Answer:
1/6
Step-by-step explanation:
To simplify the expression:
1. Change the divisor into it's reciprocal
2. Change the sign into a multiplication sign.
3. Evaluate the product of those fractions.
4. Simplify the fraction. (If possible)
Given expression:
[tex]\dfrac{1}{6^3 } \div \dfrac{1}{36}[/tex]
According to step 1, we need to convert the divisor of the expression into it's reciprocal.
[tex]\dfrac{1}{6^3 } \div \dfrac{36}{1}[/tex]
According to step 2, we need to change the division sign (÷) into a multiplication sign (×).
[tex]\implies \dfrac{1}{6^3 } \times \dfrac{36}{1}[/tex]
According to step 3, we need to determine the product of these fractions. This can be done by evaluating the exponent.
[tex]\implies \dfrac{1}{(6)(6)(6) } \times \dfrac{36}{1}[/tex]
[tex]\implies \dfrac{1}{216 } \times \dfrac{36}{1}[/tex]
Multiply the fractions as needed. [a/b × c/d = (a × c)/(b × d) = (ac)/(bd):
[tex]\implies \dfrac{36}{216 }[/tex]
According to step 4, (If possible), Simplify the product of 1/216 and 36. In this case, the product of 1/216 and 36 is 36/216. Since both are divisible by 6, we can divide the numerator and the denominator by 6 to simplify the fraction.
[tex]\implies \dfrac{36 \div 6}{216 \div 6 }[/tex]
[tex]\implies \dfrac{1}{6 }[/tex]
Therefore, the quotient of 1/6^3 and 1/36 is 1/6.
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Answer:
[tex]\large\textsf{$\dfrac{1}{6}$}[/tex]
Step-by-step explanation:
[tex]\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{36}$} \implies \normalsize \textsf{Convert 36 into a base with an exponent}[/tex]
[tex]\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{6^2}$} \implies \normalsize \textsf{Cross multiply}[/tex]
[tex]\large\textsf{$\dfrac{1 \cdot 6^2}{1 \cdot 6^3}$} \implies \normalsize \textsf{Multiply}[/tex]
[tex]\large\textsf{$\dfrac{6^2}{6^3}$}\implies \normalsize \textsf{Simplify using the Quotient of Powers Property: \normalsize\textsf{$\dfrac{x^m}{x^n} = x^{m-n}$}}[/tex]
[tex]\large\textsf6^{2-3}[/tex]
[tex]\large\textsf6^{-1} \implies \normalsize \textsf{Simplify using the Negative Exponent Property: \normalsize\textsf {${x^{-m}} = \dfrac{1}{x^m}$}}[/tex]
[tex]\large\textsf{$\dfrac{1}{6^1}$} \implies \normalsize \textsf{Simplify}[/tex]
[tex]\large\textsf{$\dfrac{1}{6}$} \implies \normalsize \textsf{Final answer}[/tex]
Hope this helps!
A bowling ball has a diameter of 8.5 inches. If it is rolled down a 60-foot bowling lane, how many complete revolutions will it make? Round to the nearest tenth.
Worth 25 points!!
Answer:
27 revolutions
Step-by-step explanation:
Things to remember :
One revolution = distance of circumference coveredcircumference = 2πrdiameter = 2 x radiusSolving
One revolution = 2 x π x d/2 = πdOne revolution = 3.14 x 8.5One revolution = 26.69 inchesNo. of revolutions = Distance / one revolutionNo. of revolutions = 60 x 12 / 26.69No. of revolutions = 720 / 26.69No. of revolutions = 27 revolutionsThe number of bacteria on your hand increases by 40% every hour. If there were initially 800 bacteria placed on your hand, how much bacteria
will be on your hand after 3 hours?
Answer:
about 2195 bacteria
Step-by-step explanation:
After one hour: 800 * 1.4 = 1120
After two hours: 1120 * 1.4 = 1568
After three hours: 1568 * 1.4 = 2195.2
A cylinder with radius 3 feet and height 5 feet is shown.
6
ft
Enter the volume, in cubic feet, of the cylinder. Round your
answer to the nearest hundredth.
Answer:
The volume of the cylinder is 141.23 cubic feet
Step by step explanation :
Given-
Radius of cylinder = 3 feet Height of cylinder = 5 feetNow, we know that
[tex] \boxed {\mathfrak \red{ volume \: of \: cylinder = \pi {r}^{2} h}}[/tex]where, r is the radius of the cylinder & h is the height of the cylinder.
