Answers
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = ax
Where a>0 and a is not equal to 1.
x is any real number.
If the variable is negative, the function is undefined for -1 < x < 1.
Here,
“x” is a variable
“a” is a constant, which is the base of the function.
An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
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Related Questions
Simplify 4X•1/x^-5•x^-3
Answers
The simplified form of the given expression, [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] is equal to [tex]4x^{9}[/tex]
What are Exponents?
Powers or exponents are quantities that indicate how many times to multiply a base number by themselves.The base is the integer being raised by a power, while the exponent or power is the superscript number above it.For example, in the expression [tex]7^{5}[/tex], 7 is the base and 5 is the exponents, which implies that 7 multiplies 5 times by itself.What is the Product of Powers rule?
The Product of Powers rule is one of the seven major Laws of Exponents.According to this rule, if the bases are the same, then when multiplying two bases with different exponent value, the resulting answer is found by adding the exponents.It can be mathematically expressed using the formula, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]In this question, the expression is [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] ------(1)
Multiplying the values in the numerator, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5} \times x^{-3} }[/tex]
Now, the values in the denominator can be simplified using the Product of Powers rule.
The formula for the Product of Powers rule is given as, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]
Simplifying the given expression using the Product of Powers rule, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5+(-3)} }\\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-8} }[/tex] -----(2)
The formula for the Quotient of Powers rule is given as, [tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]
Simplifying the expression in (2) using the Quotient of Powers rule, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{1-(-8)} \\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{9}[/tex]
Therefore, the simplified form of the given expression is [tex]4x^{9}[/tex]
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You and a classmate have been paired to solve an equation. Your partner says they got an answer but the solution they found does not work when they checked it. Here is their work:
6 (8-3x )− 3 (9x−1 )+ 60
54 - 18x = −27x − 3 + 60
54 - 18x = −27x + 57
-18x = -27x + 3
9x = 3
x= 1/3
Explain all of the mistakes your partner made and how to correct them. After correcting the mistakes, write the correct answer for this equation.
Answers
Answer: -45x + 111 or -3(15x-37)
Step-by-step explanation:
Instead of :6 (8-3x )− 3 (9x−1 )+ 60
54 - 18x = −27x − 3 + 60
54 - 18x = −27x + 57
-18x = -27x + 3
9x = 3
x= 1/3
Corrected :
6 (8-3x )− 3 (9x−1 )+ 60
First Simplify : 54 - 18x -27x - 3 + 60
Combine Like terms Like 54, - 3, and 60 : 111 - 18x -27x
Combine Like Terms Like -18x and -27x : 111 -45x
Rearrange It So The Variable Is First : -45x + 111
So, the answer is -45x + 111 or if you want you can still simplify it by finding the common factor which you will get -3(15x-37)
Corrections : The friend is wrong because he turned the equation into an inequality instead of simplifying it. He turned the equation into an inequality by adding an equal sign in the middle then he tried to solve it like how you solve inequalities.
P.S : So, correct me if I am wrong but i will try my best to answer. Hope it helps.
What is the average rate of change of the function f(x)= 4x^2 + 3x on the interval [1,5]
Answers
Answer:
The average rate of change of f(x)= 4x^2 + 3x on the interval [1,5] is 18.
Jon Begins jogging at a steady 3 m/sec down the middle of lane one of a straight track. Laura starts even with him in the cneter of lane two but moves at 4 m.sec. At the instant they begin, Ellis is loacted 100 meters down the track in lane four, and is heading towards them in his at 6 m.sec. After how many seconds will the runners lie in a straight line?
a) Let t be the number of seconds the three have been running. Write expressions for the number of meters each has run after t seconds.
b) Consider the location of each runner as a point on a graph. What quantity might you use as the x-coordinate? What quantity might you use as the x-coordinate? What quantity might you use as the y-coordinate?
c) How can you tell if three points are on a line? Use this to solve the problem.
Answers
Answer:
The runners will be in a straight line after 1/2 seconds.
