lim [f(x) - g(x)] is9.
What is a limit of a function?Generally, In mathematics, a limit is a value that a function "approaches" as the input of the function "approach" some value.
More formally, given a function f(x) and a value L, we say that "the limit of f(x) as x approaches a is L" if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a, but not equal to a.
In other words, the limit of a function describes the behavior of the function as the input gets arbitrarily close to a particular value, but doesn't necessarily equal that value
The limit of the difference between the two functions is the difference of their individual limits. So,
lim [f(x) - g(x)] = lim f(x) - lim g(x)
= 7 - (-2)
= 9.
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in exercises 11 and 12, determine if b is a linear combination of subscript[a, 1], subscript[a, 2], and subscript[a, 3].
Yes b can be written as linear combination of 3 vectors
What is linear combination of vector?A linear combination of vectors is a sum of scaled vectors, where the scaling factors are scalars. In other words, it's a linear combination of the form a_1v_1 + a_2v_2 + ... + a_n*v_n, where v_1, v_2, ..., v_n are vectors and a_1, a_2, ..., a_n are scalars. This is a fundamental concept in linear algebra and vector spaces and is used in many areas of mathematics and physics.
if b is linear combination of [tex]a_1,a_2,a_3[/tex]
then [tex]xa_1+ya_2+za_3=b[/tex]
from here we got :
x+5z = 2
-2x+y-6z = -1
2y + 8z = 6
after solving the above equation we get the solution as
{x,y,x} = {2,3,0} is a solution to the above equation so b is a linear combination of [tex]a_1,a_2,a_3[/tex]
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Complete question:
determine if b is a linear combination of [tex]a_1,a_2,a_3[/tex]
[tex]a_1[/tex] = [tex]\left[\begin{array}{ccc}1\\-2\\0\end{array}\right][/tex] , [tex]a_2 = \left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex] , [tex]a_3 = \left[\begin{array}{ccc}5\\-6\\8\end{array}\right][/tex] , b= [tex]\left[\begin{array}{ccc}2\\-1\\6\end{array}\right][/tex]
Charlie’s runs 8 miles in 74 minutes. How many minutes does he take per mile?
Answer: 9.25
For this equation you will need to use division. 74min. divided by 8mi.
To double check your answer is correct you have to multiply. 9.25min times 8mi.
Water is flowing from a horizontal pipe 48 feet above the ground. The falling stream of water has the shape of a parabola whose vertex (0, 48) is at the end of the pipe (see figure). The stream of water strikes the ground at the point (10 sqrt3 , 0). Find the equation of the path taken by the water
The water stream's parabola has the equation y = 48 - (x2)/(20*sqrt(3)), with the vertex at (0, 48) and the point of impact at (10sqrt(3), 0).
The equation of the parabola created by the water stream has a vertex at (0, 48), which is where the pipe ends. It is a quadratic equation. The pipe serves as the middle of the parabola's base, which is symmetrical and has a vertex at that location. The vertex form of a parabola can be used to determine the equation of the parabola, which is y = 48 - (x2)/(20*sqrt(3)). The parabola opens downward, with the highest point at (0, 48) and the lowest point at (10sqrt(3), 0), where the water stream hits the ground, according to the equation. The parabola's vertex and point of impact with the ground are described by the equation for the water's journey.
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Is this sequence arithmetic or geometric?
List at least 5 terms of the sequence
Write a recursive definition for the sequence
This formula states that each term in the sequence is equal to the previous term plus 3.
