The simplification of the given expression is obtained as 1/216.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given expression is 6⁻³.
It can be simplified as below,
Rewrite the given expression as,
6⁻³ = ((6)⁻¹)³
Now, (6)⁻¹ = 1/6
⇒ 6⁻³ = (1/6)³
⇒ 1/6 × 1/6 × 1/6 = 1/216
Hence, the given expression can be simplified as 1/216.
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There are 90 students in Grade 5, and 10% of them were absent today.In Grade 6, 15% of the 80 students were absent today.What was the total number of students in the two grades who were present today?
Answer:
21 students
Step-by-step explanation:
90 x .10 = 9
80 x .15 = 12
9 + 12 = 21 students
which ratio forms a proportion with 18/27
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The given ratio is [tex]\frac{18}{27}[/tex]
9 is the common factor of 18 and 27
divide numerator and denominator by 9
[tex]\frac{18/9}{27/9} =\frac{2}{3}[/tex]
hence [tex]\frac{2}{3}[/tex] is proportion with [tex]\frac{18}{27}[/tex]
Combine the like terms to create an equivalent expression. 3n+7−2
Answer:
3n+5
Step-by-step explanation:
What is 2pi/ 5radians in degrees
Answer:
2/5 * pi radians = 72 degrees
Step-by-step explanation:
To convert radians to degrees, we multiply by 180/pi
2 * pi/5 * 180/pi =
The pi/pi cancels leaving
2/5 * 180
360/5
72
2/5 * pi radians = 72 degrees
I need help!!!!
Can someone help me
Answer:
D
Step-by-step explanation:
note that the values in the domain map to the values in the domain as
- 1 → 2 ( that is 1 + 3 = 2 )
3 → 6 ( that is 3 + 3 = 6 )
5 → 8 ( that is 5 + 3 = 8 )
In each case 3 is added to the value in the domain(x) to obtain the value in the range ( y = f(x) )
Hence f(x) = x + 3 → D
4. FLOWERS Bethany placed a bouquet of roses in a vase full of water. Each day she recorded how much water had evaporated from the vase before refilling it. The results are shown in the table below. Over the course of five days how much water had evaporated? Use mental math to find your answer.
Answer:
A x 5
Step-by-step explanation:
Answer:
take all evaporation numbers and add them together to get the answer u r looking for
Step-by-step explanation:
In a geometric sequence {an}, if a1 = 4 and r = 0.2, the first 4 terms in the sequence are A) {4, .8, .16, .032,...}. Eliminate B) {4, 20, 100, 500,...}. C) {4, 4.2, 4.4, 4.6,...}. D) {4, 3.8, 3.6, 3.4,...}.
Hey man, your answer is (A) I took the test!!!
The first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }Further explanationFirstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
Given:
a = 4
r = 0.2
Solution:
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_1 = 4 \times 0.2^{1-1} = 4 \times 1 = 4[/tex]
[tex]T_2 = 4 \times 0.2^{2-1} = 4 \times 0.2 = 0.8[/tex]
[tex]T_3 = 4 \times 0.2^{3-1} = 4 \times 0.04 = 0.16[/tex]
[tex]T_4 = 4 \times 0.2^{4-1} = 4 \times 0.008 = 0.032[/tex]
Therefore , the first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
what three things must a ordered pair have?
Answer: An x and y value, parenthesis around the values, and a comma in between them.
Examples of ordered pairs: (2, 5), (1872, 1683), (-3, 7), (7/8, -10/2)
PLS HELP!!!!!! NOW PLS!!!!
Given that the points (-1, 5) and (2, 1) are vertices of a rectangle with sides parallel to the axes, how much longer is the length than the width?
A. 1 Unit
B. 2 Units
C. 3 Units
D. 4 Units
Answer:
The right answer is 1 unit or A
Step-by-step explanation:
the area of kens rectangular yard is 480 square feet. the yard is 24feet wide. in order to fence in the garden completely on all four sides,how many feet of fencing would ken need to buy.
Answer:
88 ft
Step-by-step explanation: Start with the formula for the area of a rectangle:
A = L*W, where L is the length and W is the width.
Here, the width is W = 24 ft, and the area i s 480 ft^2. Thus,
A = 480 ft^2 = L (24ft), which yields L = (480/24) ft = 20 ft.
The length of the fencing required is actually the perimeter of the yard, which is P = 2L + 2W.
