The probability of rolling a 1 and spinning section A on the spinner is 1/24.
To find the probability of rolling a 1 and spinning section A on the spinner, we need to first determine the total number of possible outcomes for the experiment. The number cube has 6 possible outcomes, and the spinner has 4 possible outcomes. Therefore, the total number of possible outcomes for the experiment is 6 x 4 = 24.
Next, we need to determine the number of outcomes that meet the criteria of rolling a 1 and spinning section A. Rolling a 1 has a probability of 1/6, and spinning section A has a probability of 1/4.
The probability of both events occurring simultaneously is the product of the two probabilities, which is (1/6) x (1/4) = 1/24.
This means that out of the 24 possible outcomes, only one outcome will result in rolling a 1 and spinning section A on the spinner.
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Complete Question:
A number cube numbered (1, 2, 3, 4, 5, 6) is rolled and a spinner with 4 sections (A, B, C, D) is spun. Find the probability of P(1 and A).
Does there exist a triangle with side lengths 12 , 5 , 15 ?
Answer:
yes, a triangle with the side lengths 12, 5, and 12 does exist.
Step-by-step explanation:
side a = 12
side b = 5
side c = 12
area = 29.34In
during the lunch rush, a fast food joint sold 10 sodas and earned $30 which is the rate of dollars per soda?
Answer:
1:3 is your rate for dollars per soda
Step-by-step explanation:
Prove that cyclic trapezium is always isosceles and its diagonal are equal
In our proof, as the trapezium are congruent and the rest of the sides are equal ∴AC = BD. Hence, the cyclic trapezium is isosceles and its diagonals are equal.
How do we prove cyclic trapezium is always isosceles and its diagonal are equal?Step 1:
The diagonals are AC and BD, and the line CE is parallel to AD.
We know that a parallelogram's opposite angles are equal.
∠D = ∠AEC......(1)
We also know that the sum of a cyclic quadrilateral's opposite angles is 180 degrees.
∠D + ∠ABC = 180..........(2)
We can deduce from (1) and (2) that
AEC + ABC = 180....... (3)
AEC and CEB are now a linear pair.
AEC + CEB = 180................. (4)
We can conclude from (3) and (4) that,
CEB = ABC
The sides opposite the equal angles are also equal, as we know.
CEB = ABC
CE = CB ... (5)
However, because AECD is a parallelogram, opposite sides must be equal.
∴CE = AD ... .(6)
From equation (5) and (6), we can conclude that
AD = CB ......(7)
As a result, the cyclic trapezium ABCD is isosceles.
Step 2:
Establishing that its diagonals are equal.
We have AC and BD as diagonals.
In triangle DBA and CBA,AD = CB from (7)⇒AB = AB (common side).
ADB + ACB (angles in the same segment of a circle are equal). As a result of the SAS rule, ABD and ABC are congruent.
Because they are congruent and the other sides are equal, AC = BD. As a result, a cyclic trapezium is isosceles and has equal diagonals.
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In a school, 220 students offer Biology or Mathematics or both. 125 offer biology and 110 Mathematics. How many offer Biology but not Mathematics?
The number of students are 110 students offer Biology but not Mathematics.
Let's use a Venn diagram to solve this problem. We know that 125 students offer Biology and 110 offer Mathematics, and we want to find out how many offer Biology but not Mathematics.
First, we can fill in the number of students who offer both Biology and Mathematics, which is the overlap between the two circles. We can do this by subtracting the total number of students who offer both from the total number of students who offer either:
220 (total) - (125 + 110) = 220 - 235 = -15
Wait a minute! A negative number of students doesn't make sense in this context. What this tells us is that there must be some double-counting going on - in other words, some students are being counted twice, once in each of the Biology and Mathematics categories.
