Using exponent properties, the equivalent expression is given as follows:
[tex]\left(\frac{2}{3}\right)^14[/tex]
What is the equivalent expression?Two thirds to the fourth power is given by:
[tex]\left(\frac{2}{3}\right)^4[/tex]
Two thirds to the third power is given by:
[tex]\left(\frac{2}{3}\right)^3[/tex]
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
[tex]\left(\frac{2}{3}\right)^4 \times \left(\frac{2}{3}\right)^3 \left(\frac{2}{3}\right)^{4 + 3} = \left(\frac{2}{3}\right)^7[/tex]
Then, this entire expression is raised to the second power, meaning that:
[tex]\left[\left(\frac{2}{3}\right)^7\right]^2 = \left(\frac{2}{3}\right)^7 \times \left(\frac{2}{3}\right)^7 = \left(\frac{2}{3}\right)^{7+7} = \left(\frac{2}{3}\right)^14[/tex]
[tex]\left(\frac{2}{3}\right)^14[/tex] is the equivalent expression.
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3) Which two recipes have equivalent ratios of cups of flour needed to the number
of cookies?
Recipes
Peanut Butter
Sugar
Chocolate Chip
Macadamia Nut
7th Grade Home Study Due 09/21/22
Cups of Flour Needed
3
4
2
3
Number of Cookies
48
64
25
27
Math-Aids Com
14+6divided by 2=20 divided by 2
=10
is your cousin correct?
(Answer needed)
Answer:
No
Step-by-step explanation:
Following pemdas (parentheses exponents multiplication addition subtraction) you would do division first so 6/2 equals 3 then 14+3=17 divided by 2 equals 8.5
if (x)=5x+4 find (3)?
Joel noticed that when he runs, his heart begins to beat rapidly. Joe wants to do an experiment to see if his heart beats faster the longer he runs. Which is the best design for Joel‘s experiment?
a. Joel should get a group of people to run. Then he should ask them what their heart rates were after one minute.
b. Joe should ask someone to run at one speed. Then he should run the same amount of time at another speed.
c. Joel should run at a constant speed and measure his heart rate after different amounts of time has passed.
d. Joel should run different amounts of time at many different speeds and measured the heart rate during each run.
Answer:
C
Step-by-step explanation:
We can go through the process of elimination to solve the question.
A is incorrect because they are only running for a minute and the variation between time and heart rate cannot be measured.
B is incorrect because there are too many variables to account for and they are both running for the same amount of time.
D is incorrect because there are too many variables to account for and it is not a fair test as he is running at many different speeds (you can only change the independent variable which is the time).
Hence, C is the answer. It is a fair test as he is running at different speeds and keeping everything else the same.
Write an explicit and a recursive formula for the sequence.
1, 7, 13, 19, 25, ...
Write an explicit formula. ▸
an (Simplify your answer.)
Answer:
The common difference equals: 6
The sum of the sequence equals: 176
The explicit formula of this sequence is: a_n=1+(n-1)*6
The recursive formula of this sequence is: a_n=a_((n-1))+6
1,7,13,19,25,31,37,43,49,55,61...
Step-by-step explanation:
nice :0
How to write one billion,three hundred million,two hundred and sixty six thousand in figure
Answer:
1,300,266,000
Step-by-step explanation:
Billion - 1
Hundred Million - 3
Ten Million - 0
Million - 0
Hundred Thousand - 2
Ten thousand - 6
Thousand - 6
Hundred - 0
Tens - 0
Unit - 0
4/6 ÷ 4 i need to use division to figure this out
Answer: 1/6
Step-by-step explanation:I hope i have helped u have a wonderful day or night!
3-4x=23
I’m stuck and need help
Answer:
Step-by-step explanation:
Simplifying
3 + -4x = 23
Solving
3 + -4x = 23
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + -4x = 23 + -3
Combine like terms: 3 + -3 = 0
0 + -4x = 23 + -3
-4x = 23 + -3
Combine like terms: 23 + -3 = 20
-4x = 20
Divide each side by '-4'.
x = -5
Simplifying
x = -5
Use the table to find how many quarts are equivalent to 7 gallons.
There are
quarts in 7 gallons.
