The units on a base area calculations is known to be cm² or m² while units on your volume calculations is known to be m³ or cm³.
Why use the unit about?The unit above is used because in base area calculation, only 2 sides are calculated while in volume calculation, 3 sides are involved.
Note that in base area, square unit is often used in its calculations via the use of two dimensions length and breadth (cm² or m² ).
In terms of volume, cubic unit is used in its calculations through the use of three dimensions length, breadth and height ( m³ or cm³.).
Note also that Area is seen as the space taken by a two dimensional flat object while volume is seen as the space taken by the three-dimensional object and as such The units on a base area calculations is known to be cm² or m² while units on your volume calculations is known to be m³ or cm³.
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Question Help
Reasoning A cone with radius 6 and height 9 has its radius quadrupled. How many times greater is the
volume of the larger cone than the smaller cone?l
Let's see
For initial cone
r=6h=9Volume
1/3πr²h1/3π(6)²(9)3(36)π108π units³For new cone
r=4(6)=24h=9Volume
1/3π(24)²(9)3(576)π1728πSo
1728π/108π16timesAnswer:
16 times
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h[/tex]
Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.
ProofGiven:
radius = 6height = 9Substituting the given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units[/tex]
If the radius is quadrupled:
radius = 6 × 4 = 24height = 9Substituting the new given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units[/tex]
To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:
[tex]\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16[/tex]
So the volume of the larger cone is 16 times greater than the volume of the smaller cone.
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The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
What is the Mean, Median, and Interquartile Range of a Data?Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
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Which is the solution set of the compound inequality 3.5 x minus 10 greater-than negative 3 and 8 x minus 9 less-than 39 negative 2 less-than x less-than 3 and three-quarters negative 2 less-than x less-than 6 2 less-than x less-than 6 2 less-than x less-than 3 and three-quarters
Answer:
The solution for the compound inequality is x \in(2,6)
Step-by-step explanation:
To find the solution set for these compound inequalities, we need to solve the inequality.
First, we shall solve the inequality
Adding both sides of the equation by 10, we have,
Dividing both sides by 3.5, we get,
Now, we shall solve the inequality ,
Adding both sides of the equation by 9, we have,
Dividing both sides by 8, we get,
The solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.
What is the general equation of a Straight line inequality?
The general equation of a straight line inequalities are -
[y] < [m]x + [c]
[y] > [m]x + [c]
[y] ≥ [m]x + [c]
[y] ≤ [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the following compound inequality -
3.5x - 10 > - 3
8x - 9 < 39
We have -
3.5x - 10 > - 3
8x - 9 < 39
3.5x - 10 > - 3
3.5x > 7
x > 2
AND
8x - 9 < 39
8x < 48
x < 6
Solution inequality -
2 < x < 6
Therefore, the solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.
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Ida's ice-cream stand has increasing profits each week during the hot summer months. Ida finds that each week during the summer her profits increase by 15% over what they were the previous week. In her first week of business, her profits were $600.How much money will she make in all over 5 weeks
Answer:
4045.43
Step-by-step explanation:
If a is real and the product of (a+6i)(5-3i) is a real number, the find a.
PLS HELP ASAP WILL MARK BRAINLIEST
Answer:
5a−3ai+30i+18
Step-by-step explanation:
i just did this
Part a
describe the process you could use to find the probability that jake will earn at least 30 points on a throw, given that he hits the target? note: assume that it is equally likely that he will hit any region in the target.
The probability that Jake will earn at least 30 points on a throw is 0.335
How to describe the process?The attached image represents the missing part of the question.