To correct for this, we need to add back in the number of students who are counted twice, which is the overlap between the two circles. We can calculate this by adding the number of students who offer Biology and Mathematics together:
125 + 110 = 235
Now we can redo the calculation:
220 (total) - 235 (double-counted) = -15
This tells us that there are 15 students who are being counted twice. To find the number of students who offer Biology but not Mathematics, we need to subtract this number from the number of students who offer Biology:
125 - 15 = 110
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Answer: if im correct i think its 95
Rachel, Sam and Thomas applied for a common position at the company. Only one of them will be hired for the position. The probabilities that each of them is hired for the role are given by 1 out of 7, 2 out of 7, and 4 out of 7 respectively.The probabilities that Rachel, Sam and Thomas can help boost the company’s revenue are given by 4 out of 5, 1 out of 2, and 3 out of 10 respectively if they are hired.(a) Find the probability that Thomas is selected for the position given that the company’s revenue did not improve.(b) Find the probability, p, that the company’s revenue will generally improve.Rachel, Sam and Thomas interviewed at another company for another position. The probabilities that each of them is hired for the role are now given by x, 2x and 4x respectively.It can be assumed that the hiring process for each individual candidate are independent of one another.(c) Suppose there is no limit to the number of hires the company can make (i.e. the company can hire any one of them, any two of them, all three of them or no one at all). Find an inequality that must satisfied by x.
(a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.
(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position.
This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.
(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role.
For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.
For further information on (a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.
(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position. This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.
(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role. For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.
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If a person walks 1 2 2 1 mile in each 1 4 4 1 hour, compute the unit rate in miles per hour.
The unit rate is 8.4 miles per hοur.
What dοes distance means?Distance and displacement are twο quantities that seem tο mean the same but are distinctly different with different meanings and definitiοns. Distance is the measure οf “hοw much grοund an οbject has cοvered during its mοtiοn” while displacement refers tο the measure οf “hοw far οut οf place is an οbject.”
Tο find the unit rate in miles per hοur, we need tο divide the distance by the time.
The distance is 1 2 2 1 miles and the time is 1 4 4 1 hοurs.
Sο, the unit rate in miles per hοur is:
(1 2 2 1 miles) / (1 4 4 1 hοurs) = 8.4 miles per hοur (rοunded tο οne decimal place)
Therefοre, the unit rate is 8.4 miles per hοur.
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Alex’s printer can print 8 photos in 12 minutes. Khalid printer can print 24 photos in 1 hour. which process could you use to help determine how much longer will it take khalils printer to print 120 photos than Alex’s. select all that apply.
A. write an equation that adds the number of photos that each print prints in 1 hour
B. make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference
C. Subtract the number of photos that khalil printer prints in two hours from the number of photos that alex’s printer print in 2 hours.
D. graph a table of values for each printer and compare the number of minutes when the number of photos is 120.
Answer:
B. Make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference would be an appropriate process to determine how much longer it will take Khalil's printer to print 120 photos than Alex's.
Step-by-step explanation:
To use this process, we can set up a table showing the ratio of photos printed to time taken for each printer. Then we can use these ratios to find how long it would take each printer to print 120 photos, and find the difference between the two times to determine how much longer it would take Khalil's printer.
Which points are solutions to the linear inequality y < 0. 5x +
2? Select three options.
The three points that are solutions to the linear inequality y < 0.5x + 2 are (-3, -2), (-1, -2), and (1, -2)
To check which points are solutions to the linear inequality y < 0.5x + 2, we can substitute the coordinates of each point into the inequality and check whether the inequality is true or false.
For the point (-3, -2):
y < 0.5x + 2
-2 < 0.5(-3) + 2
-2 < -0.5
This inequality is true, so (-3, -2) is a solution.
For the point (-2, 1):
y < 0.5x + 2
1 < 0.5(-2) + 2
1 < 1
This inequality is false, so (-2, 1) is not a solution.
For the point (-1, -2):
y < 0.5x + 2
-2 < 0.5(-1) + 2
-2 < 1.5
This inequality is true, so (-1, -2) is a solution.
For the point (-1, 2):
y < 0.5x + 2
2 < 0.5(-1) + 2
2 < 1.5
This inequality is false, so (-1, 2) is not a solution.
For the point (1, -2):
y < 0.5x + 2
-2 < 0.5(1) + 2
-2 < 2.5
This inequality is true, so (1, -2) is a solution.
Therefore, the three points that are solutions are (-3, -2), (-1, -2), and (1, -2).
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The given question is incomplete, the complete question is:
Which points are solutions to the linear inequality y < 0. 5x +2? Select three options. (-3,-2) (-2,1) (-1,-2) (-1, 2) (1,-2)
Averi was trying to factor 4x^2+20x-164x
2
+20x−164, x, squared, plus, 20, x, minus, 16. She found that the greatest common factor of these terms was 4 and made an area model:
What is the width of Averi's area model?