To solve this problem, we can set the y-coordinates of each runner equal to each other and solve for t. The y-coordinate represents the lane number, and if the lane numbers are equal, the runners are on a straight line.
Jon: y = 1
Laura: y = 2
Ellis: y = 4
Jon: 3t = 1
Laura: 4t = 2
Ellis: 6t = 4
Solving these equations simultaneously, we find that t = 1/2 seconds. This means that after 1/2 seconds, the runners will be in a straight line.
Write y=2/3x+7 in standard form
Answers
Step-by-step explanation:
y = 2/3x + 7
Multiply both sides by 3 to get rid of the fraction 2/3
3y = 2x +21
subtract 2x from both sides
3y - 2x = 21
Answer ofc is 3x - 2y = 21
Please rate if you get the answer right.
Graph the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and its image after a dilation with scale factor k=3
Answers
The image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and scale factor k=3.
Now, X(-3, 2)→3(-3, 2)→X'(-9, 6)
Y(2, 3)→3(2, 3)→Y'(6, 9)
Z(1,-1)→3(1, -1)→Z'(3, -3)
Vertices of X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
Therefore, the image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
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How do I Solve this:
Answers
Answer:
x = 20
Step-by-step explanation:
x + 2x + 6x = 9x / 180
x=20
triangles = 180
angle 1 = ?
angle 2 = 160?
angle 3 = 20
g ten random numbers are drawn from a standard normal distribution. what is the probability that at least one will exceed 2.66? round your answer to three decimal places.
Answers
The probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.
This can be calculated using the complementary probability formula, which is 1 - P(x ≤ 2.66), where P(x ≤ 2.66) is the probability that all ten numbers are less than or equal to 2.66.
The probability that all ten numbers are less than or equal to 2.66 can be calculated using the normal distribution function, which gives the probability that a random variable x follows a normal distribution with mean μ and standard deviation σ. For a standard normal distribution, the mean is 0 and the standard deviation is 1, so the probability that all ten numbers are less than or equal to 2.66 can be calculated as:
P(x ≤ 2.66) = Φ(2.66)^10where Φ(x) is the normal distribution function.
Substituting this value into the complementary probability formula, we get:
1 - P(x ≤ 2.66) = 1 - Φ(2.66)^10 = 0.045Thus, the probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.
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(c) The sum of the ages of two brothers is 31 years and the age of older brother is 5 years more than the younger brother. Find their present ages.
Answers
Answer:
Here is your answer,
Step-by-step explanation:
(c)
x + y = 31 ------ (i)
x - y = 5 ------ (ii)
We have subtract eqn (ii) from eqn (i). Here we get the equation as,
2y = 26
y = 13 ------(iii)
Put eqn (iii) in eqn (i), we get -
=> x + y = 31
=> x = 31 - 13
=> x = 18
Therefore, their present ages of younger brother & older brother is 13 yrs & 18 yrs respectively.
For linear function f,f(2)= 0 and ƒ(4) = -6.
Write function f in slope-intercept form.
Answers
Answer:
Step-by-step explanation:
(2, 0), (4, -6)
(-6 -0)/(4 - 2)= -6/2= -3
y - 0 = -3(x - 2)
y = -3x + 6
or
f(x) = -3x + 6
Answer:
Step-by-step explanation:y= -3x + 6
In need of help like rn pls nd thanks!!!!!!!!!!!!!!!
Answers
Answer: His work shows that the answer is an F. E. Which means a False Equation.
Step-by-step explanation:
This happens when an equation cannot be solved. Here is an example of a false equation answer:
Let's say that 3=6, in the equation or expression, all the letters like "x, y, z..." have been undone.
Therefore we can no longer undo, so the answer to your question is a False Equation.
