Heidi has to walk her bike for (1/8) mile to complete the loop.
Given that:-
Total distance of the loop = 7/8 mile
Distance Heidi rode on her bike before she stopped for rest = 1/2 mile
Distance Heidi rode on her bike after taking the rest = 1/4 mile.
We have to find the distance Heidi has to to walk to complete the loop because she had a flat tire.
Let the distance Heidi has to to walk to complete the loop because she had a flat tire is x miles.
We know that,
Total distance of the loop = Distance Heidi rode on her bike before she stopped for rest + Distance Heidi rode on her bike after taking the rest + distance Heidi has to to walk to complete the loop because she had a flat tire.
Hence, by adding the fractions, we get
7/8 = 1/2 + 1/4 + x
7/8 = (2+1)/4 + x
7/8 = 3/4 + x
7/8 - 3/4 = x
7/8 - 6/8 = x
1/8 mile = x
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1/4 g(x)=-4x-8 if g (-3)
Answer:
16
Step-by-step explanation:
x=-3
g(x)=4(-4(-3)-8)
g(x)=4(4)
g(x)=16
The sum of 5 times a number m and 12 is equal to 27
The value of m is 3
How to calculate the value of m ?The expression can be written as follows
The sum of 5 times a number m and 12 is equal to 27
5m + 12 = 27
collect the like terms
5m= 27-12
5m= 15
Divide both sides by the coefficient of m which is 5
5m/5 = 15/5
m= 3
Hence the value of m is 3
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Are the compositions of f(x) = 1 and g(x) = 2 commutative? Why or why not?
They are commutative, because f(x) and g(x) are constant functions.
They are commutative, because f(g(x)) and g(f(x) are constant functions.
They are not commutative, because f(x) and g(x) are not equal.
They are not commutative, because f(g(x)) and g(f(x) are not equal.
Answer:
first option
Step-by-step explanation:
They are cumulative because they are constant functions.
Is o.227 a rational number explain
Answer: 227 is a rational number because it can be expressed as the quotient of two integers: 227 ÷ 1.
Step-by-step explanation:
Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute. How many liters of water are in Tank A after the following amounts of time have passed?
4 minutes
80 seconds
minutes
How many minutes have passed, , when Tank A contains the following amounts of water?
151 liters
191.5 liters
270.25 liters
liters
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after the following amounts of time?
30 seconds
7 minutes
minutes
For how many minutes, , has the water been draining when Tank B contains the following amounts of water?
75 liters
32.5 liters
18 liters
liters
1)
In this question, we have been given Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
1 minute = 9 liters
⇒ 60 seconds = 9 liters
⇒ 20 seconds = 3 liters
We need to find the amount of water in the tank A
a) when 4 minutes
Given that, 1 minute = 9 liters
Let y1 liters of water in the tank A after 4 minutes
So, we get an equation,
y1 = 9 × 4
y1 = 36 liters
36 + 124 (initial water level) = 160 liters
Hence, 160 liters of water in the tank A after 4 minutes been passed.
b) when 80 seconds
From given information, 20 seconds = 3 liters
Let y2 liters of water in the tank A after 80 seconds
So, we get an equation,
20 (y2) = 3 × 80
y2 = 12 liters
12 + 124 (initial water level) = 136 liters
Hence, 136 liters of water in the tank A after 80 seconds been passed.
Now we need to find the amount of time passed when Tank A contains the following amounts of water.
i) 151 liters
151 - 124 = 27 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 27
t1 = 27 / 9
t1 = 3 minutes
This means, 3 minutes have passed when Tank A contains 151 liters of water.
ii) 191.5 liters
191.5 - 124 = 67.5 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t2 be the required time.
so, we get an equation,
9 × t2 = 1 × 67.5
t2 = 67.5 / 9
t2 = 7.5 minutes
t2 = 7 minutes 30 seconds
This means, 7 minutes 30 seconds have passed when Tank A contains 191.5 liters of water.
iii) 270.25 liters
270.25 - 124 = 146.25 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 146.25
t3 = 146.25 / 9
t3 = 16.25 minutes
t3 = 16 minutes 15 seconds
This means, 16 minutes 15 seconds have passed when Tank A contains 270.25 liters of water.
