The simplified value of the exponential expression [tex]16^4 ~and ~16^{17}[/tex]is:
65,536 and 36,893,488,147,419,103,232.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To simplify the exponential expressions, we can use the rule that states:
[tex]a^m \times a^n = a^{m+n}[/tex]
[tex]16^4[/tex]can be simplified as follows:
[tex]16^4[/tex] = 16 x 16 x 16 x 16
[tex]= (2^4) \times (2^4) \times (2^4) \times (2^4)[/tex]
(since 16 = 2^4)
[tex]= 2^{4+4+4+4}\\= 2^{16}\\= 65,536[/tex]
Therefore, [tex]16^4[/tex] simplifies to 65,536.
[tex]16^{17}[/tex] can be simplified as follows:
[tex]= 16^{17} = 16^{16} \times 16^1\\= (2^4)^{16 \times 2^1 }\\= 2^{4\times 16 \times 2^1}\\= 2^{64} \times 2^1\\= 2^{65}[/tex]
Therefore, [tex]16^{17}[/tex] simplifies to 36,893,488,147,419,103,232.
Thus,
The simplified value of the exponential expression [tex]16^4 ~and ~16^{17}[/tex]is:
65,536 and 36,893,488,147,419,103,232.
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Write the sentence as an equation. 84 is equal to the quotient of 165 and y
Answer:
84=165/y
Step-by-step explanation:
What are the outputs of the function below?
X
g(x)
O-1, 0, -3, 4
O-1, 0, 7, 10
O6, 2, -3, 4
6, 2, 7, 10
-1
6
0
2
7
3
10
4
Answer:
it a i think
Step-by-step explanation:
The outputs of the function are 6, 2, 3, 4, and the inputs of the function are -1, 0, 7, and 10.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
here,
We have:
x g(x)
–1 6
0 2
7 -3
10 4
The table shows the input and output of the function g(x)
g(-1) = 6
g(0) = 2
g(7) = -3
g(10) = 4
The set of equivalent y-values for the function shown in the table is as follows: 6, 2, 3, 4.
Thus, the outputs of the function are 6, 2, 3, 4, and the inputs of the function are -1, 0, 7, and 10.
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How many pairs of angles are marked as congruent in the figures below?
ДД
X M
0 3
00
2
01
N
Answer: 2 pairs
Step-by-step explanation: You can tell which angles are congruent based on the curved markings. Pairs of congruent angles have matching markings. Since two of the angles are congruent to each other, we can assume that the third angles on the triangles are also congruent to each other, but it is not marked as such. So, there are only two marked pairs of congruent angles.
In which of these pairs of numbers is 2 greater than the first and less than the second? 2.1, 2.3 2, 2 2.7, 3 2 , 2
Answer: most likely 2,2 I believe
Step-by-step explanation:
In 1920, the record for a certain race was 46.4 sec. In 1970, it was 45.4 sec. Let R(t)=the record in the race and t= the number of years since 1920.
a) Find a linear function that fits the data.
b) Use the function in (a) to predict the record in 2003 and in 2006.
c) Find the year when the record will be sec.
The year will be 2018, the predicted record of 43.74
1920, the record for a certain race was 45.9 sec.
In 1950, it was 45.0 sec.
Let R(t)= the record in the race and t= the number of years since 1920.
How to calculate slope
The equation of slope of any line can be calculated using the following formula, m = rise/run = tanθ = Δy/Δx = (y2 - y1)/(x2 - x1) where, m is the slope. Δy is the change in y-coordinates.
slope = (45-45.9)/30 = -0.9/30 = -0.03
EQUATION:
R(t)= -0.03t + 45.9
b) The predicted record for 2003
t = 83 in 2003
R(83) = -0.03*83 + 45.9
R(83) = 43.41
The predicted record for 2006
t = 86 in 2006
R(86) = -0.03*86 + 45.9
R(86) = 43.32
C) Solve for t
-.02t + 45.7 = 43.74
-.02t = 43.74 - 45.7
-.02t = -1.96
t = +98
1920 + 98 = 2018, the predicted record of 43.74
This type of equations are called linear equations
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
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Simplify 9-{X -(7+X)}
A. 16
B. -2x +2
C.-2x +16
D. 2x +2
1-131. Lindsay has a paper bag full of Fruiti Tutti Chews in three different fruit flavors. She says, “If you reach into the bag, you have a chance of pulling out a Killer Kiwi. There is a chance that you will get Crazy Coconut.”
