3×3×3×3×3 in exponential form is 3⁵.
When we represent a number in the exponential form then we can say that its power has been raised by an exponent. The exponential form is an easier way of representing repeated multiplication involving base and exponents.
For example, If we have to write the exponential form of a×a×a×a×a, we can write it as a base and the number of a's as the power that is
a×a×a×a×a = a⁵
Where
a is the base
5 is the power of a
We can simply write 3×3×3×3×3 in exponential form by raising the power to the base 3,
3×3×3×3×3 = 3⁵
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Points A and B are 200 miles apart. A cyclist starting at point A and a motorcyclist starting at point B move toward each other. The speed of the cyclist is 17 mph and the speed of the motorcyclist is 83 mph. what distance from point A will they meet.
Answer:
34 miles from A
Step-by-step explanation:
Find time to cover 200 miles at ( 17 + 83 mph) = 200/100 = 2hours
cyclist will be at 2 * 17 = 34 miles from A
Pls answer fast first to answer correct is the gets brainliest
Answer:
The answer is the first option; 6^1/12
Step-by-step explanation:
We can simplify the question by using the radical rule to rewrite it as
6^1/3 ÷ 6^1/4
Then we use exponent rule which states that when we are dividing exponents of the same base, we have to subtract them. We see that the exponents are 1/3 and 1/4. So we use basic fractional division, here's the subtraction:
= 1/3 - 1/4
= 4/3 - 3/4 (we criss-crossed)
= 1/12 (we subtracted the denominators and multiplied the denominators)
Now that we have subtracted the exponents, we can write the answer as 6^1/12
Answer:
Option #1: [tex]6\frac{1}{2}[/tex]
Step-by-step explanation:
#1: Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] and [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]:
[tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}} * \frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]
#2: Combine and simplify the denominator:
- Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] by [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] = [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6} \sqrt[4]{6}^3}[/tex]
- Raise [tex]\sqrt[4]{6}[/tex] to the power of 1
- Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6}^{1+3}}[/tex]
- Add 1 and 3
- Rewrite [tex]\sqrt[4]{6}^4[/tex] as 6: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^3}{6}[/tex]
#3: Simplify the numerator:
- Rewrite the expression using the least common index of 12: [tex]\frac{\sqrt[12]{6^4} \sqrt[12]{216^3}}{6}[/tex]
- Combine using the product rule for radicals: [tex]\frac{\sqrt[3]{6^4 *216^3}}{6}[/tex]
- Rewrite 216 as [tex]6^3[/tex]: [tex]\frac{\sqrt[3]{6^{4}*(6^{3})^{3}}}{6}[/tex]
- Multiply the exponents in [tex](6^{3})^3[/tex]: [tex]\frac{\sqrt[12]{6^{4}*6^{9}}}{6}[/tex]
- Use the power rule [tex]a^{m}a^{n}=a^{m+n}[/tex] to combine exponents and add [tex]4+9[/tex]:
[tex]\frac{\sqrt[12]{6^{13}}}{6}[/tex]
- Raise 6 to the power of 16: [tex]\frac{\sqrt[12]{13060694016}}{6}[/tex]
- Rewrite 13060694016 as [tex]6^{12}*6[/tex]: [tex]\frac{\sqrt[12]{6^{12}*6}}{6}[/tex]
- Pull terms out from under the radical: [tex]\frac{6\sqrt[12]{6}}{6}[/tex]
#4: Cancel the common factor of 6:
[tex]\frac{\sqrt[12]{6}}{6}=6\frac{1}{2}[/tex]
The correct simplified answer for [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] is Option #1: [tex]6\frac{1}{2}[/tex].
The diameter of a varicocele measures more than _____ millimeters (mm). * 5 points 5 3 4 2
Answer:
A varicocele measures more than 2 mm in diameter.
Step-by-step explanation:
pampiniform plexus veins measuring more than. 2 mm in diameter at rest and which increased in diameter by 1 mm, and subjective color Doppler.