----------------------------------------------------------------------------------------------------
2)
In this question, Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute.
⇒ 1 minute = 2.5 liters of water drained
⇒ 60 seconds = 2.5 liters
⇒ 10 seconds = 0.42 liters
We need to find the amount of water drained from tank B
a) after 30 seconds
Let x1 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
10 (x1) = 30 × 0.42
x1 = 3 × 0.42
x1 = 1.26 liters
b) after 7 minutes
Let x2 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
x2 = 7 × 2.5
x2 = 17.5 liters
Now, we need to find the time in which the water is draining when Tank B contains
i) 75 liters
80 - 75 = 5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t1 be the required time.
so, we get an equation,
2.5 × t2 = 5
t1 = 5 / 2.5
t1 = 2 minutes
This means, after 2 minutes Tank B contains 5 liters of water.
ii) 32.5 liters
80 - 32.5 = 47.5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t2 be the required time.
so, we get an equation,
2.5 × t2 = 47.5
t2 = 47.5 / 2.5
t2 = 19 minutes
This means, after 19 minutes Tank B contains 32.5 liters of water.
iii) 18 liters
80 - 18 = 62 liters of more water filled.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t3 be the required time.
so, we get an equation,
2.5 × t3 = 62
t3 = 5 / 2.5
t3 = 24.8 minutes
t3 = 24 minutes 48 seconds
This means, after 24 minutes 48 seconds Tank B contains 18 liters of water.
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An advantage of a weighted moving average is that recent actual results can be given more importance than what occurred a while ago. True or false?.
An advantage of a weighted moving average (WMA) is that recent actual results can be given more importance than what occurred a while ago is a "true" statement because "Weighted moving averages could be adjusted to emphasize more recent data in forecasting."
What is moving average?Moving averages are popular tools for measuring momentum among active traders. The formula used to calculate the average is the primary distinction between a simple moving average, a weighted moving average, and an exponential moving average.
Some key features regarding the weighted moving average are-
The SMA calculates the average price above a specific time period, whereas the WMA emphasizes current data.The exponential moving average (EMA) is also weighted to reflect the most recent prices, however the rate of decrease among one price and its previous price is not constant but exponential.Weighted moving averages give more weight to recent data points as they're more relevant than data points from the distant past. The total of the weightings should equal 1 (or 100%). The weightings are distributed equally in the case of the simple moving average.To know more about moving average, here
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show your work for -4x+3(2x-5)=31
Step-by-step explanation:
[tex] - 4x + 3(2x - 5) = 31 \\ - 4x + 6x - 15 = 31 \\ 2x - 15 = 31 \\ 2x = 31 + 15 \\ 2x = 46 \\ x = 46 \div 2 \\ x = 23[/tex]
Dyani began solving the equation g = x-1/k for x by using the addition property of equality. explain dyani's error. then describe how to solve for x
Given equation g = x-1/k in terms of x would be x = 1 + gk
for given question,
we have been given an equation g = x-1/k
Dyani began solving the equation g = x-1/k for x by using the addition property of equality.
We solve given equation for x.
⇒ g = x-1/k ..........(Given)
⇒ gk = (x - 1/k)k .........(Multiply both the sides by k)
⇒ gk = x - 1
⇒ gk + 1 = x - 1 + 1 .........(Add 1 to each side)
⇒ gk + 1 = x
⇒ x = 1 + gk
Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk
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help because i paay 30 a month 4 thisssd
Answer:
2c+2
The number that will go in the green box is 2.
Step-by-step explanation:
3c-1-c+3
Combine the like terms.
3c-1-c+3=2c+2
Hope this helps!
