The statement that explains why Charlotte's submission is correct is that (4³)³ simplifies to (4⁹) and (4⁹) simplifies to 2¹⁸
How to determine why Charlotte's submission is correct?From the question, the expression is given as
(43)3
Rewrite the expression properly
So, we have the following representation
(4³)³
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 4³*³
Next, we evaluate the products
So, we have the following notation
(4³)³ = 4⁹
Solving further, we need to express 4 as the square of 2
So, we have
(4³)³ = (2²)⁹
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 2²*⁹
Next, we evaluate the products
So, we have the following notation
(4³)³ = 2¹⁸
Hence, Charlotte's expression is correct
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Possible question
Charlotte states that (4³)³ can be rewritten as 2¹⁸. Which of the following explains how she is correct? Select all that apply.
The vertices of ΔABC are A(7, 3), B(−8, 6), C(0, −5). If ∆ABC is translated along the vector <−9, 5>, what are the coordinates of the vertices of ΔA'B'C' ?
Responses
A'(−2, 8), B'(−17, 11), C'(−9, 0)
A ' ( - 2 , 8 ) , B ' ( - 17 , 11 ) , C ' ( - 9 , 0 )
A'(8, −2), B'(11, −17), C'(0, −9)
A ' ( 8 , - 2 ) , B ' ( 11 , - 17 ) , C ' ( 0 , - 9 )
A'(12, −6), B'(−3, −3), C'(5, −14)
A ' ( 12 , - 6 ) , B ' ( - 3 , - 3 ) , C ' ( 5 , - 14 )
A'(16, −2), B'(1, 1), C'(9, −10)
The coordinates of the vertices of ΔA'B'C' after the transformation are (a) A'(-2, 8), B'(-17, 11), C'(-9, 0)
How to determine the vertices of ΔA'B'C'?The coordinates of the triangle are given as
ΔABC are A(7, 3), B(−8, 6), C(0, −5).
The transformation is given as
∆ABC is translated along the vector <−9, 5>
Mathematically, this can be represented as
(x, y) ⇒ (x - 9, y + 5)
When this is applied on ABC, we have:
ΔA'B'C' = A'(7 - 9, 3 + 5), B'(−8 - 9, 6 + 5), C'(0 - 9, −5 + 5)
Evaluate the computations
ΔA'B'C' = A'(-2, 8), B'(-17, 11), C'(-9, 0)
Hence, the image of the transformation is (a) A'(-2, 8), B'(-17, 11), C'(-9, 0)
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How can I solve the problem 3+4(10-8)
Addison drove 162 miles in 8 hours. What was her speed in miles per hour?
[tex]\fbox{20.25}[/tex]
To find her miles per hour, we need to divide the total miles by the total hours to find how many miles she drives in each hour.
[tex]162\div8[/tex]
[tex]=20.25[/tex]
Three friends go grocery shopping together, and each buys the same kind of oranges. LaMar buys 2 pounds (lb) and pays $7.00. Enrico buys 5 pounds and pays $17.50. Anna buys 3 pounds and pays $10.50. Identify the graph and unit price that represent the orange costs.
The unit price of the oranges bought by the three friends is $3.50 per pound.
Lamar bought 2 pounds for $7 , unit price = 7 / 2 = $ 3.5 per pound
Enrico bought 5 pounds for $17.50 , unit price = 17.50 / 5 = $ 3.5 per pound
Anna bought 3 pounds for $10.50 , unit price = 10.5/ 2 = $3.5 per pound
Hence we can see that the unit price rate for the oranges is $3.50 .
The average price of a product is calculated by dividing the total sales income by the number of units sold. Managers must supply "similar" units when a single product is given in many variations, such as different bottle sizes.
By weighting different unit selling prices higher by unit sales mix (%) for each single variant, the determination of average pricing is made practicable. We obtain pricing per statistical unit when we employ a standard rather than a genuine range of sizes and product types.
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22 more than a number divided by 4
Answer:
X / 4 + 22
Step-by-step explanation:
22 more means we add 22. Then, we take x as our variable, in this case, it is "a number". We divide x by 4, and then we add 22. x / 4 + 22.
can yall help me with this
In solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.There are three main categories of fractions in mathematics. 'Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, the wrong step will be:
(4/7) ÷ (-1/2)Then, the next step should be:
(4/7) × (-2/1)But, the steps it is given as:
(4/7) × (-2/-1)Which makes the error.