28 quarts are equivalent to 7 gallons
How to find how many quarts are equivalent to 7 gallons?The table represents a proportional relationship or proportional linear function
A proportional linear function is represented as
y = kx
Where
k represents the proportionality constant
y represents the number of quarts
x represents the number of gallons
When x = 14 and y = 56, we have:
56 = 14k
Divide by 14
k = 4
Substitute k = 4 in y = kx
y = 4x
When x = 7, we have
y = 4 * 7
Evaluate
y = 28
Hence, 28 quarts are equivalent to 7 gallons
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You deposit money in an account that earns simple
interest at an annual rate of 6%. After 8
years, the account earns $360 in interest. How much money did you deposit in the account?
By writing an exponential equation, we can conclude that the initial deposit is of $606.22
How much money did you deposit in the account?Here we know that we have an annual rate of 6%, so if you deposit an initial amount of A, the amount of money that the account has after t years is:
M(t) = A*(1 + 6%/100%)^t = A*(1.06)^t
Now, you know that after 8 years you earn (in interest) $360, then we can write:
M(8) - A = 360
A*(1.06)^8 - A = 360
Now we can solve that equation for A.
A*( (1.06)^8 - 1) = 360
A = 360/( (1.06)^8 - 1) = 606.22
The initial deposit is of $606.22
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4.) Connor went to the fair with $22. He bought a hot dog and a coke for $5 and planned to spend the rest of his money on rides that cost $1.50 each. Write and solve an inequality to represent the number of rides that Connor can afford.
The inequality represents the number of rides that Connor can afford is 1.50x+5≤22 and he can ride 11 rides
The amount Connor had when he went to the fair = $22
The cost of a hotdog and coke = $5
The cost of each ride = $1.50
Consider then number of rides he ride as x
Then, the equation of the inequality is
1.50x+5≤ 22
Solve the inequality
1.50x+5≤ 22
1.50x ≤ 17
x ≤ 11.33
He can afford 11 rides with the money he has
Hence, the inequality represents the number of rides that Connor can afford is 1.50x+5≤22 and he can ride 11 rides
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Which of the following functions is graphed below?
(Picture included)
Answer:
B. y=|x+6|-3
A square has side lengths that measure units 2√5 units
We get the perimeter 8 √ 5 units as and the area as 10 units² .
We are given that a square has side lengths that measure 2√5 units.
We know that, the perimeter of square is:
P = 4 × side units
P = 4 × 2 √ 5 units
P = 8 √ 5 units
We also know that the area of square is:
A = side²
A = ( 2 √ 5 units ) ²
A = 2 × 5 units²
A = 10 units²
Therefore, we get the perimeter 8 √ 5 units as and the area as 10 units² .
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Your question was incomplete. Please find the content below.
A square has side lengths that measure 2√5 units. Find perimeter and area.
Solve. Round your answer to the nearest tenth.
90.97 ÷ 8.6
Please show all of your work
Answer:
10.6
Step-by-step explanation:
Answer:
10.6
Step-by-step explanation:
90.97 divided by 8.6 = 10.57790697
rounded to the nearest tenth = 10.6
Find the 98th term of the arithmetic sequence 8, 24, 40, ...8,24,40,...
Answer:
1576
Step-by-step explanation:
The arithmetic sequence goes up by 16 each term. So if you are trying to find the 98th term, multiply 16 by 98. This results in the number 1568. Now because the arithmetic sequence starts at 8, simply add 8 to the number, and the answer is 1576
Write an expression for the total length of the line segments, and simplify it.
z z 8 and x x x
HELPPP PLEASEEEE
Step-by-step explanation:
Please help me fast. Trying to figure this out. Answer a-C. You don’t need to explain
Answer:
The value of b would be $25 since it's the initial amt. The value of m would be $8. The equation would be y=8x+25
PLEASE HELPPP
You are given a bag with 3 cubes (1 green and 2 white). You put all 3 cubes in a bag and shake the bag and pick a cube. If you pick a green cube, you get 2 points. If you pick a white cube, you get 1 point.
If you play the game 15 times, how many times do you expect to select a green cube?
a)
5
b)
10
c)
15
d)
20
Answer: a) 5
Step-by-step explanation:
Answer:
A:5
Step-by-step explanation:
I say 5 times because you said '1 green cube and 2 whites' it is very possible you can get green 5 times but 10, 15, and 20 times seems a bit lucky is maybe the word i'm looking for but overall i say 5 because 5 is possible. Virtual smile ; )
I really hope i helped
Find the distance between two points.