Is this sequence arithmetic or geometric?This sequence is arithmetic, because the difference between consecutive terms is consistent.The first five terms of the sequence are 1, 3, 5, 7, and 9.The recursive definition of the sequence is a(n) = a(n-1) + 2, where a(1) = 1.This sequence appears to be arithmetic, as the difference between consecutive terms is constant.This can be seen by looking at the graph, where the y-values of each point are regularly spaced apart.The first five terms of the sequence are 2, 5, 8, 11, and 14.A recursive definition of the sequence is a formula that can be used to generate subsequent terms of the sequence.In this case, the recursive definition of the sequence is a(n) = a(n-1) + 3, with a(1) = 2.For example, the fourth term in the sequence (11) is equal to the third term (8) plus 3, and the fifth term (14) is equal to the fourth term (11) plus 3.This sequence appears to be arithmetic, as each consecutive term increases by the same amount. The difference between each term is constant, so this is a defining characteristic of arithmetic sequences.The first five terms of this sequence are 0, 2, 4, 6, 8.\A recursive definition of this sequence is a formula that describes the relationship between each term and the preceding term. The recursive definition of this sequence is an_n = a_(n-1) + 2, where a_n is the nth term of the sequence and a_1 = 0. This definition states that each term is two more than the previous term.To learn more about the sequence refer to:
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If there are 24 apples and 12 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made
Answer:
Step-by-step explanation:
for every 24 apples there is 12 bananas
so if you dived it by 2 it will be 12 apples 6 bananas
so it will always be half amount of bananas
On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The
triangle has an area of 28 square units. Select all of the points where F could be.
(5,-4)
(1, 10)
(7,4)
(-6, 10)
On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The possible point F are (5,-4), (1, 10), (7,4), (-6, 10).
How many points does a F earn?Since we are aware that the triangle's area is 28 square units and that the base is the segment DE, which has a length of 8 units, we can construct the equation:
Area equals (1/2) × base × height = (1/2) × 8 × height=28
We can calculate the height and discover that it is 7 units.
Point F must be situated 7 units above or below the line DE since the triangle's height is perpendicular to the base DE. Therefore, any position that is 7 units above or below the line DE, which is determined by the equation y = 3, is considered to be at point F.
So the possible point F are (5,-4), (1, 10), (7,4), (-6, 10)
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Complete question -
On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The
triangle has an area of 28 square units. Select all of the points where F could be. (5,-4), (1, 10), (7,4),(-6, 10)
A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24-hour period in New York City. What is the range of this set of data?
The range of this set of data is 30 ≤ y ≤ 80.
What is a range?In Mathematics, a range is the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown above, we can reasonably and logically deduce the following domain and range:
Domain = 0 ≤ x ≤ 24 or [0, 24].
Range = 30 ≤ y ≤ 80 or [30, 80].
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Consider the slope field shown: (a) For the solution that satisfies y(0) 0,sketch the solution curve and estimate the following: y(I) ~ 0.75 and y(-1) 0.5 (b) For the solution that satisfies Y(O) = 4, sketch the solution curve and estimate the following: Y(0.5) -0.5 and Y(-1) 0.75 (c) For the solution that satisfies Y(O) = -1, sketch the solution curve and estimate the following: Y(I) ~ and y(-1) ~
For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5.
(a) To sketch the solution curve for the given slope field, beginning at the point (0, 0) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of y(1) is 0.75 and y(-1) is 0.5.
(b) To sketch the For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5. curve for the given slope field, beginning at the point (0, 4) and following the arrows, draw a curved line that gradually moves from right to left, gradually decreasing in value and then slowly increasing. The estimated value of Y(0.5) is -0.5 and Y(-1) is 0.75.
(c) To sketch the solution curve for the given slope field, beginning at the point (0, -1) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of Y(1) is and y(-1) is -1.5.
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If a plane can travel 490 miles per hour with the wind and 430 miles per hour against the wind, find the speed of the plane in still air.
Answer:
460
Step-by-step explanation:
Let b = base speed and w = wind power.
Here's what we know:
b + w = 490
b - w = 430
From here, we can use the elimination method. If we treat each variable and constant as columns, we do the following:
b + b = 2b
w - w = 0
490 + 430 = 920
Leaving us with:
2b = 920
Divide by 2:
2b / 2 = b
920 / 2 = 460
So b = 460 mph
Visitors to a carnival pay an admission fee and must buy a ticket for each ride they go on.
Last year the total cost for a visitor to go on n rides was modeled by the expression 4.00 +1.50n.
This year, the carnival doubled the cost of a ride ticket but kept the admission fee the same.
Which expression models the total cost for a visitor to go on n rides at the carnival this year?
The expression models the total cost for a visitor to go on n rides (c) is 4.00+1.50n
What is Expressions?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
total cost for a visitor to go on n rides (c) = 4.00+1.50n
Admission fee = 4.00
Cost of each ride = 1.50
Now the cost of each ride is doubled.