Please mark as brainliest if correct!
Three consecutive even integers such that the sum of the smallest integer and twice the middle integer is 20 more than the largest integer. What is the largest integer?
14 is the largest integer.
Let x, x+2 & x+4 be the 3 integers.
x + 2 (x+2)= (x+4)+20
x + 2x + 4 = x + 4 + 20
3x + 4 = x + 24
3x - x = 24 - 4
2x = 20
x = 20/2
x=10 for the smallest integer.
10 + 2 = 12 for the middle integer.
10 + 4 = 14 for the largest integer.
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Q.5 - Solve the equation 3(2x - 4) = 8 + 2x + 6. Show your work.
Answer: x=6.5
Step-by-step explanation:
3(2x - 4) = 8 + 2x + 6
6x-12=14+2x
4x-12=14
4x=26
x=26/4
x=6.5
Find an equation for the perpendicular bisector of the line segment whose endpoints are (−4,−1) and (8,-5)
An equation for the perpendicular bisector of the line segment whose endpoints are (−4,−1) and (8,-5) is [tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]
Find the line [tex]$y=m x+b$[/tex] passing through [tex]$(-4,-1),(8,-5)$[/tex]
Compute the slope [tex]$(-4,-1),(8,-5): \quad m=-\frac{1}{3}$[/tex]
Compute the [tex]$y$[/tex] intercept: [tex]$\quad b=-\frac{7}{3}$[/tex]
Construct the line equation [tex]$y=m x+b$[/tex] where [tex]$m=-\frac{1}{3}$[/tex] and [tex]$b=-\frac{7}{3}$[/tex]
[tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]
A perpendicular bisector can be defined as a line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. We can draw a perpendicular bisector using a rule, a compass and a pencil.
Two lines are said to be perpendicular to each other when they intersect each other at 90 degrees or at right angles. And, a bisector is a line that divides a line into two equal halves. Thus, a perpendicular bisector of a line segment AB implies that it intersects AB at 90 degrees and cuts it into two equal halves.
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90° angle.
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PLEASEE HELP!! I WILL MARK BRAINLIEST!
Write the expression as a number in scientific notation. quantity 5 times 10 squared end quantity times quantity 4.2 times 10 to the fourth power end quantity all divided by quantity 6 times 10 cubed 3.5 x 103 3.5 x 105 3.2 x 103 3.2 x 105
The expression in scientific notation is given as follows:
3.5 x 10³.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
For this problem, the expression is given by:
[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}[/tex]
When two factors of a multiplication have the same base and different exponent, we keep the base and add the exponents, hence:
[tex]10^2 \times 10^4 = 10^6[/tex]
5 x 4.2 = 21, hence the expression is:
[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}[/tex]
When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3[/tex]
Which is the simplified expression.
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What transformations of the graph of (x)=|x| are applied to graph the function g?
The function g(x) = - |x| + 2 is the result of applying a reflection about the x-axis and a translation 2 units up.
What transformation must be applied to modify the absolute value function?
In this problem we find a resulting expression, that is, the function g(x) = - |x| + 2. This is the result of a sequence of rigid transformations done on the parent absolute value function, that is, the function f(x) = |x|. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved in the entire function.
After a quick inspection, we find that two rigid transformations were used in the following order:
Reflection around the x-axis.Translation 2 units up.Now we proceed prove this procedure:
f(x) = |x|
Step 1
f'(x) = - |x|
Step 2
g(x) = - |x| + 2
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Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hours. relative to its type, which candle burned faster?
The cinnamon-scented jar candle brunt faster.
What does relative speed means ?Relativity means observing some action with different perspective.
Suppose you are moving in a bus at 100 km/hr and you are reading a book.To an observer which you are passing by you and the book he observes moving at a speed of 100 km/hr.But for you the book is not moving at all because both you and the book is moving at a speed of 100 km per hour.
According to the given question Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hours.