P(5\sqrt{x} 3,7\sqrt{x} 5),Q(\sqrt{x} 3,-\sqrt{x} 5)
The distance between the two points is approximately 19.18 units
The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance formula is usedto calculate the distance between two points.
In 1731, the distance formula itself was first made public. Pythagorean distance is another name for Euclidean distance. The Pythagoras is used to derive the distance formula.
If two point are given as A [tex](x_1,y_1)[/tex] and B [tex](x_2,y_2)[/tex] then the distance between the two points or the length of AB is calculated using the formula:
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
The co ordinates of the two points are given as [tex](5\sqrt{3},7\sqrt5 )[/tex] and [tex](-\sqrt{3},-\sqrt{5} )[/tex].
Therefore distance between the points will be given by:
[tex]=\sqrt{(5\sqrt{3} - \sqrt{3} )^2 + (7\sqrt{5} -(-\sqrt{5} )^2}\\=\sqrt{(4\sqrt{3})^2+(8\sqrt{5})^2 }\\=\sqrt{48+320}\\=\sqrt{368}\\\approx19.18[/tex]
The distance between the two points is approximately 19.18 units.
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ANSWER THE FOLLOWING WITH COMPLETE SOLUTIONS:
The solution of the rational inequality are-
x ≤ 9 x > 1What is meant by the rational inequality?A rational inequality is one that includes a rational expression.
To solve a rational inequality, first locate the zeroes (from the denominator) and also the undefined points (from the denominator). These zeroes and undefined points are used to divide this same number line into intervals. Then you locate the rational's sign on each interval.1. (3x - 1)/(x + 4) ≤ 2
Solving the equation.
3x - 1 ≤ 2(x + 4)
3x - 1 ≤ 2x + 8
Placing the constants and the variable on different side.
3x - 2x ≤ 8 + 1
x ≤ 9
Thus, the value of 'x' is less than equal to 9.
2. 2x/(x + 1) > 1
Simplifying;
2x > x + 1
Placing the constants and the variable on different side.
2x - x > 1
x > 1
In this, the value of the x is less than 1.
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The graph above shows the graphs of the cost (in green) and revenue (in blue) functions for a company that manufactures and sells small radios.
a) How many radios must be produced and sold to break even?
Answer:
b) What is the dollar amount coming in and going out if the company just breaks even?
Answer:
c) Use the formulas to write the company's profit function, (), from producing and selling radios.
(Notice in this problem, you must enter the entire function, not just the right hand side)
Answer:
d) How much profit will the company earn if it produces and sells 500 radios?
Answer:
The company must sell 400 radios to break even, i.e, when the revenue function and cost function is same.
The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.
The cost function is the total cost of production of the item which includes the cost of raw materials, labor, transport and establishment costs.
The cost function and the revenue function is given as:
Cost function is C(x) =5000 + 7.5x
And the revenue function is R(x) = 20x
a)In the break even point cost will be equal to revenue
so, C(x)=R(x)
or,5000+7.5x=20x
or,12.5x=5000
or, x=5000÷12.5
or, x=400
The number of radios produced to break even is 400.
(b)When the company breaks even then x=400
∴R(200)=200×20=8000
So the amount of money is dollars that is coming in or going out is given by 8000.
(c)We know that the profit=Revenue - cost
So the required profit function is given by:
p(x)=R(x)-C(x)
or, p(x)=20x-5000-7.5x
or,p(x)=12.5x-5000
(d)The company sells 500 radios
Therefore profit will be given by
p(500)=12.5×500-5000
or,p(500)=6250-5000
or, p(500)=1250
So on selling 500 radios the company will earn $1875.
Disclaimer: The revenue and cost function of the equation are
C(x) =5000 + 7.5x and R(x) = 20x .
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Find the values of x and y.
PLEASE HELP ME I DONT GET THIS
Answer:x=60 y=61
Step-by-step explanation:
lmk if you want an explanation
Can someone help me please
Answer: B': (-3, 4)
C': (-3, 0)
D': (-2, 0)
E': (-2, 4)
Step-by-step explanation:
270 degrees counterclockwise=
(360-270) degrees clockwise=90 degrees clockwise
In a 90 degree clockwise rotation about the origin for this rectangle, the x and y coordinates of the rectangle's edges are swapped, but the y-coordinates are negated. This is because the transformation is happening over the x-axis, where the y-values will be changing signs while the x-values will still have the same signs.
