The equivalent expression for 10⁶ / 10⁴ will be equal to 10²
Given,
Exponents: 10⁶ and 10⁴
We have to find an equivalent expression for 10⁶ / 10⁴
Equivalent expression:
In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are plugged into the formula.
Here,
aˣ / aⁿ = x - n
So,
10⁶ / 10⁴ = 6 - 4 = 2
That is,
The equivalent expression for 10⁶ / 10⁴ will be equal to 10²
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simplify the square root of 217
Answer: 14.73091
Step-by-step explanation:
The square root of 217, (or root 217), is the number which when multiplied by itself gives the product as 217. Therefore, the square root of 217 = √217 = 14.730919862656235.
(x^2-9/x+4=3-(x-3)/x+4
Answer:
x = 2.579248
Step-by-step explanation:
x^2 - 9/x + 4 = 3 - (x - 3/x) + 4
a) Multiply both sides by x.
x^3 + 4x - 9/x = 6x + 3
b) Multiply both sides by x.
x^4 + 4x^2 - 9x = 6x^2 + 3x
x^4 + 4x^2 - 9x - (6x^2 + 3x) = 6x^2 + 3x - (6x^2 + 3x)
x^4 - 2x^2 - 12x = 0
x(x^3 - 2x - 12) = 0
x = 0 or x^3 - 2x - 12 = 0
x = 0 or 2.5792479999999998
PLEASE HELP WITH THIS!
a rectangular piece of metal is 10 in longer than it is wide. squares with sides 2 in long are cut from the four corners and the flaps are folded upward to form an open box. if the volume of the box is 671 in, what were the original dimensions of the piece of metal?
The length and width of the piece of metal are 28 and 18 inches respectively.
What is volume?
The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Dimension of the rectangle;
Width(w)
Length,L= 10 + w
volume of the box = length * width * height
Dimension of the box;
length of box, (x + 10) - 4 = x + 6
width of box,(x - 4)
height of box = 2
The volume of the box is 672 in³;
⇒V=lwh
⇒V=2 (x -4)( x + 6)
⇒672 in³ = 2x² + 4x - 48
⇒2x² + 4x - 720 = 0
⇒x^2 + 2x - 360 = 0
⇒(x +20)(x - 18) = 0
⇒x = 18
⇒x=-20 (value of the dimension will not be negative.
The width of an original piece of metal is;
Width,w=18 inches
length,l= 28 inches
Hence. the length and width of the piece of metal are 28 and 18 inches respectively.
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A data set includes the following numbers: eighteen over 5, two and four fifths, 97%, and 1.74.
Part A: What is the order of the numbers from least to greatest? Write your answer using the numbers in their original form.
Part B: Did you use estimation or rewrite the numbers in equivalent forms? Please explain your answer.
Answer quick please I appreciate it.
The order of the numbers from least to greatest will be 97%, 1.74, 2 4/5, and 18/5.
I rewrite the numbers in equivalent forms, this was illustrated in decimals to make it easier.
How to illustrate the information?From the information, the data set includes the following numbers: eighteen over 5, two and four fifths, 97%, and 1.74. This will be:
18/5 = 3.6
2 4/5 = 2.8
97% = 0.97
1.74
The arrangement will be 97%, 1.74, 2 4/5, and 18/5.
Therefore, it should be noted that rewriting then in decimal is important to effectively convey the information better.
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Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
Answer:
252
Step-by-step explanation:
Altogether, Luis, Dayja, and Michael read 279 pages.
How do we get the total number of pages read by each person?We can get the total number of pages read by each person by building from the number of pages read by Dayja.
Dayja read 84 pages
Luis read 75% more pages than Dayja and this is equal to:
84 + 84 × 75/100
84 + 84 × 0.75
84 + 63
= 147 pages.
Dayja read 75% more pages than Michael.
Believing that Michael read x number of pages.
84 = 175 ÷ 100 × x
8400 = 175x
x = 8400/175
x = 48
So, Michael read 48 pages.
