What is the maximum number of 1 cubic centimeter cubes you can fit into a box with a volume of 32 cubic centimeters?
The maximum number of 1 cubic centimeter cubes that will fit into a box with a volume of 32 cm³ is: 32 cubes.
What is the Volume of a Cube?The volume of a cube = s³, where s is the edge length of the cube.
Given the following:
Volume of 1 cube = 1 cubic centimeters
Box volume = 32 cubic centimeters
Number of cubes that will fit into the box = 32/1 = 32 cubes.
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Convert the following functions.
Convert the exponential function,
12^3=x^4 y^3 z^6
, to its corresponding logarithmic function.
Write the log form from Part A into the expanded log form. **expression must be fully expanded for
The logarithmic function is the inverse of the exponential function
The logarithmic equivalent of the exponential function is log(12) = [tex]\frac 43[/tex]log(x) + log(y) + 2log(z)
How to convert the function?The exponential function is given as:
12^3=x^4 y^3 z^6
Take the logarithm of both sides
log(12^3) =log(x^4 y^3 z^6)
Apply the product rule of logarithm
log(12^3) =log(x^4) + log(y^3) + log(z^6)
Apply the power rule of logarithm
3log(12) = 4log(x) + 3log(y) + 6log(z)
Divide through by 3
log(12) = [tex]\frac 43[/tex]log(x) + log(y) + 2log(z)
Hence, the logarithmic equivalent of the exponential function is log(12) = [tex]\frac 43[/tex]log(x) + log(y) + 2log(z)
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Perfomance task pre-cal
Part 1: Determine the limits of a function given a graph
The value of limits and function values for a, b, c, d, e, f, g, h, i, and j are 3, -1, does not exist, 3, 1, 2, does not exist, 2 +∞, and -∞ and doesn't follow continuity conditions and its jump continuity.
What is the limit?A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have a graph of a function:
For [tex]\lim_{x \to -1^{-1}} f(x)[/tex]
As we can see x approaches -1 and it is a left-hand limit.
[tex]\lim_{x \to -1^{-1}} f(x) = 3[/tex]
For [tex]\lim_{x \to -1^{+1}} f(x)[/tex]
The x approaches the +1 and it is the right-hand limit.
[tex]\lim_{x \to -1^{+1}} f(x) = -1[/tex]
For [tex]\lim_{x \to -1} f(x)[/tex]
Since the left hand and right-hand limits are not the same,
[tex]\lim_{x \to -1^{+1}} f(x)[/tex] = does not exist
From the graph:
f(-1) = 3
Similarly, we can find further values of the limits and functions value:
[tex]\lim_{x \to 2^{-1}} f(x) = 1[/tex]
[tex]\lim_{x \to 2^{+1}} f(x) = 2[/tex]
For [tex]\lim_{x \to 2^{}} f(x)[/tex]
Since the left hand and right-hand limits are not the same,
[tex]\lim_{x \to 2^{}} f(x)[/tex] = does not exist
f(2) = 2
[tex]\lim_{x \to -\infty} f(x) = +\infty[/tex]
[tex]\lim_{x \to +\infty} f(x) = -\infty[/tex]
There are three conditions a graph must follow:
1) function value defined at any given point.
2) left-hand limit and right-hand limit must be equal
3) function value at the point and limit value at the same point must be the same.
In the given function the graph doesn't follow these conditions and its jump continuity.
Thus, the value of limits and function values for a, b, c, d, e, f, g, h, i, and j are 3, -1, does not exist, 3, 1, 2, does not exist, 2 +∞, and -∞ and doesn't follow continuity conditions and its jump continuity.
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A cylinder has a volume of 100π cubic meters.
a. What is the volume of the cylinder if the height is halved? Explain
b. What is the volume of the cylinder if the diameter is halved? Explain
Answer:
a) V/2 ; b) V/4
Step-by-step explanation:
a) V = πR²h
If h --> h/2 the new volume V' = πR²h/2 = V / 2
b) πR²h
If D --> D/2 then R --> R/2 and the new volume V" = π(R/2)²h = π(R)²h/4 = V/4
PLEASE ANSWER AS SOON AS POSSIBLE WILL GIVE BRAINLESS TO THE FIRST CORRECT PERSON!!!
Find the value of x. Write your answer in the simplest form.