Now,
Volume of the cylinder = [tex] \frac{22}{7} \times {3}^{2} \times 5[/tex]
[tex] = \frac{22}{7} \times 3 \times 3 \times 5[/tex]
[tex] = \frac{990}{7} [/tex][tex] = 141.428571[/tex] ( approximately )
[tex] = \boxed{ 141.43 \: \mathfrak { {ft}^{3}} }[/tex]
What is the result when the number 44
is increased by 75%?
Answer:
77
Step-by-step explanation:
75% of 44 = 33
33 + 44 = 77
Answer:
77.
Step-by-step explanation:
75% of 44
= 3/4 * 44
= 33
33+44
= 77.
HELP ASAP !!!!!Consider the function f(x) = 10x and the function g(x), which is shown below. How will the graph of g(x) differ from the graph of f(x)? A. The graph of g(x) is the graph of f(x) shifted 6 units down. B. The graph of g(x) is the graph of f(x) shifted to the right 6 units. C. The graph of g(x) is the graph of f(x) shifted to the left 6 units. D. The graph of g(x) is the graph of f(x) shifted 6 units up.
Answer:
the answer is B, the graph of g(x) is the graph of f(x) shifted to the right 6 units. hope this helps!
Answer:
C. The graph of g(x) is the graph of f(x) shifted to the left 6 units.
Hope this helps and good luck!
Parallelogram Properties - Diagonals
delta math
Answer:
DE=18
Step-by-step explanation:
The reason is because that parallelogram ABCD has most of the sides equal to each other.
The length of DB = 36 and half of 36/2 gets us DE.
DE=36/2=18
DE=18 also equals to BE=18
Diagonals of a parallelogram bisect each other
So
DE+BE=DBPutting DE=BE
2DE=DBDE=DB/2DE=36/2DE=18In the diagram, ABCDE is a regular pentagon.
(a) Calculate /BAE.
(b) What is the name of the quadrilateral ABCD?
(c)The sides AE and CD are produced to meet at X.
(i) Calculate /EDX.
(ii) What type of quadrilateral is BDXE? Explain your answer.
The shape ABCDE is a regular pentagon with five sides, such that the five sides are congruent
Part A: Calculate ∠BAEThe angle BAE is a vertex angle, and it is calculated using:
BAE = 180 * (n - 2)/n
Where n= 5; i.e. the number of sides.
This gives:
BAE = 180 * (5 - 2)/5
Evaluate
BAE = 108°
Hence, the measure of angle BAE is 108°
Part B: The name of the quadrilateral ABCDWhen the vertices A and B are joined together, the shape becomes a trapezoid.
Hence, the name of the quadrilateral ABCD is a trapezoid.
Part C (i) Calculate ∠EDXSee attachment for the new figure.
From the attached figure, we have:
∠EDX + ∠EDC = 180° ---- the sum of angles on a straight line
Where:
∠EDC = ∠BAE = 108°
So, we have:
∠EDX + 108° = 180°
Subtract 108° from both sides
∠EDX = 72°
Hence, the measure of angle EDX is 72 degrees
Part C (ii) What type of quadrilateral is BDXE?The quadrilateral BDXE is a parallelogram.
This is so because the opposite sides of BDXE are parallel, but not congruent
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what is the distance between -45 and 35
Answer:
10
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
-45 minus 35 is -80 so that's 80 units. and including zero it's 81 units
Someone please help and answer this please
Answer:
1) surface area = 2 · π · r · (r + h)
2) 8x5x6x14x8.94
3) surface area = 2 · π · r · (r + h)
4) 8x14x6
5) 4x4x8
6) 7x8.95x13
7) 3x4x11x3.61 divide by 2
8) 6x6x6 = 36x6 = 216
9) 3x4x10
Step-by-step explanation:
Graph f(x) = 4[x] +5.
a.
b.
X
C.
d.
r
16
Answer:
C
Step-by-step explanation:
When p = 12, t = 2, and s = one-sixth, r = 18. if r varies directly with p and inversely with the product of s and t, what is the constant of variation? one-eighth one-half four and one-half 18
The constant of variation given that r varies directly with p and inversely with the product of s and t is one-half
From the question given above,r ∝ p ∝ 1/st
r ∝ p / st
r = Kp / st
Cross multiply
r × st = Kp
Divide both side by p
K = rst / p => constant of variation
How to determine the constant of variation p = 12t = 2 s = one-sixth = 1/6r = 18Constant of variation (K) =?K = rst / p
K = (18 × 1/6 × 2) / 12
K = 6 / 12
K = 1 / 2 = one-half
Learn more about variation:
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1) lan's new Mercedes cost him $75,000. From the
moment he drives it off the lot, it will depreciate
by 20% each year for the first five years. What will
be the car's value be at the end of five years?