Altogether we will have, 84 + 48 + 147 pages.
= 279 pages.
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Area of a triangle with a vertical height of 1/2 m and base of 1/4 m.
Answer:
1/16 squared meters
Step-by-step explanation:
The formula to find the area of a triangle is [tex]\frac{Base * Height}{2}[/tex]
We can form an equation if we substitute the values (base and height).
[tex]\frac{1/2*1/4}{2}[/tex]
1/2 * 1/4 = 1/8
and [tex]\frac{1/8}{2}[/tex] = 1/16
Therefore, the area of a triangle with a vertical height of 1/2 m and a base of 1/4 m is 1/16 meters squared.
Use the number line below, where RS=9y+3, ST=5y+8, RT=67 a. What is the value of y? b. Find RS and ST.
The value of y on the number line is 4.
How to find the side of a number line?A number line is a series of numbers placed on a straight line in order from least to greatest.
The number line is RT.
The point S is in between RT.
Therefore,
RT = RS + ST
Hence,
RT = 67
RS = 9y + 3
ST = 5y + 8
Therefore,
RT = RS + ST
67 = 9y + 3 + 5y + 8
67 = 9y + 5y + 11
67 = 14y + 11
subtract 11 from both sides of the equation
67 = 14y + 11
67 - 11 = 14y + 11 - 11
56 = 14y
divide both sides by 14
y = 56 / 14
Therefore,
y = 4
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what is it please :)
The surface area of the sphere to the nearest square foot is 2463 feet.
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the given point is its center.So, the surface area of the sphere:
The formula of the surface area of the sphere: 4πr²Radius = diameter/2 ⇒ 28/2 ⇒ 14Now, substitute the radius in the formula as follows:
4πr²4π14²2463.00864Rounding off: 2463 feet
Therefore, the surface area of the sphere to the nearest square foot is 2463 feet.
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this is a little difficult for me
Answer:
Step-by-step explanation:
the answer and steps are down below to check it out have a wonderful wonderful day and apologize if the answer is wrong
Find the sum of the first 888 terms in the following geometric series.
2+8+32+...2+8+32+...
Answer:
Step-by-step explanation:
Nice question!!! It should be ####. and that's the answer that you want
william and drebra Pierce are celebrating thier 20th anniversery by having a reciptionan a local reciption hall.They have budgeted $3,500 for their recipetion. If the reciption hall charges $70 cleanup plus $33 per person, Find the greatest number of people that they may invite and still stya within their budget
drebra and William Pierce is hosting a reception at a nearby reception hall to commemorate their 20th anniversary. The number of people are invited in the reception are 104.
Given that,
drebra and William Pierce is hosting a reception at a nearby reception hall to commemorate their 20th anniversary. $3,500 has been set aside for their reception. If the prison's recreation center charges $70 for cleanup and $33 per person.
We have to determine how many guests they can invite while staying inside their budget.
The total budget of the party = $3500
Reception hall charges for clean up =$70
Extra fee per person =$33
Let us assume that the number of people are invited in the reception are be x.
Given in the question the be the clean up charge and $33 be fee per person.
We know,
The equation become
⇒ 70 +33x = 3500
33x = 3500-70
33x = 3430
x = 3430/33
x=104
Therefore, The number of people are invited in the reception are 104.
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(02.05 MC)
A group of seniors decide to spend their spring break away from home, attending at least one major event. The following table summarizes their
preferences.
Stay in state
214
Travel out of state 391
O 41.93%
What percent want to attend a festival, given that they want to stay in state?
031.72%
ous Question
Attend a concert Attend a festival
46.5%
75.92%
186
59
When considering their desire to go outside of their state, 6.94% of people say they would like to attend a festival.
A percentage is what?
A percentage of 100 is represented as a number or ratio known as a percentage.
