Answer:
£9.40
Step-by-step explanation:
Given variables:
f = fixed amount for each journey (in pounds)p = pence per mileDefined variables:
Let x = number of miles.Let y = total cost (in pounds).1 pound = 100 pence ⇒ 1 pence = 0.01 pounds
Therefore, the equation that models the given scenario is:
[tex]y = 0.01px +f[/tex]
Given:
A 4-mile journey costs £5.40A 7-mile journey costs £7.80Substitute the given information into the equation to create two equations:
[tex]\implies f+0.01(4)p=5.40[/tex]
[tex]\implies f+0.01(7)p=7.80[/tex]
Therefore:
[tex]\implies f+0.04p=5.40[/tex]
[tex]\implies f+0.07p=7.80[/tex]
Subtract the first equation from the second to eliminate f:
[tex]\implies 0.03p=2.40[/tex]
Solve for p:
[tex]\implies \dfrac{0.03p}{0.03}=\dfrac{2.40}{0.03}[/tex]
[tex]\implies p=80[/tex]
Substitute the found value of p into one of the equations and solve for f:
[tex]\implies f+0.04(80)=5.40[/tex]
[tex]\implies f+3.20=5.40[/tex]
[tex]\implies f=2.20[/tex]
Substitute the found values of p and f into the equation to create an equation for the cost of x miles:
[tex]\implies y=0.8x+2.2[/tex]
To find the cost of a 9-mile journey, substitute x = 9 into the found equation:
[tex]\implies 0.8(9)+2.2=9.40[/tex]
Therefore, the cost of a 9-mile journey is £9.40.
A teacher recorded unit 4 test scores from her class.
58, 64, 66, 70, 71, 75, 77, 80,
84, 85, 87, 90, 93, 95, 96.
Find the percentile rank of a score of 71 on this street -
Victor is in the 60th percentile, what was his score?
The percentage score for a 71 on the test is 27, and the winning score is 71.
What is Statistics?The science of statistics focuses on creating and researching strategies for gathering, evaluating, interpreting, and reporting empirical data.
As per the given information in the question,
The given scores are:
5, 4, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, and 96.
A percentage is a number in a range of one to 100 that represents the percentage of a range that falls inside or above it.
Formula for calculating percentile rank on a test score of 71,
R₁₀₀ = [100(N <) + 1/2]/N
=100 × 4 + 1/2(1)/15
=400 + 0.5/15
=400.5/15
=26.7=27th
Now we need to find the score of victor who has 60th percentile.
60 = Score/15
Score = 71
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List all of the integer values that could take that would satisfy the inequality shown on the number line below.
List all of the integer values that could take that would satisfy the inequality shown on the number line below.
(-2 , 1.5)
a liner function contains the following points. what are the slope and y-intercept of this function (0,2) (-3,4)
The function is actually (0,-3)(2,4)
Slope:
slope = y2-y1 = 4-(-3) = 7/2
x2-x1 2-0
y intercept: (0,-3)
There were 794 fih at 9:00 A. M. The dolphin were fed at 5:00 P. M. There were 209 fih left etimate how many fih the dolphin ate
the number of fih at 9:00 A.M. (794), which yields 209 fih, the number of fih left at 5:00 P.M. is 585 fih
Subtract the number of fih at 9:00 A.M. (794) from the number of fih left at 5:00 P.M. (209).
794 - 209 = 585
Therefore, the dolphin ate 585 fih.
To estimate how many fih the dolphin ate, we must first subtract the number of fih at 9:00 A.M. (794) from the number of fih left at 5:00 P.M. (209). This gives us 585 fih, which is the estimated number of fih that the dolphin ate. This calculation can be verified by subtracting the number of fih the dolphin ate (585) from the number of fih at 9:00 A.M. (794), which yields 209 fih, the number of fih left at 5:00 P.M.
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The heights of the starting 5 players (not including the libero) on a volleyball team like karasuno high school are 60 inches, 67 inches, 64 inches, and 65 inches. If the balance point of the players is 65, what is the height of the 5th player?.