(Round to the nearest whole number.)
Answer: The answer to this is 3000,
Step-by-step explanation:
I think this is the answer because when you find out what 20% of 75000 is, (which is 15000) you can divide 20% by 5 and there is your answer, i hope this helps
what is the surface area of this?
Answer:
Surface Area = 96
Step-by-step explanation:
Area of Triangle: Area = 1/2 * Base * Height
Top Triangle:Area = 1/2 * 6 * 2 = 6
Bottom Triangle:Area = 6
Area of Rectange: Area = Length * Height
Left Rectangle:Area = 7 * 3 = 21
Mid RectangleArea = 7 * 6 = 42
Right RectangleArea = 21
Surface Area = TopTri + BotTri + LeftRect + MidRect + RightRect
Surface Area = 6 + 6 + 21 + 42 + 21 = 96
whats the y intercept and rate of change ill give 20 pt please help me thank u
Answer:
y-intercept= (0,7) and rate of change=
Step-by-step explanation:
The y-intercept of a graph is the point on the graph where it intersects the y-axis or where x=0. In this case it is (0,7) so that is the y-intercept. The rate of change is equal to y2-y1 divided by x2-x1. Basically, just pick 2 random points on the line and subtract their y coordinates, then subtract their x-coordinates and divide the answers with each other. So, one point is (0,7) and another point is (2,4). Therefore, rate of change is 7-4 divided by 0-2. This gives us a rate of change of -3/2
Factorise the following:
A. 4xy-16
B. xy+2xy-x
C. 2x²-18x+12
D. 5xy+20x-9y-36
=4(xy−4)
B. xy+2xy-x3xy−x
=x(3y−1)
C. 2x²-18x+122x²−18x+12
=2(x²−9x+6)
D. 5xy+20x-9y-365xy+20x−9y−36
=(y+4)(5x−9)
5.7.PS-7
Solve the inequality. Then graph the solutions on a number line.
6< - 3(2x-6)
A. X≥
• B. X >
O C. X <
O D. XS
the answer is a x equal to or greater than
The first thing you should do in solving a word problem is estimate what you think the answer would be.
True
False
Answer:
The answer is True.
Step-by-step explanation:
Estimate the Answer Before Solving Having a general idea of a ballpark answer .Or the problem lets students know if their actual answer is reasonable or not.In a large company, 45% of the employees wear khaki pants on a daily basis. Which calculation finds the probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees
The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees is 0.18.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
In a large company, 45% of the employees wear khaki pants on a daily basis.
40% of employees wearing khaki pants in a random sample of 50 employees
So, 40% of 45% x 50
= [tex]0.40 \times 0.45 \times 50 \\ \\9[/tex]
The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees.
= 9 /50
= 0.18
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Please help i need answer asap
Answer:
14x+6+(5x+30+=2190
Step-by-step explanation:
5x+11x using distributive property
[tex]5x+11x=16x[/tex]
What is Distributive Property?To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Distributive Property:
[tex](5x+10x)+(5x+1x)[/tex]
/ \ / \
[tex](16x)[/tex] [tex](6x)[/tex]
Therfore, by using the distributive property, [tex](5x+10x)+(5x+1x)[/tex], We get [tex]16x[/tex].
Learn more about the Distributive Property here:
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How much would a 20% tip be on a $65 restaurant bill?
Answer:
13 dollars would be the answer you're welcome lol
The area of a circle is 49 pi cm^2 what is the radius of a circle
Answer:
The radius is 7 cm
Step-by-step explanation:
We know the area of a circle is given by
A = pi r^2
49 pi = pi r^2
Divide each side by pi
49 = r^2
Take the square root of each side
sqrt(49) = sqrt(r^2)
7 = r
The radius is 7 cm
Answer:
radius = 7 cm
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
given A = 49π , then
πr² = 49π ( divide both sides by π )
r² = 49 ( take square root of both sides )
r = [tex]\sqrt{49}[/tex] = 7
Which graph represents the function
f(x) = (x + 4)(x + 1)(x - 3)
?
