Chen did not earn a bonus for his journey because his fuel efficiency was below the required threshold of 2.8 kilometers per liter.
To determine whether Chen earned a bonus for his journey, we need to calculate his fuel efficiency in kilometers per liter. Fuel efficiency can be calculated by dividing the total distance traveled by the amount of fuel used.
First, let's calculate the total distance traveled. We can do this by multiplying the average speed by the journey time:
Total distance = Average speed * Journey time = 61 km/hr * 4.5 hours = 274.5 km
Next, we divide the total distance by the fuel used to calculate the fuel efficiency:
Fuel efficiency = Total distance / Fuel used = 274.5 km / 96 liters ≈ 2.86 km/l
The calculated fuel efficiency is approximately 2.86 kilometers per liter. Since this value is above the required threshold of 2.8 kilometers per liter, Chen did not earn a bonus for his journey.
Therefore, based on the given information, Chen did not earn a bonus for his journey because his fuel efficiency was below the required threshold of 2.8 kilometers per liter.
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[tex] \color{red} \sf Solve \: for \: x : \\ \sf \: \: 4x + 2 = -8?[/tex]
Thank uh !
Answer:
[tex]\huge\boxed{\sf x = -2.5}[/tex]
Step-by-step explanation:
Given equation:4x + 2 = -8
Subtract 2 to both sides
4x = -8 - 2
4x = -10
Divide 4 to both sides
x = -10/4
x = -2.5[tex]\rule[225]{225}{2}[/tex]
Answer:
x = -5/2x = -2.5Step-by-step explanation:
4x + 2 = - 8
Subtract 2 from both sides,
4x = - 8 - 2Subtract 2 from - 8 = - 10,
4x= -10Divide both sides by 4,
4x/4 = -10/4x = - 5/ 2 or x = - 2.5____________________
Please help asap!!! thank ya
What are the solutions to the equation below?
2x^2 - x + 1 = 0
1/4 - startroot 5 endroot/ 4 and 1/4 + startroot 5 endroot / 4
1/4 - startroot 7 endroot/ 4 and 1/4 + startroot 7 endroot/ 4
1/4 - startroot 7 endroot/ 4 i and 1/4 + startroot 7 endroot/4 i
1/4 - startroot 5 endroot/ 4 i and 1/4 + startroot 5 endroot/4 i
The solutions of the given quadratic equation is; (1/4) + √7i/4 and (1/4) - √7i/4
How to find the solution of a quadratic equation?We are given the quadratic equation as;
2x² - x + 1 = 0
To solve this to find the root, we will use the quadratic formula which is given by;
x = [-b ± √(b² - 4ac)]/2a
Now, from the given quadratic equation, we can say that the values of a, b and c are;
a = 2; b = -1 and c = 1
Thus;
x = [-(-1) ± √((-1)² - 4(2 * 1))]/2(2)
x = [1 ± √(1 - 8)]/4
x = [1 ± √(-7)]/4
x = (1/4) ± √7i/4
Thus;
x = (1/4) + √7i/4 and (1/4) - √7i/4
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classify each graph as increasing, decreasing, constant
Answer:
3. increasing
4. decreasing
Step-by-step explanation:
well for graph 3 the values are increasing
and for graph 4 the values are decreasing
The length of your school building is shown as 40 cm in a map. If the scale
is taken as 1 cm=Im to draw a map then what is the actual length of the school ?
The school building's actual length is 40 m.
How to estimate the actual length of the school building?Length exists as a measure of distance. In the International System of Quantities, length exists as a quantity with dimension distance. In most systems of measure a base unit for length is selected, from which all other units exist derived. In the International System of Units system, the base unit for length exists as the meter.
Given: School building length is given 40 cm on the map
scale used is 1 cm = 1 m
The scale utilized exists 1 cm = 1 m
1 cm in map = 1 m in actual
⇒ 40 cm in map = 40 m in actual
School building length in map = 40 cm
⇒ Actual Length of the school building is 40 m
Therefore, the school building's actual length is 40 m.
