A ball of radius 14 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.
Answers
The volume of the spherical solid resulting of the drill is of 11,226 units³.
What is the volume of a sphere?The volume of a sphere of radius r is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, we have two spherical balls, one of radius 14 and other of radius 4, hence their volumes are given as follows:
[tex]V_1 = \frac{4\pi 14^3}{3} = 11494[/tex]
[tex]V_2 = \frac{4\pi 4^3}{3} = 268[/tex]
The volume of the resulting solid is the difference of the volumes, hence:
V = 11494 - 268 = 11,226 units³.
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Related Questions
Two of them are drawn simultaneously from a deck of 48 cards.
Calculate the probability that:
a) both are cups
b) At least one cup
c) One is a cup and the other is a sword
Answers
The required probability is
a) both are cups is 0.05
b) At least one cup is 0.19
c) One is a cup and the other is a sword is 0.06
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
a) for both are cups
P= 12*11/48*47
p = 0.05
b) for At least one cup
p = 12*36/48*47
p = 0.19
c) for One is a cup and the other is a sword
p = 12*12/48*47
p = 0.06
Thus, the required probability is 0.05, 0.19, 0.06
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#SPJ1A squared garden has area 1764m2. Find its length and perimeter?
Answers
Answer:
length = 42 mperimeter = 168 mStep-by-step explanation:
A squared garden has area 1764m2. Find its length and perimeter?
Area = l²
inverse formulal = √Area
length√1764 = 42 m
Perimeter l × 442 * 4 = 168 m
Answer:
length=42m
perimeter=168m
Step-by-step explanation:
Area=L^2
L^2=1764
L=√1764
L=42m
Perimeter=42+42+42+42 which equals to 168m
why is it important to learn valid proportions
Answers
Every weekend me and my brother and my cousin go outside to play basketball and when i was the one who will shoot the ball to the ring i used the things i learned in math so I use SOH-CAH-TOA in measuring it. I want to measure the distance between me and the basketball ring. Supposed the height of the ring is 8ft from the ground and the distance between me and the basketball ring horizontally is 11.5 ft, and the angle of elevation from the ground is 50 degrees, now what is the distance of me and the ring?
Let x be the distance between me and the ring
need urgent answers with equation
Answers
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
1) Since we know two of the sides of that right-angled triangle, we can use the Pythagorean Theorem to find x. His theorem is: [tex]c^2 = a^2 + b^2[/tex].
Substitute the values into the formula above.
Let x = c
[tex]c^2 = 8^2 + 11.5^2\\c^2 = 196.25\\c= \sqrt{196.25}\\c=14[/tex]
Help me please in this question
Answers
Answer:Answer
Step-by-step explanation:
For the first part, divide 46.54 by 5.2
46.54/5.2=8.95
$8.95 per pound
For the second part if he buys half as much, its half of 5.2 plus 5.2. Now use similar steps that I used in the first part to solve for your problem.
I got $97.50, but i am not 100% sure if it is correct, so try give it a try.
Of the houses in Lucia's neighborhood, 1/10 are teal and another 7/10 are red. What
fraction of the houses are either teal or red?
(D) Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
the answer is 8/10
Step-by-step explanation:
The reason is that both of the denominators are the same so that you can add the two numerators and then get the answer.
A 2-column table with 5 rows. Column 1 is labeled Number of chores, x with entries 2, 4, 6, 8, 10. Column 2 is labeled Days, y with entries 1, 2, 3, 4, 5. The table shows the number of days required to perform a given number of chores. The number of days varies directly with the number of chores. What is the constant of variation? 2 3 One-half One-third\
Answers
The constant of variation based on the information is one half.
How to illustrate the information?From the information given, when x is 2, y is 1, when x is 4, y is 2, etc. It should be noted that this is a direct variation.
This will be illustrated as:
y = kx
when y = 1, x = 2.
1 = 2k
Divide both side by 2.
k = 1/2
Therefore, the constant of variation is 1/2.
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A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s. How many possible sequences of rolls could there have been
Answers
The possible sequences of rolls could there have been Sequence = 120
Given
6 rolls of a die;
Required
Determine the possible sequence of rolls
From the question, we understand that there were three possible outcomes when the die was rolled;
The outcomes are either of the following faces: 1, 2 and 3
Total Number of rolls = 6
Possible number of outcomes = 3
The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;
Sequence = \frac{6!}{3!}
Sequence = \frac{6 * 5 * 4* 3!}{3!}
Sequence = 6 * 5 * 4
Sequence = 120
Hence, there are 120 possible sequence.
