The reminder of 2 to the 100th power divided by 5 is 1
What is the reminder when 2 raised to the power of 100 is divided by 5?2 to the 100th power is:
[tex]2^{100}[/tex] = 1,267,650,600,228,229,401,496,703,205,376
Then dividing 2 to the 100th power by 5:
1,267,650,600,228,229,401,496,703,205,376 / 5 = 253,530,120,045,645,880,299,340,641,075 (without considering the decimal value)
This tells us how many times 5 can divide 2 to the 100th power.
Next, we need to multiply the answer obtained from the division by 5 (since we used 5 to divide):
253,530,120,045,645,880,299,340,641,075 x 5 = 1,267,650,600,228,229,401,496,703,205,375
Lastly, subtracting our last answer from the value of 2 to the 100th power will give us the reminder:
1,267,650,600,228,229,401,496,703,205,376 - 1,267,650,600,228,229,401,496,703,205,375 = 1
Therefore, the reminder when 2 raised to the power of 100 is divided by 5 is 1.
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What’s the answer plss
Answer: 8.4cm
Step-by-step explanation:
sin cos tan
SOH CAH TOA
It is cos because CAH does not have opposite (o) in it and we want to find the opposite.
O is opposite (opposite angle)
A is adjacent (next to angle)
H is hypotenuse (opposite right angle)
This is how I remember it
Cos(61)*17.4=8.435
8.4cm
Given mn, find the value of x.
(5X+28)°
(7x-4)°
Answer:
x = 16
Step-by-step explanation:
Kadeem and Quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles and hour. Quinn drives at a constant of 75 miles an hour. Who takes longer to drive 25 miles? How much longer?
Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.
Who takes longer to drive 25 miles?
Remember the relation:
Speed*time = distance.
Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.
Here we know that:
Kadeem drives at a constant speed of 50mi/h
Quinn drives at a constant speed of 75 mi/h.
Replacing that in the equation:
Kadeem's case:
(50 mi/h)*t = 25mi
t = (25 mi)/(50 mi/h) = 0.5 hours.
Quinn's case:
t = (25mi)/(75 mi/h) = 0.33 hours.
So Kadeem takes longer.
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jim is six feet tall, and his shadow is $16$ feet long. the flagpole he is standing next to casts a shadow that is $72$ feet long. how tall is the flagpole, in feet?
The height of the flagpole is 27 feet.
Given,
If two triangles are similar, sides of these triangles will be proportional.
Height of the flagpole = h feet
Shadow castes by the flagpole = 72 feet
Height of the person = 6 feet
Shadow casted by the person = 16 feet
By using the property of similar triangles,
Hence, h/6 = 72/16
h = (6×72)/ 16
h = 27 feet
Therefore, The height of the flagpole is 27 feet.
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The table shows the inputs and outputs for the function f (x) = -7x-5.Input-10-5O5Output65?-5-40What is the output value of the function when the input is –5?403050
Answer:
30
Explanation:
To know the output value of the function, we need to replace x by -5 and calculated f(x). So:
[tex]\begin{gathered} f(x)=-7x-5 \\ f(-5)=-7(-5)-5 \\ f(-5)=35-5 \\ f(-5)=30 \end{gathered}[/tex]Therefore, if the input x is -5, the output f(x) is 30
So, the answer is 30.
What does dilation mean,
Answer: Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.
Answer: a transformation, which is used to resize the object
Step-by-step explanation:
the shape changes size but not shape
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
Responses
A 18
B 18 2/3
C 19
D 19 2/3
Answer:
the answer for your question is option A
Answer:b
Step-by-step explanation:
Can someone please help solve the attached :) it's on simultaneous equations combined with congruent triangles
Answer:
2a + b = 180
a + b = 118
a = 64, b = 56
Step-by-step explanation:
If you look at the triangle on the top right of the diagonal, there are 3 angles a, a and b. Since the 3 angles of a triangle add up to 180°
a + a + b = 180
=> 2a + b = 180.......(1)
We are given that the largest angle is 118°
The largest angle of the parallelogram is a + b. Remember that opposite angles of a parallelogram are equal and the sum of the angles add up to 360
Therefore a + b = 118 ....(2)
Given equations (1) and (2), subtract (1) from (2):
Eq (1) - Eq(2) :
2a + b - (a + b) = 180 - 118
a = 62
Substitute for a in equation (2) to get
a + b = 118
62 + b = 118
b = 118 - 62 = 56
So the two angles are a = 64° and b = 56°
Answer:
a = 62, b = 56
Step-by-step explanation:
given the largest angle is 118° , then
a + b = 118 ( subtract b from both sides )
a = 118 - b → (1)
the sum of the interior angles of a quadrilateral = 360°
the angle adjacent to a is b ( alternate angles ) , then
a + b + a + a + b + a = 360
4a + 2b = 360 → (2)
substitute a = 118 - b into (2)
4(118 - b) + 2b = 360
472 - 4b + 2b = 360
472 - 2b = 360 ( subtract 472 from both sides )
- 2b = - 112 ( divide both sides by - 2 )
b = 56
substitute b = 56 into (1)
a = 118 - 56 = 62
a = 62 and b = 56
Select all the equations that have no solution. (Select all that apply.)