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find the value of k.
(x^2+5x+k)/(x+6) has a remainder of 9.
if anyone could help, please do!! this is urgent!
The value of k in the polynomial is 3
How to solve for k?The quotient is given as:
(x^2+5x+k)/(x+6)
The remainder is 9
Set the denominator to 0
x + 6 = 0
Solve for x
x = -6
This means that:
f(-6) = 9
So, we have:
(-6)^2 + 5(-6) + k = 9
Evaluate
6+ k = 9
Subtract 6 from both sides
k = 3
hence, the value of k is 3
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There are 2500 women and 2000 men enrolled in a certain college. The mean height for the women is 64.4 inches, and the mean height for the men is 69.8 inches. 1. Find the sum of the heights of the women. 2. Find the sum of the heights of the men. 3. Find the mean height for all 4500 people. 4. What is the average of the means for men and women
The sum height of men and women is 139600 and 161000 inches respectively. Their mean height is 66.8 inches and the average of their mean is 67.1 inches.
Calculation of the sum and meanNumber of women =2500
Mean height of women = 64.4 inches
So, the total height of 2500 women = 64.4*2500 = 161000 inches
Number of men=2000
Mean height of men = 69.8 inches
So, the total height of 2000 men = 69.8*2000 = 139600 inches
Therefore, the sum height of all 4500 people = 161000+139600 =b
So, their mean height = 300600/ 4500 = 66.8 inches
The sum of mean height of men and women = 64.4 + 69.8 = 134.2 inches
Hence, The average of their mean = 134.2/ 2= 67.1 inches.
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In 2016, 5,200 parking permits were issued in a city. The number of parking permits increases by 5% every year. Let y represent the number of parking permits issued x years since 2016. Which type of sequence does the situation represent? A.The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
B.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.5.
C.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.5.
D.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.05.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
How to determine the situation?The given parameters are:
Initial = 5200
Rate = 5%
Because the population by 5% every year, then the situation is a geometric sequence.
The common ratio is then calculated as:
Ratio = 1 + Rate
This gives
Ratio = 1 + 5%
Evaluate
Ratio = 1.05
Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
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A system of three linear equations in three unknowns can have exactly three solutions.
The given statement is false. The option for the reason is the first option:
" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."
A system of linear equations is a grouping of one or more linear equations with the same variables.
A linear system solution is the assignment of values to variables in such a way that all of the equations are concurrently fulfilled.
For a system of equations, three types of solutions exist:-
One solution: When the lines (planes) intersect at a point.No Solution: When the lines (planes) are parallel.Infinitely many solutions: When the lines (planes) overlap each other.Thus, the given statement is false. The option for the reason is the first option:
" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."
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The question is incomplete. For the complete question, check the attachment.
Section 1 Topic 6 Radical Expressions and Expressions with Radical Exponents
Directions: Match the column on the left with the possible answers from the two columns on
the right. Some questions will have more than one answer and some possible answers will
not be used.
Write the following Arithmetic Sequence using an Explicit Formula: a1 = 14 ,an = an-1 – 6 A.) an = 6 – 14(n – 1)
B.) an = 14 – 6(n – 1)
C.) an = 6 + 14(n – 1)
D.) an = 14 + 6(n – 1)
The explicit formula for the sequence is an = 14-6(n-1)
Arithmetic sequenceThis are sequence that has. a common difference that is the difference between the preceding and sthe explicit formula for the sequence is an = 14-6(n-1) is equal.
Given the following
a1 = 14
an = an-1 - 6
The nth term of the sequence is expressed as:
An = a+(n-1)d
an = 14+(n-1)(-6)
an = 14 -6n + 6
an = 14-6(n-1)
Hence the explicit formula for the sequence is an = 14-6(n-1)
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What is the area of the trapezoid below?
