The multiplication of the given expression in the simplified is 5000/ 729 and in mixed form is [tex]6\frac{626}{729}[/tex].
How to multiply fractions with mixed numbers?To multiply fractions with mixed numbers, first convert the mixed number into an improper fraction. Then, multiply the numerators of the fractions separately, and then multiply the denominators separately and simplify the result to obtain the answer.
A whole number and a legal fraction are combined to form a mixed number. An improper fraction is created by multiplying a mixed number by its denominator, keeping the denominator, and adding the resulting number to the proper fraction's numerator.
The given expression is
3 × (5/9) ×(5/3) × (8/9) ×[tex]1\frac{6}{9}[/tex] × [tex]1\frac{2}{3}[/tex]
= 3 × (5/9) ×(5/3) × (8/9) × (1×(9/6))/9 × ((1×3)+2))/3
= 3 × (5/9) ×(5/3) × (8/9) × (15/9) × (5/3)
= 45000/6561
= 5000/729
= [tex]6\frac{626}{729}[/tex]
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The complete question is:
"Multiply the whole number and fraction. Simplify your answer and write it as a mixed number 3 × (5/9) ×(5/3) × (8/9) ×[tex]1\frac{6}{9}[/tex] × [tex]1\frac{2}{3}[/tex]"
a car travels 120120 miles from aa to bb at 3030 miles per hour but returns the same distance at 4040 miles per hour. the average speed for the round trip is closest to:
The Average Speed of car for the round trip is 346.28 km/ hr.
Average Speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.
If a car travels a distance d at rate r₁ and return the same distance at rate r₂, then,
Average Speed = total distance ÷ total time
= 2d ÷ d/r₁ + d/r₂
= 2d ÷ r₂d + r₁d / r₁r₂
= 2r₁r₂ / r₁ +r₂
∴ x = 2× 3030×4040/ 3030 +4040
= 2448240 ÷ 707
= 346.28 km/hr
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I inserted a picture so it can be more clear. This is for Algebra 2, Unit 2
The inverse function of f(x) = 3x-4 when x = -1 will be 1.
According to the question,
We have the following function:
f(x) = 3x-4
Now, to find its inverse we will convert this function into a linear equation:
y = 3x-4
Now, we will change variable from x to y and y to x:
x = 3y-4
Now, we have to find the value of y, which will be the inverse of the given function:
Moving 4 from the right hand side to the left hand side will result in the change of signs:
x+4 = 3y
3y = x+4
Dividing by 3 on both the sides:
y = (x+4)/3
Now, we have:
[tex]f^{-1} (x)[/tex] = (x+4)/3
Putting the value of x = -1:
(-1+4)/3
3/3
1
Hence, the inverse function of f(x) = 3x-4 when x = -1 will be 1.
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following and propo Out of 250 coins, 50 are in mint condition. What is the ratio of mint condition coins to the total number of coins?
Reason:
We have 50 mint condition coins out of 250 total
This forms the ratio 50:250, in which we divide both parts by the GCF 50 to end up with 1:5
The ratio 1:5 tells us that the total is 5 times that of the number of mint condition.
Does x + 2 = -3(x+1) have exactly one solution?
Answer:
Yes
Step-by-step explanation:
the solution would be -5/4
Answer:
yes have on solution
Step-by-step explanation:
Decimal
=-1.25
Fraction
=[tex]-\frac{5}{4}[/tex]
Mixed fraction
=[tex]-1\frac{1}{4}[/tex]
x ≥0
y ≥0
4x+3y ≤36
x+y ≥3
A. Find the value of the objective function at each corner of the graphed region
B. use the values in part A to determine the maximum value and the value of X and Y at which the maximum occurs
Maximum value of the objective function is:
find the values of x and y at which the maximum occurs:
x=
y=
The value of x and y are 45 and 48 when the system of inequality are 4x+3y≤36 and x+y≥3.
Given that,
The system of inequality are,
4x+3y≤36 and x+y≥3
We have to find the x and y values of system of inequality.
Take the system of inequality,
4x+3y≤36 ---> equation(1)
x+y≥3 ---> equation(2)
Take the equation(2)
x+y≥3
x≥3-y
Substitute in equation(1).
4x+3y≤36
4x+3y≥-36 (To get the greater than are equal to )
4(3-y)+3y≥-36
12-4y+3y≥-36
12-y≥-36
-y≥-36-12
-y≥-48
y≥48
Substitute in equation(1)
x+y≥3
x+48≥3
x≥3-48
x≥-45
Therefore, The value of x and y are 45 and 48 when the system of inequality are 4x+3y≤36 and x+y≥3.
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Please also provide the solution so i can understand the question better! ^^ Also when they say estimate they mean if the answer is closer to 0 , 1/2 , or 1 whole.
On yesterday beth walked farther. She walk 1/6 farther than the another day.
beth walked on yesterday = 1/2 of a miles
beth walked on today = 1/3 of a miles
which day she walked farther?on yesterday she walked = 1/2 of a miles = 0.5 miles
on today she walked = 1/3 of a miles = 0.3 miles
This shows she walk farther on yesterday.
and how far is calculated as :
= 1/2 - 1/3
= (3 - 2)/ (2x 3)
= 1/6
she walked 1/6 farther on yesterday than today.
On yesterday beth walked farther. She walk 1/6 farther than the another day.
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Please help I tried multiple times but still can't get it right
Answer:
-3
Step-by-step explanation:
You want the slope of the line through points (1, 2) and (3, -4).
SlopeThe slope of the line is its "rise" divided by its "run." The values of these can be found several ways. Perhaps the easiest is to count the squares on the graph.
The bottom point on the graph is 2 grid squares to the right of the top point, and 6 grid squares below it. The "rise" is -6 (down is negative), and the "run" is 2. The slope is ...
slope = rise/run = -6/2 = -3
You can also use the slope formula with the coordinates of the points.
m = (y2 -y1)/(x2 -x1)
m = (-4 -2)/(3 -1) = -6/2 = -3
The slope of the line is -3.
If this net were to be folded into a
cube, which number would be
opposite of the number 1?
6
3
5 1
4
2
If the given net was folded into a cube, the number that would be opposite of 1 would be number 6.
How to find the opposite number?If the net was folded into a cube, it would be done such that 1 would be at the bottom of the cube. 4 and 3 would raised to be on the sides of the cube. 2 and 5 would also be raised as well. This would then put 6 on the top of the dice.
With 6 being on top of the dice, this means that it would be the opposite of 1 which is at the bottom. 3 and 4 would be opposites and 5 and 2 would be opposites.
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Find the missing values for the exponential function represented by the table below.
To find the missing values for the exponential function represented by the table above.
An exponential function is in general form, that is
[tex]f(x) = y = a(b)^{x}[/tex]
Now, given points are (-2,8), (-1,12), (0,18)
First let us consider
f(x) = 8 at x = -2
[tex]f(x) = a(b)^{x}[/tex]
[tex]f(-2) = a(b)^{-2}[/tex] = 8
[tex]\frac{a}{b^{2} } = 8[/tex]
So, [tex]a = 8b^{2}[/tex] lets consider this as equation 1
second let us consider
f(x) = 12 at x = -1
[tex]f(-1) = a(b)^{-1} = 12[/tex]
[tex]\frac{a}{b} = 12[/tex]
a = 12b lets consider this as equation 2
From equations 1 & 2, we have
[tex]8b^{2} = 12b[/tex]
[tex]8b^{2}-12b = 0[/tex]
4b(2b-3) = 0
b = 0 or [tex]\frac{3}{2}[/tex]
This is not possible otherwise function will not remain exponential.
[tex]b = \frac{3}{2} ,[/tex] so putting b in equation 1
we have [tex]a = 12b = 12x\frac{3}{2} = 18[/tex]
therefore a = 18
therefore [tex]f^{n} = f(x) = 18(\frac{3}{2})^{x}[/tex]
1. [tex]f(1) = 18(\frac{3}{2})^{1} = 27\\[/tex]
f(1) = 27
2. [tex]f(2) = 18(\frac{3}{2})^{2} = \frac{81}{2} = 40.5[/tex]
f(2) = 40.5
Hence the answer is the missing values is 27, 40.5
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Write an equation of a line
that passes through the
point (-5, 1) and is
perpendicular to y = -x - 3
A) y = x + 6
B) y = -x - 5
C) y = -x-4
D) y = x + 4
E) y = x - 6
From perpendicular line, we have m1
Knowing m1 * m2 = -1 for perpendicular lines gives us
-1 *m2 = -1
m2 = 1
Using y-b = m(x-a) with the point provided gives
y-1 = 1(x--5)
y = x+6
Therefore (A) is the correct answer
Point C is in between D and E and DE = 61 . What is DC equal to? *Screenshot of question below*
Step-by-step explanation:
DE = 61.
great.
both sub-segments together must be as long as the whole line.
so,
(x - 4) + (2x + 5) = DE = 61
x - 4 + 2x + 5 = 61
3x + 1 = 61
3x = 60
x = 60/3 = 20
so,
DC = x - 4 = 20 - 4 = 16
Derek Jeter, the short stop for the New York Yankees, a major league baseball team, played in 159 games in 2012 and hit 15 home runs. If he plays a total of 1272 games in his career, approximately how many home runs will he hit?