New cost of each ride = 2×1.50 = 3.00
New cost model (C') for n rides = 4.00+ 3n
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the bus has a maximum capacity of 30 passengers write as an inequality
The inequality of the statement is x ≤ 30
How to determine the inequalityFrom the question, we have the following parameters that can be used in our computation:
The bus has a maximum capacity of 30 passengers
Represent the bus capacity with x
This means that the value of x cannot exceed 30
The term cannot exceed implies less than or equal to
So, we have
x ≤ 30
Hence, the inequality is x ≤ 30
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on Saturday there was a -4 change in inventory. How many phones were In inventory on Sunday?
Answer:
14
Step-by-step explanation:
First we can find Wednesdays inventory by doing 16-5, giving us 11
We can do the same thing for Saturday. Doing -2+20 because the change was positive 20, not negative. That brings Saturdays inventory to 18
They said Saturdays change was -4
So taking the 18 and subtracting 4 gets you Sundays inventory of 14
Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1). Therefore, option B is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, three softball players discussed their batting averages after a game.
Probability:
Player 1: 4/7 =0.57
Player 2: 5/8 =0.625
Player 3: 3/6 =0.5
Therefore, option B is the correct answer.
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Rob runs at a constant speed of 3.4 meters per second for one half hour. Then, he walks at a rate of 1.5 meters per second for one half hour. How far did Rob run and walk in 60 minutes?
The total distance that rob ran and walked for 60 minutes is; 8820 meters
How to calculate the distance covered?The parameter for the constant speed is that Rob runs at a speed of 3.4 meters per second for one half hour. Thus;
V1 = 3.4 m/s
t1 = 1.5 hours =
30 * 60 = 1,800 seconds.
The distance he runs at that speed and time is;
S1 = V1 * t1
= 3.4 * 1,800
= 6,120 meters
He walks at V2 = 1.5 m/s for t2 = 1,800 seconds.
The distance he walks;
S2 = V2 * t2
= 1.5 * 1,800
= 2,700 meters
The total distance he runs and walks;
S = S1 + S2
= 6120 + 2700
= 8820 meters
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Draw the graph of y=f(x) and y= 1/f(x) on the same axes.
f) f(x) = -(x+4)²+1
are there any specific steps to get the answers here?
Answer: To graph y = f(x) = -(x+4)²+1 and y = 1/f(x) on the same axes, you can follow these steps:
Plot the y-intercept of y = f(x) which is (0,-1)
For y = f(x), the parabola opens downward since the coefficient of x² is -1, thus the vertex is at (-4,1)
Plot the x-intercepts of y = f(x) which are x = 4 and x = -8
The parabola of y = f(x) is symmetric about the y-axis, so the graph will be reflected about the y-axis.
For y = 1/f(x), the x-intercepts will be the same as y = f(x) and the y-intercept is (0,1)
To graph y = 1/f(x), we can start by plotting the x-intercepts and the y-intercept, and then connecting the points.
Label the x-intercepts, y-intercepts, and vertex for both graphs
Shade the regions above the parabola of y = f(x) and below the graph of y = 1/f(x)
Note: It is important to remember that the graph of y = 1/f(x) is a reflection of the graph of y = f(x) across the x-axis, so the y-intercept of y = 1/f(x) is (0,1)
Step-by-step explanation:
The land area of Statesville, NC, is 20.7 square miles. If the entire US population (currently about 322.9 million) were put inside the city limits of Statesville, determine the number of square feet that each person would have. Round your answer to two decimal places. [Hint: Remember that a mile is 5,280 feet, so a square mile is (5,280 x 5,280) square feet.]
In the land area of Statesville, NC there would be 133.54 persons per square foot.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, One mile is 5280 feet so a square mile is
(5280 × 5280) = 27878400 square feet.
Therefore, The number of persons in each square foot should be,
= 322900000/27878400 persons per square foot.
= 3229000/278784 persons per square foot.
= 133.54 persons per square foot.
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Please help me find each measure!! Thank you
6 1/2 divided by 1 2/3 as a mixed number in simplest form
The value of 6 1/2 divided by 1 2/3 is 3 9/10
How to determine the quotient of the numbersFrom the question, we have the following parameters that can be used in our computation:
6 1/2 divided by 1 2/3
When represented as an expression, we have
6 1/2 / 1 2/3
Convert to improper fractions
13/2 / 5/3
Express as products
13/2 * 3/5
So, we have
39/10
Express as mixed number
3 9/10
Hence, the solution is 3 9/10
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what is the y-interpect on this graph
Answer:
16
Step-by-step explanation:
It's the number where the line crosses the y-axis
Question 23 of 41
Which of the following is equivalent to the product below?
√9.√5√2
OA. 18√5
OB. 10√3
OC. 3√10
OD. 5√18
It is a cold, dark, and stormy winter morning. Your boss has called a 5 a.m. meeting before she leaves to catch a flight to the Bahamas for her vacation, and there is a power outage. Your alarm does not go off and you sit up in bed with a fright at what you guess is about 4:45 a.m. You are trying frantically to get dressed and you need to reach into your sock drawer to get two matching socks in the dark. Naturally, your mind wanders to solving probability equations. Your sock drawer contains 20 total socks which consist of 10 matched pairs of socks. All of them are only black or white and they are loose, disorganized randomly, and not bound together. This means you have 10 black socks and 10 white socks in your disorganized drawer. You do not have a light source because your phone did not charge and you cannot find a flashlight or a candle. You are completely in the dark! You have to get dressed and go! You have to math fast! 1. Think for a minute and describe your optimal strategy for solving this problem in 50 words or less. 2. Let’s say for a moment that all 20 socks are different colors meaning that none match. What is the total number of different ways they could be combined in pairs? 3. Now consider all the socks are only black and white. What is the total number of different ways they could be combined in pairs? (Suggestion: You might consider listing the sample space of all possible outcomes.) For the remaining problems, let’s go back to the assumption that there are 20 total socks, 10 white and 10 black. This makes 10 total matching pairs of 5 pair of white and 5 pair of black.
1. Optimal strategy for solving this problem would be to feel for the socks, and grab two socks of the same color at random, as they have a 50% chance of being a match.
2. The total number of different ways they could be combined in pairs, assuming all 20 socks are different colors, is calculated by using the formula (nCr) = n! / (r! * (n-r)!)
So, the total number of different ways they could be combined in pairs would be (20*19)/2 = 190.
3. The total number of different ways they could be combined in pairs would be 10, as there are 10 black and 10 white socks, and they can only be paired with one another.
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Using trial and improvement, find the numbers that should replace A and B in the
rule for this sequence.
Rule:
Start at 6
Multiply by A then subtract B each time
6-8->
-36->
Using trial and improvement the numbers that should replace A and B is 20 and 34.
What is the trial and improvement process?If you are unable to solve a problem using standard algebraic techniques, try using the trial and improvement approach. If you want to get a C in math, you must comprehend this question because it typically is worth 3 marks.
According to the topic
6 = A * 2 - B = 2A - B
SZ = A - S - B = SA - B {Find the relationship}
:: 3A = 36 - 8 = 28
/ A = 28/3 = 9
; B = 2A - 8 = 18 - 8 = 10
the rule expression. 14n-10
: n = 3 , 10 . 3 - 10 = 20
n = 4 11 . 4 - 10 = 34
Using trial and improvement the numbers that should replace A and B is 20 and 34.
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Which graph shows the new image of the rectangle after a translation of two units to the left?
The new image of the rectangle after a translation of two units to the left is of option D
How to draw a shifted figure if the shifts are provided?Suppose the graph is drawn on the coordinate plane.
Let the shifting be (x,y) → (x+a, y+b)
Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.
The resultant set of new points will be plotted.
Given;
A rectangle area on graph with coordinates (1,0), (6,0),(6,2), (1,2)
Now after the shift of 2 unit left, the x coordinates will be affected;
=(1-2,0), (6-2,0),(6-2,2), (1-2,2)
=(-1,0), (4,0),(4,2), (-1,2)
Therefore, the coordinates of shifted graph will be (-1,0), (4,0),(4,2), (-1,2)
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GIVING 50 POINTS FOR THE RIGHT ANSWER!!!!
What is 34 + 4/9 x 1/2
Answer:
308/9
Step-by-step explanation:
Answer: 34 + 4/9 x 1/2 = 34 + 2/9 = 36/9.
Decimal Form: 34 + 4/9 x 1/2 in decimal form is 34.22222222.
Step-by-step explanation:
Solve the equation on the
interval [0, 2π).
2sin(x) + √3 = 0
X =
?]π
5TT
The equation on the interval [0, 2π).x is 4π / 3 ,5π / -2
How should an interval equation be written?Intervals are expressed using parentheses or rectangular brackets, and a comma is used to separate two integers. The two numbers are referred to as the interval's endpoints. The least element or lower bound is shown by the number on the left. The biggest element or upper bound is shown by the number on the right.
As a result, when x = 4 and 5 4, f (x) has its maximum value of 1, which is 1.
A range of numbers between two specified numbers that include all real numbers in that range is known as an interval.
2sinx+ [tex]\sqrt{}[/tex]3 =0
⇒sinx= [tex]\sqrt{}[/tex] 3− 2
⇒x=nπ+(−1) ^-n 4π /3 (∵sin3 4π = [tex]\sqrt{}[/tex]3/-2 )
X =?]π5TT
x = 4π / 3 ,5π / -2
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The sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7: 6. The store donates 24 soccer balls. How many basketballs does the store donate?
The number of basketballs that were donated is equal to 28 basketballs.
How to determine the number of basketballs that were donated?In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.
This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;
7:6 = x:24
7/6 = x/24
Cross-multiplying, we have the following:
6x = 7 × 24
6x = 168
x = 168/6
x = 28 basketballs.
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at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. which of the following is closest to the proportion of orders that are processed in less than 240 seconds? following is closest to the proportion of orders that are processed in less than 240 seconds?
А
0.17
B
0.25
0.36
D
083
E
0.95
As per the interpolation method, the proportion of orders that are processed in less than 240 seconds is 0.17
The interpolation method is defined as a method of deriving a simple function from the given discrete data set such that the function passes through the provided data points.
Here we have given that at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds.
And the proportion of orders that are processed in less than 240 seconds is calculated as,
Here we know that 1 standard deviation below mean = 16% = M - d
Then we apply the value on it, then we get,
=> 276 s - 38 s = 238 s
Here we know that the mean of distribution is,
=> 50% which is equal to 276 s
And the proportion less than 240 s is consider that x%, then by using the interpolation method it can be calculated as,
=> (240 - 238) / (276 - 238) = (x - 16) / (50 - 16)
When we simplify this one then we get,
=> 1/19 = x - 16 / 34
Which can be rewritten as,
=> 19(x - 16) = 34
=> 19x - 304 = 34
=> 19x = 338
=> x = 17.78%.
Therefore the closest to the proportion of orders that are processed in less than 240 seconds is 17% that is equal to the value of 0.17.
Hence the correct option is (A).
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10 pts.!!!!!
You select a marble without looking and then put it back. If you do this 7 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
ASAPPPPPPPPP PLSSS ITS GRADED
The best prediction possible for the number of times you will pick a marble that is not orange, is 7 times.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
There are 4 pink marbles and 3 orange marbles.
The probability of not picking orange marbles,
= 4/(3 + 4)
= 4/7
If you do this 7 times,
the best prediction possible for the number of times you will pick a marble that is not orange,
= 4/7 x 7
= 4 times
Therefore, number of times is 4.
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The complete question:
There are 4 pink marbles and 3 orange marbles.
You select a marble without looking and then put it back. If you do this 7 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 22 by 29 ft brick patio installed.
Answer:
1,547
Step-by-step explanation:
15' x 20' = 300 square feet
2,275 / 300 = $7.583 per square foot
12 x 17 = 204 square feet
204 x 7.583 = 1,547
Marissa bought 7 ounces of yogurt for $3.50.
What is the unit price?
$0.35 per ounce
$0.50 per ounce
$3.50 per ounce
$5.00 per ounce
Answer:
$0.50
50 cents per ounce.
Step-by-step explanation:
To get the unit price, you take the cost of the package divided by the parts it has. Since Marissa has a package of yogurt that costs $3.50 and there are seven ounces in the package we have this equation:
($3.50)/(7 ounces)= $0.50 = 50 cents = the second answer available.