Answer:
Step-by-step explanation:
The graph that represents the function
f(x) = (x + 4)(x + 1)(x - 3)
crosses the x-axis three times: at x = -4, x = -1, and x = 3
because we apply the zero product rule and found the roots -4, -1, and 3
x+ 4= 0 → x = -4
x+1 = 0 → x = -1
x-3 = 0 → x = 3
solve by completing the square: x^2+18x+45=0
Answer:
x = -3 , - 15
Step-by-step explanation:
Given:
x² + 18x + 45 = 0
Solve:
[tex]x_{1,\:2}=\frac{-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45}}{2\cdot \:1}[/tex]
Simplify
[tex]-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45=12[/tex]
[tex]x_{1,\:2}=\frac{-18\pm \:12}{2\cdot \:1}[/tex]
Separate the solution
[tex]x_1=\frac{-18+12}{2\cdot \:1},\:x_2=\frac{-18-12}{2\cdot \:1}[/tex]
[tex]x_1=\frac{-18+12}{2\cdot \:1}=-3[/tex]
[tex]x_2=\frac{-18-12}{2\cdot \:1}=-15[/tex]
Thus, the answer are:
[tex]x=-3,\:x=-15[/tex]
Kavinsky
What two-dimensional shape is formed by the cross section shown below?
Answer:
I believe rectangle.
Step-by-step explanation:
help me with this question, please
Answer:
Part 1: [ -4 = -8 ]
Part 2: Inconsistent
Step-by-step explanation:
Part 1
1. Move all terms that don't contain x to the right side:
3x - 6y+6y = -12+6y
= 3x = -12 + 6y
2. Isolate x:
[tex]\frac{3x}{3} = \frac{-12+6y}{3}[/tex]
x = -4 + 2y
3. Substitute the new expression into the original:
-4 + 2y - 2y = -8
4. Simplify:
-4 + 0 = -8
[ -4 = -8 ]
Part 2
The two solutions are not equal in value, so, we can conclude that the system of equations has no solution, or is inconsistent.
hope this helps!
Can someone please give me the (Answers) to this? ... please ...
I need help….
Answer:
see explanation
Step-by-step explanation:
2 chords intersecting inside a circle , then the product of the parts of one chord is equal to the product of the parts of the other chord.
6
BE × ED = AE × CE , that is
10 × 3x = 12(2x + 1) ← distribute parenthesis by 12
30x = 24x + 12 ( subtract 24x from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
then
ED = 3X = 3(2) = 6
7
RJ × JP = SJ × JQ , that is
6 × 3x = 4(4x + 1) ← distribute parenthesis by 4
18x = 16x + 4 ( subtract 16x from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
then
RP = RJ + JP = 6 + 3x = 6 + 3(2) = 6 + 6 = 12
An item on sale costs 15% of the original price. The original price was $97
Answer:
$14.55
Step-by-step explanation:
help me i need help.
Answer:
The value of a side = 5
Step-by-step explanation:
By using PGT theoram
H² = P² + B²
=> 13² = a² + 12²
=> 13² - 12² = a²
=> 169 -144 = a²
=> 25 = a²
=> √25 = a
=> 5 = a
Answer:
a = 5
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
a² + 12² = 13²
a² + 144 = 169 ( subtract 144 from both sides )
a² = 25 ( take square root of both sides )
a = [tex]\sqrt{25}[/tex] = 5
solve each logarithmic equation. Round your answer to two decimal places.
Teach me this one? I want to work on the next and will submit it once I have it done.
7 log9 (x + 8) = 7
Answer:
[tex]\sf \boxed{\bold{x=1}}[/tex]
Explanation:
[tex]\rightarrow \sf 7 log_9 (x + 8) = 7[/tex]
divide both sides by 7
[tex]\rightarrow \sf \dfrac{7\log _9\left(x+8\right)}{7}=\dfrac{7}{7}[/tex]
simplify the following
[tex]\sf \rightarrow \log _9\left(x+8\right)=1[/tex]
apply log rules [tex]\underline{The \ rule}: \ \bold{log_{b} (a)= c} \ \ \Longrightarrow \sf a = b^c[/tex]
[tex]\sf \rightarrow x+8 = 9^1[/tex]
simplify
[tex]\sf \rightarrow x+8=9[/tex]
subtract both sides by 8
[tex]\sf \rightarrow x=1[/tex]
[tex]\\ \rm\Rrightarrow 7log_9(x+8)=7[/tex]
[tex]\\ \rm\Rrightarrow log_9(x+8)=1[/tex]
[tex]\\ \rm\Rrightarrow x+8=9^1[/tex]
a^1=a[tex]\\ \rm\Rrightarrow x+8=9[/tex]
[tex]\\ \rm\Rrightarrow x=9-8[/tex]
[tex]\\ \rm\Rrightarrow x=1[/tex]