Substituting 20 ft for L and 24 ft for W, we get:
P = perimeter of yard = amount of fending needed:
P = 2(20 ft) + 2(24 ft) = 88 ft
Ken would need 88 ft of fencing to enclose his entire yard.
Ken needs to buy 88 feet of fencing to enclose his rectangular yard, which has an area of 480 square feet and is 24 feet wide.
To find out how much fencing Ken would need to buy to enclose his rectangular yard, we first need to calculate the dimensions of the yard. We know the area of the yard is 480 square feet and the width is 24 feet.
To find the length, we use the following equation for the area of a rectangle (Area = length imes width):
480 square feet = length x 24 feet
By dividing both sides by 24 feet, we obtain:
length = 480 / 24
length = 20 feet
Now, to calculate the total amount of fencing needed, we add together the lengths of all four sides:
Total fencing = 2 imes (length + width)
Total fencing = 2 imes (20 feet + 24 feet)
Total fencing = 2 imes 44 feet
Total fencing = 88 feet
Therefore, Ken needs to buy 88 feet of fencing to enclose his yard completely on all four sides.
70% of a number is what fraction
It's going to be 7/10
You earn $8.60/hr. You work 32 hr/wk and your deductions are FICA (7.65%), federal tax withholding (10.6%), and state tax withholding (8.25%). How much do you have direct-deposited bi-weekly?
The amount that is direct-deposited bi-weekly is 404.30.
To calculate the bi-weekly direct deposit amount, we need to follow these steps:
1. Calculate the gross pay for a week:
Gross pay per week = Hourly wage * Hours worked per week
Gross pay per week = $8.60/hr * 32 hr/wk
Gross pay per week = $275.20
2. Calculate the total deductions per week:
Total deductions rate = FICA rate + federal tax rate + state tax rate
Total deductions rate = 7.65% + 10.6% + 8.25%
Total deductions rate = 26.5%
Total deductions per week = Gross pay per week * Total deductions rate
Total deductions per week = $275.20 * 26.5%
Total deductions per week = $73.049
3. Calculate the net pay for a week:
Net pay per week = Gross pay per week - Total deductions per week
Net pay per week = $275.20 - $73.049
Net pay per week = $202.151
4. Calculate the bi-weekly net pay:
Bi-weekly net pay = Net pay per week* 2
Bi-weekly net pay = $202.151 * 2
Bi-weekly net pay = $404.302
Since the net pay is calculated to the nearest cent, we can round the bi-weekly net pay to the nearest cent as well:
Bi-weekly net pay (rounded) = $404.30
Therefore, the amount that is direct-deposited bi-weekly is 404.30.
The answer is: $404.30.
A customers photo cell phone bill this month is $50 and 50 Cent the company charges a monthly fee of $18 +5 cents for each car used in to represent the number of calls
Which number sentence is true
Answer:
B is the right one i bet u 100 point s
Answer:
B is the correct answer.
The brackets ║ represent absolute value. Absolute value is ALWAYS positive. I hope this helps you!
-Mikayla
an aquarium tank is 3 feet long, 1 foot wide, and 2 feet high. how many gallons of water would it take to fill the tank two-thirds full?
Answer: the answer is 6ft
Step-by-step explanation:
3 times 1 times 2 = 6ft
Number of gallons of water would it take to fill the tank two-thirds full is,
⇒ 30 gallons
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
An aquarium tank is 3 feet long, 1 foot wide, and 2 feet high.
Hence, Volume of tank is,
⇒ V = 3 x 1 x 2
⇒ V = 6 feet³
Hence, Number of gallons of water would it take to fill the tank two-thirds full is,
⇒ 2/3 of 6
⇒ 4 feet³
⇒ 4 × 7.5
⇒ 30 gallons
Thus, Number of gallons of water would it take to fill the tank two-thirds full is,
⇒ 30 gallons
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What is the 41st term in sequence 8,10,12,14,.....?
A lot is in the shape of a trapezoid. The sum of the bases is 280 feet. If the area of the lot is 8,400 square feet, what is the distance across the lot, i.e., the altitude of the figure? The altitude of the trapezoid is feet.
Answer:
The altitude of the trapezoid is 60 feet.
Step-by-step explanation:
Trapezoid
Sum of the bases: B+b=280 feet
Area of the trapezoid: A=8,400 feet^2
Altitude of the trapezoid: h=?