The probability of choosing a Kiwi or a coconut is 14/15.
There has to be another flavor in the bag. The probability of picking the third flavor is 1/15.
There can be 15 candies in the bag. There can be more than one possibility.
What is the probability?Probability calculates the odds that a random event would occur. The odds that the random event happens lie between 0 and 1. The more likely the event is to occur, the closer the probability value is to 1. If the probability value is 0.5, it is equally likely and unlikely that the event would happen or not happen. The sum of all probabilities should add up to 1.
The probability of choosing a Kiwi or a coconut = chances of picking a kiwi + chances of picking a coconut
1/3 + 3/5
(5 + 9) / 15 = 14/15
There has to be another flavor in the bag because the sum of the probabilities of picking a coconut or a kiwi does not add up to 1.
The probability of getting another flavor = 1 - sum of the probabilities of picking a kiwi or a coconut
1 - 14/15
15/15 - 14/15 = 1/15
The total number of candies in the bag would be a multiple of 15. The multiple of a number is the product of the number and another number. The possible number of candies are 15, 30, 45, 60, 75, 90
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in an arcade game, nick can earn up to 10 tickets depending on which slot his coin goes through. if he plays the tournament six times what is the most significant number of tickets nick earn
Answer:
This answer is most likely 60
The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = -8 and x = -2. Use the line segment to determine the average
rate of change of the function f(x) on the interval -8 ≤ x ≤-2.
Answer:
1x+mx=b
Step-by-step explanation:
1*15+3*15=60
Which of the following represents the area of a rectangle whose length is 5x − 3 and whose width is x + 7?
Use f (x) = |x|
f (x) is shifted left 5 and shifted up 2 to create g(x). Write the equation g(x)
Assuming that f(x)=x, we need to shift f(x) to the left by 5 and up by 2 in order to get g. (x). The equation g(x) may be written in mathematical terms as
G(x)=(x+5)+2
This is further explained below.
What is a function?Generally, In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.
In conclusion, Assuming f(x)=x, f (x) is shifted left 5 and shifted up 2 to create g(x). the equation g(x) is mathematically given as
G(x)=(x+5)+2
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Please show work, and brainliest will be yours.
2,094.1 nearest tenth
Answer:
The possible answer i giot when solving was: 2094.1
when rounded to the nearest tenth.
Carlos is moving his 14 books. He has packed and equal number of books into each of 3 empty boxes. How many books are in each box? How many books are left over
Answer:
The total ways the textbooks can be arranged in the 3 boxes is , which is equivalent to . If all of the math textbooks are put into the box that can hold  textbooks, there are  ways for the other textbooks to be arranged. If all of the math textbooks are put into the box that can hold  textbooks, there are  ways to choose the other book in that box, times  ways for the other books to be arranged. If all of the math textbooks are put into the box with the capability of holding  textbooks, there are  ways to choose the other 2 textbooks in that box, times  ways to arrange the other 7 textbooks. , , and , so the total number of ways the math textbooks can all be placed into the same box is . So, the probability of this occurring is . If the numerator and denominator are both divided by , we have . Simplifying the numerator yields , and dividing both numerator and denominator by  results in . This fraction cannot be simplified any further, so  and . Therefore, .
Answer:
Step-by-step explanation:
Parallel, Perpendicular, or neither? y=3x+3 y=3x-4
Type a digit that makes this statement true. 366,5_4 is divisible by 8.