Therefore, in solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
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what are the domain and range or this exponentiAl function y=1/6.8×
We want to identify the domain and range of the following function
[tex]\frac{1}{6}\cdot8^x[/tex]Recall that the domain of a function is the set of values for the variable x, for which the function is defined. Note that we can see this function as the product of two different functions
[tex]\frac{1}{6}[/tex]and
[tex]8^x[/tex]Note that the first part (1/6) does not depend on x, so this means that it is always defined. Also, note that 8^x is always defined for any value of x. That is, if you replace x by any number, you will get another number.
So, this means that the the original function is defined for every value of x. So the domain of this function is the set of all real numbers.
If we define the equation
[tex]y=\frac{1}{6}\cdot8^x[/tex]the range is the set of all possible values that y can take. Taking a look at the functions we already identified (1/6, and 8^x) we can see that 1/6 is always a positive number, and we can also see that for every value of x, the number
8^x is always positive.
That means that the product
[tex]\frac{1}{6}\cdot8^x[/tex]is always a positive number. So, this means that the range of the function is all positive real numbers. That is the set of y such that y>0
What is the equation of the line that passes
through the point (-6, -7) and has an
undefined slope?
A line with an undefined slope would be x=___, in which you would put the x value of the coordinate. So, the equation would be x = -6
Crispy Clover, a popular vegetarian restaurant, introduced a new menu that has 20\%20%20, percent more dishes than the previous menu. The previous menu had DDD dishes.
The number of dishes the crispy clover has in his new menu can be expressed as D + (1/5)D.
Define expression.A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, and subtraction operations.
Given data -
20% more dishes are available on the new menu than the old one.
D foods were on the previous menu.
As 20% more dishes are added,
Therefore we can also write it as (20/100)D
Now the total dishes in the new menu can be expressed as
= D + (20/100)D
= D + (1/5)D
Therefore the number of dishes the crispy clover has in his new menu can be expressed as D + (1/5)D.
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The complete question is:
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has?
17. a = -3: Yes/No?
4a + 3 = -9
How many simple random samples of size 3 can be selected from a population of size 7.
By using combination, it can be obtained that
Number of simple random samples of size 3 that can be selected from a population of size 7 = 35
What is combination?
Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.
Here, concept of combination is used
Number of simple random samples of size 3 that can be selected from a population of size 7 = [tex]{7 \choose 3}[/tex] = 35
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Which of the following ratios is equivalent to 25:18?
The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .
In the question ,
it is given that ,
the ratio is 25:18 , we need an equivalent ratio .
the ratio is 25:80 which can be written in fraction as 25/80 .
writing the factors of 25 and 80 .
= (5×5)/(5×16)
we can see that 5 is the common factor in both the numerator and the denominator .
= 5/16
which can be written as
= 5:16
the equivalent ratio is 5:16 .
Therefore , The ratio that is equivalent to 25:80 is 5:16 , the correct option is (d) .
The given question is incomplete , the complete question is
Which of the following ratio is equivalent to 25:80 ?
(a) 2:5
(b) 8:5
(c) 16:5
(d) 5:16
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For which inequality is x= 5 a solutionx < 2x > 9x < 18x > 42
Let's check each inequality if the value x = 5 is part of the solution:
a. x < 2
5 is a value greater than 2, so it isn't part of the solution of this inequation.
b. x > 9
5 is lesser than 9, so it isn't part of the solution of this inequation.
c. x < 18
5 is lesser than
What is 14 3/4 - 4 1/8
The mixed fraction is express as :
[tex]a\frac{b}{c}=\frac{a\times c+b}{c}[/tex]The given expression is :
[tex]14\frac{3}{4}-4\frac{1}{8}[/tex]Simplify the mixed fraction into decimal form :
[tex]\begin{gathered} 14\frac{3}{4}=\frac{14\times4+3}{4} \\ 14\frac{3}{4}=\frac{59}{4} \\ 14\frac{3}{4}=14.75 \end{gathered}[/tex][tex]\begin{gathered} 4\frac{1}{8}=\frac{4\times8+1}{8} \\ 4\frac{1}{8}=\frac{33}{8} \\ 4\frac{1}{8}=4.125 \end{gathered}[/tex]Substitute the value and then subtarct :
[tex]\begin{gathered} 14\frac{3}{4}-4\frac{1}{8}=14.75-4.125 \\ 14\frac{3}{4}-4\frac{1}{8}=10.625 \end{gathered}[/tex]Answer : 14 3/4 - 4 1/8 = 10.625
Answer:
5/8
Step-by-step explanation:
3/4 can be multiplied by 2 to get 6/8 and now you have common denominators so you do 4 6/8 - 4 1/8
4-4= 0
6/8 - 1/8 = 5/8 so 5/8 is the answer
what 82 x 82 x 82 x 82
Answer:45212176
Step-by-step explanation:calculator
Answer:
82x82x82x82, or 82 squared to the 4th power, is 45212176.
Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 20.a. Find the standard deviation for the numbers of peas with green pods in the groups of 20
Given
Probability that a pea has green pods = 0.75
Sample of the offspring peas , n = 20
Find
Standard deviation for the numbers of peas with green pods in the groups of 20
Explanation
as we have given ,
Probability that a pea has green pods , p = 0.75
Probability that a pea do not have green pods , q = 1 - 0.75 = 0.25
n = 20
in binomial distribution ,
standard deviation is given by
[tex]\sqrt{npq}[/tex]so,
[tex]\begin{gathered} S.D=\sqrt{20\times0.75\times0.25} \\ S.D=\sqrt{3.75} \\ S.D=1.93649167\approx1.94 \end{gathered}[/tex]Final Answer
Hence , the standard deviation for the number of peas with green pods in the group of 20 is 1.94
8. Brendan ran a total of 88 miles over the course of 44 track practices.
How many track practices would it take for Brendan to run 1010 miles?
Solve using unit rate?
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
the question is about distance.
what do we use to measure distance ? things like feet, yards, meters, ...
definitely not square feet (areas) or cubic feet (volume).
it is a right-angled triangle. so Pythagoras applies
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle). in our case the 48 ft side.
a and b are the legs. in our case x and x+6.
the saved walking distance is the difference between 48 ft and the sum of the legs (which would be the walking distance, when they cannot get though the lot).
48² = x² + (x + 6)² = x² + x² + 12x + 36
2304 = 2x² + 12x + 36
1152 = x² + 6x + 18
x² + 6x - 1134 = 0
the solution for such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a) =
= (-6 ± sqrt(6² - 4×1×-1134))/(2×1) =
= (-6 ± sqrt(36 + 4536))/2 =
= (-6 ± sqrt(4572))/2 =
= -3 ± sqrt(4572/4) = -3 ± sqrt(1143) =
= -3 ± sqrt(9×127) = -3 ± 3×sqrt(127)
x1 = -3 + 3×sqrt(127) = 30.80828301...
x2 = -3 - 3×sqrt(127) = -36.80828301...
negative numbers for a distance don't make any sense, so
x = 30.80828301... is our solution.
that means the 2 legs are
30.80828301... ft
36.80828301... ft
in total they are
67.61656602... ft
and so they save
67.61656602... - 48 = 19.61656602... ft ≈
≈ 19.617 ft
by walking across the lot.
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
helpp me fast thank u pleasee
The value of x from the given equations is 0.6.
The given equations are y=4x and y=-x+3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Here, 4x=-x+3
⇒ 4x+x=3
⇒ 5x=3
⇒ x=3/5
⇒ x=0.6
Hence, the value of x from the given equations is 0.6.
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5.2=
5.2=
\,\,620(0.5)^{\frac{x}{10}}
620(0.5)
10
x
Answer:
D
Step-by-step explanation:
A number is squared. This is added to fifteen and the product of eight and the number, to give zero.
A number is squared. This is added to fifteen and the product of eight and the number, to give zero.
the algebraic expression is
Let
x ----> the number
x^2+(15+8x)=0
therefore
x^2+8x+15=0
solve the quadratic equation
Solve by using calculator
x=-5 and x=-3
A) (18,-2)
B) (18,2)
C) (15,-2)
D) (15,2)
Answer: Location of T' on the coordinate axis will be (16,7).
T (6,4) → T' (16,7).
Step-by-step explanation:
coordinate vertices of points in rectangle JKLM are:
J (-8,-8)
K (-4,-8)
L (-4,-5)
M (-8,-5)
and coordinate vertices of points in rectangle J'K'L'M' are:
J' (2,-5)
K' (6,-5)
L' (6,-2)
M' (2,-2)
coordinate vertices of points in Quadrilateral STUV are:
S (1,4)
T (6,4)
U (4,6)
V (2,6)
transformation in coordinate vertices from rectangle JKLM to rectangle J'K'L'M' is:
J (-8,-8) → J' (2,-5)
⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.
and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.
similarly for
K (-4,-8) → K' (6,-5)
⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.
and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.