The formula to calculate the area of a Trapezoid is:
A = (1/2) (B+b) h
Replacing the given values:
8,400 feet^2 = (1/2) (280 feet) h
(1/2) (280 feet) = (140 feet)
8,400 feet^2 = (140 feet) h
Solving for h: Dividing both sides of the equation by 140 feet:
8,400 feet^2 / (140 feet) = (140 feet) h / (140 feet)
60 feet = h
h = 60 feet
Answer: The altitude of the trapezoid is 60 feet.
Answer:
60
Step-by-step explanation:
what is 3/20 as a percentage
Answer:
15%
Step-by-step explanation:
Percent means out of 100. Lets get the denominator out of 100
3/20 * 5/5 = 15/100
This is 15%
Final answer:
To convert the fraction 3/20 to a percentage, first convert it to a decimal by dividing 3 by 20. Then, multiply the decimal by 100 to get the percentage.
Explanation:
To express 3/20 as a percentage, you can multiply the fraction by 100. The calculation is (3/20) * 100 = 15%. Therefore, 3/20 as a percentage is 15%. This means that 3 out of every 20 parts represent 15% of the whole. In percentage terms, it provides a convenient way to compare the fraction to 100, making it easier to understand its relative size or portion in relation to the total. In this case, 15% indicates the proportion of the whole that is represented by the fraction 3/20.
A building is casting a 140 foot shadow at the same time a nearby post is casting a 10 ft shadow. If the post is 18 feet tall how tall is the building
Answer: 252 feet tall
Step-by-step explanation:
1) make a proportion
x/18=140/10
2)solve
10x=140*18
x=140*18/10
x=14*18
x=252
3) Answer
The building is 252 feet tall
A regular dodecagon has 12 sides. What is the smallest angle of rotation about its center that carries a dodecagon onto itself?
Answer:
30°
Step-by-step explanation:
No. of sides in dodecagon = 12
No. of angles = 12
Since its regular, all sides and all angles are equal.
total rotational angle = 360°
since no. of angles = 12
and all angles are equal,
rotational angle at which, it will co - incide with itself = [tex]\frac{360}{12}[/tex]
= 30°
A regular dodecagon will be onto itself it is rotated about the central angle 30°.
Answer: 30°
Step-by-step explanation:
7 1/3 ∙ x = 1.6 ÷ 6/11
x = __
Please Help!
Answer:
x= 0.4
Step-by-step explanation:
We need to solve and find the value of x
7 1/3x = 1.6 ÷ 6/11
Converting mixed fraction into improper fraction
22/3 x = 1.6 ÷ 6/11
Converting ÷ sign by X and reciprocating the term
22/3 x = 1.6 * 11/6
Now divide both sides by 3/22
x = 1.6 * 11/6 * 3/22
x = 1.6 * 1/2 * 1/2
x = 1.6/4
x = 0.4
S0, x= 0.4
Answer fast!!!!!!!!!!!
i’m in algebra 2 and it’s long division please help
[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)[/tex]
[tex]_+\begin{matrix}(5x^4&+&10x^3&-&7x&+&1)&:&(x+2)&=5x^3-7\\-5x^4&-&10x^3\end{matrix}\\\overline{_+\begin{matrix}\ \ =&&&&=&\ \ \ -&7x&+&1\\&&&&&&7x&+&14\end{matrix}}\\\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\ 15}[/tex]
[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)=5x^3-7+R(15)\\\\5x^4+10x^3-7x+1=(x+2)(5x^3-7)+15[/tex]
Final answer:
Long division is a method used to divide two polynomials in algebra. It involves arranging the dividend and divisor, determining the term of the quotient, subtracting and repeating until there are no more terms left to bring down.
Explanation:
In algebra, long division is a method used to divide two polynomials. It is especially useful when the dividend (the polynomial being divided) has a higher degree than the divisor (the polynomial dividing the dividend).
Here's a step-by-step explanation:
Arrange the dividend and divisor in descending order.Determine the term of the quotient by dividing the leading terms of the dividend and divisor.Multiply the entire divisor by the term of the quotient and subtract it from the dividend.Repeat steps 2 and 3 until there are no more terms left to bring down.The result is the quotient and any leftover terms are the remainder.Let me know if you need further assistance or if there's anything else I can help you with!
use the law of cosines to find each missing side
Answer:
29.03 units
Step-by-step explanation:
x^2 = 10^2 + 19^2 - 2*19*20 cos 122
= 100 + 361 - 720 * -0.52992
= 842.54
x = 29.03
can someone help me and explain how you did it?