From the given data of burning hours we can observe that berry-scented pillar candle that burned for 888888 hours which is more that of Andrei had cinnamon-scented jar candle that brunt for 303030 hours because
30303030 < 888888.
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Without random selection, we cannot appropriately apply the laws of probability to perform inference. True or false?.
Answer:
true
Step-by-step explanation:
needed to eliminate bias
a house is drawn to the scale of 1/4in = 5 ft. Its rectangular kitchen measures
4.5 inches by 6.5 inches on the blueprints. What is the actual length and width of the kitchen?
Find the actual area of the kitchen.
Answer:
1 : 4 1/2 :: 8 1/5 : x proportion
x = (4 1/2)(8 1/5) product of means/extremes
x = (9/2)(41/5) change improper fraction
x = 369/10 multiply
x = 36.9 change to decimal
On a coordinate plane, a parabola with equation f (x) = squared minus 4 x + 2 opens up. It goes through (0, 2), has a vertex at (2, negative 2), and goes through (4, 2).
Consider the function shown. How can you restrict the domain so that f(x) has an inverse? What is the equation of the inverse function?
x > –2; f Superscript negative 1 Baseline (x) = 2 minus StartRoot x + 4 EndRoot
x > –2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
x > 2; f Superscript negative 1 Baseline (x) = 2 minus StartRoot x + 4 EndRoot
x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
The domain at which the function f(x) = x² - 4•x + 2, and the inverse of the function, f(x), is given by the option;
x > 2; [tex] f^{-1}(x) = 2 + \sqrt{x + 2} [/tex]How can the inverse function and the domain of the inverse function be found?The given function is f(x) = x² - 4•x + 2.
The points through which the parabola passes are;
(0, 2)(2, -2), which is the vertex(4, 2)The inverse of the function is found as follows;
f(x) = x² - 4•x + 2
The standard form of a quadratic equation is f(x) = a•(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
a = The coefficient of x²
Comparing, we have;
(h, k) = (2, -2)
a = 1
Which gives;
f(x) = x² - 4•x + 2 = (x - 2)² - 2
f(x) = (x - 2)² - 2
Let f(x) = y
y = (x - 2)² - 2
y + 2 = (x - 2)²
x - 2 = √(y + 2)
x = √(y + 2) + 2 = 2 + √(y + 2)
x = 2 + √(y + 2)
Therefore, f(x) has an inverse when y > -2, which gives;
The domain where f(x) has an inverse is x > 2, given that the expression, 2 + √(y + 2), is always positive.
The inverse of the function is obtained by changing x to [tex] f^{-1}(x) [/tex] and y to x in the equation, x = 2 + √(y + 2), to give;
[tex] f^{-1}(x) = \mathbf{2 + \sqrt{x + 2}} [/tex]The correct option is therefore;
x > 2, f superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
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Answer:
Its D.x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
Step-by-step explanation:
What is d if [tex]\frac{3d-2}{8} = -d+16\frac{1}{4}[/tex]
Answer: d=12
Step-by-step explanation:
[tex]\displaystyle\\\frac{3d-2}{8} =-d+16\frac{1}{4} \\\\\frac{3d-2}{8} =-d+\frac{16*4+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{64+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{65}{4}[/tex]
Multiply both parts of the equation by 8:
[tex]\displaystyle\\3d-2=(-d+\frac{65}{4} )(8)\\\\3d-2=-8d+65*2\\\\3d-2=-8d+130\\\\3d-2+2=-8d+130+2\\\\3d=-8d+132\\\\3d+8d=-8d+132+8d\\\\11d=132\\[/tex]
Divide both parts of the equation by 11:
[tex]d=12[/tex]
Which is the order from least to greatest of the following: four thirds, 0.8, one fifth, thirty percent?
four thirds, 0.8, one fifth, thirty percent
thirty percent, four thirds, 0.8, one fifth
one fifth, four thirds, thirty percent, 0.8
one fifth, thirty percent, 0.8, four thirds
The order from least to greatest of the numbers will be D. one fifth, thirty percent, 0.8, four thirds.