The height of the 5th player would be 69 inches
To find the Height, first, we have to calculate the mean value.
No. of players=5
The height of 4 players is 60 inches, 67 inches, and 64 inches, 65 inches.
Mean =Sum of observations/No of observations
Mean of the 5th players=65
To find, Height of 5th player
As we know,
Assuming the height of the 5th player is x
Mean =Sum of observations/No of observations
65=(60+67+64+65+x)/5
65*5=60+67+64+65+x
325=256+x
x=69
Thus, the height of the 5th player is 69 inches.
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Which of the following terms represents the situation shown in the graphic below?
a glide a reflection a glide reflection
None of these choices are correct.
The term that represents the situation shown in the graphic below is B. a reflection
What is a a reflection?A glide reflection or transflection is a symmetry operation in two-dimensional geometry that combines a reflection over a line with a translation along that line into a single operation.
An exchange of points from one side of a line with points on the other side of the mirror at the same distance from the mirror occurs when a mirror line is fixed in the plane. There is a mirror line in every reflection. A mirror reflection is followed by a translation that is parallel to the mirror to create a glide reflection.
Here, the shape is mirrored in the reflection. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
In conclusion, based on the information given, it should be noted that the correct option is B.
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If a rectangle and a quare have the ame perimeter then which one will have a larger area
The area of the square is bigger than the Area of the rectangle.
Suppose the sum of all the sides in a square is this: 4 x A and the same is true of a rectangle, too.
Then, first, the area of the square is A^2.
And next, assuming that we have this: 0 < X < A and that one side in the rectangle is this: (A - X)
we can say that the side next to (A - X) is this: (A + X) because the sum of all the four sides in the rectangle has to be this: (4 x A), which equals the sum of all the sides in the square.
So now, the area of the square is this: A^2, whereas the area of the rectangle is this: (A^2 - X^2), which equals this: (A + X)(A - X).
You know thus now, which of the two areas is bigger, and it’s the area of the square. And the difference between the two areas is this: X^2.
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The city planner wants to put recycling bins at the circumcenter of the park. What are the coordinates of the recycling bins?.
The coordinates of the recycle bin will be = ( -1, 2.5 )
According to the information given in the question,
The coordinates of the vertices of the park are,
( 1, 1 ), ( 1, 4 ), and ( -3, 4 )
We have to find the coordinates of the recycle bin.
Let us consider the equation of the circle,
[tex]x^{2} +y^{2}+Dx + Ey+ F =0[/tex]
So putting the values of the coordinates into the equation,
First Equation,
[tex]1^{2}+1^{2} + D + E + F = 0[/tex]
Second Equation,
[tex]1^{2} +4^{2} +D + 4E + F=0[/tex]
Third Equation,
[tex](-3)^{2} + 4^{2} - 3D+4E+F=0[/tex]
Subtracting the first equation from the second,
[tex]1^{2} +4^{2} +D + 4E -E=0[/tex]
15 + 3E = 0
3E = -15
E = -5
Subtracting the third equation from the second,
1 + 16 - 9 - 16 + D + 3D = 0
4D = 8
D = 2
Putting the values of E and D in the first equation,
1 + 1 + D + E + F = 0
F = -2 - D - E
F = 1
So now the equation of the circle becomes,
[tex]x^{2} +y^{2}+2x - 5y+ 1 =0[/tex]
By expanding the above equation we can find the standard equation,
[tex]x+2x+1^{2} +y^{2} -5y+ 2.5^{2}- 1^{2} -2.5^{2} +1 =0[/tex]
[tex](x+1)^{2} + (y - 2.5)^{2} = 1^{2} + 2.5^{2} -1[/tex]
[tex](x+1)^{2} + (y - 2.5)^{2} = 2.5^{2}[/tex]
So the required circumcenter will be = ( -1, 2.5 )
Therefore, the coordinates of the recycle bin will be = ( -1, 2.5 )
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A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (1,4), and (-3,4). The city planner wants to put recycling bins at the circumcenter of the park. What are the coordinates of the recycling bins?
the audit team is planning to examine a sample of control policies and procedures. assume that, based on the intended degree of reliance on internal control, the audit team wishes to control the risk of overreliance to 5%. in addition, based on prior engagements, the audit team anticipates an expected deviation rate of 2%. what would be the impact of reducing the tolerable rate of deviation from 7% to 5% on the sample size?
