The ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1 and the volume of the medium box is 5832 cubic inches.
Let's denote the side length of the small cube as "s". Since it is a cube, all sides are equal.
Given that the volume of the small box is 216 cubic inches, we can set up the equation;
Volume of small box = s³ = 216
Taking the cube root of both sides, we get;
s = ∛216 = 6 inches
So, the side length of the small cube is 6 inches.
For the medium box, the length, width, and height are all tripled, so the new side length of the medium cube is 3 times the side length of the small cube:
Side length of medium cube = 3s = 3 × 6 = 18 inches
Now, let's calculate the ratio of the sides, area of the bases, and volumes of the small and medium boxes;
Ratio of sides: Side length of medium cube / Side length of small cube = 18 / 6 = 3
Ratio of area of bases: (Side length of medium cube)² / (Side length of small cube)² = (18)² / (6)² = 9
Ratio of volumes: (Volume of medium box) / (Volume of small box) = (Side length of medium cube)³ / (Side length of small cube)³ = (18)³ / (6)³ = 27
So, the ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1.
The volume of the medium box is given by;
Volume of medium box = (Side length of medium cube)³ = 18³
= 5832 cubic inches
Therefore, the volume of the medium box is 5832 cubic inches.
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7. Which inequality matches the graph below.
Find the area of the triangle ABC with the given parts. Round to the nearest tenth when necessary
The area of the triangle is equal to 1337 square feet. (Correct choice: A)
How to determine the area of the triangle
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:
s - Semiperimetera, b, c - Sides of the triangle.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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use the Pythagorean theorem to find the missing length and then round the result to the nearest ten
a=12, b=12, c=
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:
Which point is located at (4, –2)? On a coordinate plane, point A is 2 units to the left and 4 units up. Point B is 4 units to the right and 2 units down. Point C is 4 units to the left and 2 units up. Point D is 2 units to the right and 4 units down. A B C D Mark this and retu
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).
Find the measure of minor arc BC (labeled as x)
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°.
answer questions in picture please
Evaluate f(-8), f(0),
f(-8)
f(x)
=
f(0) =
f(4) =
and f(4) for the piecewise defined function.
√x + 4 if x < 0
2-x if x 20
Sketch the graph of the function.
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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The diamond suit from a standard deck of cards are taken out. You draw 2 cards from only the diamonds. What are the chances that you draw a king on your first draw and an ace on your second?
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
Determine two pairs of polar coordinates for the point with 0 < theta <360
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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Find the volume for each figure. Use 3.14 for Pi
2.
V=
r = 6 in
Round your answer 2 decimal places if possible.
1
2 3
4
10
5
6
7 8
9
Answer:
V = (4/3)π(6^3) = 288π square inches
= 904.78 square inches
Using 3.14 for π, V = 904.32 square inches.
A list of the outcomes in a sample space and the number of times each outcomes occurs is a
A. Frequency table
B. Conditional probability
C. Cumulative probability
D. Probability distribution
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 variables y and x have a proportional relationship, and y = 28 when x = 21.
What is the value of y when x = 36?
O y = 14
O y = 48
O y = 36
O x = 64
How do I solve this? It says there is an error somewhere but doesn't say what it is. Can anyone tell me?
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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What value of x satisfies the equation
(793x)3 = 343q36?
The value of x satisfies the equation is 4
What are index forms?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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find the height of right triangular prism
The side x of the triangular base prism is 0.4 centimetres.
How to find the side of a triangle prism?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
a and b are the other legsc is the hypotenuse sideTherefore,
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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Can you help me with this question?
Kyla finds a pair of roller blades that she would like to purchase. They are originally priced at $110 but are marked 30% off. What is the final price Kyla will pay for the roller blades if the tax rate is 5%?
To find the final price Kyla will pay for the roller blades, we first need to calculate the amount of the discount.
Discount = 30% of $110Discount = 0.30 x $110Discount = $33So 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.
Pre-tax price = Original price - DiscountPre-tax price = $110 - $33Pre-tax price = $77So 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.
Tax amount = 5% of $77Tax amount = 0.05 x $77Tax amount = $3.85Final price = Pre-tax price + Tax amountFinal price = $77 + $3.85Final price = $80.85Therefore, the final price Kyla will pay for the roller blades, including tax, is $80.85.New homeowners hire a painter to paint rooms in their house. The painter pays $100 for supplies and charges the homeowners $25 for each room they want painted.
Which of the following graphs shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints?
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 0
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 negative 100 through the point 4 comma 0
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
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 negative 100 through the point 4 comma negative 200
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).
What is a Graph?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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At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1252 with a standard deviation of 39 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.
(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between
and
A.D.
(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between
and
A.D.
(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between
and
A.D.
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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Helpppppppppppppppppp
Answer:
use symbolab it will help you with almost anything
what is area of rectangular 1 5/6 ,4 1/3
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)
Find the ratio specified in the picture.
Find sin A.
A
12
13
C 5 B
The value of sin A using trigonometric ratios is: 12/13
How to solve trigonometric ratios?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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What is the length of BD
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
An angle of 60 radians can be converted to an angle of____
degrees. (Give an exact answer as a fraction, not a decimal approximation.)
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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Highschool geometry 8-12
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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In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
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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Please help !!!!!!!!!!!!!
The error that Martell made in determining the scale factor was using point K and point A when they weren't similar points.
How to find the scale factor ?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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What are the solutions of 3x^2- x +7=0?
O A. x =
о
B. x =
O C. x =
2-9i
2+9i or x = 2-⁹⁰
6
6
1+iv83 or x =
6
-i√/83
6
1+9i
1-9i
¹+9 or x = 1-⁹
O D. x = 2+√83 or x = 2-i√/83
6
6
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.
Quadratic formulaThe 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]
<95141404393>
Nicholas and his father went fishing.
Nicholas caught a fish that weighed
14 1/2 pounds. His father caught a fish
that weighed half as much as the fish
Nicholas caught. What was the total
weight of the fish Nicholas and his
father caught, in pounds? Enter the
weight as an improper fraction.
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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A box has 7 blue and 7 green jelly beans. A bag has 6 blue and 4 green jelly beans. A jelly bean is selected at random from the box and placed in the bag. Then a jelly bean is selected at random from the bag. If a green jelly bean is selected from the bag, what is the probability that the transferred jelly bean was green? (Round your answer to three decimal places.)
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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the ratio of ducks to geese on a pond is 3:2. which is true. A. there are 2 fewer geese than duck pond. B. There are 13 ducks and 12 geese on the pond. C. There are a total of 20 birds on the pond, of which 8 are ducks. D. There are a total of 45 birds on the pond, of which 27 are ducks
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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Please help me solve question 19!
Answer:
Step-by-step explanation: