When 2 to the power of hundred is divided by 5 it show s remainder of 1
How to calculate the value of 2 to the 100th power divided by 52 to the 100th power is solved as follows
2 ^ 100 = 1.2676506 * 10^30
This is solved using a calculator and the solution means that
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2 (2 multiplying itself till the number of 2's are up to 100)
This gives the value = 1.2676506 * 10^30
Division of the 2^100, by 5
2^100 / 5
2^1 / 5 remainder =2
2^2 / 5 remainder = 4
2^3 / 5 remainder = 3
2^4 / 5 remainder = 1
2^5 / 5 remainder = 2
2^6 / 5 remainder = 4
2^7 / 5 remainder = 3
2^8 / 5 remainder = 1
2^9 / 5 remainder = 2
2^10 / 5 remainder = 4
2^11 / 5 remainder = 3
It can be seen that it generates a pattern which is
1243The pattern counts in 4's. If we follow the pattern and count to 2^30
= 100 / 4
= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1
This is to say
2^97 / 5 remainder = 2
2^98 / 5 remainder = 4
2^99 / 5 remainder = 3
2^100 / 5 remainder = 1
Hence 2^100 divided by 5 will give a remainder of 1
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Estimate what fraction of the 900-mile trip the car has traveled. Write your answer in simplest form.
Based on the distance of the entire trip, the fraction of the trip that the car has travelled is 514 ²/ ₇.
How far has the car gone?The diagram is divided into 7 parts which means that each part can be said to be:
= 1/7 of the journey
The car is in the 4th part so that means that the fraction of the trip that has been traveled is:
= 4 / 7
Given the total miles of the trip, this would be:
= 4/7 x 900
= 514.29
= 514 + 29 / 100
= 514 ²/ ₇
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math is not fun please help
Answer:
∠ RST = 22°
Step-by-step explanation:
since ∠ RSU = 91°
and ∠ TSU = 69°
so ∠ RST = 22°
HOW:
given that;
∠ RSU = 91°
and
∠ TSU = 69°
we would subtract 69° from 91°
91°-69°= 22°
Match each expression on the left with its equivalent on the right. Some answer choices on the right will not be used.
1,500 × 100
15
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Explain about the expression?You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.
The idea of an expression number makes use of the method of allocating single-digit numbers (1 to 9) to the letters of the English alphabet, starting with A. The main mathematical advancements utilizing these number patterns are highlighted in the next section.
An expression is, for instance, 3x - 2. While an equation, on the other hand, denotes the connection between two separate expressions via an equal to sign.
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PLEASE HELP ME ASAP :,)
Answer:
154 feet squared
Step-by-step explanation:
1. Divide 14 by 2
2. Use the equation pie times radius squared
3. Answer is 153 foot squared
Roger and Rita each drive at a constant speed between Phoenix and San Diego. Each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. Who had a head start, and how many miles was the head start?
If each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. The person that had a head start is: Rita had a 28-mile head start.
Determining the speedSlope for speed = (y² - y1) / (x² - x1)
Slope for speed = (130 - 65) / (2 - 1)
Slope for speed= 65 / 1
Slope for speed= 65 mph
Determining Roger's starting position if Roger distance is 65.
Hence,
Mile of head start = Slope of speed - Roger distance
Mile of head start = 65 mph - 65 miles
Mile of head start = 0 miles
Rita starting position if Rita distance is 93
Slope for speed = (y² - y1) / (x² - x1)
Slope for speed = (158 - 93) / (2 - 1)
Slope for speed = 65 / 1
Slope for speed = 65 mph
Mile of head start = Slope of speed - Rita distance
Mile of head start = 93 - 65
Mile of head start= 28 miles
Therefore we can conclude that Rita has a head start of 28 miles.
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Answer:
Rita had a 28-mile head start.
Step-by-step explanation:
EDGE
How do the laws of exponents apply to algebraic expressions
The laws of exponents are useful to solve algebraic expression as shown below.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
The laws of exponents (sometimes referred to as the rules of exponents) allow us to simplify expressions by using our understanding of what an exponent implies.
The goal is to write algebraic expressions as simply as you can in both situations.
Recall that an exponent indicates the number of times to multiply a number, variable, or expression by itself.
[tex]x^4=x \cdot x\cdot x\cdot x[/tex]
and, [tex](x+5)^3=(x+5)(x+5)(x+5)[/tex]
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Find the solutions to the equations 20+brainliest
The solutions to the rational equation x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1) are 7 and - 4, respectively.