A ship's destination is 30 miles north and 12 miles east. At what angle should it head to go straight to its destination?
a) 22°east of north b) 24°east of north
c) 31°east of north d) 66°east of north
Answers
The angle should it have to go straight to its destination is 66° east of north. The correct option is D.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that a ship's destination is 30 miles north and 12 miles east. The angle will be calculated as,
tanθ = 30 / 12
θ = tan⁻¹ ( 30 / 12)
θ = 66°
The angle is θ = 66°
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Simplify the expression. fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 as A.the denominator ten fourths. B.negative ten fourths C.8 D.−8
Answers
The expression fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is simplified to give 8
How to simplify the fraction expressionThe fraction: negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is written in words
Rewriting the fraction
-4( (2 - ∛8 * 6) / 5)
The equation is simplified as
= -4( (2 - ∛8 * 6) / 5)
= -4( (2 - 2 * 6) / 5)
= -4( (2 - 12) / 5)
= -4( (-10) / 5)
= -4( -2)
= 8
Option C, 8 is the correct answer
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John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year.
Number of Lease Offices 0 1 2 3 4 5
Probability 10/33 1/33 7/33 1/11 4/33 8/33
If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars)
a) E(X) = $29,130.91
b) E(X) = $29,090.91
c) E(X) = $29,170.91
d) E(X) = $29,070.91
e) E(X) = $29,100.91
Answers
AE(X) = $23,333.33 could John expect to collect in yearly leases for the whole building in a given year.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The given table is:
Number of Lease Offices : 0 1 2 3 4 5
Probability : 5/18 1/4 1/9 1/18 2/9 1/12
The expected probability is
Expected probability [tex]$=\sum_{i=0}^5 x_i p\left(x_i\right)$[/tex]
Expected probability [tex]$=0 p(0)+1 P(1)+2 P(2)+3 P(3)+4 P(4)+5 P(5)$[/tex]
Expected probability [tex]$=0 \cdot\left(\frac{5}{18}\right)+1 \cdot\left(\frac{1}{4}\right)+2 \cdot\left(\frac{1}{9}\right)+3 \cdot\left(\frac{1}{18}\right)+4 \cdot\left(\frac{2}{9}\right)+5 \cdot\left(\frac{1}{12}\right)=\frac{35}{18}$[/tex]
It is given that the yearly lease [tex]$=\$ 12,000$[/tex].
The yearly leases for the whole building in a given year is
Yearly leases [tex]$=\frac{35}{18} \times 12000=23333.3333333 \approx 23333.33$[/tex]
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Laney walks 2 1/3 miles to school from her house and rides the bus home. If she attended school five days last week, how many total miles did Laney walk?
Answers
The total miles that Laney walked is 11 2/3 miles.
How many total miles did Laney walk?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this situation, Laney walks 2 1/3 miles to school from her house and rides the bus home and she attended school five days last week.
The total miles that Laney walked will be:
= 2 1/3 × 5
= 7/3 × 5
= 35/3
= 11 2/3 miles
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There are 5,280 feet in a mile. There are 3 feet in a yard. How many yards are there in a mile? Please help this is due tomorrow
Answers
In mile there are 63360 inches.
The number of inches in a mile is equal to the number of inches in a foot times the number of feet in a mile
We multiply 528 by 12 and add one zero to the right of the result.
Use vertical form to perform the multiplication.
So. 12 × 5280=63360
∴ 5280/6336
= 1056
The number of inches in a mile = 12 × 5280
We multiply 528 by 12 and add one zero to the right of the result.
Use vertical form to perform the multiplication:
528 × 12 = 1056
1056 + 5280 = 6336
So, 12 × 5280 = 63360 miles
Therefore, in mile there are 63360 inches.
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mike rents a car for a total of$445.
the rental charges are$145 for the first day and $60 for the first day after that
for how many days did mike rent the car?
Answers
Answer:
6 days
Step-by-step explanation:
total is 445
first day charge is 145
so, 445-145 = 300
second day onwards its 60.
so, 300/60 = 5 days
so total 5+1 = 6 days.
I hope I helped you
What is the equation of the line (in slope intercept form) passing through X(1,-4) perpendicular to line YZ with Y(1,3) and Z(-3,-1)
(Please enter fraction as decimals rounded to the nearest tenth)
Answers
The equation for the line we want to get is:
y = -x + 3
How to get the equation of a line?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular of the product between the slopes of the two lines is -1.
