When a smaller, upside-down cone is placed inside a larger cone, both cones being similar and the vertex of the smaller one being at the center of the base of the larger one, the smaller cone would occupy 1/8 or 12.5% of the volume of the larger cone.
Explanation:The relationship between the volume of the larger cone and the smaller, upside-down cone placed inside it is represented through the formula for the volume of a cone, which is 1/3 * π * r² * h, where 'r' is the radius of the base and 'h' is the height. If you manage to place the smaller cone such that it has the largest possible volume (which will happen when the smaller cone is similar to the larger cone), the smaller cone will have a height and radius proportionately smaller than the larger one.
Thus, the volumes are proportional to the cube of their corresponding proportions, so the smaller cone will occupy 1/n³ of the volume of the larger cone, where 'n' is the proportion between their linear dimensions. In this particular set-up, the 'n' will equal 2 because when the vertex of the smaller cone is at the center of the base of the larger cone, the smaller cone's height is half that of the larger cone. Hence, the smaller cone will occupy 1/2³ = 1/8 or 12.5% of the volume of the larger cone.
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If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?
A. 5,3
B. 4,5
C. 5,5
D. 4,3
Factor completely x^2 + 16.
(x + 4)(x + 4)
(x + 4)(x − 4)
Prime
(x − 4)(x − 4)
factor the trinomial x^2+6x-16
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Letter grades earned by a particular student in history class.
a. qualitative/nominal
b. qualitative/ordinal
c.quantitative/continuous
d.quantitative/ discrete
i think the answer is d
What are the slope and the y-intercept of the linear function that is represented by the graph?
The y-intercept is the point where the line cuts the y-axis, hence the y-intercept is (0,3)
Slope and intercept of a lineThe formula for calculating slope of a line is expressed as:
Slope = y2-y1/x2-x1
Using the coordinate points (0, 3) and (4, 0)
Slope = 0-3/4-0
Slope = -3/4
Since the y-intercept is the point where the line cuts the y-axis, hence the y-intercept is (0,3)
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Choose the correct simplification of the expression a to the 7th power times b to the 8th power all over a to the 4th power times b to the 4th power
−12.7=y−3.4
Can you guys please help me solve this. Thanks!
Select the correct product. ( a + 8)( b + 3)
ab + 8 a + 3 b + 24
ab + 3 a + 8 b + 24
11 ab
24 ab
Answer:
ab + 3 a + 8 b + 24
Step-by-step explanation:
just did this question
Joseph squares a number and subtracts 8 from the answer. He then divides this result by 7. Finally he adds 12 and the result is now 20. What was Joseph's original number?
Final answer:
We use reverse operations to solve Joseph's equation and find that the original number could have been either 8 or -8.
Explanation:
The question asks us to determine Joseph's original number based on a series of mathematical operations. We can set up an equation to represent the problem statement: let x be the original number. The sequence of operations given is:
Square x and subtract 8.
Divide this result by 7.
Add 12 to the result from step 2.
The final result is 20.
Representing this mathematically: ((x2 - 8) / 7) + 12 = 20. To find x, we need to work backward through these operations:
Subtract 12 from both sides: ((x2 - 8) / 7) = 8.
Multiply both sides by 7: x2 - 8 = 56.
Add 8 to both sides: x2 = 64.
Take the square root of both sides: x = 8 or x = -8 (considering both positive and negative square roots).
Therefore, Joseph's original number could have been either 8 or -8.
How can you find the number of inches in 1 mile, show your work.
The value of number of inches in 1 mile is,
⇒ 15,096 inches
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
To find the number of inches in 1 mile.
Since, We know that;
1 mile = 1258 foot
And, 1 foot = 12 inches
Thus, The value of number of inches in 1 mile is,
⇒ 1258 x 12
⇒ 15,096 inches
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the graph that represents 4 ≤ x
Answer:
Refer attachment.
Step-by-step explanation:
Given: Equation as 4 ≤ x
We have to plot the graph for that represents the given equation 4 ≤ x.
