A ball of radius 17 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.
Answer:
19,133.067Step-by-step explanation:
Volume of the ball (spherical in nature) Vb = 4/3πrb³
Volume of the hole Vh = 4/3πrh³
rb is the radius of the ball
rh is the radius of the hole
If a ball of radius 17 has a round hole of radius 7 drilled through its center, the volume of the resulting solid will be expressed as:
V = Vb - Vh
V = 4/3πrb³ - 4/3πrh³
factor out the like terms;
V = 4/3π(rb³-rh³)
Given
rb = 17
rh = 7
V = 4/3π(17³-7³)
V = 4/3π(4913-343)
V = 4/3π(4570)
V = (4π*4570)/3
V = 57,399.2/3
V = 19,133.067
Hence the volume of the resulting solid is 19,133.067
How are fractions, decimals, and percents related?
Answer:
yes bc they all have sum to do wit eachother
Step-by-step explanation:
$75 jacket: 5% markup
Answer:
75*1.05 = $78.75
Step-by-step explanation:
You can just multiply by 1.05 or go the long route and divide by 100 and multiply by 105.
3x>9
Which of the following sentences is the word equivalent of the expression above?
The product between 3 and a number is no less than 9
The product between 3 and a number is greater than 9
The product between 3 and a number is no more than 9
The product between 3 and a number is less than 9.
Answers to the entire test:
Step-by-step explanation:
1. C. a<b
2.A. x >_0
3. A. The product between 3 and a number is greater than 9
4. B. The difference of 16 and the product of 5 and a number is no less than 1
5.B. 6(x-4)<_20
Auto sales in a country increased from 16.5 million in 2014 to 17.5 million in 2015. Find the percent increase in auto sales from 2014 to 2015. Round to the nearest tenth of a percent._______%
Answer:
6.1%
Step-by-step explanation:
Amount increase=17.5-16.5
=1million
% increase= amount increase/original×100% amount
= 1/16.5×100%
= 6.1%
The percentage increase in auto sales is 6.1 %
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
The auto sales of the country in 2014 = 16.5 million
The auto sales of the country in 2015 = 17.5 million
The increase in auto sales in 2015 from 2014 =
Auto sales of the country in 2015 - Auto sales of the country in 2014
The increase in auto sales in 2015 from 2014 = 17.5 million - 16.5 million
= 1 million
Now , the percentage increase in auto sales =
( Increase in auto sales / Auto sales of the country in 2014 ) x 100
The percentage increase in auto sales = ( 1 / 16.5 ) x 100
= 6.06 %
Therefore , the percentage increase is 6.1 %
Hence , the percentage increase in auto sales if 6.1 %
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May y'all please help me
Answer:
2x^2 - 11x + 6
Step-by-step explanation:
2x^2 + 4x - 3 * (5x - 2)
Distribute -3 between the parentheses like so.
2x^2 + 4x - 15x + 6
And then add like terms 4x and 15x together.
2x^2 - 11x + 6
-11, -8,-5, -2...
What is the 100th term in this sequence?
Answer:
298.
Step-by-step explanation:
formula- n in the next term is (n+3)
basically adding three
3x100=300
-2+300=298
Ignore the marked answer, accidentally clicked it
From the Pythagoras's Theorem, we know that:
(Hypotenuse)² = (base)² + (perpendicular)²
We are Given:
We are given that the 2 legs (Base and Perpendicular) of the triangle are (m²-n² and 2mn)
Solving for the Hypotenuse:
replacing the variables in the Pythagoras's theorem, we get:
Hypotenuse² = (m²-n²)² + (2mn)²
Hypotenuse² = (m⁴ -2m²n² + n⁴) + (4m²n²) [(a-b)² = a² - 2ab - b²]
Hypotenuse² = m⁴ -2m²n² + n⁴ + 4m²n²
Hypotenuse² = m⁴ + 2m²n² + n⁴
Hypotenuse² = (m²)² + 2m²n² + (n²)²
Hypotenuse² = (m² + n²)² [a² + 2ab + b² = (a+b)²]
taking the square root of both the sides
Hypotenuse = m² + n²
Richmond High School purchased 90 graphing calculators for $110
each. The school received a manufacturer's rebate of $10 per
calculator. After the rebate, what was the total cost of the
calculators?
Answer:
$9000
Step-by-step explanation:
110 x 90 = 9900
90 x 10 = 900
9900 - 900 = 9000
The chart below shows the numbers of endagered and threatened species both here in the United States and abroad
Endangered Threatened
United States Foreign United States Foreign
Mammals 68 251 10 20
Birds 77 175 13 6
Reptiles 17 67 22 19
Anphibians 11 8 10 1
Find the probability that it is:
a. Threatened and in the United States
b. An endangered foreign bird
c. A mammal or a threatened foreign species
Answer:
a. 0.071
b. 0.226
C. 0.4849
Step-by-step explanation:
We add up all endangered and foreign species to get 775
A.
Probability of threatened in united States.
= 10+13+22+10 = 55 divided by total species
= 55/775
= 0.070967
= 0.071
B
An endangered foreign bird
Total number of foreign birds = 175
Probability = 175/775
= 0.2258
= 0.226
C.
Please check attachment for the calculation of answer part c.
Thank you!
Solve the equation.
3/4x+3-2x=-1/4+1/2x+5
Answer:
x=-1
Isolate the variable by dividing each side by factors that dont
contain the variable
(34+ (9 x 2)) divide2 = _
Answer:
26
Step-by-step explanation:
9 x 2= 18
18+34= 52
52/2= 26
Find the midpoint of the segment with the following endpoints.