You are performing an experiment in your lab. to compare with other experiments your results must be in moles. during your final step you burn a strip of magnesium (mg), which results in 187 grams of magnesium oxide (mgo). how should you enter your results?
4.6 moles in 187 grams of magnesium oxide (mgo).
What is mole explain with example?One mole is defined as the amount of substance containing as many elementary entities (atoms, molecules, ions, electrons, radicals, etc.) as there are atoms in 12 grams of carbon - 12(6. 023×1023). The mass of one mole of a substance equals to its relative molecular mass expressed in grams.The relative formula mass of a compound is calculated by adding together the relative atomic mass values for all the atoms in its formula. Moles are units used to measure substance amount. Chemistry (Single Science) Atomic structure.
To solve ,
number of moles is equals to the mass in grams divided by RFM
RFM=16+24.3=40.3
=187/40.3
=4.6 moles of MgO
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Annual starting salaries for college graduates with degrees in business administration are generally expected to be between and . Assume that a confidence interval estimate of the population mean annual starting salary is desired. a. What is the planning value for the population standard deviation
The planning value for the population standard deviation is 4330.
Given the confidence interval 20000 and 35000.
We have to find the planning value of standard deviation.
Standard deviation is measuring dispersion of data. Uniform probability distribution has two bounds a and b. The standard deviation is given by :
s=[tex]\sqrt{(b-a)^{2}/12 }[/tex].
Annual starting salaries for college graduates be between 20000 and 35000.
It is uniform in the interval so, a=20000, b=35000.
Now we have to just put the values of a and b in the above formula to get the value of standard deviation.
s=[tex]\sqrt{(35000-20000)^{2} /12}[/tex]
=[tex]\sqrt{(15000)^{2} /12}[/tex]
=[tex]\sqrt{225000000/12}[/tex]
=[tex]\sqrt{18750000}[/tex]
=4330
Hence the planning values for the population standard deviation is 4330.
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Question is incomplete as it should includes the confidence interval of $20000 and $35000.
Which of the following are like terms?
3x and 5x²
4xy and 2x²y
6x and -3x
7x and 7y
An artist charges a $50 supply fee, plus $35 per hour for classes. write an equation to represent the total cost, c, based on the number of hours, h, of the lesson. what will be the total cost if you take a 5 hour art lesson?
The total cost in 5 hours is $225
Given that the charges of a supply fee of an artist is $50
The charges per hour classes is $35
The total cost is expressed by c
The number of hours expressed by h
We need to calculate the total cost in 5 hour lesson
As per the given statement ,
C= 50 +35h
Where h is the number of hours
h = 5 hours
C = 50 + 35h
C = 50 + 35(5)
C = 50 +175
C = $225
The total cost in 5 hours is $225
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Balu had a collection of coins. 1/2 of the coins are from asian countries, 1/3 of them from european countries, 36 are from america, how many asian coins are there
The total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.
We assume the total coins with Balu to be x.
The fraction of coins from Asian countries = 1/2.
Thus, the number of coins from the Asian countries = 1/2 of x = x/2.
The fraction of coins from European countries = 1/3.
Thus, the number of coins from the European countries = 1/3 of x = x/3.
The number of coins from America = 36.
Thus, the total number of coins = x/2 + x/3 + 36.
But, we assumed that the total number of coins is x.
Thus, we get a linear equation in one variable as follows:
x = x/2 + x/3 + 36.
We solve this equation as follows:
x = x/2 + x/3 + 36,
or, x - x/2 - x/3 = 36,
or, (6x - 3x - 2x)/6 = 36,
or, x/6 = 36,
or, x = 36*6 = 216.
Thus, the total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.
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A combination lock uses three integers in the combination, and the dial is numbered with the integers 0, 1, 2 and 3. If adjacent numbers in the combination cannot be the same, how many possible combinations are there
There can be 36 combinations.
How to find the total number of combinations?The total number of combinations of the dial can be found by using permutations without any number repeating.