We've got
Take in a performance Attend a concert and a festival
Remain in state 214 and 186
Travel outside of state 391 and 59
The amount of groups planning to visit a state while attending a concert=214
The amount of groups planning to leave the state to attend a concert=391
The amount of groups planning to visit a state while attending a festival=186
The amount of groups planning to leave the state to attend a festival=59
The proportion of festival-goers that desire to travel outside of their state:
= Total number of groups from all four conditions/ Number of groups wishing to attend an event while remaining outside the state.
= 59 / ( 214 + 391 + 186 + 59 ) x 100
= 59 / 850 x 100
= 6.94%
Therefore, When considering their desire to go outside of their state, 6.94% of people say they would like to attend a festival.
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it costs $45 to rent a car each day there is also a fee of $12. how much does it cost to rent a car for 5 days including fee
Answer:
it would cost $285
Step-by-step explanation:
Answer:
285 po answer
Step-by-step explanation:
Pa brainlest po plsss
Each of my children has at least two
brothers and one sister. Find the least
number of children I might have.
Answer:
4 kids.
Step-by-step explanation:
There could be 2 boys and 2 girls. Each of the 2 boys has at least one sister, and each of the 2 girls has at least two brothers.
Hope this helps!
a car travels 3.5 miles in 5 minutes. work out the average speed in miles per hour
The average speed of the car which travels 3.5 miles in 5 minutes is 42 miles per hour.
What is the average speed of the car?Speed is simply referred to as distance traveled per unit time. It is expressed mathematically as;
Speed = Distance ÷ time.
Given the data in the question;
Distance travelled = 3.5 milesTime elapsed = 5 minutesAverage speed = ?First, we convert unit of the elapsed time from minutes to hours.
Time = 5 min = ( 5/60 )hr = 5/60hr
Now, plug the given values into the speed formula and solve for speed.
Speed = 3.5 ÷ 5/60
Speed = 3.5 × 60/5
Speed = 210/5
Average speed = 42 mph
Therefore, the average speed of the car 42 mph.
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What does it mean to cube the number 18?
It means to find the cube root of 18.
It means to raise the number 18 to the exponent 2.
It means to find the square root of 18.
It means to raise the number 18 to the exponent 3.
Answer:x+y=36
xy=256
x=256/y
256/y + y = 36
256/y + y²/y = 36y/y
y² - 36y +256 = 0
use the quadratic formula to get 18+2√17 and 18-2√17. ugly numbers but they work!
Step-by-step explanation:
Question is in the picture
Answer:
(a) D = 72.05 dB (2 d.p.)
(b) I = 2.51 W/m² (2 d.p.)
Step-by-step explanation:
Given function:
[tex]\boxed{D(I)=10 \log_{10}(I)+120, \quad I\geq 0}[/tex]
where:
D is the sound intensity level (in dB).I is the sound intensity (in W/m²).Part (a)Given:
[tex]I=1.6 \times 10^{-5}\; \sf W/m^2[/tex]Substitute the given value of I into the given function and solve for D:
[tex]\begin{aligned}\implies D(1.6 \times 10^{-5}) & =10 \log_{10}(1.6 \times 10^{-5})+120\\& = 10 \log_{10}(0.000016)+120\\& = 10 (-4.795880017)+120\\& = -47.95880017+120\\&=72.04119983\\&=72.04\; \sf dB\;(2\:d.p.)\end{aligned}[/tex]
Part (b)Given:
D = 124 dBSubstitute the given value of D into the given function and solve for I:
[tex]\begin{aligned}\implies 124 & =10 \log_{10}(I)+120\\4 & =10 \log_{10}(I)\\10 \log_{10}(I)&=4\\\log_{10}(I)&=0.4\\10^{\log_{10}(I)}&=10^{0.4\\I&=2.511886432\\I&=2.51\; \sf W/m^2\; (2\:d.p.)\end{aligned}[/tex]
What is the domain of this relation?
Answer:
{-4, 0, 2, 5}
Step-by-step explanation:
The domain of a relation in a graph is a list of all the x values from the points plotted on it.