The width of Averi's area model is 4 units.
The area model for factoring 4x²+20x-16 is shown above. The width of Averi's area model is 4 units. To factor the given expression, Averi used an area model.
In this model, the width represents the greatest common factor of the given expression while the length represents the remaining factors of the expression. Averi determined that the greatest common factor of 4x²+20x-16 was 4.
Therefore, she created a rectangle with a width of 4 and a length of (x²+5x-4). The dimensions of the rectangle are determined by the factors of the given expression.
The area of the rectangle represents the original expression. Therefore, the area of the rectangle can be calculated by multiplying the width and length of the rectangle. The area of the rectangle is equal to: Area of rectangle = width x length Area of rectangle = 4(x²+5x-4)Area of rectangle = 4x²+20x-16
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*3 SIMPLE GEOM QUESTIONS!!*
please help me with this study guide!
I appreciate it!
Thank you so muchhh <3
Therefore , the solution of the given problem of coordinates comes out to be the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).
Explain coordinate.By utilising one or even more variables or coordinates, a coordinate system is able to precisely locate points or other mathematical items on such a room, including Euclidean space. Coordinates, which seem to be pairs of integers, are used to locate a point or object on a double plane. The y and x vectors are used to represent the position of a point on a two-dimensional surface. a group of figures used to designate particular places.
Here,
G(3, -2) will have the following coordinates after being reflected across the y-axis:
=> (-3, -2).
A point's x-coordinate changes sign when it is reflected across the y-axis, but its y-coordinate stays the same.
Consequently, the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).
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The coordinates of the resulting point after the reflection across the y - axis will be G'(3, 2) and The coordinates of the resulting point after the reflection across the x - axis will be G'(3, 2).
What do you mean by reflection of coordinates?A reflection on the coordinate plane (x , y ) is a type of transformation. It takes a geometric figure such as a line, segment, point or shape and transforms it into a congruent geometric figure called the image.
a. It is given that a point (-3, 2) reflected across the y - axis.
Now, when any given coordinate is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.
Therefore, the coordinates of the resulting point after the reflection across the y - axis will be G'(3, 2)
b. It is given that a point (3, -2) reflected across the x - axis.
Now, when any given coordinate is reflected across the x - axis then, the sign of the y - coordinate is inverted and the x - coordinate remains same.
Therefore, the coordinates of the resulting point after the reflection across the x - axis will be G'(3, 2).
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which way does shift
g(x)=lx+9l-5
Answer:
g(x) was shifted 9 units to the left and 5 units down
Step-by-step explanation:
Horizontal shifts take place when the x value is changed within the parentheses, or in this case, absolute value.
The graph is shifted 9 units left because of the + 9.
Vertical shifts happen when the entire equation is added or subtracted to.
The graph is shifted 5 units down because of the - 5.
See the graph for a visualization.
12.
Find the Volume of the solid below;
Round to the nearest one hundredth
Use your pi #button when applicable.
10 ft
17 ft
6 ft
8 ft
The volume of the given solid above which is a triangular prism would be = 510 ft³.
How to calculate the volume of the solid shape ?To calculate the volume of the given prism the formula should be used such as;
Volume = 1/2 × base× height × length
Where base = 10ft
height = 6 ft
length = 17ft
Volume = 1/2 × 10×6×17
= 5×6×17
= 510 ft³
Therefore the volume of the given shape above would be = 510 ft³ when the formula for triangular prism is used.
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HELP PLEASE!! URGENT!!
Measure your own height and arm span (from finger-tip to finger-tip) in inches. You will likely need some help from a parent, guardian, or sibling to get accurate measurements. Record your measurements on the "Data Record" document. Use the "Data Record" to help you complete Part Two of this project.
Measure 11 additional people, and record their arm spans and heights in inches. You may use the sample data provided in the table if you do not have 11 people to measure.
Arm Span (inches) Height (inches)
58 60
49 47
51 55
19 25
37 39
44 45
47 49
36 35
41 40
46 50
58 61
Part Two: Representation of Data with Plots
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word processing document.