Answer:
Step-by-step explanation: To find a y intercept you must find what y is when x is 0 so because it already tells you on the table the y intercept is 4. To find slope take 2 x intercepts and 2 y intercepts. For this well take the 0,4 and 5,1. The take the y from both pairs and minus them so it will look like 4 minus 1. Then draw a line under the equation under this line do the same thing but with the x's from both pairs so 0-5 then you will get as a result of both -3/5 as your slope.
Answer:
slope: -3/5
y-intercept: (0, 4)
slope-intercept form: y = -3/5x + 4
Step-by-step explanation:
Finding the slopeTo find the slope of this line, you would take two points from the table and substitute their coordinates into the slope formula.
Slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
I'm going to use the points (0, 4) and (5, 1). You can really use any point from the table. Substitute these points into the formula to find the slope.
(0, 4), (5, 1) → [tex]\frac{1-4}{5-0} \rightarrow \frac{-3}{5}[/tex]
This means the slope of the line is -3/5.
Finding the y-interceptThe y-intercept will always have the value of x be 0 (so the point is solely on the y-axis), so by looking at the table we can see that the y-intercept is at (0, 4).
Finding the slope-intercept formSince we have the slope and a point of the line, we must use point-slope form to find the equation of the line in slope-intercept form. Substitute in the point (0, 4) --you could use any point from the table-- and the slope -3/5 into the point-slope form equation.
point-slope form: y - y1 = m(x - x1) --you'll be substituting the point coordinates and slope into y1, x1, and m.
y - (4) = -3/5(x - (0))
Simplify.
y - 4 = -3/5x
Add 4 to both sides.
y = -3/5x + 4 is the equation of the line in slope-intercept form (you have both the slope and the y-intercept in this form).
Drag each tile to the correct box.
A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Order the samples by their average growth rate over the interval [1, 3], from least to greatest.
Answer: C < B < A
Step-by-step explanation:
First, let's evaluate the growth rate of A from [1, 3]
[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^1[/tex]
= 300
coordinate is (1, 300)
[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^3[/tex]
= 675
coordinate is (3, 675)
Average growth rate (AGR) is: [tex]\dfrac{675-300}{3-1} = \dfrac{375}{2} = 187.5[/tex]
AGR (A) = 187.5
*************************************************************************************
Next, let's evaluate the growth rate of B from [1, 3]
The coordinates are already provided as (1, 120) and (3, 480)
Average growth rate (AGR) is: [tex]\dfrac{480-120}{3-1} = \dfrac{360}{2} = 180[/tex]
AGR (B) = 180
*************************************************************************************
Lastly, let's evaluate the growth rate of C from [1, 3]
f(x) = 600(1.2)ˣ
f(x) = 600(1.2)¹
= 720
coordinate is (1, 720)
f(x) = 600(1.2)³
= 1036.8
coordinate is (3, 1036.8)
Average growth rate (AGR) is: [tex]\dfrac{1036.8-720}{3-1} = \dfrac{316.8}{2} = 158.4[/tex]
AGR (C) = 158.4
please view my question down below
[tex]\frac{422}{8}=52.75mph[/tex]
A.
[tex]average=\dfrac{distance}{time}\\\\\text{We have}\\\\distance=422\ miles\\\\time=8\ hours.\\\\\text{Substitute:}\\\\\boxed{x=\dfrac{422\ miles}{8\ hours}=52.75\ mph}[/tex]
If y = 2x − 8, what is the value of x when y = 0?
What is the equation of the graph below?
Answer:
[tex]y=cos(x+\pi )[/tex]
Step-by-step explanation:
From the graph, we can see that y = -1 when x = 0.
So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.
1. y = cos(x + pi/2) = cos(0 + pi/2) = 0
2. y = cos(x+2pi) = cos(0+2pi) = 1
3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5
4. y = cos(x+pi) = cos(0+pi) = -1
Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.
The letters in the word Mississippi are put into a bag. What’s the probability of randomly selecting a vowel from the bag ?
- 3/11
- 2/11
- 1/11
- 4/11