Therefore, we can take the coordinates of each point, and list all the x values. (You can't use the same number more than once)
Once you list all the x values, you put them in order from least to greatest, and then you're done! (make sure to use swirly brackets)
Good luck on your math journey! ^-^
6x+26x-10=8(4x+10) write a word problem that this equation,or any of its equivalent forms,represents.
6x+26x-10=8(4x+10) quadratic equation has no solution.
First, Simplify the equation:
6x + 26x + (-10) = 8(4x + 10)
Now, reorder the terms:
(-10) + 6x + 26x = 8(4x + 10)
Combine the like terms:
6x + 26x = 32x
-10 + 32x = 8(4x + 10)
Then, reorder the terms:
-10 + 32x = 8(10 + 4x)
-10 + 32x = (10 × 8 + 4x × 8)
-10 + 32x = (80 + 32x)
Add '-32x' to each side of the equation.
-10 + 32x + -32x = 80 + 32x + -32x
Again, Combine like terms:
32x + -32x = 0
-10 + 0 = 80 + 32x + -32x
-10 = 80 + 32x + -32x
Repetitively, Combine like terms:
32x + -32x = 0
-10 = 80 + 0
-10 = 80
After Solving,
-10 = 80
Thus, there is no further variable to solve.
∴ This equation is invalid, the left and right sides are not equal, therefore there is no solution.
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a heap of rubbish in the shape of a cube is being compacted into a smaller cube. given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters.
-1/16 meters per minute is the rate of change of an edge.
What is the rate of change?The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.So, the Volume of the cube: V = r³
Where the edge of the cube is represented as r.Differentiate with respect to t (time) as follows:
[tex]\frac{d V}{d t}=3 r^2 \frac{d r}{d t}[/tex]dV/dt = -3 : Cubic meters per minute
Also, V = 64 ⇒ r = ∛64 = 4Now, substitute the values:
-3 = 3(4)² dr/dt-3 = 48 dr/dtdr/dt = -3/48 = -1/16Therefore, -1/16 meters per minute is the rate of change of an edge.
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Decimal equivalent to three and nine hundredths
Answer: this bc well it decimals and those are kinda easy
3.09
Of the teacups in lexi’s tea shop, 1/6 are teal and another 2/3 are red. What fraction of the teacups are either real or red?
The fraction of the teacups that are either teal or red is 5/6.
What are fractions?A number that represents a portion of a whole is used to denote a fraction in mathematics. Any number, an amount, or an object can be a whole; a fraction is a portion or segment taken from that whole. The number is represented mathematically as a quotient, where the numerator and denominator are split. The p/q is the form used to represent fractions.Given:
Fraction of teal teacups = 1/6
Fraction of red teacups = 2/3
Fraction of the teacups are either teal or red = Fraction of teal teacups + Fraction of red teacups
= 1/6 + 2/3
= (1+4)/6
= 5/6
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PLS ANSWER PART (f) ASAP
There are a total of 54 men.
Let's take x new men who joined the club, then according to the question (22-x) new women who joined the club.
[(98 × (5 ÷ 5 + 9)) + x ÷ [(98 × (9 ÷ 5 + 9)) + (22 - x)] ÷ [(98 × (9 ÷ 5 + 9)]= 9 ÷ 11
[(98 × (5 ÷ 14)) + x ÷ [(98 × (9 ÷ 14)) + (22 - x)] ÷ [(98 × (9 ÷ 5 + 9)]= 9 ÷ 11
[35 + x] ÷ [63 + (22 - x)] = 9 ÷ 11
11 × (35 + x) = 9 × (85 - x)
385 + 11x = 765 - 9x
11x + 9x = 765 - 385
20x = 380
x = 19.
Therefore, 19 new members have joined the club.
So, Step 10: 10 + (98 × (5 ÷ 5 + 9)) = 19 + 35 = 54.