As per the impact of reducing the tolerable rate of deviation from 7% to 5% on the sample size is 93.
The term deviation is defined as a measure that is used to find the difference between the observed value and the expected value of a variable.
Here we have given that the audit team is planning to examine a sample of control policies and procedures. assume that, based on the intended degree of reliance on internal control, the audit team wishes to control the risk of overreliance to 5%.
And we need to find sample size.
While we looking into the given question, we know that the tolerable rate of deviation from 7% to 5% on the sample size.
Let us consider that 100 be the sample size, then the reduction in 7% to 5%, tell that there is an 2% decrement in the sample size.
Therefore, it can be calculated as,
=> 100 x 2/100
=> 2
Here we already know that the risk of overreliance to 5%.
Then the total value is
=> 5 + 2 = 7.
Then the sample size is
=> 100 - 7
=> 93.
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114=6p
x/4=16
75=y-25
answer pls
Answer:
p = 19
x = 64
y = 100
Step-by-step explanation:
114 = 6p
Divide by 6 into both sides
p = 19
x/4 = 16
Times 4 into both sides
x = 64
75 = y - 25
Add 25 to both sides
y = 100
(a) how many 4-permutations are there of a set of six objects? (b) how many 2-permutations are there of a set of nine objects?
There will be a total of 720 4- permutations of a set of six objects. And there will be a total of 72 2- permutations of a set of nine objects.
The calculation for 4-permutations of a set containing six objects
P(6,4)! = 6! / (6-4)1
P(6,4)! = 6×5×4×3x2
P(6,4)! = 720
Therefore, there will be a total of 720 permutations.
The calculation for 2- permutation of a set containing 9 objects
P(9,2)! = (9,7)! = (9-2) = 9! / 7!
P(9,2)! = 9×8x7! / 7!
P(9,2)! = 72
Therefore, there will be a total of 72 permutations.
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which graph represent 5x-2y=3
Answer:
The answer is below; I have put the equation and graphed it!
Step-by-step explanation:
Graph the line whose equation is given in Point slope form. y+7=2(x-4)
Some of the coordinates on the graph are (0, -15), (1, -13), (2, -11).
The graph of the equation is given below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates of the equation y + 7 = 2 (x - 4).
y + 7 = 2 (x - 4)
y = 2(x - 4) - 7
y = 2x - 8 - 7
y = 2x - 15
For x = 0,
y = - 15
(0, -15)
For x = 1,
y = 2 - 15 = -13
(1, -13)
For x = 2,
y = 4 - 15 = -11
(2, -11)
And so on...
Thus,
The graph of the equation is given below.
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19a - 6 = 4a please help me solve this! this is due in two days and the entire paper has 50 questions, this is only question 27!!
Answer:
a=6/15
Step-by-step explanation:
19a-6=4a
(19-4)a=6
a=6/15
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Answer:
a= 2/5 =0.4
Step-by-step explanation:
19a−6=4a
Subtract 4a from both sides.
19a−6−4a=0
Combine 19a and −4a to get 15a.
15a−6=0
Add 6 to both sides. Anything plus zero gives itself.
15a=6
Divide both sides by 15.
a= 6/15
Reduce the fraction 6/15 to lowest terms by extracting and canceling out 3.
a=2/5
help me with this math question
Answer:
Step-by-step explanation:
y = -5 (x² + 1 - 2x) + 5
y = -5x² + 10x - 5 + 5
y = -5x² + 10x
maximum height = y coordinate of the vertex of the parabola
x = -10/-10
x = 1
y = -5 (1)² + 10 (1)
y = -5 + 10
y = 5
5 meters
b) the x coordinate of the vertex is 1
1 meter
c) since the term without x is 0, the ball was kicked from the ground
0 meters
d) we have to find the x-intercept
-5x² + 10x = 0
-5/-5 x² + 10/-5 x = 0/-5
x² - 2x = 0
x(x-2) = 0
x = 0
x = 2
2 meters
Given that f(x) = 2x^2 + 9x and p = f(-3), what is the value of 3p?