a. 2t+1=1+ 2t
b. 2t+1 = 2t
c. 2(t+1) = 2t + 1
d. 2t+t=2t+1
e. 2t = 1
The equations that have No solution are2t + 1 = 1 + 2t , 2t + 1 = 2t and 2(t+1) = 2t + 1 , the correct options are (a) , (b) and (c) .
In the question ,
equations are given ,
we have to find which equation have NO Solution .
So,
(a) First equation is given as
2t + 1 = 1 + 2t
On rewriting the terms , we get
2t - 2t = 1 - 1
0 = 1-1 ,
we cannot find the solution of x .
hence this equation has No solution .
(b) equation is
2t + 1 = 2t
On rewriting the terms , we get
2t -2t = -1
0 = -1
hence ,this equation have No Solution .
(c) equation is 2(t+1) = 2t + 1
2t + 2 = 2t + 1
2t - 2t = 1 - 2
0 = -1
hence , this equation have No Solution .
(d) equation is 2t+t=2t+1
3t = 2t + 1
3t - 2t = 1
t = 1
hence , this equation have Unique Solution .
(e) equation is 2t = 1
So, t = 1/2
hence , this equation have Unique Solution .
Therefore , The equations that have No solution are 2t + 1 = 2t and 2(t+1) = 2t + 1 , the correct options are (a) , (b) and (c) .
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Which expressions are equivalent to 46 ?Choose all answers that apply:A6 + 2(b + 26)B36 +62(26)
hello
to solve this question, we just have to find the expression that is equal to 4b
option A
[tex]b+2(b+2b)=b+2b+4b=7b[/tex]option a is incorrect
let's look at option B
[tex]3b+b=4b[/tex]option B is correct
and finally option C
[tex]2(2b)=4b[/tex]option C is correct
from the calculations above, option B and C are the right answers
an= a(n-1) +15; a1=8
Answer:
an=7/2
Step-by-step explanation:
an=a(n-1)+15
given a1=8
multiply; a(n-1)
a(n-1)=an-a1
enter an-a1 in the equation
an=an-8+15
an=an+7
collect like terms;
an-an=(-7)
divide by negative both side
an-an/(-)=(-(-7)
2an=7
divide by 2 both side
2an/2=7/2
therefore the answer is an=7/2
the population of elk in a national forest was measured to be 12,000 in 2003, and was measured again to be 12,700 in 2004. if the population continues to grow linearly at this rate, what will the elk population be in 2014?
The elk population in 2014 will be 19,700 ,A population is an identified grouping of objects with the purpose of analysis and data collection.
What is population?A population is an identified grouping of objects with the purpose of analysis and data collection. Examples include people and animals. It comprises of a related collection of species that live in a specific area and have the ability to interbreed.
The population increased by 12,700-12,000 = 700 between the two measures, however, it did so over a period of 1 year, from 2004 to 2003. Divide 700 elk by 1
The elk population in 2014 will be 19,700We must first establish the method
2014=700 should add 10 times then we will get the 2014th year population.
so the population of 2014th will 19700
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The area of a rectangular field is 5082 yd². If the length of the field is 77 yards, what is its width?
Answer:
The width is 66 yardsStep-by-step explanation:
Area of rectangle formula:
A = lw, where l- length, w- widthGivenA = 5082 yd²,l = 77 yd.SolutionFind the width by substituting the given values:
5082 = 77ww = 5082/77w = 66 ydLast year the debate club had 25 members. This year there are 37 members in the club. Estimate the percent change in the number of club members.
Answer:
There was a 48% increase from last year.
Step-by-step explanation:
Last year the debate club had 25 members. This year there are 37 members in the club. Estimate the percent change in the number of club members.
= (37 - 25) / 25
= -12 / 25
= 0.48 or 48%
There was a 48% increase from last year.
check:
25 * 1.48 = 37
In one year, a school uses 13,480 pieces of white paper, 7,880 fewer pieces of blue paper thanwhite paper, and 1,500 fewer pieces of yellow paper than blue paper. How many pieces of paperdoes the school use in all?