[A] Write a proportion that is defined by this situation.
[B] Explain how the cross product is used to solve the problem.
[C] Answer the question.
a. The the proportion that would be used is: 159/15 = 1272/x
b. See explanation for the cross product below.
c. Approximately 120 home runs will be hit.
What is a Proportion?A proportion can be defined as an equation that involves comparing two equal ratios that are equivalent to each other or set equal to each other.
a. To write a proportion that defines the situation described above, let x represent the number of runs he will hit in his career.
Therefore, we would have the following proportion:
159:15 = 1272:x
or
159/15 = 1272/x
b. Using the cross product, we can find the value of x as shown below:
159 × x = 1272 × 15
159x = 19,080
Divide both sides by 159
159x//159 = 19,080/159
x = 120
c. The number of runs he will hit in his career is: 120.
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f a national survey finds candidate A leads candidate B by 5 percent in the upcoming election and the margin of error in the survey is 3 percent, it means that:
candidate A leads candidate B by anywhere between 2 and 8 percentage points.
If the margin of error for the electoral poll is 3%, then candidate A has an advantage over candidate B of between 2 and 8 points.
Define the term margin of error?Your results will deviate by how many percentage points from the actual population value, according to your margin of error.
It is considered as a very small percentage that is allowed for error in calculations.
As the question stated-
A candidate would receive more or fewer points than the margin of error, which is the number of points.In this scenario, if one candidate has 5% more voting intentions than the other, it suggests that he is likely 5 points in front.The candidate is leading by three points, more or less, if the margin of error is three percent.This leads us to the conclusion as candidate A is 2 or 8 points ahead of voter intentions.This suggests that if the margin of error for the electoral survey is 3%, candidate A is leading of candidate B by 2 to 3 percentage points.
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The complete question is-
If a national survey finds candidate A leads candidate B by 5 percent in the upcoming election and the margin of error in the survey is 3 percent, it means that-
candidate A leads candidate B by exactly 5 percentage points. candidate A leads candidate B by anywhere between 2 and 8 percentage points. candidate A leads candidate B by exactly 3 percentage points.Would someone help me? This is due tomorrow
Answer: Someone already answered this but he said:
True, the product of three positive integers is positive.
What is a positive integer?
A positive integer is a non-negative whole number which belong to real numbers.
Examples of positive integer
1, 2, 3, 4, 5, 6, etc
Product of three positive integers
1 x 2 x 3 = 6
Thus, we can conclude that the product of three positive integers is positive.
The person is this guy: brainly.com/question/1367050
Answer: True
Step-by-step explanation:
If all the integers are positive, the only answer you get when multiplying them all is positive. If one of the three integers is negative, then the product is negative because if you have 2*3*(-1), the answer would be -6. But if you have 2*3*1, the answer is 6. If two of the three integers are negative, then the product is positive given the third integer is positive because a negative times a negative is a positive.
When we are writing in expanded form what digit do we put in the places in front of the digit given?
random signs or 0
When we are writing in expanded form we put zero (0) in the places in front of the digit given.
As we all know, zero (0) doesn't add any value or make any difference in the number while putting in front.
Hence, putting 0 in the front won't make any difference to the number
So, we put 0 in the front.
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Answer: Depends on the number!
Step-by-step explanation:
The digit to put in front of the given digit depends on the number. For example, if the given digit is an 8, then a 0 should be placed in front of it to indicate that it is a two-digit number. If the given digit is a 3, then a 0 should be placed in front of it to indicate that it is a three-digit number.
registrants at a large convention are offered 6 sightseeing tours on each of 3 days. in how many ways can a person arrange to go on a sightseeing tour planned by this convention?
The registrants would be able to see the 6 sightseeing tours in 18 ways.
Here it is given that the convention has organized the 6 sightseeing tours on 3 days each.
This implies that the 6 sightseeing tours are available on all three days.
Hence, the registrants would be able to book the tour on any of the one days.
Hence, on day 1
the registrants will be able to tour in ways
On day 2
the registrants would again be able to tour in 6 ways,
Similarly on day 3, they will again be able to tour in 6 ways.
Since they need to choose either of the days given, the total number of ways to tour will be
no.of ways for day 1 + no. of ways for day 2 + no. of d6ays for day 3
= 6 + 6 + 6
= 18 ways
Hence, they can go on a sightseeing tour in 18 ways.
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What score is a 12 out of 30?.
Can someone help me really quick
(Please Explain how you know this is correct.)
Answer:
It's b because 4 is half of 8 and 15 is half of 30.
Step-by-step explanation:
if u help me u will get brainlist for giving me the answer and explaining
Answer:78.