There are four integers on the dial. They are 0, 1, 2, and 3.
It is also given that the numbers shouldn't repeat on the adjacent dial.
Therefore, we can say that there are 4 possible numbers on the first.
Similarly, on the second dial, only 3 numbers are possible since no two adjacent dials can have the same.
This is also the case for the third dial. It can also have 3 possible numbers.
Therefore, the total number of combinations is given by 4*3*3 = 36 combinations.
Therefore, we have found that there can be 36 combinations.
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Which of the following exponential functions is represented by the graph?
OA)
A) f(x) = -2x
B) f(x) = 2x
C) f(x) = (¹/2)-x
OD) f(x) = (¹/2)*
Answer:
D) f(x) = (1/2)^x
Step-by-step explanation:
at least that is what I think answer D is supposed to be.
I guess the other answer options are actually
A) f(x) = -2^x
B) f(x) = 2^x
C) f(x) = (1/2)^-x
let's look at the most interesting point here : (1, 1/2).
when x=1, then y = 1/2
A fails. because for x = 1 we get y = -2.
B fails. because for x = 1 we get y = 2.
C fails. because for x = 1 we get (1/2)^-1
and that is 1 / 1/2 = 2
so, the only function giving us (1, 1/2) is D, as
(1/2)¹ = 1/2
ALL U NEED TO TO IS IDENTIFY THE PROPERTYS OF EACH PROBLEM. PLS
Your Overall grade is calculated by adding 35% of your Minor grade to 65% *
of your Major grade. If your Minor grade is 84 and your Major grade is 61,
what would your overall grade be (rounded to the nearest percentage)?
A. 62
B. 67
C. 65
D. 80
E. 69
Answer:
69%
Step-by-step explanation:
Overall grade = 0.35*minor grade + 0.65*major grade
major grade: 0.65*61 = 39.65
minor grade: 0.35*84 = 29.4
total: 39.65+29.4 = 69.05
Rounded = 69%
What is the parameter of interest to compare the proportions from two populations?.
Answer:
also known as the population parameter of interest the parameter of interest is a practical value that gives you more information about the research sample or population being studied in other words these parameter define the describe the search population
what is parameter answer is given above
what is the length of side AB of the triangle?
BC is 3 across & CA is 3 up, but this creates a right-angle triangle. So, Pythagoras Theorem is used to find AB
AB = root 3^2 + 3^2
AB = 3 root 2
or 4.242640687
Thus, AB is 4.24 to 2d.p
(root means square root)
Hope this helps!
The product of three different positive integers is 8 what is the sum of these integers
Answer:
(4)(2)(1)=
4+2+1=
explanation:
Ethan donated 20% of his savings for charity. if the amount he donated was $920, then find his savings.
Total Saving of Ethan is = $4600
Saving after donating 20% = $4600-$920
=$3680
What is Percentage ?
As a fraction of 100, a percentage is a number or ratio. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent sign ("percent") is frequently used to indicate it. A % has no dimensions and no associated unit of measurement.
How to calculate percentage?
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. The formula for percentage calculation is (value/total value)100%
Solution :
Let the Saving be 100%
Donated salary 20% = $920
finding 80% of the saving
Formula for percentage:
[tex]\frac{value}{total value} *100[/tex]
=[tex]\frac{20}{100} *920[/tex]
= [tex]5*920[/tex]
= [tex]4600[/tex]
Then the Total saving =$4600
The Total saving after donating 20% = $3680
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Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents lolas purchase
The graph that represents Lola's Purchase is as shown in the attached file.
How to interpret Inequality Graph?Lola bought x pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
Representing expense in the equation form gives us;
Expense on pencils + expense on erasers < 3
Thus;
0.25X + 0.50Y < 3
Dividing through by 0.25, we have;
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
From the standard equation of line in slope intercept form, we can deduce that; Slope of this line is = (-1/2)
The correct graph is attached below.