From the attached image, we can see that:
For Jake to earn at least point, he must hit the three circles (starting from the inner circle)
The radius of the yellow circle is:
Radius = 3
While the width of the other circles is:
Width = 4
The total area of the sections that give a point of at least 30 is:
A₁ = π * (3 + 4 + 4)² = 121π
The total area of all the sections is:
A₂ = π * (3 + 4 + 4 + 4 + 4)² = 361π
The probability of getting at least 30 points is:
P(At least 30) = 121π/361π
Evaluate
P(At least 30) = 0.335
Hence, the probability that Jake will earn at least 30 points on a throw is 0.335
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2/3 - 5/4 + 7/3 whats the4 answer pls
Answer:
7/4Step-by-step explanation:
2/3 - 5/4 + 7/3
=8/12 - 15/12 + 28/12 (LCM=12)
(8 - 15 + 28)/12
=21/12
=7/4
The table shows the solution to the equation |2x - 3| -1 = 2:
Step 1
|2x - 3|= 2 + 1
Step 2
|2x - 3|= 3
Step 3
2x - 3= 3 or 2x + 3 = 3
Step 4
2x = 6 or 2x = 0
Step 5
x = 3 or x = 0
Which is the first incorrect step?
The first incorrect step is step 2 because this step did not take the two signs positive and negative.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation in a mod function;
|2x - 3| - 1 = 2
Step 1:
|2x - 3| = 3
Step 2:
2x - 3 = 3 or 2x - 3 = -3
(after removing mod, we get two same values but opposite in sign)
The first incorrect step is step 2 in which did not take the two sign,
2x - 3= 3 or 2x + 3 = 3 (wrong)
Thus, the first incorrect step is step 2 because this step did not take the two signs positive and negative.
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Hello Brainly, The Question is Find the Area of this Parallelogram. Please Help! Thank You!
Answer:
24 ft sq
Step-by-step explanation:
find area of triangles
6×4=24
24/2=12
add areas together
12+12=24
he triangles below are similar. Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters. Which similarity statement expresses the relationship between the two triangles? Triangle Z Y X is similar to triangle C A B Triangle Z Y X is similar to triangle A C B Triangle Z Y X is similar to triangle C B A Triangle Z Y X is similar to triangle A B C
And
AB=12BC=6AC=14Check
AB/YX=BC/ZY=AC/XZ12/6=6/3=14/72=2=2Hence
ABC=XYZOr
ZYX≈CBAOption C
if three times a certain number is increased by 4 the result is 28
Answer:
The number is 8
Step-by-step explanation:
Let x be the number
3x+4 = 28
Subtract4 from each side
3x+4-4 = 28-4
3x= 24
Divide by 3
3x/3 =24/3
x = 8
Calculate the mean of 1,2,3,4,5,6
Answer:
mean = 3.5
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{1+2+3+4+5+6}{6}[/tex] = [tex]\frac{21}{6}[/tex] = 3.5
Answer:
The mean of 1 , 2 , 3 , 4 , 5 , 6 is 3.5
Given :
The observations 1 , 2 , 3 , 4 , 5 , 6
To find :
The mean of 1 , 2 , 3 , 4 , 5 , 6
Solution :
Step 1 of 2 :
Calculate sum of the observations
Here the given observations are 1 , 2 , 3 , 4 , 5 , 6
Number of observations = 6
Sum of the observations
= 1 + 2 + 3 + 4 + 5 + 6
= 21
Step 2 of 2 :
Find the mean
The required mean
The scatter plot below shows the number of enrollments, N, in a sports club, t years after the year 2005.
The equation of the line of best fit is
N = 62t + 35.
What does the why intercept of the line of best fit represent?
A. The number of enrollments in the year 2006 were 97
B. The number of enrollments in the year 2005 were 35
C. Each year the number of enrollments increases by 35
D. Each year the number of enrollments increases by 62
−6×(−8)= what is the answers
Answer:
48
Step-by-step explanation:
when you multiply a negative times a negative (or divide a negative by a negative), it equals a positive!
-6 times -8 will equal 48!
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The speed of light is roughly 186,000 miles per second. How many minutes does it take for light to arrive from the sun, which is 93,000,000 miles away?