L (-4,-5) → L' (6,-2)
⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.
and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.
M (-8,-5) → M' (2,-2)
⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.
and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.
So, the location of T' of the Quadrilateral S'T'U'V' on the coordinate plane will be:
along x axis the Quadrilateral will shift towards right by 10 units
So, 6 → 6+10=16
and along y axis the Quadrilateral will shift upwards by 3 units
So, 4 → 4+3=7
⇒ T (6,4) → T' (16,7).
Step-by-step explanation:
40. If you want a poll to have a margin of error of 3.06%, how large will your sample have to be? Round your answer to the nearest whole number. people
Margin of Error:
[tex]=\pm\frac{100}{\sqrt[]{n}}[/tex]ANSWER: 1068
[tex]\begin{gathered} \text{Margin of Error}=\pm\frac{1}{\sqrt[]{n}} \\ 0.0306=\pm\frac{1}{\sqrt[]{n}} \\ \sqrt[]{n}\cdot0.0306=1 \\ \frac{\sqrt[]{n}\cdot0.0306}{0.0306}=\frac{1}{0.0306} \\ \sqrt[]{n}=32.67973856 \\ (\sqrt[]{n})^2=32.67973856^2 \\ n=1,067.965312 \end{gathered}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
A Town has a population of 20000 and grows at 4% every year. What will be the population after 6 years? To the nearest whole number
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=20000(1 + 0.04)^{6} \implies A=2000(1.04)^6\implies A \approx 25306[/tex]
Find the slope and y-intercept of the line below
Mr. Peasley wrote an expression that is equivalent to
20 ÷ 1 + 4 on the board. Which expression could be the one Mr. Peasley wrote?
Responses
A 3 • 12 – 3 • 43 • 12 – 3 • 4
B 36 ÷ 3 • 2 + 1 36 ÷ 3 • 2 + 1
C 5 • 6 + 2 • 3 ÷ 2 • (1 + 5)5 • 6 + 2 • 3 ÷ 2 • (1 + 5)
D 6 + 6 • (10 + 2)
20 ÷ 1 + 4 on the board is 36 ÷ 3 • 2 + 1 36 ÷ 3 • 2 + 1.According to the order of operations, you should execute addition and subtraction last and multiply and division first, proceeding from left to right
How can addition, subtraction, multiplication, and division be calculated?According to the order of operations, you should execute addition and subtraction last and multiply and division first, proceeding from left to right. Divide and multiply from left to right as you continue. After that, add and subtract starting from the left.Remind them, if necessary, that addition and subtraction occur after multiplication and division in the order of operations.Mathematics has created standards (agreements) for how we interpret mathematical expressions in order to avoid these and other potential ambiguities. A writer who intended the contrary interpretation would have to write the sentence differently: 10 (5 2). One of these conventions stipulates that when all of the operations are the same, we go left to right. Therefore, 10 5 3 = 2.To learn more about mathematical expressions refer to:
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Simone paid $13 for an initial year's subscription to a magazine. The renewal rate is $8 per year. This situation can be represented by the equation y = 8x + 13, where x represents the number of years the subscription is renewed and y represents the total cost, in dollars. Part 1 out of 4 Complete the table of values for this situation. x (number of years renewed) 0 1 2 3 4 y (total cost in dollars) Next
Data Input
Simone paid $13 for an initial year's
The renewal rate is $8 per year
Equation
y = 8x + 13
Table
x (number of years renewed) | (total cost in dollars)
0 -> 13 dollars
1 -> 21 dollars
2 -> 29 dollars
3 -> 37 dollars
4 -> 45 dollars
It takes 5 workers 12 hours to unload one truck. How long would it take 6 workers to unload the truck?
Which points define the solution set of this linear-quadratic system of equations?
A. point A and point B
B. point D and point F
C. point C and point E
D. point B and point D
Answer:
C. C and E
Step-by-step explanation:
The solutions for a system of equations is the point of intersection of the two graphs of those equations. Here, there are two points of intersection, that is, two points where the graphs cross. The graphs cross at point C and point E.
C and E are the solutions to this system.