Answer:
required digit is 0.
if we want two answers then 0 &8
Step-by-step explanation:
it is divisible by 8 if last three digits are divisible by 8
504÷8=63
so 366,504 is divisible by 8.
366,504÷8=45813
next term is 584
584÷8=73
so 366,584 is divisible by 8.
Why should I probably get my first credit card from the same institution that has my checking and/or savings account?Because building a relationship with a financial institution makes good OA sense You should not. You should get your first card at one of those really cool OB. student websites. A better idea is to pick your credit card company based on which gift I like Oc the best. OD Because local institutions offer better gifts
I probably get my first credit card from the same institution that has my checking and/or savings account because that is the right thing to do.
What is a credit card?The credit card is a type of card that could be used to pay for utilities. The credit card is a thin plastic card that is issued by a person's financial institution and is recognized for financial transaction.
However, the credit car should be used with caution so that a person do not accumulate a lot of debt on the credit card that could lead to the bankruptcy of the individual that is using the cards in question.
Now, I probably get my first credit card from the same institution that has my checking and/or savings account because that is the right thing to do.
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Which of the following is NOT a voluntary response sample?
***
Choose the correct answer below.
A. A local dentist asks her patients to fill out a questionnaire and mail it back to determine the quality of the care received during an office
visit.
B. Quiz scores from a college level statistics course are analyzed to determine student progress.
C. A radio station asks for call-in responses to a question concerning city recycling.
OD. A survey is taken at a mall by asking passersby if they will fill out the survey.
Of the given options, the one that is NOT a voluntary response sample is B. Quiz scores from a college level statistics course are analyzed to determine student progress.
What is a voluntary response sample?A voluntary response sample refers to a sampling method where those who are to be in the sample are asked to be in the sample. They will have a choice on accepting the offer to be in the sample.
When quiz scores from a college level statistics course are used as the sample, this is not a voluntary response sample as the students who had the scores were not consulted.
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PART B ONLY
Given: Evaluate the integral
∫x^12ln(x) dx
Solved: 1/13ln(x)x^13 - 1/169x^13 + C
(b) The application of integration by parts corresponds to applying the product rule to what product: [ ??? ]
Using integration by parts, the application of integration by parts corresponds to applying the product rule to the product of functions u(x) = ln(x) and v(x) = (x^13)/13.
What is the integration by parts?Integration by parts is similar to the inverse of the product rule, and is given as follows:
[tex]\int u dv = uv - \int v du[/tex]
Hence it is the product of functions u and dv. To identify function u, the precedence is given is as follows:
L: Logarithmic.I: Inverse.A: Arithmetic.T: Trigonometric.E: Exponential.In this problem, we have a logarithmic and an arithmetic function, hence:
Function u is the logarithmic function ln(x).Function g is ∫x^12 dx, hence x^13/13.The application of integration by parts corresponds to applying the product rule to the product of functions u(x) = ln(x) and v(x) = (x^13)/13.
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Debbie has 340 dimes in three boxes. she says that there are 4 times as many dimes in the first box as in the second and 3 times as many in the third box as in the first how much money in dollars does she have in each box
The amount of money in the first box is 8 dollars
The amount of money in the second box is 2 dollars
The amount of money in the third box is 24 dollars
Solving equationsFrom the question, we are to determine how much money there are in each box
From the given information,
"Debbie has 340 dimes in three boxes"
Let x represents the number of dimes in the first box
y represent the number of dimes in the second box
and z represent the number of dimes in the third box
Thus,
x + y + z = 340
Also, from the given information
"she says that there are 4 times as many dimes in the first box as in the second"
x = 4y
and
"3 times as many in the third box as in the first"
z = 3x
Substitute the second and third equations into the first equation
x + y + z = 340
4y + y + 3x = 340
4y + y + 3(4y) = 340
4y + y + 12y = 340
17y = 340
y = 340/17
y = 20
Substitute the value of y into the second equation
x = 4y
x = 4(20)
x = 80
Substitute the value of x into the third equation
z = 3x
z = 3(80)
z = 240
Thus,
There are 80 dimes in the first box
80 dimes = 8 dollars
There are 20 dimes in the second box
20 dimes = 2 dollars
There are 240 dimes in the third box
240 dimes = 24 dollars
Hence,
The amount of money in the first box is 8 dollars
The amount of money in the second box is 2 dollars
The amount of money in the third box is 24 dollars
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Solve negative four and one third ÷ two and one fifth.
