The solutions to the equation ax² +bx +c = 0 are given by the formula ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The given equation has a=3, b=-1, c=7, so the solutions are ...

  [tex]x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(7)}}{2(3)}=\dfrac{1\pm\sqrt{-83}}{6}\\\\\\\boxed{x=\dfrac{1+i\sqrt{83}}{6}\quad\text{or}\quad x=\dfrac{1-i\sqrt{83}}{6}}[/tex]

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The value of x satisfies the equation is 4

Index forms are described as mathematical forms that are used to represent numbers or values that are too large or small in more convenient ways.

From the information given, we have that;

(7q³ˣ)³ = 343q³⁶

expand the bracket for the values

7³. q⁹ˣ = 343q³⁶

Now find the common exponents, we have;

7³. q⁹ˣ= 7³. q³⁶

Divide the values, we have;

q⁹ˣ = q³⁶

Equate the exponents, we get;

9x = 36

Divide both sides by the coefficient of x, we get

9x/9 = 36/9

Divide the values

x = 4

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30% of the pennies in the roll were made before 1985.

To find the percentage of pennies made before 1985, we need to divide the number of pennies made before 1985 by the total number of pennies and then multiply by 100 to convert the answer into a percentage.

Number of pennies made before 1985 = 15

Total number of pennies = 50

Percentage of pennies made before 1985

= (15/50) x 100%

= 30%

Therefore, 30% of the pennies in the roll were made before 1985.

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The list of the outcomes in a sample space and the number of times each outcomes occurs is a frequency table

Given data ,

The outcomes in a sample space and the frequency with which each event happens are displayed in a frequency table, which is a tabular representation of data.

It shows the frequency or count of each result, which makes the data distribution easier to see. In statistics and probability, frequency tables are frequently used to compile and analyze data from experiments, surveys, or other data-generating activities.

Hence , the solution is frequency table

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The polar coordinates for the point (5, 5) are (5√(2), 45 degrees) or (5√(2), 225 degrees) since 225 degrees is also a valid angle between 0 and 360 degrees that corresponds to the same point.(option c)

For the point (5, 5), we can find its polar coordinates by first finding the distance r from the origin using the Pythagorean theorem:

r = √(5² + 5²) = √(50) = 5√(2)

Next, we can find the angle θ that the line connecting the origin to the point makes with the positive x-axis using trigonometry:

tan(θ) = y/x = 5/5 = 1

θ = arctan(1) = π/4 radians

Since 0 < θ < 360, we can express θ in degrees as θ = 45 degrees.

Hence the correct option is (c).

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Answer:

Step-by-step explanation:

The value of total weight of the fish Nicholas and his father caught, in pounds is,

⇒ 87/4 pounds

We have to given that;

Nicholas caught a fish that weighed 14 1/2 pounds.

And, His father caught a fish that weighed half as much as the fish Nicholas caught.

Hence, The weight of fish caught  by his father is,

⇒ 14 1/2 ÷ 2

⇒ 29/2 × 1/2

⇒ 29/4

Thus, The value of total weight of the fish Nicholas and his father caught, in pounds is,

⇒ 14 1/2 + 29/4

⇒ 29/2 + 29/4

⇒ 58/4 + 29/4

⇒ 87/4 pounds

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Answer:

use symbolab it will help you with almost anything

Answer:

Area = 7 7/18 or 39/2 square units

Step-by-step explanation:

To find the area of a rectangle, you need to multiply its length by its width.

Given:

Length = 1 5/6

Width = 4 1/3

Convert mixed numbers to improper fractions:

Length = (6 + 5) / 6 = 11/6

Width = (3 x 4 + 1) / 3 = 13/3

Area = Length x Width

Area = (11/6) x (13/3)

Area = (143/18)

Simplify the result to mixed number or improper fraction:

Area = 7 7/18 or 39/2 square units (if we want the answer in fraction form)

Answer:

Point B is 4 units to the right and 2 units down

Step-by-step explanation:

Since our x is positive, we are going to the right of the x-axis (where positive values lay).

Since our y is negative, we are going down in the y-axis (where negative values lay).

Answer:

V = (4/3)π(6^3) = 288π square inches

= 904.78 square inches

Using 3.14 for π, V = 904.32 square inches.

Answer:80°

Step-by-step explanation:

We can use the given angle, 50, to determine the other angles of the triangle opposite to the arc that we need to find the measure of.

Because the entire inscribed figure is rectangular, we can use our given angle to determine the other angles of the triangle represented by the given angle, which are 50 and 80.