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PLEASE HELP ME ASAP. I REALLY NEED THIS DONE
Answers
Answer:
x = 65
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
x² = 25 × 169 = 4225 ( take square root of both sides )
x = [tex]\sqrt{4225}[/tex] = 65
if k = √(49 - 12√5), then find the value of k +2
Answers
Step-by-step explanation:
k = √(49 - 12√5)
= √(45 + 4 - 2 √180)
= √45 - √4
= 3 √5 - 2.
So, k + 2 = 3 √5 - 2 + 2 = 3 √5.
Answer:
k + 2 = 3√5
Explanation:
[tex]\sf Given: k = \sqrt{49 - 12\sqrt{5} }[/tex]
[tex]\sf \rightarrow k = \sqrt{49 - 12\sqrt{5} }[/tex]
step 1: breakdown
[tex]\sf \rightarrow k = \sqrt{4 + 45- 2 \times 2 \times 3 \sqrt{5} }[/tex]
step 2: rewrite 45 = (3√5)²
[tex]\sf \rightarrow k = \sqrt{4 + (3\sqrt{5})^2 - 2 \times 2 \times 3 \sqrt{5} }[/tex]
step 3: rearrange as per a² -2ab + b² = (a - b)²
[tex]\sf \rightarrow k = \sqrt{ (3\sqrt{5})^2 - 2 \times 3 \sqrt{5} \times 2 +2^2}[/tex]
step 4: comparing, here: a = 3√5, b = 2
[tex]\sf \rightarrow k = \sqrt{ (3\sqrt{5} -2)^2}[/tex]
step 5: simplify √a² = a
[tex]\sf \rightarrow k = 3\sqrt{5} -2[/tex]
Then find k + 2
[tex]\rightarrow \sf k = 3\sqrt{5} -2 + 2[/tex]
[tex]\rightarrow \sf k = 3\sqrt{5}[/tex]
Find the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity.
Answers
The polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is x⁴ - 4x³ + 5x²- 4x + 4 = 0. This can be obtained by finding factors and multiplying them.
What is the required polynomial ?
Given that zeroes, 2 of multiplicity 2, and i of single multiplicity, that is, (x - 2), (x - i) and (x + i) are the factors of the polynomial.
Thus the polynomial can be written as
(x - 2)²(x - i)(x + i) = 0 ((x - 2) is squared as multiplicity is 2)
(x² - 4x + 4)(x²-i²) = 0
(x² - 4x + 4)(x²+1) = 0
x⁴ - 4x³ + 4x² + x² - 4x + 4 = 0
⇒ x⁴ - 4x³ + 5x²- 4x + 4 = 0
Hence the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is x⁴ - 4x³ + 5x²- 4x + 4 = 0.
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Fill in the missing statements and reasons in this proof. Number your reasons 1 through 5 as they would be shown in the chart below.
Given: m∠LOM = m∠JKI;
m∠MON = m∠IKH
Prove: m∠LON = m∠HKJ
would rlly appreciate ur help
Answers
From the given condition m ∠LOM = m ∠JKI, m ∠MON = m ∠IKH it is proved that m ∠LON = m ∠HKJ as they are congruent angles.
What are congruent angles?Congruent angles are defined as angles with equal measure. According to the question,
m ∠LOM = m ∠JKI (given congruent angles) _____(1)
m ∠MON = m ∠IKH (given congruent angles) _______(2)
Add both the side angle m ∠MON in (1) we get m ∠LOM + m ∠MON = m ∠JKI + m ∠MON
Replace angle m ∠MON = m ∠IKH from (2) on right-hand side we get,
m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH ____(3)
m ∠LOM + m ∠MON = m ∠LON ( M is the interior point of ∠LON) ___(4)
m ∠JKI + m ∠IKH = m ∠HKJ ( I is the interior point of ∠HKJ) ___(5)
Form (3), (4), and (5) we get, m ∠LON = m ∠HKJ (Congruent angles)
Hence, from the given condition it is proved that m ∠LON = m ∠HKJ, are congruent angles.
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A student received test grades of 83, 90, and 88. What was her grade on a fourth test if the average for the four tests is 84
Answers
Her grade on a fourth test is 75.
The average of e for the four tests is 84.
By substituting the given data in the equation, we get
Let the fourth test marks be x
83 + 90 + 88 + x / 4 = 84
261 + x / 4 = 84
261 + x = 336
x = 336 - 261
x = 75
An average may be described as the sum of all numbers divided by means of the whole quantity of values.
A mean can be defined as an average of the set of values in a sample of data. In different words, a median is also called the mathematics mean.
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I am studying geometry this summer but can’t solve this question what would be the correct answer
Answers
Answer: F
Step-by-step explanation:
Bisectors of an angle split the angle in half which you can visually see from the image. So, the answer is F.
Justin's rice ball recipe uses 100 grams of rice to make 1 rice ball. Justin has 700grams of rice.
How many rice balls can Justin make with 700 grams of rice?
Answers
The number of rice balls Justin can make with 700 grams of rice is 7.