Answer:
9[tex]\sqrt{2}[/tex]/2
Step-by-step explanation:
Since this is a right triangle designated by the square box in the right side, we know 2 of the angles. 45 and 90. Add these 2 angles and subract them from 180 which turns out to be 45.
We can use the law of sines to solve.
sin90/9 = sin45/x
x = 9sin45 = 6.36 = 9[tex]\sqrt{2}[/tex]/2
The value of x + x(x^x) when x = 2 is:
(a) 10,
(b) 16
(c) 18,
(d) 36,
(e) 64
the value of x + x(x^x) when x = 2.
solution:x + x(x^x)
by putting the value of x = 2 in the above expression we get:
2 + 2(2^2)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
therefore, the value of x + x(x^x) when x = 2 is 10.
answer= option a
Answer is option a) = 10
have a great day
hope this helps
Help help help help
Answer: 1
Step-by-step explanation:
We can start by dividing both sides by 5. This gives us
[tex]6 + s = 7[/tex]
Subtracting 6 from both sides gives us
[tex]s = 7-6=1[/tex]
To check, we can put 1 back in the equation:
[tex]5(6+1) = 35[/tex]
[tex]5(7) = 35[/tex]
Since 5 * 7 is 35, 1 is the answer.
A bag with 10 marbles has 2 yellow marbles, 4 blue marbles, and 4 red marbles. What is the probabillity that it chosen at random and is yellow?
Answer:
1/5 = 0.2 = 20%
Step-by-step explanation:
Given:
Yellow marbles = 2Blue marbles = 4Red marbles = 4Total marbles = 10[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(yellow) = \dfrac{2}{10}=\dfrac15[/tex]
This can also be written as 0.2 or 20%
Answer:
[tex]Probability=0.2[/tex]
Step-by-step explanation:
Step 1: List the given information
[tex]Total\ Marbles = 10[/tex]
[tex]Yellow\ Marbles = 2[/tex]
[tex]Blue\ Marbles = 4[/tex]
[tex]Red\ Marbles = 4[/tex]
Step 2: Determine the probability of choosing yellow
[tex]Probability=\frac{Yellow\ Marbles}{Total\ Marbles}[/tex]
[tex]Probability=\frac{2}{10}[/tex]
[tex]Probability=\frac{1}{5}[/tex]
[tex]Probability=0.2[/tex]
Answer: [tex]Probability=0.2[/tex]
Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS not risking a virus
help me please :c :C
Answer:
214 square inch is the area of the figure
which graphed line represents an equation of a line with a slope of -2 and a point of line of (-1, 2)
A red line
B blue line
C green line
D purple line
Answer:
D
Step-by-step explanation:
by looking at the point you can see what has a slope.
it is also a decreasing slope
2 out of 5 bought pizza there were 30 students in total how many students did not get pizza as a ratio
Answer:
75%
Step-by-step explanation:
graph the linear equation -x+2y=2
The graph of the given linear equation, y = 1/2x + 1 (-x+2y=2), is given in the diagram attached below.
What is the Graph of a Linear Equation?The graph of a linear equation is a straight line graph, and it is represented, in slope-intercept form as, y = mx + b, where m is the slope and b is the y-intercept of the graph.
Given the linear equation, -x+2y=2, rewrite in slope-intercept form:
-x+2y=2
2y = x + 2
y = x/2 + 2/2
y = 1/2x + 1
Thus, the graph of the linear equation is drawn as shown in the image attached below.
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The area of a rectangle is 45 square inches. One dimension is 5 inches. What is the perimeter
Answer:
28 inches
Step-by-step explanation:
To begin, the area of a rectangle is base · height. Since we are given one of the sides already, you can make an equation to solve for the other value.
5 · x = 45
5x = 45
x = 9
A rectangle has two pairs of parallel sides, or in easier terms, two sets of sides that are the same. So, the perimeter is going to be two lengths plus two widths.
2 · 5 + 9 · 2 = 10 + 14 = 28
Select the correct answer.
Simplify the following expression.
Answer:
A. 1/49, or 0.02040
When the shadow of a flagpole is 36 m long, a 1.8-m fencepost casts a shadow that is 3 m long. How tall is the flagpole?
Answer:
21.6 m long
Step-by-step explanation:
To do this, we find the scale factor of the fencepost and the shadow.