Step-by-step explanation:
A fortune wheel has 5 sections of equal size with the colours: red, green and white. The probability to get a red sector if you turn the wheel once is 40% Work out the number of red sectors .
The number of red sectors is given as 2.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
The total number of sectors on the fortune wheel is 5.
And, the probability of getting red colour is 40%.
Which is equivalent to 40/100 = 0.4.
The probability of getting red is given as,
P(red) = Number of red sectors ÷ Total number of sectors
=> 0.4 = Number of red sectors ÷ 5
=> Number of red sectors = 5 × 0.4
= 2
Hence, the number of red sectors are 2.
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Question Progress
2
لیا
5
Homework Progress
10/29 Marks
The nth term of a sequence is 25 - 3n
a) Work out the first three terms of the sequence.
9
7
b) Work out the value of the first negative term of the sequence.
8
First three terms of sequence are 25,22,19 and first negative term of the sequence is -2.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The nth term of a sequence is 25 - 3n
Twenty five minus three times of n.
25 - 3n
the first three terms are
the first term is 25
25-3=22
25-6=19
25-9=16
The first three terms are 25,22,19.
25-3(9)=25-27=-2
The first negative term of the sequence is -2.
Hence, first three terms of sequence are 25,22,19 and first negative term of the sequence is -2.
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A line passes through the points (–20, –18) and (–2, –18). What is its equation in slope-intercept form?
Answer:
slope: -18+18/-2+20
slope: 0:
y = -18
A boy cycles 12x km in 5 hours. How far can he cycle in 3y hours at the same average speed?
Answer:
Step-by-step explanation:
this is the Answer:
xy/180 km
Step-by-step explanation:
Mathematically, we have it that;
Speed = distance/ time
If he cycles x km in 3 hours
We know that ; 60 minutes = 1 hr
3 hours = 3 * 60 = 180 minutes
So the speed in km per minutes will be;
x km/180 minutes = x/180 km/minute
Recall,
Distance = speed * time
= x/180 * y = xy/180 km
HOPE THIS HELP !!!!!!!!!!!!!!!!!!!!!!!! :D
In the coordinate plane, line p has slope 13 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r?.
In the coordinate plane, line p has slope 13 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin.
Line P
Slope (m) = 13
y intercept is (0,2)
Equation is
y = mx+y
y= 13x+2
Dilated by scale factor of 3 with center at (0,3)
First make the centre at origin (0,0) by shifting the line 3 units downwards.
y = (13x+2)-3
y = 13x-1
In case of dilation, slope remains same only the y-intercept gets multiplied.
New equation is y = 13x-(1x3)
y = 13x-3
Now again take this line 3 units upwards
y = (13x-3)+3
y = 13x+0
Hence line r has slope of 13, y intercept is (0,0)
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If your job pays you a 10% commission based on your sales, how much
commission would you make if your sales were $20,000?
$200
$2,000
$20,000
$22,000
select all that apply. the probability of rolling an even number with a six-sided, equally weighted die is group of answer choices 1/3. 1/2. 1/6. 3/6.
Using the sample space, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.
In the given question we have to find the probability of rolling an even number with a six-sided dice.
The sample space of dice through the experiment is
{1,2,3,4,5,6}
The even numbers is {2,4,6}.
The probability of rolling an even number with a six-sided dice is
P(E)=Total number of even outcome/Total number of outcome
P(E)=3/6
P(E)=1/2
Hence, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.
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Factor the expression. 4x + 16. The factored expression is
Answer: 4(x+4)
Step-by-step explanation:
4 can be factored out because 4*x is 4x and 4*4 is 16
A table represents a relation that is also a function if it shows that every ____ value is assigned to _____ one ___ value
A table represents a relation that is also a function if it shows that every input value is assigned to exactly one output value
What is function?A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|If every element in set A has exactly one and only one image in set B, then the relation is said to be a function.A function is a relation from a non-empty set B such that its domain is A and it never has the same first member in two different ordered pairs.To learn more about function, refer to
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A new bank customer with 5000$ wants to open a money market account. The bank is offering a simple interest rate of 1.2 %.
a. How much interest will the customer earn in 20 years?
b. What will the account balance be after 20 years?
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i will give the brainliest answer for the first t answer ans help me get it right. do this if your smart i bet your not. it is worth 100 points
Francis heard that a car stereo system was on sale for 30%off. If the sale price was %57.75, what was the original price of the stereo?
Answer:
Original Price = Sale Price / ( 1 - Percent Off / 100 )
= 57.75 / (1 - 30/100)
= 57.75 / (1 - 0.3)
= 57.75 / 0.7
= $82.50
Original price = $82.50