Part Three: The Line of Best Fit
Include your scatter plot and the answers to the following questions in your word processing document:
Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
Write the equation of the line of best fit using the slope-intercept form of the line y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Test the residuals of two other points to determine how well the line of best fit models the data.
Use the line of best fit to help you to describe the data correlation.
Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
According to your line of best fit, what is the arm span of a 74-inch-tall person?
The equatiοn οf the line οf best fit is ŷ= 0.96x+3.79
The slοpe is 0.96
The y-intercept is 3.79
The heights οf peοple that have arm spans οf 66 inches is 67.15 inches and the heights οf peοple that have arm spans οf 74 inches is 74.83 inches.
What is y-intercept?When the line tοuches the y-axis, it fοrms a y-intercept. Find the y when x = 0 tο find these. The y-intercept pοint will have the shape οf (0,y) When the line tοuches the x-axis, it fοrms an x-intercept.
We have the fοllοwing cοmputatiοn summary frοm the graphing calculatοr:
Sum οf X = 486
Sum οf Y = 506
Mean X = 44.1818
Mean Y = 46
Sum οf squares (SSX) = 1225.636
Sum οf prοducts (SP) = 1171
Hence, the fοrmula fοr the line οf best fit is ŷ= 0.96x+3.79
A linear regressiοn equatiοn is mentiοned
ŷ=mx+b
Where m is the slοpe, and b is the y-intercept
Sο, the slοpe is 0.96 and the y-intercept is 3.79
The heights οf peοple that have arm spans οf 66 inches and 74 inches
This means that:
x = 66 and x = 74
When x = 66,
y=0.96*66+3.79=67.15
When x = 74,
y=0.96*74+3.79= 74.83
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Answer this ASAP will give the brainliest answer
Given that y = 11 cm and θ = 38°, work out x rounded to 1 DP.
x ≈ 17.8 cm (rοunded tο 1 decimal place).
What is trigοnοmetric functiοn ?The trigοnοmetric functiοns in mathematics are real functiοns that relate the angle οf a right-angled triangle tο the ratiοs οf its twο side lengths. They are alsο knοwn as circular functiοns, angle functiοns, οr gοniοmetric functiοns.
All geοsciences, including navigatiοn, sοlid mechanics, celestial mechanics, geοdesy, and many οthers, use them extensively. They are sοme οf the mοst straightfοrward periοdic functiοns, and as a result, Fοurier analysis is frequently used tο study periοdic phenοmena.
Tο sοlve fοr x, we can use the trigοnοmetric functiοn cοsine since we have the adjacent side and the hypοtenuse.
cοs(θ) = adjacent/hypοtenuse
cοs(38°) = x/hypοtenuse
We knοw that the perpendicular is y = 11 cm, sο we can use the Pythagοrean theοrem tο find the hypοtenuse:
[tex]\rm hypotenuse^2 = perpendicular^2 + base^2[/tex]
[tex]x^2 = y^2 + (adjacent)^2[/tex]
[tex]x^2 = 11^2 + (x cos(38^\circ))^2[/tex]
[tex]x^2 = 121 + (x 0.7880107536)^2[/tex]
[tex]x^2 = 121 + 0.6201117996x^2[/tex]
[tex]0.3798882004x^2 = 121[/tex]
[tex]x^2 = 318.5022183[/tex]
x ≈ 17.84 cm (rounded to 1 decimal place)
Therefore, x ≈ 17.8 cm (rounded to 1 decimal place).
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This question has two parts. First, answer Part A. Then, answer Part Part A SOFTWARE A software company releases two products: a home version of their photo editor, which costs $20, and a professional version, which costs $45. The company sells 1000 copies of the photo editing software, earning a total revenue of $38,075. Write and solve a system of equations to determine how many home versions and professional versions of the software the company sold. Let h = the number of home versions sold and D = the number of professional versions sold
A system of equations to determine the number of home versions and professional versions of the software the company sold is given by:
20h + 45p = 38,075
h + p = 1000
The number of home versions sold is 277 and the number of professional versions sold is 723.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the number of home versions sold and the number of professional versions sold respectively, and then translate the word problem into a linear equation as follows:
Let the variable h represent the number of home versions sold.Let the variable p represent the number of professional versions sold.Since a home version of their photo editor cost $20, and a professional version, cost $45, a linear equation that models the situation is given by:
20h + 45p = 38,075
Additionally, the company sold 1000 copies of the photo editing software;
h + p = 1000
Solving the equations simultaneously, we have:
20h + 45(1000 - h) = 38,075
20h + 45,000 - 45h = 38,075
25h = 6,925
h = 277 home versions.
p = 1000 - h
p = 1000 - 277
p = 723 professional versions.