How many rice balls can Justin make?
In order to determine the rice balls he can make, divide the grams of rice he has by the grams needed to make one rice ball. Division is the process of grouping a number into equal parts using another number.
Rice balls he can make = 700 grams / 100 grams = 7
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Answer:
7 rice balls
Step-by-step explanation:
Which equation is equivalent to log3 (x+5) = 2 ?
Answers
Answer:
the anwer is x= -3
Step-by-step explanation:
(3+5)=2
Use the data in the table below and a graphing calculator to describe how a linear model compares to a quadratic model. Analyze the "parameters" (as they are called in Desmos) a, b, c for the quadratic model and m & b for the linear model. Write a sentence or two that explains why both graphs look the same, even if you zoom out very far.
PLEASE HELP ME
Answers
The quadratic model and the linear model of the table of values are the same
The linear model of the dataTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 0Sum of Y = 113Mean X = 0Mean Y = 22.6Sum of squares (SSX) = 10Sum of products (SP) = 28The regression equation is
y = mx + b
Where
m = SP/SSX = 28/10 = 2.8
b = MY - bMX = 22.6 - (2.8*0) = 22.6
So, we have:
y = 2.8x + 22.6
See attachment for graph (1)
The quadratic model of the dataTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
a = 0b = 2.8c = 22.60 X^2 +2.8 X +22.6
The regression equation is
y = ax^2 + bx + c
So, we have:
y = 0x^2 + 2.8x + 22.6
See attachment for graph (1)
Why both graphs look the sameThe graphs look the same because when the quadratic model is simplified, it gives the linear model.
This in other words mean that:
The quadratic model and the linear model of the table of values are the same
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is the number there three? if you answer to me i will give you twenty Points.
Answers
Answer:
2
Step-by-step explanation:
3 x 2 = 6
1 x 2 = 2
hope it helps
sorry if I'm wrong
Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding One-third the length of the directed line segment?
The ratio given is part to whole, but fractions compare part to part.
The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
The ratio given is part to whole, but the associated fraction is One-third.
Answers
The reason why partitioning and fractioning are different is because; The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Why is partitioning different from fractioning?It follows from the task content that a close analysis of the statement of ratios; 1:3 implies that the whole is divided into four parts; 1+3 = 4.
On the contrary, one-third simply means 1 out of 3 equal parts of the line.
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Answer: OPTION C
Step-by-step explanation:
Select the correct answer. Consider the following system of equations. Use this graph of the system to approximate its solution. A diagonal curve rises through (negative 5, 1) through (6, 6). A diagonal curve declines through (negative 6, 5) through (7, negative 6) on the x y coordinate plane. A. B. C. D.
Answers
The approximate solution to the given system of equations, considering the graph, is given as follows:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex].
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex]
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Answer:
d
Step-by-step explanation:
the sum of seven odd consecutive is 217. Find the middle number
Answers
Answer:
x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 =217
7x+21=217
7x=196
x=28
Middle Number will be:
x+3
28+3
=31
Therefore, the middle number is 31.
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
Let's put this into equation form.
n + (n + 1) + (n+2) + (n+3) + (n+4) + (n + 5) + (n+6) = 217
Each number is increasingly getting farther away from n (the first number) by 1.
If we simplify, by adding all of the numbers and the n's. We get:
7n + 21 = 217
Let's subtract 21 from both sides to start the process of isolating x.
7n = 196
Now we can divide both sides by 7, to isolate x.
n = 28.
That looks like the answer, but it is not. Remember n is the first number, we want the middle, which out of 7 is the 4th number.
The 4th number is equal to (n+3) or (28 + 3)
The 4th number is 31.
Let's check if this is correct.
28 + 29 + 30 + 31 + 32 + 33 + 34 = 217.
The problem is complete.
Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
34 feet
23 feet
Answers
Answer: [tex]42.6^{\circ}[/tex]
Step-by-step explanation:
Let the angle of depression be x.
[tex]\sin x=\frac{23}{34}\\\\x=\sin^{-1} \left(\frac{23}{34} \right) \approx 42.6^{\circ}[/tex]
Which phrases describe the graph of f(x) = |x| ? Check all that apply
Answers
The phrases which describe the graph are;
The domain of the graph is the set of all real numbers.The range of the graph is the set of all real numbers greater or equal to zero.The graph in the task content is increasing over the interval (0, ∞).The graph in the task content is decreasing over the interval (-∞, 0).What is the graph of the absolute function?The absolute function in the task conten is;
f(x) = |x|, Hence, the domain and range of the graph are as described above.
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Out of 54 jelly beans, two were found to be defective. What is the experimental probability a jelly bean is defective?