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Answer:
19
Step-by-step explanation:
Originally there are 98 members
Ratio of men to women = M:W = M/W = 5/9
The ratio of men to total number of members = M/(M + W) and this should be the same as 5/(5+9) = 5/14
Since 5/14 th of the total membership of 98 members is the number of men,
Actual number of men
= 98 x (5/14)
= 35
After 22 members join the club, the total club membership is 98 + 22 = 120
The new ration M/W = 9/11
Actual number of men members
= 120 x 9/(9+11)
= 120 x 9/20
= 6 x 9
= 54
Increase in the membership of men = 54 - 35 = 19
Michelle was fishing in her canoe at point A in the lake depicted above. After trying
to fish there, she decided to paddle due east at a steady speed of 15 miles per hour,
As she paddled, a wind blowing due south at 7 miles per hour caused a change in
her direction. To the nearest tenth of a mile, what is the velocity, represented by
vector AC, of her canoe?
A. 8.0 miles per hour
C. 16.6 miles per hour
B16.34 miles per hour
D15.0 miles per hour
Answer:
Step-by-step explanation:
Find the volume of the triangular prism,
Answer:
280 cm^3
Step-by-step explanation:
formula
1/2 * b * h * l
1/2 * 5 * 8 * 14
1/2 * 560
wikipedia
i’m not sure what the answer is help pls
Answer:
x = 33
Step-by-step explanation:
( x + 20 ) + ( 4× - 5) = 180 {m||n}
5×+20 - 5 = 180
5×+15 = 180
5× = 165
× = 33
which fraction is equivalt to 2/10
Answer: 1/5
Step-by-step explanation:
Answer:
[tex]{ \sf{ \frac{1}{5} }} \\ [/tex]
Step-by-step explanation:
[tex]{ \sf{ \frac{2 \div 2}{10 \div 2} \equiv \frac{1}{5} }} \\ [/tex]
LEAST TO GREATEST
PLS HELP
Answer:
A. {2.82, √8, √11, 3 1/2}
Step-by-step explanation:
A. {2.82, 2.83, 3.32, 3.5}
√8 = 2.82842712475 or 2.83 when rounded to the nearest hundredth.
√11 = 3.31662479036 or 3.32 when rounded to the nearest hundredth.
To find the square root you multiply a factor of a number by itself in order to get that number.
3 1/2, or 7/2 = 3.5
To convert a fraction into a decimal you divide the numerator by denominator.
B. {2.24, -2.45, 2.5, -3}
√5 = 2.2360679775 or 2.24 when rounded to the nearest hundredth.
-√6 = -2.44948974278 or -2.45 when rounded to the nearest hundredth.
2 1/2, or 5/2 = 2.5
C. {-4, -4.12, -4.24, -4.36}
-√16 = -4
-√17 = -4.12310562562 or -4.12 when rounded to the nearest hundredth.
-√18 = -4.24264068712 or -4.24 when rounded to the nearest hundredth.
-√19 = -4.35889894354 or -4.36 when rounded to the nearest hundredth.
D. {3.16, 4, 2, 1.5}
√10 = 3.16227766017 or 3.16 when rounded to the nearest hundredth
√4 = 2
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Two families went to a baseball game. The first family bought 5 pretzels and 4 sodas, which totaled $22. The second family bought 6 pretzels and 6 sodas, which totaled $30. How much did one soda cost?
$2
$3
$4
$5
Answer:
3
Step-by-step explanation:
Question:Two families went to a baseball game. The first family bought 5 pretzels and 4 sodas, which totaled $22. The second family bought 6 pretzels and 6 sodas, which totaled $30. How much did one soda cost?
first family bout 5 PRETZELS and 4 SODAS and the second family bought 6 PRETZELS and 6 SODAS
So immanently 5 is wrong because that would be too much and not fit the amount that the families spent
4 is also incorrect because the price is not reasonable it’s to high and out of budget for both of the families
3 is the only right answer also 2 is wrong (wrote this in rush)