Now we can use the 80° angle <DPA, which is also equal to <CPB.
This means that the center angle <CPB is also 80°, and it means that the corresponding arc X is also 80°.

The correct graph is: a coordinate grid with the x-axis labeled rooms painted and the y-axis labeled amount of money earned and a line going from the point (0,100) through the point (4,200).

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

The painter pays $100 for supplies, which is a fixed cost, and charges $25 for each room painted, which is a variable cost.

Therefore, the relationship between the amount of money the painter earns and the number of rooms he paints can be represented by a linear equation in slope-intercept form:

Amount earned = (price per room) x (number of rooms painted) + (fixed cost)

In this case, the price per room is $25, the number of rooms painted is the x-value, and the fixed cost is $100. Thus, the equation is:

Amount earned = 25x + 100

To graph this equation, we can plot two points and draw a line through them. One point is when no rooms are painted, which gives the painter $100 for the fixed cost:

(0,100)

The other point is when four rooms are painted, which gives the painter:

Amount earned = 25(4) + 100 = 200

So the other point is:

(4, 200)

The correct option :

a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.

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Answer:

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Hence, we use this formula to solve for the missing length:

c^2 = a^2 + b^2

Plugging in the given values, we get:

c^2 = 12^2 + 12^2 c^2 = 144 + 144 c^2 = 288 c ≈ √288

Rounding √288 to the nearest ten gives 17. Therefore, the missing length is approximately 17.

Hence, c ≈ 17 is the answer.

Step-by-step explanation:

The side x of the triangular base prism is 0.4 centimetres.

The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,

c²= a² + b²

where

Therefore,

x² = 0.5² - 0.3²

x² = 0.25 - 0.09

x = √0.16

x = 0.4 cm

Therefore,

x = 0.4 centimetres.

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Answer:

The angle -90 degrees is equivalent to -π÷2 radians.

How we convert the angle −90∘ into radians?

To convert an angle from degrees to radians, we use the formula: radian measure = degree measure * π/180. In this case, we want to convert -90 degrees to radians. So, we substitute -90 into the formula and get:

radian measure = -90 × π÷180

Simplifying this expression, we can cancel the factor of 90 and get:

radian measure = -1÷2 × π

This means that -90 degrees is equivalent to -π÷2 radians. We can leave our answer in terms of π since it is exact. The reason why we use radians to measure angles is because they are a more natural unit for measuring angles in calculus and other mathematical contexts.

Therefore, -90 degrees is equivalent to -π÷2 radians. We can leave our answer in terms of π since it is exact.

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The probability that the  transferred jelly bean was green is P ( G ) = 0.636

Given data ,

Let the probability that the  transferred jelly bean was green be P ( G )

Now , There are 7 blue and 7 green jelly beans in the box, so the probability of selecting a green jelly bean from the box is 7/(7+7) = 0.5, and the probability of selecting a blue jelly bean from the box is also 0.5

A jelly bean is chosen from the box and then put in the bag. Say someone chooses a green jelly bean from the package and puts it in the bag. Currently, there are 6 + 1 = 7 green jelly beans and 4 + 0 = 4 blue jelly beans in the bag.

Now , Since there are 7 green jelly beans and 4 blue jelly beans in the bag, the probability of selecting a green jelly bean from the bag is P ( G )

where P ( G ) = 7/(7+4)

P ( G ) = 0.636

Hence , the probability is 0.636

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a) The range of years centered about the mean in which about 68% of the data in between 1291 or 1213.

b) The range of years centered about the mean in which about 95% of the data in between 1330 or 1174.

c) The range of years centered about the mean in which about 95% of the data in between 1369 or 1135.

We have,

Mean= 1252

Standard deviation= 39

a) The range of years centered about the mean in which about 68% of the data

= 1252 ±39

= 1252 + 39 or 1252 -39

= 1291 or 1213

b) The range of years centered about the mean in which about 95% of the data

= 1252 ± 2(39)

= 1252 + 78 or 1252- 78

= 1330 or 1174

c) The range of years centered about the mean in which about 95% of the data

= 1252 ± 3(39)

= 1252 + 117 or 1252- 117

= 1369 or 1135

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The error that Martell made in determining the scale factor was using point K and point A when they weren't similar points.

The process that Martell used to find the scale factor was correct, however, he should not have used points A and K because they are not similar sides in the triangles.

Point A is similar to point H while point D is similar to point K.