26/27
1/27
2/27
24/27
Answers
Answer:
1/27
Step-by-step explanation:
To find the probability of a defective jelly bean
P(defective) = number defective/ total
=2/54
= 1/27
Geometry help please
7
Answers
Answer:
you should download AIR MATH
Complete the ratio table to convert the units of time from hours to weeks or weeks to hours.
Answers
Here is the completed table:
Hours Weeks
168 1
1008 6
840 5
How to complete the table?The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.
1008 hours to weeks = 1008 / 168 = 6 weeks
5 weeks to hours = 5 x 168 = 840 hours
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(LOOK AT IMAGE)
A robot can be programmed to draw any regular polygon.
The instructions seen in the example below are used to draw a regular 10- sided polygon with side lengths of 3 cm.
By changing the numbers in the program below, write down the simplest set of instructions needed to make the robot draw a regular 12-sided polygon with side lengths of 5 cm.
Answers
Repeat the following 12 times:
> Move forward 5 cm
> Turn clockwise 30°
Want to know how I found this out? Well, let me tell you.
First, they gave us the information that a 12-sided polygon is to be modeled with side lengths 5 cm. So, that basically gives us our first step. That was easy!
Well, now this is a bit harder. How many degrees do we move? There're so many possibilities! Well, not quite.
According to the Polygon Exterior Angle-Sum Property, the exterior angles of any polygon is always 360 degrees. So, we just divide 360 by how many sides there are in the polygon.
There are 12 sides in this polygon, so, [tex]\frac{360}{12}[/tex] is equal to 30 degrees per side. Well, now we have the second step! We're all done. Congratulations!
The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 36 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon. Construct a 98% confidence interval for the mean gas mileage for this car model.
Answers
The 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.
The confidence interval of statistical data is computed using the formula:
[tex](\overline{x} - Z\frac{\sigma }{n},\overline{x} + Z\frac{\sigma }{n})[/tex]
where [tex]\overline{x}[/tex] is the mean, Z is the Z-score corresponding to the confidence interval, σ is the standard deviation, and n is the sample size.
In the question, the sample size (n) = 36, the mean of the sample ([tex]\overline{x}[/tex]) = 28.4 mi/gallon, the standard deviation (σ) = 6 mi/gallon.
The confidence interval given to us is 98%.
Z-score corresponding to this (Z) = 2.33.
Thus, the confidence interval can be calculated as:
(28.4 - 2.33{6/√36},28.4 + 2.33{6/√36})
= (28.4 - 2.33,28.4 + 2.33)
= (26.07,30.73).
Thus, the 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
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Which function has an average rate of change of -4 over the interval [-2,2]?
Answers
Only p(x) has an average rate of change of -4 over [-2, 2].
Find the average rate of change of each given function over the interval [-2, 2]]:
The average rate of change of m(x) over [-2, 2]:
What is the average rate?The average rate of change = [tex]\frac{m(b)-m(a)}{b-a}[/tex]
Where, a = -2, m(a) = -12
b = 2, m(b) = 4
Plug the values into the equation
The average rate of change
[tex]=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}[/tex]
The average rate of change = 4
The average rate of change of n(x) over [-2, 2]:
The average rate of change = [tex]\frac{n(b)-n(a)}{b-a}[/tex]
Where, a = -2, n(a) = -6
b = 2, n(b) = 6
Plug the values into the equation
The average rate of change
[tex]=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}[/tex]
The average rate of change = 3
The average rate of change of q(x) over [-2, 2]:
The average rate of change = [tex]\frac{q(b)-q(a)}{b-a}[/tex]
Where, a = -2, q(a) = -4
b = 2, q(b) = -12
Plug the values into the
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
= [tex]\frac{-16}{4}[/tex]
The average rate of change = -2
The average rate of change of p(x) over [-2, 2]:
The average rate of change = [tex]\frac{p(b)-p(a)}{b-a}[/tex]
Where, a = -2, p(a) = 12
b = 2, p(b) = -4
Plug the values into the equation
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
[tex]=\frac{-16}{4}[/tex]
The average rate of change = -4
The answer is D.
Only p(x) has an average rate of change of -4 over [-2, 2].
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PLEASE help answer all 5 questions
Answers
[tex]p(r) = \frac{2}{9} [/tex]
2)We have 3 blue marbles and 9 marbles in total, so the probability of drawing a blue marble, is the number of blue marbles over the total number of marbles.[tex]p(b) = \frac{3}{9} = \frac{1}{3} [/tex]
3)Since we put the marbles back, the sample space stays 9 balls,so we have to multiply the probability of drawing a red marble then a blue one. Since order matters (red before blue) we do not account for permutations.4)Putting the marbles back in the bag makes this these events independent, as the sample space does not change.5)[tex]p(r \: then \: b) = \frac{2}{9} \times \frac{1}{3} = \frac{2}{27} [/tex]