Answers:
The new volume is 1/8 of the old volume
The new surface area is 1/4 of the old surface area
======================================================
Explanation:
Volume:
Let's say the diameter is d = 60
That would make the radius r = d/2 = 60/2 = 30
The volume of the sphere is
V = (4/3)pi*r^3
V = (4/3)*pi*(30)^3
V = (4/3)*(30)^3*pi
V = 36000*pi
Now consider that d = 30 which is half of the original diameter.
So r = d/2 = 30/2 = 15
And also,
V = (4/3)pi*r^3
V = (4/3)*pi*(15)^3
V = (4/3)*(15)^3*pi
V = 4500*pi
The old volume was 36000pi and the new volume is 4500pi
Comparing the two volumes, we see that the reduction factor is
(new volume)/(old volume) = (4500pi)/(36000pi) = 1/8
The new volume is 1/8 of the old volume
smaller volume = (1/8)*(larger volume)
This is equivalent to saying the larger volume is 8 times that of the smaller volume.
------------------------------------------------------
Surface Area:
We'll use the same d and r values from earlier.
The diameter d = 60 leads to r = 30. We'll use this to find the surface area
SA = 4pi*r^2
SA = 4*pi*30^2
SA = 3600pi
For the smaller sphere (d = 30 and r = 15), we have
SA = 4pi*r^2
SA = 4*pi*15^2
SA = 900pi
The reduction factor is (900pi)/(3600pi) = 1/4
The smaller sphere has its surface area 1/4 that of the larger sphere.
smaller surface area= (1/4)*(larger surface area)
This is equivalent to saying the larger surface area is 4 times that of the smaller surface area.
Convert 32/7 into a mixed number.
32/7 to a mixed number is 4 and 4/7
What are the coordinates?
Answer:
Coordinates are numbers which determine the position of a point or a shape in a particular space (a map or a graph).
In primary school children are taught Cartesian coordinates, which they are introduced to in Year 4. Points are marked by how far along they are on the x axis (the horizontal axis) and how far up they are on the y axis (the vertical axis).
Step-by-step explanation:
Is change always positive?
Answer:
no
Step-by-step explanation:
it depend on the question
Step-by-step explanation:
No it's not Change may be positive and negative. For example, negative change may seem all rotten but a lot of the time there are wonderful things in it. To begin with, getting sick is negative but it is also positive.hope it helps..stay safe healthy and happy..in a college biology class, only half of the class earned a passing grade, Out of all the students
and passed. What is the probability of someone having studied, given that they passed?
All 60%
b. 30%
6, 2%
d. 70%
Answer:
b 30% is the right answer
witch expressions are equivalent to x + 2y + x +2
Answer:
[tex]2(x + y + 1)[/tex]
Step-by-step explanation:
[tex]x + 2y + x + 2[/tex]
[tex]x + x = 1x + 1x[/tex]
[tex](1 + 1)x = 2x[/tex]
[tex]2x + 2y + 2[/tex]
[tex] = 2(x + y + 1)[/tex]
help !!!! what is the m and b ?????
Answer:
m is the slope and b is the y intercept
Step-by-step explanation:
SOMEONE PLEASE HELP!
PLEASE!!
Answer:
55-9
Step-by-step explanation:
you subtract
Define a Variable and write an iequallity to model the given situation.
A restaurant can hold no more than 160 people.
If p is the restaurant's capacity, which of the following models the situation?
p < 160
p > 160
p ->(negative greater than less that symbol) 160
p -<(neg greater than less than symbol) 160
Answer:
Variable data is defined as information and figures used to build control charts. Variable data can be used to create average (X-bar) charts, range charts, and sample standard deviation charts or "S-charts."
Answer:
D. p ≤ 160Step-by-step explanation:
A restaurant can hold no more than 160 people, it means it can hold 160 people or less.
This is shown as:
p ≤ 160Correct choice is D
_______is the process of paying off a debt with regular fixed payments.
Order the racers from first place to fifth place based on the clues.
Susan finished the race in second place.
The swimmers who placed first and fourth have names that start with the same letter.
Maria finished immediately after Janice.
Jennifer finished before Emily.
Answer:
Jennifer - 1st
Susan - 2nd
Emily - 3rd
Janice - 4th
Maria - 5th
Step-by-step explanation:
Susan is 2nd.
Places 1, 3, 4, and 5 are left.
Janice and Jennifer both start with J. None of the other swimmers start with the same first letter. One is 1st and one is 4th.
Since Maria finished immediately after Janice, and Janice must be 1st or 4th, Janice can't be first since 2nd place is already taken. This means that Janice is 4th and Maria is 5th.
Places 1 and 3 are left.
We know Jennifer is 1st or 4th and since 4th is taken, Jennifer is first.
Place 3 is left.