Using the similar points of A (4, 2 ) and H ( 6, 3 ), we find the scale factor to be:

= 6 / 4

= 1. 5

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The statement that is true about the ratios is:

There are 2 fewer geese than ducks on the pond.

Option A is the correct answer.

We have,

The ratio of ducks to geese on a pond is 3:2.

This means,

Number of ducks = 3x

Number of geese = 2x

And,

If the total number of ducks and geese = 10

So,

(3x + 2x) = 10

5x = 10

x = 2

Now,

Number of ducks = 3x = 3 x 2 = 6

Number of geese = 2x = 2 x 2 = 4

This means,

There are 2 fewer geese than ducks on the pond.

Thus,

The statement that is true about the ratios is:

There are 2 fewer geese than ducks on the pond.

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The values of x and y in the given triangle are 41.4° and 114.5°

We have to  values of x and y by using law of cosine

Using the Law of Cosines, we can find the values of x and y:

For angle x⁰:

cos(x⁰) = (a² + c² - b²) / (2ac)

cos(x⁰) = (15² + 18² - 12²) / (540)

cos(x⁰) = 0.75

x⁰ = cos⁻¹(0.75)

x⁰ = 41.4°

For angle y:

cos(A) = (b² + c² - a²) / (2bc)

cos(A) = (12² + 15² - 18²) / (360)

cos(A) = -0.4

A = cos⁻¹(-0.4)

y=114.5°

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The sum of the series converges absolutely by alternate series test

Given data ,

Let the sequence be represented as A

Now , the value of A is

A = ∑n=1 to ∝ ( 1/6n³ )

On simplifying , we get

Taking the common factor out , we get

A = ( 1/6 ) ∑n=1 to ∝ ( 1/n³ )

Now , from the alternate series test ,

A = ( 1/6 ) ( converges )

Hence , the series A converges

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Answer:

There are 13 diamonds in a deck of cards, including one king and one ace.

The probability of drawing a king on the first draw is 1/13, since there is one king among 13 diamonds.

Assuming that the king is not replaced, there are now 12 diamonds left, including one ace. The probability of drawing an ace on the second draw is 1/12, since there is one ace among 12 diamonds.

The probability of drawing a king on the first draw and an ace on the second draw is the product of these probabilities:

P(king first, ace second) = P(king first) * P(ace second|king first not replaced)

P(king first, ace second) = (1/13) * (1/12)

P(king first, ace second) = 1/156

Therefore, the chances of drawing a king on your first draw and an ace on your second draw, when drawing 2 cards from only the diamonds, is 1/156.

Step-by-step explanation:

Branliest please

The area of the triangle is equal to 1337 square feet. (Correct choice: A)

In this problem we must determine the area of the triangle given the lengths of all sides, this can be done by using Heron's formula:

A = √[s · (s - a) · (s - b) · (s - c)]

s = 0.5 · (a + b + c)

Where:

If we know that a = 47 ft, b = 59 ft and c = 65 ft, then the area of the triangle is:

s = 0.5 · (47 ft + 59 ft + 65 ft)

s = 85.5 ft

A = √[(85.5 ft) · (85.5 ft - 47 ft) · (85.5 ft - 59 ft) · (85.5 ft - 65 ft)]

A = 1337.252 ft²

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Answer:

BD = 3 units

Step-by-step explanation:

since AB is a tangent to the circle, then the angle between the tangent and the radius at the point of contact A is 90°

Then Δ ABC is right

using Pythagoras' identity in the right triangle

BC² = AC² + AB² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )

BC = [tex]\sqrt{56.25}[/tex] = 7.5

now CD is a radius of the circle = 4.5

Then

BD = BC - CD = 7.5 - 4.5 = 3 units

The value of the function are f(-8) = -4, f(0)= 2 and f(0)= 2.

We have the function,

f(x) = { x + 4 ,     x<0

          2 - x ,     x≥0

First, f(-8)

= (-8)+ 4

= -4

and, f(0)

= 2 - 0

= 2

and, f(4)

= 2 - 4

= -2

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To find the final price Kyla will pay for the roller blades, we first need to calculate the amount of the discount.

So Kyla will get a discount of $33 off the original price of $110.

Next, we need to calculate the pre-tax price of the roller blades after the discount.

So the pre-tax price of the roller blades after the discount is $77.

Finally, we need to calculate the final price Kyla will pay, including the 5% tax.

The value of sin A using trigonometric ratios is: 12/13

There are three main trigonometric ratios in right angle triangles and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We want to find sin A and as such using trigonometric ratios on the attached right angle triangle, we have:

sin A = 12/13

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