How to calculate the value?It should be noted that 1/5 = 0.2
It should be noted that 30% = 0.3
It should be noted that 4/3 = 1.33
Therefore the order from least to greatest of the numbers will be one fifth, thirty percent, 0.8, four thirds
In conclusion, the correct option is D.
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56+85+95+42= i need help from Zoe witthans
Answer:
278
Step-by-step explanation:
First, add 85+95=180.
Then, add 56+42=98
Add 180+98=278
9n-22=4n + 3
And please explain how you got your answer, I’ve gotten this far (look at image) but I don’t know what to do now
Complete each function table,then graph the function
The y values from:
1. ₋6
2. ₋3
3. 0
4. 3
Given the x values and y value as y = 3x
1. when x = ₋2 then y = 3x
y = 3(₋2)
y = ₋6
2. when x = ₋1 then y = 3x
y = 3(₋1)
y = ₋3
3. when x = 0 then y = 3x
y = 3(0)
y = 0
4. when x = 1 then y = 3x
y = 3(1)
y = 3
therefore we get the points as (₋2 , ₋6) (₋1 , ₋3) (0,0) (1 , 3).The graph is pltted and attached.
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Rename the fraction as a decimal.
1/50 =
-
Answer:
0.02
Step-by-step explanation:
whats 4x5x6x32x4x4x4x4
Answer:
983,040
Step-by-step explanation:
4×5=20
6×32=192
4×4=16
4×4=16
20×192×16×16
=983,040
square root 147 simplified
Answer:
7√3
Step-by-step explanation:
What is 424.4 ÷ 8? show your work
Answer: 53.05
Step-by-step explanation: Simply divide both using the division method. Show your work as the method. (would recommend drawing out the problem)
Answer:
60.5
Step-by-step explanation:
60.5
8 424
-42
0
4.0
4.0
0
Find the difference between simple interest and annual compound interest on Rs 9,600 for 2 yers at the rate of 5 % per annum.
Answer:
Rs 984
Step-by-step explanation:
Principal (P) = Rs 9,600
Time (T) = 2 years
Rate (R) = 5%
Simple Interest (SI) = [tex]\frac{PTR}{100}[/tex]
SI = [tex]\frac{9600*2*5}{100}[/tex]
SI = [tex]\frac{9600}{10} = Rs 960[/tex]
Compound Interest (CI) = 9600 * [tex]\frac{41}{100} = 24*41 = Rs 984[/tex]
Two shops rent pairs of skis for a rental fee plus a fee
per hour. The table shows the total costs (in dollars)
for different numbers of hours at Shop A. The total
costy (in dollars) for x hours at Shop B is
represented by the equation
y = 2x + 8.
Which shop charges less per hour?
• Shop A
O Shop B
How many hours must a pair of skis be rented for the total costs to be the same?
The total costs are the same when a pair of skis is rented for
hours.
PLS HELP
Using linear functions, it is found that:
Shop B charges less per hour.The total costs are the same when a pair of skis is rented for 3 hours.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For Shop A, we have that the slope is of 3, as the cost increases by $3 an hour, hence:
yA(x) = 3x + b.
When x = 1, y = 8, hence we find the intercept b as follows:
8 = 3 + b
b = 5.
Hence:
yA(x) = 3x + 5.
For Shop B, the rule is given as follows:
yB(x) = 2x + 8.
Due to the lower slope, we have that:
Shop B charges less per hour.
The costs will be the same when:
yA(x) = yB(x).
Hence:
3x + 5 = 2x + 8
x = 3.
The total costs are the same when a pair of skis is rented for 3 hours.
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A party of 17 comes in the door. What is the leastnumber of tables needed to seat them together?
Answer: 1
Step-by-step explanation:
How big is the table? 1 table can fit all 17 people if the table is big enough.