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What is the answer?
The expression which is equivalent to [tex](\frac{3}{2})^8[/tex] is [tex]$\frac{3^6}{2^8}$[/tex] . So, correct option is C.
Describe Exponential Expression?An exponential expression is a mathematical expression that involves a base raised to an exponent. The base is usually a fixed number, and the exponent represents the number of times the base is multiplied by itself. For example, in the expression [tex]2^3[/tex] the base is 2 and the exponent is 3. This means that 2 is multiplied by itself three times, resulting in the value of 8.
Exponential expressions are commonly used in many areas of mathematics and science, as well as in everyday life. For example, they can be used to represent growth rates, decay rates, population growth, radioactive decay, and compound interest.
Exponential expressions can be simplified using the laws of exponents, which allow us to combine or simplify expressions with the same base. Some common laws of exponents include:
Product law: [tex]a^m x a^n = a^(m+n)[/tex]
Quotient law: [tex]a^m / a^n = a^(m-n)[/tex]
Power law: ([tex]a^m)^n = a^(mn)[/tex]
Negative exponent law: [tex]a^(-m) = 1 / a^m[/tex]
Zero exponent law: [tex]a^0 = 1[/tex]
Exponential expressions can also be graphed on a coordinate plane, producing a curve called an exponential function. The shape of the curve depends on the value of the base and the sign of the exponent, and can be used to model a wide range of real-world phenomena.
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Max builds rail fences for one style of the fence each section uses 3 vertical fence posts and 6 horizontal rails how many rails does he need for a fence that has 27 posts completely the rules and use the rules to complete the table
Max needs 54 horizontal rails to build a fence with 27 vertical posts.
The problem states that each section of the fence uses 3 vertical fence posts and 6 horizontal rails. This means that for every section of fence, there are 3 vertical posts and 6 horizontal rails.
To find out how many horizontal rails Max needs for a fence with 27 vertical posts, we need to figure out how many sections of fence Max needs to build.
Since each section of fence has 3 vertical posts, apply unitary method, we can divide the total number of vertical posts by 3 to find out how many sections of fence Max needs to build:
27 / 3 = 9
So Max needs to build 9 sections of fence.
Since each section of fence has 6 horizontal rails, we can multiply the number of sections by 6 to find out how many horizontal rails Max needs in total:
9 x 6 = 54
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Quantity of fuel uterlized by water tanker March 2022
The quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres. The total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.
To determine the quantity of fuel utilized by the water tanker in March 2022, we need to first calculate the total distance that the water tanker has covered in March 2022.
The total distance covered can be calculated using the formula:
distance = rate × time
From Annexure A, we can see that the water tanker was supplied to the construction site on the following dates in March 2022:
March 1, 2, 3, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, and 31
Counting the number of days, we get a total of 23 days. Since the water tanker was supplied every day, we can assume that it covered the same distance every day.
The rate of fuel consumption of the Mercedes water tanker averages 5 km/l, which means that it can travel 5 km for every litre of fuel it consumes. Therefore, the distance covered by the water tanker on a full tank of fuel is:
distance = rate × fuel capacity
= 5 km/l × 460 litres
= 2300 km
So, the total distance covered by the water tanker in March 2022 is:
distance = 23 days × 2300 km/day
= 52,900 km
Next, we can determine the quantity of fuel utilized by the water tanker in March 2022 using the formula:
quantity of fuel = distance ÷ rate
Using the values we have calculated, we get:
quantity of fuel = 52,900 km ÷ 5 km/l
= 10,580 litres
Therefore, the quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres.
To determine the total amount of money that was utilized on fuel for the water tanker in March 2022, we can multiply the quantity of fuel utilized by the fuel price in March 2022:
total cost = quantity of fuel × fuel price
From the problem statement, the fuel price in March 2022 was R19.55 per litre. Substituting the values we have calculated, we get:
total cost = 10,580 litres × R19.55/litre
= R206,929.00
Therefore, the total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.