negative nine and eight fifteenths
negative eight and one fifteenth
negative one and 32 over 33
one and 32 over 33
Answer:
Step-by-step explanation:
answer b
Answer: Its C not B
Step-by-step explanation:
Consider the line y=
1
2x+2.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
If the equation of a line is [y = (12x + 2)], then the slope of a line parallel to this line will be (Tan θ = 12) and, slope of a line perpendicular to this line will be [Tan θ = [tex](\frac{-1\1}{12})[/tex]].
As per question statement, the equation of a line is [y = (12x + 2)].
We are required to find out the slope of a line parallel to this line and the slope of a line perpendicular to this line.
To solve this question, firstly, we need to know about the standard equation of a line which goes as [tex][y = (mx +c)][/tex] where, "m" is the slope of the line and "c" is the y-intercept.
Comparing our given equation [tex][y = (12x +2)][/tex] with the above mentioned standard equation of [tex][y = (mx +c)][/tex], we get (m = 12) and (c = 2).
Hence, slope of our concerned line is 12. And since slopes of all parallel lines are equal, therefore, the slope of any line parallel to the line [tex][y = (12x +2)][/tex] will be 12 or (Tan θ = 12).
Also, we know that, the product of the slopes of two perpendicular lines, (say m₁ and m₂) is equal to (-1), i.e., [m₁*m₂ = (-1)].
Therefore, the line perpendicular to [tex][y = (12x +2)][/tex] will have a slope of [tex](\frac{-1}{m})[/tex], i.e., ([tex]\frac{-1}{12}[/tex]).
Equation: An equation is a mathematical statement that consists of two separate expressions, connected by an equal signSlope: Slope of a line is defined as the inclination of the line along the positive (x- axis) and is calculated by the formula [tex][m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}} ][/tex] where (x₁, y₁) and (x₂, y₂) are two points on the line.To learn more about Slopes (of Lines), click on the link below.
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The coordinates of triangle MNP and triangle QRS are shown in the table.
Triangle MNP
Triangle QRS
M(2, 5) N(6, 4) P(6, 8)
Q(–2, -5) R(–6, -4) S(–6, -8)
Which BEST describes the relationship, in terms of congruency, between triangle MNP and triangle QRS?
Using translation concepts, it is found that the triangles are congruent, as triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.
From the vertices of the triangles MNP and QRS, the following transformation was applied:
(x,y) -> (-x,-y).
Which is a 180º rotation about the origin, that is, triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.
Rotations do not change the side lengths, only the orientation of the triangle, hence the triangles QRS and MNP are congruent.
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You buy a carton of milk and two sandwiches for $10.One sandwich costs twice as much as a carton of milk.Your friend buys two cartons of milk and three sandwiches. How much does your friend spend?
The total amount spent by your friend is $8
How to determine the amount spent by your friend?The given parameters are:
1 carton of milk and 2 sandwiches= $10The cost of 1 sandwich = Twice carton of milkRepresent sandwich with x and carton of milk with y
So, we have
x = 2y
This also means that
y + 2x = 10
Substitute x = 2y in y + 2x = 10
y + 2(2y) = 10
This gives
5y = 10
Divide by 2
y = 2
Recall that:
x = 2y
So, we have
x =2 * 1
x = 2
Your friend's purchase can be represented as:
2y + 3x
This gives
Total = 2 * 1 + 3 * 2
Evaluate
Total = 8
Hence, the amount spent by your friend is $8
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Can anybody help me with this
Answer:
IV
Step-by-step explanation:
All of the other ones are pointing towards the square. As you can see, the arrow is not pointing towards the square in IV, therefore that is your answer.