How to simplify a rational equationIn this problem we find a rational equation that must be solved for x by means of algebraic properties. The complete procedure is shown below:
Step 1 - We have the following expression:
x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1)
Step 2 - Factor x² + 3 · x - 4:
x / (x + 4) = 20 / [(x + 4) · (x - 1)] + 2 / (x - 1)
Step 3 - By existence of multiplicative inverse, modulative, associative and commutative properties:
[x · (x - 1)] / [(x + 4) · (x - 1)] = 20 / [(x + 4) · (x - 1)] + [2 · (x + 4)] / [(x + 4) · (x - 1)]
Step 4 - By compatibility with multiplication, existence of multiplicative inverse, modulative, associative and commutative properties:
x · (x - 1) = 20 + 2 · (x + 4)
Step 5 - By distributive property:
x² - x = 20 + 2 · x + 8
Step 6 - By compatibility with addition, distributive, modulative and associative properties:
x² - 3 · x - 28 = 0
Step 7 - Factor x² - 3 · x - 28:
(x - 7) · (x + 4) = 0
Step 8 - By understanding the factors found in the previous, we get the folowing result:
x = 7 or x = - 4 Result
The solution to the equation are 7 and - 4.
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find the solution of the system of equations
9x+y=28
3x+3y=-12
Answer:
(4, - 8 )
Step-by-step explanation:
9x + y = 28 ( subtract 9x from both sides )
y = 28 - 9x → (1)
3x + 3y = - 12
substitute y = 28 - 9x into (2)
3x + 3(28 - 9x) = - 12 ← distribute parenthesis on left side and substitute
3x + 84 - 27x = - 12
- 24x + 84 = - 12 ( subtract 84 from both sides )
- 24x = - 96 ( divide both sides by - 24 )
x = 4
substitute x = 4 into (1)
y = 28 - 9(4) = 28 - 36 = - 8
solution is (4, - 8 )
PLS BE DONE RIGHT AWAY. NO NEED TO GRAPH JUST SOLVE
Answer:
x/1
Step-by-step explanation:
8=-4x-4
4=-4x
(divide by -4)
1=x
Answer:
[tex]-1\geq x[/tex]
Step-by-step explanation:
[tex]8\leq -4(x-1)[/tex]
[tex]8\leq -4x+4[/tex]
[tex]8-4=-4x+4-4[/tex]
[tex]4\leq -4x[/tex]
[tex]\frac{4}{-4} \leq \frac{-4x}{-4}[/tex]
Inequality is reversed:
[tex]-1\geq x[/tex]
Hope this helps
Jenna buys three boxes of cocoa.
She gives one box to Keanu and one box to Jacoby.
What fraction of cocoa did Jenna give to her friends?
Answer: 2/3
Jenna had 3 boxes of cocoa and gave away 2, for each friend the fraction is 1/3 therefore 1/3 +1/3 =2/3.... the final fraction is 2/3.
Answer: 2/3
Step-by-step explanation:
total, Jenna had 3/3, then she gave 1/3 to two of her friends. Which makes the total boxes 2/3 of what she gave away with a remaining of 1/3. (1 box of the three boxes)
20, 33, 44, 53, 69, 75, 89, 90 Find the mean and the standard deviation. Round to the nearest thousandth.
The mean and the standard deviation of the following numbers 20, 33, 44, 53, 69, 75, 89, 90 are 59.125 and 22.461 respectively
What are mean and standard deviation?The mean is the average value in a collection and a standard deviation is the average amount of variability in a data.
mean= sum of data in the collection/ number of data
= (20+33+44+53+69+75+89+90)/8 = 473/8 = 59.125( nearest thousandth)
standard deviation= sum of √(x- mean)^2/ number of data while x is each number in the data
finding (x- mean)^2 for each value of x
(20-59.125)^2=848.266
(33-59.125)^2=682.516
(44-59.125)^2=228.766
(53-59.125)^2=37.516
(69-59.125)^2=102.516
(75-59.125)^2= 260.016
(89-59.125)^2= 907.516
(90-59.125)^2= 968.766
S.D= √(848.266+682.516+228.766+37.516+102.516+260.016+907.516+968.766)/8 =
√504.484
Therefore S.D =22.461 ( to the nearest thousandth)
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Maths problem in indices. Pls help
Answer:
x = 9
Step-by-step explanation:
using the rule of indices
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]5^{x}[/tex] = [tex]\frac{5^{8} }{5^{-1} }[/tex] = [tex]5^{(8-(-1))}[/tex] = [tex]5^{(8+1)}[/tex] = [tex]5^{9}[/tex]
since bases on both sides are equal, both 5 , then equate indices
x = 9
Question 3 of 5
A Galapagos penguin can walk mile in an hour. How many hours would it
take the penguin to walk mile?