Emily must be 3rd since that is the only spot left.
The words above say “the expression x-2 has a value of -5 for some value of x. For the same value of x, what is the value of the expression (x-2)*squared. Show your reasoning for this problem.” Also i said (*squared) bcuz its squared with a 2 so please dont leave that part out. D: help pls
Answer:
(1)
Step-by-step explanation:
x - 2 = - 5 Add 1 to each side
x = - 5 + 2
x = - 3
Now go to the next part
(x - 2)^2
(-3 - 2)^2
(- 5)^2
Now it's a good idea at this point to separate the squared. It means that two numbers that are the same are to be multiplied together.
(-5)(-5) Two minuses are going to give you a plus.
5 * 5 = 25
(-5) * (-5) also give you 25
The answer is (1)
Amaya wants to jog 8 miles this week.She jogged 2 1/2 miles on Monday and 3 2/5 miles on wednesday. How many miles does Amaya still need to jog?
Answer:
2 1/10 miles.
Step-by-step explanation:
8 - (2 1/2 + 3 2/5)
= 8 - (5/2 + 17/5)
= 8 - (25/10 + 34/10)
= 8 - 59/10
= 80/10 - 59/10
= 21/10
= 2 1/10 miles.
Order the number from least to greatest
1. root of seven, 2, root of 8/2
2. root of 220, -10, root of 100, 11.5
In a shipment of 180 flashlights, 30 were selected. If 2 flashlights were defective, how many would be expected to be defective in the entire shipment?
Answer:
two out of 30
30 x 6 = 180
2 x 6 = 12
if 2 out of 30 are defective, and there are 180 total, 12 should be expected to be defective
Step-by-step explanation:
Meena is helping her school librarian to arrange books on the shelves. Based on this situation, answer the following questions: (Attempt any 4 questions)
2/3 of the books are Language books and 1/5 are Science books. What can you conclude from this statement?
There are less Language books than Science books
There are more Language books than Science books
They are equal in number
Can’t say anything
If the remaining books are of Mathematics, what is the fraction of those books?
1/15 b) 4/15 c) 2/15 d) 7/15
Answer:
a) language
b) 2/15
Step-by-step explanation:
For the first part, you can start by making the denominators same
you take the LCM of 3 and 5 which is 15
Language books are now 10/15 since you multiply the nominator and denominator by 5
While science books are 3/15
10/15 : 3/15 making it obvious that language books are more
if the remaining are math books then
total books - (language + science books) = math books
10/15 + 3/15 = 13/15 (non math books)
15/15 - 13/15 are math books making 2/15 of them math books
Find the missing probability.
P(A)=13/20,P(A∩B)=13/25,P(B|A)=?
By definition of conditional probability,
P(B | A) = P(A ∩ B)/P(A) = (13/25) / (13/20) = 20/25 = 4/5
1. Find the measure of
Answer:
p = 70 degree
c = 70 degree
Help find X:_,_ Y:_,_
Clean123 Inc. is preparing its balance sheet. It has $59,000 in accounts receivable, $32,000 in accounts payable, $41,000 in notes payable, $5,100 in salaries payable, $34,000 in salaries and wages expense, and $12,000 in rent. What is the total of the company's current liabilities?
The amount of total current liabilities reported on the balance sheet equals to; $178,000.
What is Current liabilities?Current liabilities entails set of amount or responsibility owed within an accounting period.
Particulars Amount
Accounts payable $32,000
Notes payable (current portion) $41,000
Salaries and wage payable $34,000
Rent $12,000
Accounts receivable $59,000
Total current liabilities $178,000
Therefore, the amount of total current liabilities reported on the balance sheet equals to ; $178,000.
Read more about financial reporting
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Half of the smaller of two consecutive even integers is equal to two more than the larger integer. find both integers Please i will give brainliest ASAP
Answer:
-8 and -6.
Step-by-step explanation:
Let the first even integer be a.
Since the second is a consecutive even integer, it is given by (a + 2).
Half of the smaller (i.e. a) is equal to two more than the larger (i.e. a + 2). In other words:
[tex]\displaystyle \frac{a}{2} = (a + 2) + 2[/tex]
Solve for a:
[tex]\displaystyle \begin{aligned}\displaystyle \frac{a}{2} &= (a + 2) + 2\\ \\ \frac{a}{2} &= a + 4\\ \\ a &= 2a + 8 \\ \\ a &= -8 \end{aligned}[/tex]
In conclusion, the two even, consecutive integers are -8 and -6.
The sales tax in Pennsylvania is 8%. If the tax on an item is $80, find the cost of the item.