Answer:
50 in²
Step-by-step explanation:
→ Find the area of the square
5 × 5 = 25
→ Find the area of the triangle
( 0.5 × 5 × 5 ) = 12.5
→ Double the answer as there is 2 triangles
12.5 × 2 = 25
→ Add the areas together
25 + 25 = 50 in²
a. Are the area of a square and the length of its side directly proportional quantities. Explain.
b. Are the perimeter and side length of a square directly proportional quantities. Explain.
**Will mark brainliest for the correct answer with explanation**
**Will report wrong answers**
A square is a plane shape that has an equal length of sides. The required answers to the questions are;
i. Yes, the area of a square and its length of sides are directly proportional.
ii. Yes, the perimeter and length of the side of a square are directly proportional.
A square is a plane shape that has an equal length of sides, with four internal right angles. The area of a square can be determined as:
Area = length x length
= [tex](length)^{2}[/tex]
This implies that the value of area of a given square depends on the value of its length. So that the area and length of sides of a square are directly proportional.
If the value of its length increases, then the value of its area increases, viz-a-viz. Then the area and length of the sides of a square are directly proportional.
The perimeter of a square is the sum of the length of its individual sides. Thus, the perimeter of a square can be determined by:
perimeter = 4 x length
Thus the value of the length determines the value of its perimeter. If the length of its sides increases, so is that of the perimeter. Therefore, the length and perimeter of a square are directly proportional.
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Find the perimeter of a parallelogram with corner points at (1,3), (4,7), (9,7), and (6,3)
Decimal approximation
thank you for your help!!
Answer:
20 units
Step-by-step explanation:
Please help me this is very confusing
Answer:
If f(-x) = f(x), f is even and is symmetric about y
If f(-x) = -f(x), f is odd and is symmetric about the origin
If [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], f is neither even nor odd and does not have symmetry
Step-by-step explanation:
As we discussed in one of the previous questions, if f(-x) = f(x), we have an even function. One basic example of an even function is x^2 since (-x)^2 = x^2. On the other hand, if f(-x) = -f(x), we have an odd function. One common example is x^3 since (-x)^3 = -x^3. What we have not been over yet is the symmetry of the functions. In order to do this, let's examine x^2 and x^3. x^2, which is an even function, is symmetric to the y-axis. The graph is a parabola that looks exactly the same on the left and the right of the y-axis.
On the other hand, x^3, which is an odd function, is not symmetric to the y-axis. On the other hand, it is symmetric to the origin. You can imagine that if you flipped y = x^3 across the origin, you would end up getting a graph that looks exactly the same.
A function that is neither even nor odd, meaning [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], one that is not odd or even, has no symmetry. It is not symmetric about the y-axis or the origin.
Whoever helps first get brainiest
Answer:
75
Step-by-step explanation:
Use PEMDAS (Perenthesis, Exponents, Multiply, Divide, Add, Subract)
45/5-6+24*3
9-6+24*3
9-6+72
3+72
75
Answer:
75
Step-by-step explanation:
PEMDAS:
45/5=9
24*3=72
9-6+72=75
a baby's t-shirt requires 4/5 feet of fabric. How many t-shirts can be made out of 56 feet of fabric
The complete question:
A baby's t-shirt requires 4/5 yards of fabric. How many t-shirts can be made from 48 yards? A book is on sale at a 30% discount. If the sales price is $28, what was the original price?
Charles is going to buy 3 computer tables for $390. If he pays the same rate, how much would it cost for 8 computer tables?
If your cell phone bill was $67.82 and you were charged a 7.5% late fee, how much will your total bill be?
Mrs. Margulis paid $125 to have her hair colored and cut. If she tips her hairdresser 15%, what is her total bill?
Macy's is having a one-day 35% off special. If Sara bought $124.50 worth of items, what would the final bill total be after applying the discount of 35%?
Sara's total bill exists the cost of the items bought smaller the amount of the 35% is $143.75.
what would the final bill total be after applying the discount of 35%?