O A. x = hour
OB. +=
hours
O c.
hour
OD. + hours
-
Answer:
1 hour
Step-by-step explanation:
Since the penguin supposedly walks a 1 mile per hour, it would take one hour to achieve 1 mile
please fill in the missing
The spaces with inputs; 5 has an output of 16 × 4 + 6 × 25, 100 has an output of 16 × 99 + 6 × 10000, and p has an output of 16 × (p-1)+ 6 × p².
How to fill the output spaces.Following the given three examples of the outputs from inputs 1, 3 and 7, we will discover a pattern of subtracting 1 from an input, multiply the result by 16, and then add the square of the input multiplied by 6 to it.
We will derive the missing outputs as follows;
For input 5:
5 - 1= 4
16 × 4
16 × 4 + 6 × 5²
16 × 4 + 6 × 25
For input 100:
100 - 1 = 99
16 × 99
16 × 99 + 6 × 100²
16 × 99 + 6 × 10000
For input p:
p - 1
16 × (p - 1)
16 × (p - 1) + 6 × p²
Hence, the input 5 gives an output 16 × 4 + 6 × 25, input 100 gives an output 16 × 99 + 6 × 10000 and input p gives an output of 16 × (p - 1) + 6 × p² from the reasoned pattern.
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f(x)= x-6/2
g(x)=√x-4
Express the function gf in the form gf(x) = ...
Give your answer as simply as possible.
The function is given below
What is a function?
The value of a function f at an element x of its domain is indicated by f(x); the numerical value resulting from the function evaluation at a given input value is expressed by substituting x with this value; for example, the value of f at x = 4 is denoted by f(x) (4). When the function is not named and is represented by an expression E, the function's value at, say, x = 4 can be expressed by E|x=4. In science, engineering, and the bulk of the mathematical disciplines, functions are commonly used. Functions are claimed to be "the central objects of research" in most branches of mathematics.
The given function is
f(x) = x - 6/2
The function in gf is
g{f(x)} = √(x - 6/2) - 4
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The value of the required composite function is [tex]g(f(x))=\sqrt{x-\frac{6}{2} } -4[/tex].
What is a composite function?
When the result of one function is utilized as the input for another, a composite function is created.
Given that:
[tex]f(x)=x-\frac{6}{2}[/tex] and [tex]g(x)=\sqrt{x}-4[/tex]
To find the composite function [tex]g(f(x))[/tex], it is required to use the output of the first function as the input of the second function. It means that replace [tex]x[/tex] by [tex]f(x)[/tex] in the second function as:
[tex]g(x)=\sqrt{x}-4\\g(f(x))=\sqrt{f(x)}-4[/tex]
Now, substitute the value of [tex]f(x)[/tex] on the right side of the above equation as:
[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]
Hence, the required answer is:
[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]
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what is the slope of PV
Answer: -4 (-4/1)
Step-by-step explanation:
Slope is the rate of change, or rise over run. So in this case it is negative because to get from p to v we have to go down. Sow e go down 4, and across one, but we just say -4.
WATER DEPTH An echo sounder is a device used to determine the depth of water by measuring the time it takes a sound produced just below the water surface to return, or echo, from the bottom of the body of water. The accuracy of an echo sounder is the positive difference between the depth of water reading on the echo sounder and the actual depth of water w. Write two absolute value expressions equivalent to the accuracy of an echo sounder.
The absolute value expressions of the echo sounder are |r - w| and |w - r|
How to determine the absolute value expressions of the echo sounder?The statement in the question is represented as
The accuracy of an echo sounder is the positive difference between ...