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65. Find the perimeter & area:
13 cm
5 cm
12 cm
66.
Given, that the sides of a triangle are [tex]$5 \mathrm{~cm}, 12 \mathrm{~cm}$[/tex] and [tex]$13 \mathrm{~cm}$[/tex] semi-perimeter [tex]$=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$[/tex]
[tex]$$\begin{aligned}&\mathrm{s}=\frac{(5+12+13)}{2} \\&\mathrm{~s}=\frac{30}{2} \\&\mathrm{~s}=15 \mathrm{~cm}\end{aligned}$$[/tex]
Area of the triangle (according to Heron's Formula)
[tex]$$\begin{aligned}&=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \\&=\sqrt{15(15-5)(15-12)(15-13)} \\&=\sqrt{15(10)(3)(2)} \\&=\sqrt{900} \\&=30 \mathrm{~cm}^{2}\end{aligned}$$[/tex]
What is Heron's Formula?
Heron's formula was first given by Heron of Alexandria. It is used to calculate the area of various triangles such as equilateral, isosceles, and scalene triangles or quadrilaterals. When we know the sides of a triangle, we can use Heron's formula to find its area. Using Heron's formula, we find the area of a triangle by taking its semi-perimeter and side lengths.Heron's formula is used to calculate the area of triangles given the lengths of all their sides, as well as the area of quadrilaterals. It's also known as Hero's formula. This formula for calculating the area does not rely on the angles of a triangle. It is solely determined by the lengths of all triangle sides. It contains the term "s," which stands for semi-perimeter, which is obtained by halving a triangle's perimeter. Similarly, the concept of determining the area is extended to determine the area of quadrilaterals.To learn more about Hero's formula visit:
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What is the recursive formula for this geometric sequence?
4, -12, 36, -108, ...
Answer: C.
Step-by-step explanation:
The first number is a positive 4, which is your a1. Then the geometric sequence goes to a negative implying that it is multiplied by a negative. So the a1 = 4 and it is being multiplied by a negative 3.
Answer: C
[tex]\left \{ {{a_{1}=4 } \atop {a_{n}=a_{n-1}*(-3) }} \right.[/tex]
Step-by-step explanation:
The starting amount (a1) = 4
The rate is -3 because 4 * -3 = 12 and -12 and -12 * -3 = 36 etc.
What is the value of the discriminant for the quadratic equation zero equals 2x^2+x-3
Discriminant for the quadratic equation [tex]2x^2+x-3=0[/tex] is [tex]d=25[/tex]
How to find the d Discriminant of the quadratic equation ?
We know that the standard quadratic equation
[tex]ax^2+bx+c=0[/tex]
Discriminant of the equation is [tex]d=b^2-4ac[/tex]
Equation given in the question is
[tex]2x^2+x-3=0[/tex]
So we can find the values of [tex]a,b,c[/tex]
[tex]a=2\\b=1\\c=-3[/tex]
Substitute the values
[tex]d=1^2-4*2*(-3)\\d=1+24\\d=25[/tex]
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The volume, V, of a cylinder is V=r²h, where r is the
radius of the cylinder and h is the height. Using rounding
to the nearest whole number, which of the following is an
estimate of the volume of a cylinder with a radius of
3.75 inches and height of 6.21 inches?
Answer:
~87.33 in³
Step-by-step explanation:
All you have to to is pkug the numbers in the formula. You start by doing 3.75 as the r² and you get around 14.06. Then you multiply that by the height (6.21) which gets you around 87.33. I hope this helps!
A marble has a mass of 5 grams. juan has 17 marbles in his bag.
what is the total mass of the marbles?
o a. 22 grams
o b. 55 grams
o c. 57 grams
o d. 85 grams
Answer:
85 grams
Step-by-step explanation:
Marble: 5 g/marble
17 marbles in a bag: (17 marbles)*(5 g/marble) = 85 grams/bag of 17 marbles
A knight is placed at the origin of the cartesian plane it moves in an L shape what is the expected distance from the origin after 2016 moves
Answer:
Below in bold.