Complete question:
Records of the number of water tankers that were supplied to the construction site appear in the calendar on ANNEXURE A. The water tanker has a fuel capacity of 460 litres. The rate of fuel consumption of the Mercedes water tanker averages 5 km/l. The prices of fuel per litre in March and June 2022 appear below. MARCH 2022 FUEL PRICES DIESEL 50 ppm (a 4. 1) (b ) COST R19,55 JUNE 2022 FUEL PRICES DIESEL 50 ppm Source: COST R24,14 Calculate the total distance that the water tanker has covered in March 2022. Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. Determine the total amount of money that was utilized on fuel for the water tanker in March 2022. Quantity of fuel utilized by water tanker March 2022
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The most powerful volcanic eruption on earth in the last 10,000 years was approximately VEI 7.3 (Mt. Rinjani in Indonesia). The most powerful volcanic eruption in the last 100 years was the 1991 eruption of Mt. Pinatubo in the Philippines (I remember it very well). It was rated a 6.0. How much larger was the Mt. Rinjani eruption than the Mt. Pinatubo eruption?
This means that the Mt. Rinjani eruption was approximately 20 times larger and more powerful than the Mt. Pinatubo eruption.
What is exponent?An exponent is a mathematical operation that involves raising a base number to a certain power. The exponent tells how many times the base number should be multiplied by itself. For example, in the expression 2³, 2 is the base number and 3 is the exponent, and it means that 2 should be multiplied by itself three times: 2 x 2 x 2 = 8. Exponents are commonly used in algebra, calculus, and other branches of mathematics.
Here,
The Volcanic Explosivity Index (VEI) is a logarithmic scale used to measure the relative size and power of volcanic eruptions. Each increase of 1 on the VEI scale represents a tenfold increase in the eruption's size and power.
The difference in VEI between the Mt. Rinjani eruption and the Mt. Pinatubo eruption is 7.3 - 6.0 = 1.3.
To calculate the difference in size and power, we need to raise 10 to the power of 1.3:
10¹.³ = 19.95
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6. if you replace one 75-watt incandescent light bulb with fluorescent light bulb that gives the same amount of light by drawing only 20 watts. you use the light bulb for an average of 4 hours a day. a. how many kwhs of energy would you save in one day? b. how many kwhs of energy would you save in one year? c. the cost of one kwh is $0.10. how much money does the fluorescent light bulb save in one year?
On replacing the incandescent light bulb with a fluorescent light bulb (a) the energy saved in one day is 0.22 kWh, (b) the energy saved in one year is 80.3 kWh. and (c) the cost savings in one year is $8.03.
a. The energy saved in one day by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one day = Energy consumed by incandescent bulb - Energy consumed by fluorescent bulb
Energy saved in one day = (75 watts x 4 hours) - (20 watts x 4 hours)
Energy saved in one day = 300 watt-hours - 80 watt-hours
Energy saved in one day = 220 watt-hours
To convert watt-hours to kilowatt-hours (kWh), we divide the watt-hours by 1000:
Energy saved in one day = 220 watt-hours / 1000
Energy saved in one day = 0.22 kWh
b. The energy saved in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one year = Energy saved in one day x Number of days in one year
Energy saved in one year = 0.22 kWh/day x 365 days/year
Energy saved in one year = 80.3 kWh
c. The cost savings in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Cost savings in one year = Energy saved in one year x Cost per kWh
Cost savings in one year = 80.3 kWh x $0.10/kWh
Cost savings in one year = $8.03
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could use some help, think this might be right(new to precalculus
Find dxdy . y= cosx1+ tanx7dxdy =
Answer:
y= 1/cosx+7/tanx
dy/dx = 1secxtanx-cosec^2x
A circle has a radius of 6 feet and a circumference of approximately 37.70 feet. Complete the sentence to describe
how to estimate the value of 7.
Move the correct answer to each box. Not all answers will be used.
6 12 37.70
To estimate the value of x, divide
37.70/12
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Using a ruler and a pair of compass only construct:
a. Line MN =8. 8cm
b. A perpendicular to MN at N
c. Angle MNP=60 degrees,such that line NP =6. 3cm
The Construction of line MN and perpendicular at point N as well as angle MNP = 60°such that NP would be 6.3 cm is given below as image.