To solve further, we use the following representations
Depth of water reading = r
Actual depth = w
So, the statement becomes
The accuracy of an echo sounder is the positive difference between r and w
The difference can be represented as
Difference = r - w or Difference = w - r
Represented as absolute value expressions
Difference = |r - w| or Difference = |w - r|
Hence, the expressions are |r - w| and |w - r|
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please answer fast!!!!! find x
Step-by-step explanation:
the triangles are congruent out at least similar, so both have the same angles.
therefore,
2x = 80
x = 40
PLS HELP ON THIS 50-(-20)
Evaluate the expression. Explain your process. 3x+2. for x=4
Answer:
14
Explanation:
To evaluate the expression, we need to replace x by 4. So, the expression is equal to:
3x + 2
3(4) + 2
12 + 2
14
Therefore, the value of the expression is 14
Given a Figure whose points are A(9, 1), B(2, 3), C(-2, 4).
What would be the image of that figure if it goes under a translation (x, y) -> (x - 5, y + 8), what is the
coordinate of B'?
A. B'(-14, 11)
B. B'(3, 11)
C. B'(14, 11)
D. B'(-3, 11)
Answer:
B' (-3,11)
Step-by-step explanation:
B(2,3) The rule is saying subtract 5 from x and 8 add to y
(2 -5, 3 + 8)
(-3,11)
I dont know how to do this help!
Answer:
4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{48}[/tex] is not in simplest form, however, 48 contains a perfect square as a factor, that is 16 × 3
using the rule of radicals
[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then
[tex]\sqrt{48}[/tex]
= [tex]\sqrt{16(3)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]
= 4[tex]\sqrt{3}[/tex] ← in simplest form
Find the measure of each angle in the diagram
Your family used 27.5 gallons of gas to drive 654.5 miles. how many miles did you drive for each gallon?
Answer:
total distance = 654.5
Total gas used = 27.5
Distance per gallon = 654.5 ÷ 27.5 = 23.8
We drove 23.8 miles for each gallon of gas
Carmen participated in a walkathon to
raise money for the local library. Before the
hour-long event began, Carmen estimated
that she would walk 3.5 miles, but she
ended up walking 4 miles. What is the
percent error for Carmen's estimate?
Answer:
Step-by-step explanation:
12%
Answer:
12.5%
Step-by-step explanation:
Noah was asked to compute the product of two numbers. He misread the problem and entered the sum of the two numbers instead. Luckily he still got the right answer. One of the two numbers is $5$. What is the other number?
Answer:
1.25
Step-by-step explanation:
5 X 1.25 is 6.25 and 5 + 1.25 is 6.25
FAST PLS
Which brand of granola typically weighs more?
Brand A bags typically weigh more because the median of brand A is higher than that of brand B.
Brand B bags typically weigh more than brand A bags because there is a high outlier at 52.5.
Brand A bags typically weigh more than brand B bags because there are no outliers in the distribution.
Brand B bags typically weigh more because the range of weights is higher than that of brand A.
Answer:
brand A. The bag weights for brand A have less variability than the bag weights for brand B
10 Which relation is a function?
y =
X
-1
0
1
1
2
3
(1)
y
1
0
1
2
4
9
(x,-1
(x², 2
(2)
y
(3)
{(0,1), (2,3), (3,2), (3,4)}
(4)
i don't get it could you please help me? also please could it be quick because I have soccer practice too
The number of cups of bananas is represented by x
The number of cups of strawberries is represented by y
Note that:
[tex]\begin{gathered} 1\frac{2}{25}\text{ = }\frac{27}{25} \\ 5\frac{2}{5}=\text{ }\frac{27}{5} \\ 2\frac{18}{25}=\text{ }\frac{68}{25} \\ 13\frac{3}{5}=\text{ }\frac{68}{5} \end{gathered}[/tex]27/5 cups of strawberry is used for 27/25 cups of banana
1 cup of strawberry is used for x cups of banana
x = 27/25 ÷ 27/5
x = 27/25 x 5/27
x = 1/5
1/5 cups of banana is used for 1 cup of strawberry
Comparing the values of x with values of y in the table and writing the relationship in the form y = kx:
y = 5x
where k = 5
The constant of proportionality = 5
What is the value of the the 9 in 194.6
The place value of 9 in 194.6 is tens or 90.
According to the question,
We have the following expression:
194.6
Now, we know that place value of any digit can be found easily. The place value of the digit at the right most corner (of a number without any decimal point) is unit, left to this digit we have place value of tens, then we have hundred, then thousand, ten thousand, etc.
Now, in this case, we have a decimal point. So, we will look at the last digit before the decimal point because it's place value is unit place. And the next left digit to this is tens.
Hence, the place value of 9 in 194.6 is tens.
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