Step-by-step explanation:
Using the Pythagoras theorem:
Distance from the origin after 1 move = √(1^2 + 2^2) = √5.
So after 2016 distance is 2016√5 units.
This = 4507.9 units to the nearest tenth,
20 points
please help me i am in a rush
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Which geometric solids would model the tent?
cone and sphere
cylinder and cone
pyramid and rectangular prism
triangular prism and rectangular prism
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the
Answer:
10 points
Step-by-step explanation:
From the passage, we know:
1. Jay earned 15 points after spending $60
2. We want to know the number of points he can earn if he spends $40
We can set this up into proportions.
60:15 = 40:x
The x is the number of points he will get after spending $40.
15(40) = 60x
600 = 60x
x = 10
Jay will earn 10 points if he uses $40.
If a rectangular cross-section with coordinates at (1, 1), (1, 4), (3, 4) and (3, 1) is rotated about the line y = 1, what will be the resulting three-dimensional object? cone cylinder sphere pyramid
Answer:
Step-by-step explanation:
Comment
The first thing you ought to notice is that the original shape is a rectangle, with 2 of the y coordinates of the 4 points of 1. What that statement means is that two of the points (1,1) and (3,1) both sit on the line y = 1. they don't move. The other two points do move and they form a circular shape. So what you are going to get is a cylinder.
Answer: cylinder
Answer: 345
Step-by-step explanation: the alls
Which statement is true regarding the graphed functions?
141x
12-
10-
g(x)
8-
3)
6
fin
2+
7-6-5-4-3-2-12 1 2 3 4 5 6
-4
-6
-8+
ܘ
-10+
-12+
-14
f(x)
个x
X
The true statement regarding the graphed function is that f(-2) = g(-2).
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given is a graphed function.
The graph contains two functions f(x) and g(x).
From the graph, it is clear that,
The two graphs intersect at a certain point, where the both functions passes through.
The intersecting point is (-2, 4).
This point can be written as (-2, f(-2)) and (-2, g(-2)).
This implies that,
f(-2) = g(-2)
Hence the true statement is f(-2) = g(-2).
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Your question is incomplete. The complete question is as given below.
I need help!!! I don't get it.
The ship's horizontal distance from the lighthouse is 1930.59 feet. Using trigonometric ratio 'tanθ' the distance is calculated.
What are trigonometric ratios?The trigonometric ratios are used for determining the lengths of the right-angled triangle. There are six basic trigonometric ratios. they are:
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
sec θ = hypotenuse/adjacent
cosec θ = hypotenuse/opposite
cot θ = adjacent/opposite
Calculation:It is given that,
The height of the bacon-light is 135 feet above the water
Consider the horizontal distance between the boat and the lighthouse = x feet
The angle of elevation is given as 4°
Constructing a model as below in the figure.
From the trigonometric ratios, we have
tan θ = 135/x
⇒ tan 4° = 135/x
⇒ x = 135/tan 4°
∴ x = 1930.589 feet ≅ 1930.59 feet (rounding to the nearest hundredth of a foot)
Therefore, the ship's horizontal distance from the lighthouse is 1930.59 feet.
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The combination for opening a safe is a four-digit number made up of different digits. How many different comninations can you make, using only add digits?
There are 625 different 4-digit codes only made with odd numbers.
How many different combinations can you make?To find the total number of combinations, we need to find the number of options for each one of the digits.
There are 4 digits, such that each digit can only be an odd number.
For the first digit, there are 5 options {1, 3, 5, 7, 9}For the second digit, there are 5 options {1, 3, 5, 7, 9}For the third digit, there are 5 options {1, 3, 5, 7, 9}For the fourth digit, there are 5 options {1, 3, 5, 7, 9}The total number of different combinations is given by the product between the numbers of options, so we have:
C = 5*5*5*5 = 625.
There are 625 different 4-digit codes only made with odd numbers.
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