Here we want to find a line perpendicular to the one that passes through the line with Y(1,3) and Z(-3,-1), the slope of that line is:
a = (-1 - 3)/(-3 - 1) = 1
Then the slope of a perpendicular line, a', is:
a'*1 = -1
a' = -1
Then our line is like:
y = -1*x + b
To find the value of b, we use the fact that this line passes through (1, -4), then we will get:
-4 = -1*1 + b
-4 + 1 = b
-3 = b
So the linear equation is:
y = -x + 3
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Chase and Alonzo stand next to each other and throw baseballs in the air. The path of chases baseball is described by the equation y= -4x^2+5x+7. The path of Alonzo’s ball is shown by the graph whose baseball reaches a greater height
Answers
Quadratic equation :The maximum height reached by Alonzo's ball will be 9m.
What is a quadratic equation?
The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.
Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.
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Complete Question:
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
D) Non of these
Answer:
Alonzo's baseball
whompwhompwhompwhopwhompwhompwhompwhompwhompwhompwhompwhompwhompwhompwhomp
Step-by-step explanation:
What are the missing parts that correctly complete the proof? W/ picture
Answers
1. Reason: Since QA divides ∠PQR into two different parts so it is a bisector∠PQA≅∠RQA.
2. The line which divides an angle into two different angles is known as a bisector.
4. ∠QXA≅∠QYA and they are situated opposites to each other so we can say that right angles are conjugate.
5. Given, Both are situated in the same plan so QA≅QA
6.ΔQXA≅ΔQYA, by the AAS Postulate.
8. Definition of equidistant. XA=XY.
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Hi, I need help solving quadrilateral problems.
Answers
The value of x in quadrilateral JKLM is 29
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.
The sum of the interior angles in a quadrilateral is 360°
∠J + ∠K + ∠L + ∠M = 360
3X + 90 + 2X + 8 + 4X + 1 = 360
9x + 99 = 360
9x = 360 - 99
9x = 261
x = 261/9
x = 29
In conclusion 29 is the value of x in the quadrilateral.
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The diameter of a circle divides the circle into two equal sectors true or false
Answers
Answer:
NO
FALSE
Step-by-step explanation:
The diameter divides the circle into two equal part called semi– circles( the image on white)
A sector is the plane figure enclosed by two radii of a circle or ellipse and the arc between them.
( the image that is dark)
i hope this helped
Answer: No, the diameter of a circle divides the circle into two equal halves called semi circle.
Step-by-step explanation:
The line that splits a circle into two identical halves is its diameter. The widest chord that divides the circle in half exactly is called the diameter. Each component is known as a semicircle.
Find part b m of c and m if a. Please explain.
Answers
Answer:
Step-by-step explanation:
a) the opposite angles of a quadrilateral inscribed in a circle are supplementary
70 + angle D = 180
angle D = 180 - 70
angle D = 110 degrees
b) DAB is a semicircle, so angle A and angle C are two circumference angles whose sides passes through the extremes of the diameter.
The centre angle of a semicircle is 180 degrees and its circumference angle is half that measure, so its value is 90 degrees
A = 90 degrees
C = 90 degrees
5 plus what equals -6
Answers
Answer:
Step-by-step explanation:
-1
Answer:
-11
Step-by-step explanation:
Equation:
5+x=-6
melissa's null hypothesis is that the average calories in frozen mac n cheese is 350 (that is, the population average is 350). since she only has one sample, she uses the bootstrap to estimate the average and ultimately decides to create a confidence interval. she also chooses an 8% p-value cutoff. what kind of confidence interval should she use?
Answers
For 8% p-value cutoff , Melissa should use 92% confidence interval
A confidence interval calculated for a treatment effect measure shows the range in which the true treatment effect is likely to fall.
A smaller sample size or higher variability will result in a wider confidence interval with a larger margin of error. The interval width is also influenced by the level of confidence. If you want a higher level of certainty, the interval should be wider.
The width of the confidence interval and the size of the p value are related.