Answer:
8.3 minutes
Step-by-step explanation:
93,000,000 m/186,000 m/s = 500 s
500/60 = 8.333333
If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 2 ones?
[tex]\displaystyle|\Omega|=6^3=216\\A=\binom{3}{2}\cdot5=3\cdot5=15\\|A|=\dfrac{15}{216}=\dfrac{5}{72}\approx0.069[/tex]
Find the value of x.
Answer:
125 minus 81 will give me 34°
Answer:
x = 44°
Step-by-step explanation:
｡◕‿◕｡｡◕‿◕｡｡◕‿◕｡
Rectangular prism A measures 2 inches by 7 inches by 8 inches. Rectangular prism B measures 1 inches by 5 inches by 10 inches.
Rectangular Prism A:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
Rectangular Prism B:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³
Surface Area to Volume Ratio = 43/28
Mensuration of SolidsGiven Data
Rectangular prism A
Length = 2 inches
Width = 7 inches
Height = 8 inches
Surface Area
A=2(wl+hl+hw)
A=2(7*2+8*2+8*7)
A=2(14+16+56)
A= 172 inches²
Volume
Volume = L*W*H
Volume = 2*7*8
Volume = 112 inches³
Surface Area to Volume Ratio
= 172/112
= 43/28
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Which of the following situations can be defined using an exponential function?
A The value of the stocks decreased by $100 last year.
B The number of bacteria decreases by 7% each hour.
C The number of bacteria increases by 700 each hours.
D The value of the stocks increases by $10 every year you own them.
The situation which can be defined using an exponential function is "The number of bacteria decreases by 7% each hour".
What is an exponential function?An exponential function is used to represent a situation in which values of an event do not increase at a constant or linear rate.
From the above,
The value of the stocks decreased by $100 last year is a linear function.The number of bacteria increases by 700 each hour is a linear function.The value of the stocks increases by $10 every year you own them is a linear function.Learn more about exponential function:
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f(x) = x g(x) = 1
What is the domain of ( g/f ) (x)?
Answer:
Step-by-step explanation:
First one- x=0
Second=All real numbers
B
5 in.
a.
(6.257 25) in.
-
b. (6.25π – 12.5√2)in.²
d.
Find the value of x and y rounded to the nearest tenth.
C.
(6.25π- 12.5) in.2
none of these
Answer:
Step-by-step explanation:
5 in.
a.
(6.257 25) in.
-
b. (6.25π – 12.5√2)in.²
d.
Find the value of x and y rounded to the nearest tenth.
C.
(6.25π- 12.5) in.2
Evaluate
4(x+5)(x+1)
(x+3)(x-3)
for x = 5.
Answer:
3840
Step-by-step explanation:
Given expression:
4(x+5)(x+1)(x+3)(x - 3)
To:
Evaluate the expression ; for x = 5.
Solution:
4(x+5)(x+1)(x+3)(x - 3)Evaluate x = 5 :
4(5+5)(5+1)(5+3)(5 - 3)Simplify using PEMDAS rule:
P : Parentheses
E : Exponents
M : Multiplication
D : Division
A : Addition
S : Subtraction
(4)(10)(5+1)(5+3)(5−3)40(5+1)(5+3)(5−3)(40)(6)(5+3)(5−3)(240(5+3)(5−3)(240)(8)(5−3)1920(5−3)(1920)(2)3840Hence, after evaluating the given expression for x = 5 , the answer'll be 3840.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to evaluate
[tex]\large\pmb{4(x+5)(x+1)(x+3)(x-3)}[/tex] for x=5.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Use PEMDAS. With the help of this acronym, we will not make any mistakes in the Order of Operations!Here's what PEMDAS stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
So, let's start computing...
///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\//\\\///\\\///\\\///\\\\///\\\\///\\\///\\\///\
Evaluating the expression
First, substitute 5 for x:
[tex]\star~\large\pmb{4(5+5)(5+1)(5+3)(5-3)}[/tex]
Now, use the Order of Operations.