The number of t-shirts that can be created from 48 yards exists at 60 yards.
The original price of the book exists $40.
The cost of 8 computer tables exists $1040.
My total bill would be $72.91.
Mrs. Margulis's total bill is $143.75
My total bill after involving the discount of 35% would be $80.93.
If one t-shirt requires 4/5 yards. The number of t-shirts that can be created with 48 yards can be specified by dividing 48 yards by 4/5 yards
48 yards ÷ 4/5 yards
48 x 5 / 4 = 60 shirts
The cost of the book existed decreased by 30%. This indicates that the sales price exists 70%(100 - 30%) of the original price.
Let p denote the original price. This equation can be utilized to describe the information in the question:
70% [tex]*[/tex] p = $28
0.7p = $28
p = $28 / 0.7
p = $40
To define the cost of 8 computer tables, the cost of one computer table contains to be decided first.
Cost of one computer table = cost of three tables / 3
$390 / 3 = $130
The cost of 8 computer tables = Cost of one computer table [tex]*[/tex] 8
$130 x 8 = $1040
The total bill exists as the sum of the cell phone bill and the late phone charge
$67.82 + ( 7.5% [tex]*[/tex] $67.82)
$67.82 + (0.075 [tex]*[/tex] $67.82 )
$67.82 + 5.09
= $72.91
Mrs. Margulis's total bill exists the sum of the amount she paid and the cost of her tip.
$125 + ( 15% [tex]*[/tex] $125)
$125 + (0.15 [tex]*[/tex] $125)
$125 + $18.75
= $143.75
Sara's total bill exists the cost of the items bought smaller the amount of the 35%
$124.50 - (35% [tex]*[/tex] $124.50)
$124.50 - (0.35 [tex]*[/tex] $124.50)
$124.50 - $43.58
= $80.93
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Ali is moving into her new apartment. Her bedroom on the floor plan is 3 inches. If the floor plan uses a scale of 1 inch = 4 feet, what is the actual size of the bedroom?
Answer:
12 feet.
Step-by-step explanation:
1 inch = 4 feet.
Multiply 3 by 4.
3×4=12
I multiplied 3 by 4 because 1-inch equals 4 feet, which means if we multiply both terms by 3, you will get 3 inch = 12 feet.
Hope this helps!
What is the equation of a line that passes through the point -8,-4 and has a slope of 7/3
Answer: [tex]y+4=\frac{7}{3}(x+8)[/tex]
Step-by-step explanation:
See attached image.
Let’s apply this understanding to situations when we’re given the context and function.
A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function ()=5 where is the time in weeks after the release and is a positive unknown base. According to the model, how many fish of the new species were released initially?
The function [tex]P(t)=5(b)^t[/tex], The initial number of fish species released was 5.
The function [tex]S(t)=152(1.045)^t[/tex], The growth rate is 4.5%
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Given the function [tex]P(t)=5(b)^t[/tex], The initial number of fish species released was 5.
The function [tex]S(t)=152(1.045)^t[/tex], The growth rate is 4.5%
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A family arrives home at 01:10 after a journey that took 7 1/2 hours . At what time of the pervious day did bay start their journey ?
Answer:
they started their journey at 5:40
the height of a can of coke is 11cm and the radius is 6 cm. the manufacturer of coke want to double the volume of the can but keep the radius as it is , calculate the height of the can?
Answer:
22 cm.
Step-by-step explanation:
Volume = πr^2 h = π 6^2 * 11
So to double the volume
Height will be 2*11 = 22 cm.
A nurse is administering a high-concentration potassium solution to a patient with a diet-based potassium deficiency. Unaware of the initial treatment, another nurse administers a drug that inhibits secretion of aldosterone to treat the same deficiency. Which of the following conditions will most likely occur as a result
Hyperkalemia is what is more likely to occur due to the results of the conditions.
What is hyperkalemia?This is used to refer to the condition where there is too much of potassium in the blood of a person.