It is known that 4 WHOEVER ANSWERS CORRECTLY WILL BE MARKED BRAINLIEST
Answer:
jsjsjsjs
Step-by-step explanation:
sjsjsjsjdjdjdjdjdjjdjdfjjfdjjdjdjdjdjdjdjdjd
Find The Value Of X.
Answer:
X=25.5
Step-by-step explanation:
First we need to apply supplementary angles.
We see that angle EGH is 78 degrees. Since Angle BEC falls on the same line as EGH we can easily calculate the Angle for BEC
Supplementary angles add up to 180. 78+x=180
180-78 is 102
4x=102
divide both sides by 4
x=25.5
24. m/PQT if m/PQR = 25° and m/RQT = 11°.
m
13 degrees mPQT = 1 degree in internal angle .
An illustration of an internal angle?
Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three interior angles. Interior angles are sometimes defined as "angles enclosed in the interior region of two parallel lines when they are intersected by a transversal."mPQR=25 degrees , mRQT=11 degrees.
mPQT=PQR-RQT
MPQT=25-11=13 degrees
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Question 8, 11.1.21 A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 9 stocks?
Explanation:
Consider 2 stocks that either go up, down, or stay unchanged. We'd have a 3 by 3 table to show the 3*3 = 3^2 = 9 different outcomes.
This idea can be extended to 3 stocks to have 3*3*3 = 3^3 = 27 outcomes
4 stocks would have 3^4 = 81 outcomes and so on
Therefore, 9 stocks have 3^9 = 19683 outcomes
The following represent statistics of weekly salaries at Acme Corporation.
Mean = $585 Median = $581 Mode = $575
First Quartile = $552
Third Quartile = $605
a) What is the most common salary? $575
Standard deviation = $28.
86th Percentile = $612
b) What salary did half the employee's salaries surpass? $581
c) About what percent of employee's salaries is below $612?
d) What percent of the employee's salaries are above $552?
e) What salary is 2 standard deviations below the mean?
f) About what percent of employee's salaries is above $592?
g) What salary is 1.5 standard deviations above the mean?
(Round answer two decimal places, if necessary.)
P64 = $592
a) This refers to the mode = $575
b) This refers to the median = $581
c) This refers to the 86th Percentile = $612
d) This refers to the First Quartile = $552
e) The salary is that is 2 standard deviations below the mean = $529
f) About 36 percent of employee's salaries is above $592
g) $627 is 1.5 standard deviations above the mean
Given data
Mean = $585
Median = $581
Mode = $575
First Quartile = $552
Third Quartile = $605
Standard deviation = $28.
86th Percentile = $612
P64 = $592
How to find the required valuesa) What is the most common salary? $575
This refers to the mode = $575
b) What salary did half the employee's salaries surpass? $581
This refers to the median = $581
c) About what percent of employee's salaries is below $612?
This refers to the 86th Percentile = $612
d) What percent of the employee's salaries are above $552?
This refers to the First Quartile = $552
e) What salary is 2 standard deviations below the mean?
The mean is given as $585 and the standard deviation is $28
2 standard deviation below the mean is:
= 585 - 2 * 28
= 585 - 56
= $529
f) About what percent of employee's salaries is above $592?
P64 is given as $592 this refers to the percent of employee's salaries that falls under 64%. so the percent above is above 64 is given as:
= 100 - 64
= 36%
g) What salary is 1.5 standard deviations above the mean?
The mean is given as $585 and the standard deviation is $28
1.5 standard deviation below the mean is:
= 585 + 1.5 * 28
= 585 + 42
= $627
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