Answer:
–27
Step-by-step explanation:
f(x) = 2x² + 9x
f(–3) = 2(–3)² + 9(–3)
= 2(9) + –27
= 18 – 27
= –9
since p= f(–3) = –9
3p = 3 × – 9 = –27
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Mr. Harold invested $1,600 in an account
that paid him 3.25% simple interest. What
will be the balance of his account after
32 years, including interest?
A) $1,664.00
C) $16,640.00
B) $1,536.00
D) $3,264.00
Determine the value for x in the given diagram, with a || b.
35°
55°
125°
None of these choices are correct.
Answer:
125°
Step-by-step explanation:
the given problem is related to co-interior angle
so.
please show your work
d) [tex]\frac{48y^{10} }{x^{9} }[/tex] is the answer to your question
Exponents:
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64.In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6.The symbol used for representing the exponent is ^. This symbol (^) is called a carrot. For example, 4 raised to 2 can be written as 4^2 or 42. Thus, 4^2 = 4 × 4 = 16Adding exponents while maintaining the same base is the rule for multiplying like bases.exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.To know more about Exponents:
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The sum of 3 consecutive even numbers is 54 what’s the largest number
The largest number is 20 .
What is largest ?
There is a big number—a googolplex—that exists. It consists of 1 and 10100 zeros (googol). A googolduplex, which is an even larger number, is also present. It is 1 and over a googol zeros after that.
Let 'n' be any number, odd or even.
2n will always be even number. This is because, 2n has 2 as common factor. So, 2n is always even.
Eg: 2= 2×1, n=1 ; 4=2×2, n=2 etc
Numbers are even, consecutive.
Consecutive even numbers are 2n-2, 2n, 2n+2,
Eg : For consecutive even numbers, put n=2
2n-2=4-2=2
2n=4
2n+2 =4+2=6,
we get 2,4,6 which are consecutive even nos.
So, numbers are 2n-2, 2n and 2n+2
Their sum= 2n+2+2n+2n-2=6n
Sum=54
6n=54
n=54/6=9
So, n=9
Consecutive numbers are
2n-2= (2×9)-2=16
2n=2×9=18
2n+2=18+2=20.
So, numbers are 16, 18, 20. Their sum is 54.
The largest number is 20
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three less than twice an integer is greater than 1
2x - 3 > 1
x represents an integer and 3 is less than twice an integer which is 2x. So it's 2x - 3.
2x - 3 is greater than 1.
So therefore, the answer is 2x - 3 > 1
Answer:
2x-3>1
Step-by-step explanation:
lets say x is the interger
so twice an interger would be 2*x or 2x
and three less than that would be 2x-3
and 2x-3 is greater than one
so, 2x-3>1
Find the measure of each angle indicated.
A. 70 degrees
B. 110 degrees
Help!!!
Answer:
110 degrees
Step-by-step explanation:
This is because they are alternate exterior angles
So they are the same angle
The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.3 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 4600 MB. How many downloads of the standard version were there?
Answer:
The number of downloads of the standard version is 230.
Step-by-step explanation:
Let x be the number of downloads of the standard version.
The number of downloads of the high-quality version is 4x.
The total size downloaded for the standard version is 2.8x MB.
The total size downloaded for the high-quality version is 4.3(4x) = 17.2x MB.
The total size downloaded for both versions is 2.8x + 17.2x = 4600 MB.
Combining like terms, we have 20x = 4600 MB.
Dividing both sides by 20, we have x = 230 downloads of the standard version
Two cell phone plans offer differing text packages. The two plans are outlined below: Plan A: $9.25 per month charge along with a charge of $0.06 per text. Plan B: $2.50per month charge, but a charge of $0.20 per text. Is there a certain number of texts, when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.
Answer:
48
Step-by-step explanation:
Let T be the number of texts sent on each plan.