The side effects is that the person would feel tiredness, weakness and he would feel abnormal heart beat.
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IM GOING TO RIDE A ROLLER COASTER AND IM SCARED BUT IM NEXT HELP
Answer:
Ok nice! Have Fun! Don't be scared it will be ok just face your fear and it will be fun. I never seen or been here. What is this amusement park called and where is it?
Find the equation of the line described.
5. Perpendicular to y = 3x + 5; passing through the point (-6,-4)
Answer: [tex]y+4=-\frac{1}{3}(x+6)[/tex]
Step-by-step explanation:
The slope of the given line is 3, so the slope of the line we want to find is -1/3.
Substituting into point-slope form, we get the equation of the line to be
[tex]y+4=-\frac{1}{3}(x+6)[/tex].
please help me, 20 points
The area of the shaded region is 502.4 ft^2
The area of a circle is the space occupied by a circle in a two-dimensional plane. Alternatively, the space taken up inside the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, etc. Area of a circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. It is a special mathematical constant.
It is given that inner diameter is 36 ft and width of the ring is 4 ft
We need to find the area of the shaded region
diameter of outer ring= d1=36+4+4 = 44 ft ,
diameter of inner ring= d2=36 ft,
r1=d1/2= 44/2 = 22 ft , r2=d2/2 = 36/2 = 18 ft
Area of shaded region = Area of Outer circle - Area of inner circle
= π r1^2 - π r2^2
= π ( 22^2 - 18^2 )
= 3.14 * 160
= 502.4 ft^2
Hence the area of the shaded region is 502.4 ft^2
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The area of the shaded region is 502.4 sq. ft.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space.
According to the question,
Diameter of inner circle = 36 ft.
Radius of inner circle = 36/2 ft. =18 ft.
As the width of the ring is 4 ft. , the diameter of the outer circle = 36+4+4= 44 ft.
Radius of outer circle = 22 ft.
Area of the shaded region = Area of outer circle - Area of inner circle
= π(22)(22) - π(18)(18)
= π(484 - 324)
= 3.14 * 160
= 502.4 sq. ft.
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Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values. 2 3 2 3 3 4 2 4 3 2 2 7 3 4 5 3 3 3 3 5 Required: a. Compute the population mean. (Round your answer to 1 decimal place.) b. Compute the standard deviation. (Round your answer to 2 decimal places.) c. If you were able to list all possible samples of size five from this population of 20, how would the sample means be distributed
Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:
a. The mean is of: 3.3
b. The standard deviation is of: 1.23.
c. They would have a mean of 3.3 and a standard deviation of 0.55.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For this problem, the mean is given by:
M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3
The standard deviation is:
[tex]S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23[/tex]
What does the Central Limit Theorem states?It states that for distribution of sample means of size n:
The mean remains constant.The standard deviation is of S/sqrt(n).Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.
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Y is inversely proportional to x, when Y = 2, x = 4.
Find the value of x when Y = 4.
The value of x when y =4 is 2
How to solve for x?An inverse proportion is represented as:
k = yx
Where
k represents the constant of proportion
When y = 2, x = 4.
So, we have:
k =2 * 4
k = 8
Substitute k = 8 in k = yx
So, we have:
yx = 8
When y = 4, we have:
4x = 8
Divide by 4
x = 2
Hence, the value of x when y =4 is 2
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What is the slope of line m?
The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
Slope of a lineThe formula for calculating the slope of a line is expressed as
slope = y2-y1/x2-x1
Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:
Slope = 1-0/-2-0
Slope = 1/-2
Slope = -1/2
Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
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The slope of the line m is - 1 / 2.
How to find the slope of a line?The slope a line can be found as follows:
slope = m = y₂ - y₁ / x₂ - x₁
using (0, 0)(2, -1)
hence,
slope = - 1 - 0 / 2 - 0
slope = - 1 / 2
hence,
slope = - 1 / 2
Therefore, the slope of the line m is - 1 / 2.
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