Answer:
23,180 pieces
Explanation:
The number of white paper used = 13,480 pieces
Since they used 7,880 fewer pieces of blue paper than white paper
The number of blue paper used = 13,480 - 7880 =5,600 pieces
They also used 1,500 fewer pieces of yellow paper than blue paper.
The number of yellow paper used = 5,600-1500 =4100 pieces
Therefore. the total number of pieces of paper
=13,480 + 5,600 + 4100
=23,180 pieces
Identify the partial quotient in the first step of this problem, as shown:
Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
-83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
4357/21 - 4200
Take LCM as 21.
4357-88200/21
-83843/21
=-3992.5
Hence -83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
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Determine whether the given value is from a discrete or continuous data set.When a car is randomly selected, it is found to have a gas tank that can hold 19.9 gal.
Explanation
We are asked to determine if the question is a continuous or discrete data set
The discrete data set is a data set that can be counted
Continuous data set are data that can be measured
For the given question, the answer will be option A
Help me solve question 1 on my algebra homework please
Two lines are parallel if they hay the same slope.
The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph, line m passes through the points (0, 1) and (3,3), then its slope is:
[tex]m=\frac{3-1}{3-0}=\frac{2}{3}[/tex]Equation of a line in slope-intercept form
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1, y2) is a point on the line.
The new line has to pass through point P(1, -2). Substituting with this point and m = 2/3 into the general formula:
[tex]\begin{gathered} y-(-2)=\frac{2}{3}(x-1) \\ y+2=\frac{2}{3}(x-1) \end{gathered}[/tex]
in linear regression, the fitted value is the: a. predicted value of the dependent variable b. predicted value of the independent value c. predicted value of the slope d. predicted value of the intercept e. none of these options
predicted value of the slope , A regression model called simple linear regression uses a straight line to calculate the association between one independent variable and one dependent variable.
What is linear regression?
When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable, and multiple linear regression is used when there are numerous variables.
A regression model called simple linear regression uses a straight line to calculate the association between one independent variable and one dependent variable. Both variables ought to have numerical values.
When the parameters are linear, a regression equation (or function) is said to be linear in statistics. Although the predictor variables can be transformed in ways that result in curvature, the equation must be linear in the parameters.
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in linear regression, the fitted value is the: predicted value of the dependent variable
When you enter the values of the predictors, factor levels, and other inputs into a statistical model, the predicted mean response value is known as the fitted value.
What is the predicted variable called?The independent variable, commonly referred to as the predictor variable, is used to forecast dependent variables. In data science and the scientific method, predictor variables are used rather frequently.Regression models that fit data well produce predicted values that closely match the values of the actual data. If there were no useful predictor variables, the mean model, which utilizes the mean for every predicted value, would typically be employed.Researchers can anticipate or explain variation in one variable based on another variable using regression. Defined terms: The response variable is the one that scientists are attempting to predict or explain. Because it is reliant on another variable, it is also sometimes referred to as the dependent variable.To learn more about predicted variable refer to:
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What is the effect on the graph of f(x) = 1/xwhen it is transformed to
g(x) = 1/x + 17?
OA. The graph of f(x) is shifted 17 units to the left.
OB. The graph of f(x) is shifted 17 units up.
OC. The graph of f(x) is shifted 17 units down.
O D. The graph of f(x) is shifted 17 units to the right.
The correct option is option B that is "The graph of f(x) is shifted 17 units up". It is shifted 17 units up. By adding 17 to the equation, y increases by 17. If y increases by 17, the graph shifts up by 17.
What is graph?In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to connected and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other types of graphs.
What is transformation in graph?The process of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the modification of algebraic equations, it is a typical kind of algebraic problem.
It is shifted 17 units up.
By adding 17 to the equation, y increases by 17.
If y increases by 17, the graph shifts up by 17.
Option B, "The graph of f(x) is shifted 17 units up," is the answer. It is moved upward 17 units. Adding 17 to the formula causes y to rise by 17. The graph moves up 17 units if y rises by 17.
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a fence is to be built to enclose a rectangular area of 280 square feet. the fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 13 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
Fencing of any rectangular region is basically represent perimeter of that rectangular region.
For most economical fencing, length L = 21.05 feet and width W = 13.301 feet.
How to estimate the length and width of the rectangular region?Area of rectangular region is 280 square feet.
And length is L and width is W.
Area of rectangular region = L × W=280 square feet
W=280 / L
Since, The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot.
Therefore, Total cost, C = 6(2L + W) + 13W = 12 L + 19 W
Total cost, C = 12 L+ 5,320 / L
To find most economical cost, differentiate above function and equate to zero.