Answer:
10 percent
Step-by-step explanation:
Answer:
$1000
Step-by-step explanation:
Cost of item x sales tax percentage = total sales tax
x * (0.08) = 80
Divide both sides by 0.08
x = 1000
The table and the graph show information about students enrolled in spanish and french classes at a high school. use the graph to determine after how many years there will be equal enrollment in spanish and french classes
Answer:
after 6 years
Step-by-step explanation:
thats when the lines intersect, (6,300)
There will be equal enrollment in Spanish and French classes after 6 years from now.
The red line shows the number of students enrolled in French class each year from now and blue line shows the number of students enrolled in Spanish class each year from now.
The point of intersection of the lines is the point which lies in both the line.
So, it represents the point or time when there are same number of students enrolled in both French and Spanish classes.
From the graph, we can see that the two lines at a point [tex](6,300)[/tex]. The value on the [tex]x[/tex]-coordinate shows the years from now. So, we can say that there will be equal number of students enrolled in two classes after 6 years.
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Guided Practice
The number of bacteria in a lab sample triples every hour. If you start with 2 bacteria in the sample, write an equation that represents the number of bacteria, y, in the sample after x hours.
A.
y=2 · x3y equals 2 times x cubed
B.
y=3 · 2xy equals 3 times 2 superscript x baseline
C.
y=2 · 3xy equals 2 times 3 superscript x baseline
Answer:
C.
y=2 · 3xy equals 2 times 3 superscript x baseline
Step-by-step explanation:
y=2 · 3 xy equals 2 tim
Question 1 (1 point)
The school that Linda goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets
and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets.
What is the price each of one senior citizen ticket and one student ticket?
Answer:
8 & 14
Step-by-step explanation:
Let
Cost of senior tickets be x and students be y
In day 1
4x + 5y = 102
In day 2
7x + 5y = 126
Subtract both
7x + 5y - (4x + 5y) = 126 - 102
7x + 5y - 4x - 5y = 24
7x - 4x = 24
3x = 24
x = 24/3
x = 8
From 1
4(8) + 5y = 102
32 + 5y = 102
5y = 102 - 32
5y = 70
y = 70/5
y = 14
[tex]f(x)=(x+4)^2\\[/tex]
Answer:
x²+8x+16
Step-by-step explanation:
f(x) = (x+4)²
= (x+4)(x+4)
= x² + 4x + 4x + 16
= x² + 8x + 16
Solve each equation 3m-3/5=2m-1/2
Answer:
m= 1/10
Step-by-step explanation:
1. Move the terms so that will be 3m - 2m=-1/2 + 3/5
2. Subtract the m values so that will be 3m - 2m= 1 or m
3. Calculate the sum.
4. So the answer will be m= 1/10. M because we subtracted 2 from 3 which make us 1 so we say it m and 1/10 by doing 1/2 + 3/5.
Answer:
Step-by-step explanation:
3m - 3/5 = 2m - 1/2
3m - 2m = 3/5 - 1/2
m = 0.1
Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options.
x = 5
–15 = –5x
5x = 15
–15 = 5x
x = -5
Answer: Its B and C
Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options.
x = 5
–15 = –5x
5x = 15
–15 = 5x
x = -5
i need help algebra
Answer:
A. the slope value is 1/4
B. 0
C. y = 1/4x
Step-by-step explanation:
A: the slope can be calculated with the formula
[tex]m = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]
m is the slope
(x1, y1) is your first coordinate point (any point will work)
(x2, y2) is your second coordinate point (any point will work)
Plug in your values, in this case I chose (0,0) and (4,1) as the two coordinates:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - 0}{4 - 0} = \frac{1}{4} [/tex]
B: the y-intercept is the y-coordinate of where the graph touches the y-axis and in this case the coordinate is (0,0) where the y coordinate is 0.
C:
the equation of the graph is y = mx + b.
m is the slope = 1/4
b is the y-intercept = 0
Therefore the equation is y = 1/4x
the perimeter of Andy's rectangular patio is 60 feet. which equation could Andy use to find the length [L] of the patio?
The equation for the length of the rectangle is L = 30 - W.
The given parameters:
perimeter of Andy's rectangular patio = 60 feet
The formula for perimeter of a rectangle is calculated as follows;
[tex]P = 2(L+W)[/tex]
Where;
P is the perimeter
L is the length of the rectangle
W is the width of the rectangle
To find the equation for the length of the rectangle, make L the subject of the formula;
[tex]P = 2(L+W)\\\\60 = 2(L+W)\\\\divide \ both \ sides \ by \ 2\\\\\frac{60}{2} = \frac{2(L+W)}{2} \\\\30 = L+ W\\\\L = 30 - W[/tex]
Thus, the equation for the length of the rectangle is L = 30 - W.
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At the end of a 10-year term, what is the balance of a $3,000 investment at a rate of 1.5 percent compounded quarterly?
$3,485
$3,675
$3,751
$3,900