(-4,-9) and (4, -1)
Answer:
[tex](0,-5)[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point (-4, -9)
Point (4, -1)
Step 2: Find midpoint
Substitute: [tex](\frac{-4+4}{2},\frac{-9-1}{2})[/tex]Add/Subtract: [tex](\frac{0}{2},\frac{-10}{2})[/tex]Divide: [tex](0,-5)[/tex]Plz help with A and D!
Answer:
Yes it's B or C
Step-by-step explanation:
Amy received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.24 per pound. After buying the coffee, she had $38.80 left on her card. How many pounds of coffee did she buy?
Answer:
5 pounds
Step-by-step explanation:
Given that:
Amount of gift card = $80
Cost of coffee per pound = $8.24
Amount left in the card = $38.80
To find:
Number of pounds of coffee bought = ?
Solution:
Let the number of pounds of the coffee bought = [tex]x[/tex] pounds
Cost of 1 pound = $8.24
Cost of [tex]x[/tex] pounds = $8.24 [tex]\times x[/tex]
Writing the equation as per question statement:
[tex]80 - 8.24x = 38.80\\\Rightarrow 80 - 38.80 = 8.24x\\\Rightarrow 8.24x = 41.2\\\Rightarrow x = \dfrac{41.2}{8.24}\\\Rightarrow \bold{x = 5\ pounds}[/tex]
Therefore, 5 pounds of coffee was bought.
The slope of a line is -7 what is the slope of a line parallel to it
Answer: The slope is -7
Step-by-step explanation:
When a line is parallel to another line it means that they will never meet. This requires the slope to be the same, so no matter the line, if it is parallel to a line with a slope of -7, then its slope is also -7.
Please help me solve this i need help
Answer:
21
Step-by-step explanation:
Which expression is equivalent to 6x2 – 19x – 55?
Answer:
(6x + 11)(x – 5)
Step-by-step explanation:
Trust me!
use the figures below what is the ratio of AD to JM
A.2/3
B.6/5
C.3/2
If I knew what the figures looked like I could help you but since I don't. I'll just explain.
A: If 2/3 is a ratio provided then AD to JM might be 4 to 6
B: If 6/5 is a ratio provided then AD to JM might be 12 to 10
C: If 3/2 is a ratio provided then AD to JM might be 6 to 4
Can someone help me with these?
Answer:
Luzilândia baiana não ia já ouvi falar em Maranhão que e Rosa do Brasil na rocha godprl e abaixa e viu neon
Which is NOT the graph of a function?
Οε:
te
What is the probability of getting one or fewer people with a chronic heart condition in a sample of 22 if 25% of the population in this age bracket?
The question is incomplete. The complete question is :
The National Center for Health Statistics reports that 25% of all Americans between the ages of 65 and 74 have a chronic heart condition. Suppose you live in a state where the environment is conducive to good health and low stress and you believe the conditions in your state promote healthy hearts. To investigate this theory, you conduct a random telephone survey of 25 persons 65 to 74 years of age in your state.
Suppose only one person in your survey has a chronic heart condition. What is the probability of getting one or fewer people with a chronic heart condition in a sample of 25 if 25% of the population in this age bracket has this health problem?
Solution :
Chronic heart disease is a condition where a person's heart have trouble to pump blood to the body. It develops over a period of time.
In the context, we can see from the figures from National Center for Health Statistics that the expected number of persons of age 65 - 74 years having a chronic heart disease is about
25 % of 25 = 6.25
Now by Poisson's ratio, the probability of choosing the sample where only one person having heart disease is 1.4%
1) Find a unit rate for the following ratio. 135 words: 3 minutes
2 points
45 words: 1 minute
50 words: 1 minute
40 words: 1 minute
100 words: 2 minutes
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonable) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).
In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.6%. Describe the conclusion about p using an absolute value inequality.
The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that too ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥.
Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).
Answer:
|0.254 ≤ p ≤ 0.286|
Step-by-step explanation:
Given that:
In a made up poll :
Proportion of people who like dark chocolate than milk chocolate (p) = 27%
Margin of Error = 1.6%
Hence,
p ± margin of error
27% ± 1.6%
(27 - 1.6)% ; (27 + 1.6)%
25.4% ; 28.6%
0.254 ; 0.286
Therefore ;
Lower bound = 0.254
Upper bound = 0.286
Expressing p as an absolute value Inequality ;
|0.254 ≤ p ≤ 0.286|
a garden store is making seed package . Each package contains 35 seeds. There are 1960 seeds available. How many seed package can be made ?
Divide total seeds by seeds per package:
1960 / 35 = 56
56 packages can be made.
what can be visualized as a series of vertical lines around the Earth
Answer:
roads?
Step-by-step explanation:
i think thats right
Write a four digit whole number that is divisible by 2. Use a divisibility rule and explain how you know that your number is divisible by 2.
please help
compare. Write <, >, or =.
Answer:
1. <
2. >
3. >
4. =
5. <
6. <
7. >
8. >
9. >
10. <
11. >
12. <
13. <
14. =
15. =
16. =
Step-by-step explanation:
Please help needs to be rounded to the nearest hundredth
Answer: 0
Step-by-step explanation:
11 + 11= 22
22 is rounded to the nearest hundredth, which is not 100, so its 0
you bough shoes for $60. they were on sale for 40% off their original price. a. write a proportion to solve for the original price of the shoes
Answer:
$100
Step-by-step explanation:
The proportion would be [tex]\frac{60}{x} =\frac{60}{100}[/tex]. This is because you are paying for 60% of the original price and 60% is equal to [tex]\frac{60}{100}[/tex].