3/1.8 = 1.66666667
So, we know that when we take the original length and multiply it, we get the new one, so:
1.666666667 * x = 36
x being the original length. Now, we divide both sides by 1.66666667 to get x alone and find the original length.
x = 21.6
To double check, we can take the scale factor and multiply it by the original to get the shadow.
21.6 * 1.666666667 = 36
It is correct
Two methods to measure one's heart rate are:
A. Palpitation and monitor
B. None apply
C. Monitor and EKG
D. Palpitation and pulse rate
Answer:
C. Monitor and EKG
D. Palpitation and pulse rate
Explanation:
Correct me if I'm wrong:)
The tub started with
gallons of water.
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal
places.
95% confidence; the sample size is 10,000, of which 40% are successes
0.0096
0.0126
0.0072
0.0110
Ik The answer is 0.0096 but don’t know how to get that. Would someone show steps?
HELP EEEEEEEK….. please
Answer:
5
Step-by-step explanation:
If it is 18 roses for 90 dollars, what is one rose worth?
90 dollars/18 roses=5 dollar per rose
Question is in the image
Answer:
16%
Step-by-step explanation:
4 people like rock
and there are 25 ppl all together
4/25=0.16
16%
Use the drop-down menu to complete the statement. What is 3 ÷ 2 5 ? To find the quotient, jump groups of . A number line going from 0 to 3. Numbers 0, 1, 2, and 3 are marked on the line. Marks divide the spaces between each number into 5 equal parts.
2/5 on edge
Yw and pls mark me brainiest :D
when using a graph you must look at all dots? given information,? or pages
Answer:
The dots are used for dot plots, and the given Information Is to help you understand the % or number of people and things etc.
Help but pls explain you thought
Can someone help me please
I recommend using guathmath
The entire band decides to have a concert to raise the money for the trip. TIckets
for the concert will cost $7.50 each. A local business agrees to donate an ado tonal
$0.50 for each $1.00 in ticket sales to the band for their trip.
What is the least number of concert tickets the band must sell in order to raise te
rest of the money needed for the trip?
Answer:
yeah so you a g my guy
Step-by-step explanation:
Help please please!!!!!
Answer:
7/8 inch
Step-by-step explanation:
Convert 1 1/4 to improper fraction.
1 1/4 4/4 + 1/45/4Convert 5/4 to a fraction with a denominator of 8.
5/45/4 x 2/210/8Subtract 3/8 from 10/8
10/8 - 3/87/8 inch5. How far can a person run in 15 minutes if he or she runs at an
average speed of 16 km/ty? (HINT: Remember to convert minutes to
hours.)
Now
Distance=Speed ×TimeDistance=16(1/4)Distance=4kmAnswer:
4 km
Step-by-step explanation:
QuestionHow far can a person run in 15 minutes if he or she runs at an average speed of 16 km/h?
Solution1 hours = 60 minutes
[tex]\implies \sf 16 km/h = \dfrac{16\:km/h}{60\:min}=\dfrac{4}{15} km/min[/tex]
If the person runs for 15 minutes, then:
[tex]\implies \sf total\:distance\:run=\dfrac{4}{15}\:km/min \times 15\:min=4\:km[/tex]
Fill in the missing numbers to complete the linear equation that gives the rule for this table.
х y
2 -36
3 -33
4 -30
5 -27
Y= ___x - ___
Answer:
y = 3x - 42
Step-by-step explanation:
The equation of a line if y = mx + cFirst, choose two of the x values with their respective y valuesI’ll choose 2 & -36 and 3 & -33We need to find the gradient of this line (which is the m in y = mx + c)We can do this by finding the difference in the y values and divide this by the difference in the x valuesSo this would be [tex]\frac{-33--36}{3-2} = \frac{3}{1}=3[/tex]So far we have y = 3x + cUsing one of the x values and their respective y value, substitute these values into the formulaI’ll choose 4 & -30-30 = 3 × 4 + c-30 = 12 + cc = -30 - 12 = -42So the equation is y = 3x - 42!Enter the correct answer in the box.
Write the expression (x4)8 in simplest form.
Answer:
x³²
Step-by-step explanation:
When raising exponents to another power, multiply the exponents given.
That means that:
(x⁴)⁸ = x⁽⁴⁾⁽⁸⁾ = x³²