Consider the given equation 4 ≤ x.
It can be read as x takes values which is greater than and equal to 4.
So, the graph of this equation 4 ≤ x is given as shown below.
Select the correct answer. What is the LCM of the numbers 3, 6, and 9? 9 18 36 54
Answer:
18
Step-by-step explanation:
3 times 5
6 times 2
9 times 2
all 18
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. the store manager assures you that 13 of the 47 boxes on the shelf have the secret decoder ring. the other 34 boxes on the shelf have a different gift inside. if you randomly select two boxes of cereal from the shelf to purchase, what is the probability that both of them have the secret decoder ring?
The probability that both selected boxes have the secret decoder ring is approximately 7.20%
Explanation:To find the probability that both selected boxes have the secret decoder ring, we can use the concept of independent events. Since the boxes are randomly selected, the probability of selecting a box with the secret decoder ring is 13/47 for the first box. After selecting the first box, there will be 12 boxes with the secret decoder ring left out of 46 total boxes. So, the probability of selecting a second box with the secret decoder ring is 12/46. To find the probability of both events occurring, we multiply the probabilities: (13/47) * (12/46) = 156/2162 ≈ 0.07197 or about 7.20%
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"if a six sided dice is rolled 2 times. what is the probability of obtaining a 2"
A rectangle is 25 inches long and 13 inches wide. What is the area of the rectangle? Enter your answer in the box as a fraction in simplest form
Jake carries a green and yellow and a black guitar pick in his pocket he randomly chooses a guitar pick from his pocket before every concert what is the probability will he select the same color pic for two concert in a row?
Answer:
[tex]\bf\textbf{The required probability = }\frac{4}{9}[/tex]
Step-by-step explanation:
The total number of ways that he can pick a pic are 3 × 3 × 3 = 27 ways
If Jake selects the black pic in the first concert, then number of ways of success are :
B B G
B B Y
B G G
B Y Y
Total number of success = 4
If Jake selects the green pic in the first concert, then number of ways of success are :
G G B
G G Y
G B B
G Y Y
Total number of success = 4
If Jake selects the yellow pic in the first concert, then number of ways of success are :
Y Y B
Y Y G
Y B B
Y G G
Total number of success = 4
Therefore, in all the three cases total number of successes are :
4 + 4 + 4 = 12
[tex]Probability = \frac{\text{Number of successful ways}}{\text{Total number of ways}}\\\\\implies Probability = \frac{12}{27}=\frac{4}{9}[/tex]
[tex]\bf\textbf{Hence, The required probability = }\frac{4}{9}[/tex]
Answer:
For the people coming for the iready question answer, the answer is 1/3 lol
Step-by-step explanation:
WILL GIVE BRAINLIEST!!! PLEASE HELP!!! 11 POINTS!!!
Given that a function, f(x), has a domain of -70 ≤ x ≤ -15 and a range of 30 ≤ f(x) ≤ 110 and that f(-60) = 80 and f(-17) = 40, select the statement that could be true for f(x).
* f(-10) = 25
* f(-60) = 95
* f(40) = -55
* f(-65) = 90
Answer:
Step-by-step explanation:
[tex]slope=\frac{40-80}{-17+60} =-\frac{40}{43}\\f(x)-80=-\frac{40}{43}(x+60)\\\\x=40\\f(x)=-\frac{40}{43}*100+80 \approx -93+80=-13\\x=-65\\f(-65)=-\frac{40}{43}*(-15)+80 \approx 14+80=94[/tex]
A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism? Enter your answer as a simplified mixed number or a decimal
The volume of a rectangular prism is:
[tex]V=l*w*h[/tex]
Where
l=lenght,
w=width
h=height
So, as this prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches, the volume is calculated as follows:
[tex]V=l*w*h=312 in*5 in*112 in=174 720 inches^3[/tex]
what is the lateral area of the cone? base 10 yd height 12.1 yd
a. 242.6 yd2
b. 190.07 yd2
c. 603.19 yd2
d. 96.4 yd2
Please help me get this answer correct ! asap
What pair of numbers has the geometric mean of 44
The possible pair of numbers that has the geometric mean of 44 is 16 and 121 and this can be determined by using the concept of geometric progression.