The first operation here is:
[tex]\dag[/tex] P=Parentheses
So we need to perform the operations inside the parentheses first:
[tex]\star~\large\pmb{4(10)(6)(8)(2)}[/tex]
The next operation is multiplication, since we don't have any exponents here:
[tex]\star~\large\pmb{40\times6\times8\times2}[/tex]
Multiply!
[tex]\star~\Large\pmb{3840}~~\square\!\!\!\!\!\checkmark[/tex]
That's the value of the expression 4(x+5)(x+1)(x+3)(x-3) for x=5.
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What is it help pleaseee
Answer:
25.13cm
Step-by-step explanation:
formula for circumference of a circle is (2r)π with r being the radius
since the problem gave us the diameter already we can change the formula to 8π (2r is equal to the diameter since diameter is twice as long as the radius)
this gives us the circumference of 25.13
Solve 2x+6 ≤ 10 or 2x + 8 > 20.
A. x ≤2 or x>6
OB. x < 1 or x > 2
OC. x ≤ 1 or x > 6
OD.
2 and x > 2
Answer:
A. x ≤2 or x>6Step-by-step explanation:
2x+6 ≤ 10 or 2x + 8 > 20
⇔ 2x ≤ 4 or 2x > 12
⇔ x ≤ 2 or x > 6
what is the slope of the line through the points (-3,3) and (6,-8)
Answer:
[tex]\displaystyle \frac{-11}{9}[/tex]
Step-by-step explanation:
We will use the equation of change in y over change in x to solve for the slope of the line. Then, we will simplify.
[tex]\displaystyle \frac{y_{2}-y_1 }{x_2-x_1}[/tex]
[tex]\displaystyle \frac{-8-3}{6--3}[/tex]
[tex]\displaystyle \frac{-8-3}{6+3}[/tex]
[tex]\displaystyle \frac{-11}{9}[/tex]
how many Years are in 1,000
The number of years in 1000 days is = 2 . 74 years .
How many Years are in 1,000 day?Division is the arithmetic operation that is used to determine the quotient of a number. Division parts a number into equal parts with another number.
Number of years in 100 days = 1000 / 365
= 2 . 74 years
Here is the complete question:
how many Years are in 1,000 days
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A mosquito has a mass of about 0.00000225 kilograms. Which of these is the measure of the mass in scientific notation?
Answer:
2.25x 10^-6
Step-by-step explanation:
In order to find out which is the scientific notation you would want to count how many zeros are in front of the number in this case it has 6 zeros before the series of numbers meaning that it would be 10^-6
show your working please.
Offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
2 bags for £35
2 bags means 50 kg (2×25)
Each kg cost = 35/50 = £0.7 per kg
3 bags for £92.50
3 bags means 150 kg
Each kg cost = 92.50/150 = £0.61 per kg
As we can see, offer B has a low cost per kg
Thus, offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
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O is the center of the regular octagon below. Find its area. Round to the nearest tenth
if necessary.
Answer:229.1
Step-by-step explanation: to much work I thought to hard that’s the answer your welcome buddy
A keypad has only the letters A−D. What is the total number of possible outcomes if the code has 3 letters?
Answer:
9
Step-by-step explanation:
Because 3 letter to find that just do 3 times 3 which = 9
Hope This Helped
Answer:
64
Step-by-step explanation:
There are 4 options to choose from:
ABCDEach has a 1/4 chance of being picked.
For 3 times in a row, we would multiply the chance of being picked for one option, by whatever the other option's chance is.
As they all have the same chance, and it is 3 times in a row, we would do the following:
1/4 x 1/4 x 1/4
This is:
1/16 x 1/4
Which is:
1/64
Therefore, any possible combination has a 1/64 chance of occurring, meaning that there are 64 possible combinations that could be created.