The cost of Plan A can be represented as $9.25 + $0.06T.
The cost of Plan B can be represented as $2.50 + $0.20T.
We want to find the number of texts T at which the two plans cost the same amount. Therefore, we can set the two equations equal to each other and solve for T:
$9.25 + $0.06T = $2.50 + $0.20T
Subtracting $2.50 from both sides, we get:
$6.75 + $0.06T = $0.20T
Subtracting $0.06T from both sides, we get:
$6.75 = $0.14T
Dividing both sides by $0.14, we get:
T = 48.21
Therefore, the number of texts at which the two plans cost the same amount is approximately 48 texts. This means that if you send fewer than 48 texts per month, Plan A will be cheaper, and if you send more than 48 texts per month, Plan B will be cheaper.
Find the sales tax
Selling Price 70.00
Rate of Sales Tax 7%
Sales tax ?
The sales tax is [aswer]
An angle measure 8 less than the measure of its supplementary angle.what is the angle measure of each angle
Step-by-step explanation:
Let the larger angle be x.
Smaller angle = x - 8
As both angles are supplementary,
x + (x - 8) = 180°
2x - 8 = 180°
2x = 188°
x = 94°
Therefore, larger angle = 94°
Smaller angle = 94° - 8° = 86°
DISTANCE The graph represents the distance y in miles Roland is from home as a function of time x in hours. Which could very likely be true?
WHAT IS DISTANCE?
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria
You need to write complete questions in order to get good and exact answers. Here you haven't provided any graph so I could help you giving you my own graph. The relationship between speed, time and distance is as follows:
Where:
[tex]d=v t[/tex]
[tex]Where :[/tex]
[tex]d: Distance[/tex]
[tex]v:speed[/tex]
[tex]t : time[/tex]
So [tex]v[/tex] represents slope of a line that passes through the origin. In this case:
d matches the y-axis
t matches the x-axis.
So:
[tex]y=m x \rightarrow d=v t[/tex]
[tex]Where:[/tex]
[tex]\begin{aligned}& y \rightarrow d \\& m v \rightarrow v\end{aligned}[/tex]
[tex]x \rightarrow t[/tex]
The graph below (Car A) comes from the following equation:
[tex]y=\frac{5}{3} x[/tex]
And the equation for car B is:
[tex]y=\frac{5}{6} x[/tex]
By comparing them, car A moves faster than car B because:
[tex]\frac{5}{3} > \frac{5}{6}[/tex]
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Write an equation in slope-intercept form of the line that passes through (-4, 3) and (-3, 1) .
An equation is
Answer: Y=-2x-5
Step-by-step explanation:
Points: (-4, 3) & (-3, 1)
To find the slope, we use m= (y₂-y₁)/(x₂-x₁)
With these points, m= (1-3)/(-3--4)
This gives us m= -2/1, or -2
Slope-intercept form is y=mx+b
We can plug in the slope now, so y=-2x+b
B is the y-intercept, which is -5, in this case
This gives us y=-2x-5
Tell which property you used. 50x (20 x 1.3)
Answer:100x * 65
Step-by-step explanation:
distribute the 50 into 20 and 1.3 then set it up
Is the data set approximately periodic?
If so, what are its period and amplitude?
Hour
Number of bikes
O
O
not periodic
1 2 3 4 5 6
7
5 19 14 4 19 15 6
8 9 10 11 12
5 20 16
22 15
periodic with period of 3 and amplitude of about 7.5
periodic with period of 4 and amplitude of about 7.5
periodic with period of 4 and amplitude of about 5
The data is A. periodic with period of 3 and amplitude of about 7.5
How to illustrate the data?From the information, we are given the number of hours as well as the number of bikes. It should be noted that we can see that ty values are periodic as it repeats every third value.
Also, the amplitude will be the:
= Larger value - Smallest value / 3
For the first set it is 7.
For the second set it is 7.5
For the third set it is 8
For the fourth set it is:
= (20 - 5)/2
= 7.5
Therefore, the amplitude is 7.5
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