C' = 12 - 5,320 / L²
simplifying the above equation, we get
⇒ 12 - 5,320 / L² = 0
⇒ L² = 5,320 / 12
L = 21.05 feet
Therefore, L = 21.05 feet
Substituting value of L in area equation.
We get, W = 13.301 feet.
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G(x)=|x-2|
How do u solve this?
Please help quickly!! (30 POINTS)
Given f(x)=3x^2 −5x−2.
What is the value of f(−2/3)?
The value of the function f(−2/3) will give the value 8/3.
What is the answer for f(-2/3)?A function is important to show the expression that's given.
Given: f(x) = 3x^2 −5x−2.
To find f(-2/3), we substitute x = -2/3 into the equation:
f(-2/3) = 3 x (-2/3)^2 - 5(-2/3) - 2
= 3 x 4/9 + 10/3 -2
= 12/9 + 10/3 - 2
= (12 + 30 - 18) / 9
= 24 /9
= 8/3
Therefore, f(-2/3) evaluates to 8/3.
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Answer:1700
Step-by-step explanation:
Please someone answer this ty! :)
Answer:373248
Step-by-step explanation:
Answer:
Step-by-step explanation:
12*6=72
72^3=373248
What is the arithmetic mean between 15 and 7?
Answer:
11
Step-by-step explanation:
How to find the arithmetic mean:
Add all numbers together, and divide by the amount of numbers.
Ans: 15 + 7 = 22
22 ÷ by amount of numbers =
22 ÷ 2 =
11
Ans = 11
7. Solve by using extracting square roots 4a²-25= 0
pa answer po rn
w solution po
[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]
IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.
GOODLUCK!!
Your weekly base salary is $150. You earn $20 for each cell phone that
you sell.
a. What is the minimum amount you can earn in a week?
b. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $630 a week.
c. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $750 a week.
d. The company policy is that as a part-time employee, the maximum
you can earn each week is $950. Write and solve an inequality that
represents the number of cell phones you can sell each week.
The minimum that could be earned is $150. The required inequalities are solved below:
What is an inequality?
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.
(a) The minimum that could be earned is $150.
(b) The required inequality is given as 150+20x≥630
or, 20x≥630-150
or, x≥480/20
or, x≥24
(c) The required inequality is given as 150+20x≥750
or, 20x≥750-150
or, x≥600/20
or, x≥30
(d) The required inequality is given as 150+20x≤950
or, 20x≤950-150
or, x≤800/20
or, x≤40
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Which of these ordered pairs is NOT a solution to this system
Answer:
C (4,5)
Step-by-step explanation:
See the attached image.
A bag contains 3 red, 4blue, 4 yellow, and 5 green marbles only yellow marbles will be added tp the bag. how many yellow marbles should be added to the bag to make the probability of choosing yellow marble 1/3?
Two yellow marbles are added to the bag to make the probability of choosing a yellow marble 1/3 .
There is a bag containing five green marbles, three red marbles, and four blue marbles and four yellow marbles.
The probability that a given event will happen is expressed as a number between 0 and 1 where 0 means there is no chance of the event occurring and 1 means that the outcome is certain.
There are a total of 16 marbles in the bag (5 + 3+ 4+4 = 16). This means that the probability of drawing a marble of a particular color is the number of marbles of that color divided by the total number of marbles in the bag.
Let ‘x’ number of additional yellow marbles be added to the bag.
Then, the required probability will be
(4 + x )/ (16+x ) = 1/3
=> 3(4+x) =16 +x
=> 12+3x = 16+x
=> 2x =4
=> x= 2
Hence, the required number of marbles is 2.
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quick Sarah is walking diagonally across a park as modeled by the equation y = x − 1. Suppose Marcus starts walking at the point (0, 9) so his path is perpendicular to Sarah's. At what point will Sarah's path and Marcus's path intersect?
The Sarah's path and Marcus path will intersect at the point (5,4) .
In the question ,
it is given that
the park is modeled by the equation y = x − 1 .
On comparing with the slope intercept form ,
we get
the slope as 1 .
Since both the paths are perpendicular ,
the slope for Marcus path is -1 .
hence the equation of line with slope -1 and passing through the point (0,9) is y = (-1)x + c
9 = (-1)0 + c
9 = c
so equation is y = (-1)x + 9
So to find the point of intersection , we solve both the equations .
Substituting y = x − 1 in y = (-1)x + 9 ,
we get
x − 1 = (-1)x + 9
x - 1 = -x + 9
x + x = 9 + 1
2x = 10
x = 5
So, y = 5 - 1 = 4
the point of intersection is (5,4) .
Therefore , The Sarah's path and Marcus path will intersect at the point (5,4) .
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