The narrower the interval, the smaller the p value. The confidence interval, on the other hand, provides useful information about the likely magnitude of the effect under consideration as well as the accuracy of the estimate.
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Queuing system A has a utilization of 80 percent, and queuing system B has a utilization of 90 percent. Both have single server. Say, the utilization of both systems increases by 5 percent; that is, A increases from 80 percent to 85 percent while B increases from 90 percent to 95 percent. Which system is likely to experience the smaller increase in the average time in queue?
a) System A
b) System B
c) Time in queue for each system will increase by the same amount.
d) More information is needed to determine which has a bigger change in average time in queue
Answers
(b) System B is likely to experience a smaller increase in the average time in queue.
As utilization increases, the length of time in line grows more quickly. So a 5% increase in utilization has a larger effect from 90% to 95% than from 80% to 85%.
When you use something, you use it, whether it's a tool—like when you write something down with a pen—or a talent or skill—like the speed you use when you run a race. Utilization is the act of using something, such as using your voice to sing a song. It may be necessary for a team to use a gym for practices until the rain stops.
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Market reearch firm ha hired operator who conduct telephone urvey. A computer
i ued to randomly dial a telephone number, and the operator ak the anwering peron
whether he ha time to anwer ome quetion. Let Y
= the number of call made until the
firt peron replie that he i willing to anwer the quetion. I thi a binomial e
xperiment?
Explain
Answers
The random variable Y does not have a binomial distribution, therefore this is not a binomial experiment
Here, a computer is used to randomly dial a telephone number
Then the operator asks the answering person whether she has time to answer some questions.
Y is the number of calls made until the first person replies that she is willing to answer the questions
There is no independent variable the affect the value of the Y. here the number of trial are not fixed, so there wont be any binomial distribution
Therefore, this is not a binomial experiment, because y does not have a binomial distribution
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C-Town is advertising a Back-to-School sale on pencils. Pack A has 30 pencils and sells for $7.50, while Pack B has 12 pencils and costs $4.25. Find the unit price for each and determine which pack is the better buy.
The rate for Pack A and Pack B
The unit price for Pack A and Pack B
Which pack is the better buy? Explain your reasoning.
Answers
The best buy is pack of 30 .
What is cost and division ?
A cost function is a mathematical formula used to chart how production expenses will change at different output levels.
The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.
Division is the opposite of multiplication.
A division is a process of splitting a specific amount into equal parts.
Pack A has 30 pencils
sells for $7.50.
pack of 30:
7.97/30 = 0.27 per pencil
Pack B has 12 pencils
costs of $4.25.
pack of 12:
4.77/12 = 0.40 per pencil
The best buy is pack of 30 because:
0.27 < 0.40
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PLEASE HELP!!!
Which choices are equivalent to the fraction below? Check all that apply.
12/32
A. 4/10
B. 3/8
C. 10/30
D. 6/16
E. 4/9
F. 2/6
PLEASE EXPLAIN HOW TO DO IT‼️‼️‼️
Answers
Answer: the answers should be B and D
Step-by-step explanation:
so basically, this is just simplifying
B is the correct answer because the numerator 12, when divided by 4 is 3, and the denominator 32, when also diving by 4, is eight. This makes the two fractions equivalent.
Same goes for D, for if you diving the numerator and denominator by 2, you get answer choice D
it’s kind of a trial and error type problem and you have to test out all possibilities
hope this helps!
Answer:
B and D
Step-by-step explanation:
12/32 (if you divide them both by three) does not equal 4/10
12/32 fully simplified is 3/8
12/32 - subtracting is not simplifying, therefore, 10/30 is not correct
12/32 - both divided by two, a common factor, is 6/16, therefore, this answer is correct
12/32 - both of them divided by three equals 4/10.7 (rounded up to the nearest tenth), therefore, 4/9 is not a correct answer
12/32 - both divided by six equals 2/5.3 (rounded down to the nearest tenth), therefore, 2/6 is not a correct answer
97 divided by 10 and round to the nearest tenth place pleaseeeee
Answers
Answer: 9.7
Step-by-step explanation: 97 divided by 10 is 9.7