B: (-4, -3) ==> (-3, -4) ==> B': (-3, 4)
C: (0, -3) ==> C': (-3, 0)
D: (0, -2) ==> D': (-2, 0)
E: (-4, -2) ==> (-2, -4) ==> E': (-2, 4)
You walk 14 miles to a shoe store. Then you walk another 15 miles to a music store. How many miles have you walked in all?
Answer:
14+15=29 or 14x15=210
Step-by-step explanation:
.
Suppose the value of y and the value of x vary together at a constant rate of change (so that Δ y = 0.5 ⋅ Δ x ), and y = 1.5 when x = 3 . We are given that y = 1.5 when x = 3 . Plot a point on the graph to represent these values
Graph with points x=3 and y =1.5
In mathematics, a histogram can be defined as a graphical or graphical representation of data or values in an organized manner. Points on a graph usually represent a relationship between two or more things. We can also represent the data using a bar chart. The quantity of each supply is represented by bars. The higher the bar, the more supplies or items are used.The representation of information in pictures is called pictograms. Several elements are represented by each image. A bar chart is a representation of numerical data using rectangles (or bars) of equal width and variable height. Line charts use points connected by lines to show changes over a period of time. Pie charts are also known as pie charts. It shows how a whole is divided into different parts.Learn more about graph here
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The answer choices in the picture are:
A. a reflection over the line x=6
B. a dilation with a scale factor of 6
C. a 180 degrees clockwise rotation about the origin
D. a 90 degree clockwise rotation about the origin
Answer:
A. A reflection over the line x = 6
Step-by-step explanation:
You can see in the picture if you follow the line every edge has the same
Number x=6
Throwback Thursday
How much would a $75
vacuum cost with a 8%
sales tax added to it?
(Explain how to get it please)
Answer:
$.75.08Step-by-step explanation:
First you need to know how much is the sales tax
8% - 8 centsThen add the sales tax to the value of the vaccum cleaner
75 + 8 cents = $. 75.08Answer
$ 75.08On the coordinate plane, the segment from U(4, -6) to V(-8, -11) forms one side of a
rectangle. The rectangle has a perimeter of 78 units. Find the area of the rectangle.
Write your answer as a whole number, decimal, or simplified radical. Do not round.
___ square units
pls help me
The area of the rectangle = 338 square units
The co-ordinate plane has two axes X and Y.
The points in the co-ordinate plane is given as U(4, -6) to V(-8, -11).
i.e., (x₁, y₁) = (4, -6) and (x₂, y₂) = (-8, -11)
The distance between these points are considered as a side of a rectangle.
Distance between U(4, -6) and V(-8, -11) = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-8-4)^2+(-11--6)^2}[/tex]
= [tex]\sqrt{(-12)^2+(-5)^2}[/tex]
= √169
= 13 units
So the length of one side of rectangle, l = 13 units
Let 'w' be the width of the rectangle.
Also perimeter of the rectangle = 78 units
⇒ 2(l +w) = 78
⇒ l +w = 39
⇒ w = 39 -l
⇒ w = 39 - 13
⇒ w = 26 units
Area of the rectangle = length x width
= l x w
= 13 x 26
= 338 square units
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mals
For how many animals is (p V q) Ar true?
O 15
O 17
O 20
O 22
Answer:
17
Step-by-step explanation:
help me please 2-7
2. Every Tuesday that Yolanda's family has visited a specific local restaurant, the
Nids meals have been free. When Yolanda's family visits that restaurant next
Tuesday, the kids' meals will be free
The given statement about when next they visit the restaurant that the meals will be free is an example of; inductive reasoning.
What type of reasoning was used?
Inductive reasoning is a type of reasoning that involves forming general theories from specific observations. Observing something happen repeatedly and concluding that it will happen again in the same way is an example of inductive reasoning.
Deductive reasoning is a type of reasoning that involves forming specific conclusions from general premises. An example is; Everyone in this class is an English major; Jesse is in this class; therefore, Jesse is an English major.
Now, from the given question, it was observed that Every Tuesday that Yolanda's family has visited a specific local restaurant, the Nids meals have been free. Now, using that to conclude that when next he visits the restaurant that the meals will be free is an example of inductive reasoning.
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