In Euclidean geometry, an angle is a shape made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed in the plane where two rays are positioned. Moreover, when two planes overlap, angles are created. Dihedral angles are what they are called.
In geometry, two lines are considered to be perpendicular if they meet or intersect at right angles of 90°. The Latin term "perpendicularis," which denotes a plumb line, is where the word "perpendicular" originally made its appearance.
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Find the surface area of a cylinder with a base diameter of 8 feet and a height of 8 feet right your answer in terms of pi and be sure to include the correct unit
Answer:
96π cubic feet
Step-by-step explanation:
Surface area of a cylinder
A = 2πr(h+r)
where r = radius, h = height
Here
r = diameter/w = 8/2 = 4 feet
h = 8 feet
A = 2π · 4 (8 + 4)
= 8π (12)
= 96π cubic feet
Round to the nearest tenth.
Answer:
E =53.1
Step-by-step explanation:
sin=opposite ÷ hypotenuse
opposite side of E = 4
hypotenuse = 5
4÷5=0.8
sin^-1 (0.8) = 53.1
E=53.1
Suppose that \( f(x)=h^{-1}(x) \) and that both \( j \) and \( h \) are defined for all values of \( x \). Let \( h(11)=2 \) and \( f(12)=-7 \). Evaluate the following if possible. If it is not possib
h(2) + j(−7) = −7(1 + j)
Suppose that f(x) = h^−1(x) and that both j and h are defined for all values of x. Let h(11) = 2 and f(12) = −7. We need to evaluate the following. h(2) + j(−7)For finding the value of h(2), we can use f(x) = h^−1(x) where x = h(2)f(h(2)) = 2h(2) = f^−1(2)We need to find h(2). Therefore, we need to find f^−1(2). We know f(12) = −7f(h(2)) = 2⟹ h(2) = −7Substitute h(2) = −7 in h(11) = 2h(11) = h(2 + 9) = h(2) + 9 = 2 + 9 = 11Therefore, h(2) = −7 and h(11) = 2.h(2) + j(−7) = −7 + j(−7) = −7(1 + j)Therefore, h(2) + j(−7) = −7(1 + j).
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Nisha read the part of a book in 1 hour. How much part of the book will be read by
her in 3 2/5
hours?
The table summarizes results from 986 pedestrian deaths that were caused by automobile accidents.
Driver Pedestrian Intoxicated?
Intoxicated? Yes No
Yes 54 83
No 246 603
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
From the given data, the probability that the pedestrian was not intoxicated or the driver was not intoxicated is 99.7%.
To find the probability that the pedestrian was not intoxicated or the driver was not intoxicated, we can add the probabilities of the two mutually exclusive events:
Pedestrian not intoxicated and driver intoxicated
Pedestrian intoxicated and driver not intoxicated
From the table, we can see that there were 603 pedestrian deaths where the driver was not intoxicated and 54 pedestrian deaths where the driver was intoxicated, for a total of 657 deaths where the driver was not intoxicated. Similarly, there were 246 pedestrian deaths where the pedestrian was not intoxicated and 83 pedestrian deaths where the pedestrian was intoxicated, for a total of 329 deaths where the pedestrian was not intoxicated.
Therefore, probability that pedestrian was not intoxicated or driver was not intoxicated is:
P = (657 + 329) / 986
= 0.9969
Converting to percentage and rounding to one decimal place,
P = 99.7%
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PLEASE HELP ME ASAP PLEASEEE
Answer:
Step-by-step explanation:
B and E
Based on estimates from the united nations population division , in 2020 the population of estonia was 1. 33x10^6 people. In 2020 the population of India was approximately 1. 38 x10^9. About how many orders of magnitude as populated was India in 2020
The population of India in 2020 was approximately 1.38x10^9 people, while the population of Estonia in 2020 was approximately 1.33x10^6 people. This means that India was approximately 103 orders of magnitude more populated than Estonia in 2020.
To calculate the difference in orders of magnitude between India and Estonia, divide India's population (1.38x10^9) by Estonia's population (1.33x10^6). This gives a result of 1.03x10^3, or 103 orders of magnitude.
In other words, India's population was 103 times bigger than Estonia's population in 2020. This difference can also be expressed as India being 10,300,000,000 times more populated than Estonia in 2020.
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