Given :
The geometric mean of 44.
The following steps can be used in order to determine the pair of numbers that has the geometric mean of 44:
Step 1 - The concept of geometric progression can be used in order to determine the pair of numbers that has the geometric mean of 44.
Step 2 - Let the two numbers be 'a' and 'b'.
Step 3 - According to the given data, the geometric mean of 44, that is:
[tex]\rm \sqrt{ab} = 44[/tex]
Step 4 - Simplify the above expression.
ab = 1936
Step 5 - So, the possible pair of numbers that has the geometric mean of 44 is 16 and 121.
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Special-effects artists often use scale models.the actual height of a velociraptor is estimated to have been approximately 2 ft.an artist draws the dinosaur with a height of 4 in. on paper.
a. what would be an appropriate scale for a model of the velociraptor?
b. the same scale is used for a model of a tyrannosaurus, whose actual height was 16 ft.what is the height of the model?
If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to
decrease
stay the same
increase
If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to decrease.
What is the correlation of the sets?For a message to be processed by a certain orchestration, a correlation set specifies a collection of qualities and values for these properties. A maximum of three parameters are supported by each correlation set.
If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to decrease.
This means that there is an inverse relationship between the two sets, such that when one variable increases, the other variable tends to decrease.
This type of correlation is often expressed by a negative correlation coefficient,
which ranges from -1 to 0, with -1 indicating a perfect negative correlation.
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There are 8 runners in a race.
The 4 fastest runners will win trophies.
Halfway through the race, 2 of the
runners drop out of the race. What
fraction of the remaining runners will win
a trophy?
Match term with the definition
__A) shape created when a right triangle is rotated about the y-axis
__B) shape created when a rectangle is rotated about the y-axis
__C) perpendicular cross section of a cylinder
__D) parallel cross section of a sphere
__E) perpendicular cross section of a pyramid
Triangle
Rectangle
Circle
Cylinder
Cone
which expression represents the volume of the box?
use the formula v=lwh.
please help....
Judi is 9 years older than Baz.Baz is twice as old as Caleb.All their ages add up to 64.What are their ages?
Caleb is 11 years old, Baz is 22 years old, and Judi is 31 years old, which adds up to 64 years in total.
If Caleb's age is C, then Baz, being twice as old, is 2C. Judi is 9 years older than Baz, so her age is 2C + 9.
C + 2C + 2C + 9 = 64
5C + 9 = 64
Subtracting 9 from both sides gives:
5C = 55
C= 11
what are the values of x and y?
Janet has a square-shaped sheet of wrapping paper. To cover the top of a box, she cuts off 11 centimeters of the sheet along the width. The new area of the sheet is given by the expression below, where x represents the length, in centimeters, of the sheet of wrapping paper before being cut.
x^2-11x
Which statement best describes the term 11x?
the area cut from the sheet of wrapping paper
the area of the sheet of wrapping paper after being cut
the area of the sheet of wrapping paper before being cut
the width of the sheet of wrapping paper after being cut
Answer:
The correct option is 1. It means 11x is the area cut from the sheet of wrapping paper.
Step-by-step explanation:
The shape of sheet is square.
Let x represents the length, in centimeters, of the sheet of wrapping paper before being cut.
The area of a square is
[tex]A=a\times a[/tex]
Where, a is side length.
The area of sheet before being cut is
[tex]A=x\times x=x^2[/tex]
The width of the piece cut from the sheet is 11 and length is x. So, the area of piece is
[tex]A=x\times 11=11x[/tex]
The remaining area of sheet is
[tex]A=\text{Area of sheet}-\text{Area of piece cut from the sheet}[/tex]
[tex]A=x^2-11x[/tex]
Therefore correct option is 1. It means 11x is the area cut from the sheet of wrapping paper.