The equation is c = 31 + 0.13x and total cost on driving 180 miles is $54.4.
Firstly we will form the equation using one time charge and the product of number of miles and charge per mile. Then we will keep the value in equation to find the total cost.
Forming the equation -
c = 31 + 0.13x
Keep the value of x in formula for calculation of total cost.
c = 31 + 0.13×180
Performing multiplication on Right Hand Side of the equation
c = 31 + 23.4
Performing addition on Right Hand Side of the equation
c = $54.4
Thus, the equation for calculation of total cost is c = 31 + 0.13x and total cost is $54.4.
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A rectangular garden has a length of 60 feet (ft), a width of w ft, and a perimeter of 200 ft.
Which of the following equations best models the garden's perimeter?
The width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200.
A rectangular garden has a length of 60 feet (ft)
a width of w ft
and a perimeter of 200 ft.
The formula of perimeter of a rectangle is 2(lenght + width)
The equation that represents the garden's perimeter is 2(60 + w) = 200
2(60 + w) = 200
120 + 2w = 200
2w = 200 - 120
2w = 80
w = 40
Therefore, width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200
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Find the slope of the line that passes through (4,2) and (2,1)
Given
Points (4,2) and (2,1)
Find
Slope of the line
Explanation
Slope of line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]so ,
[tex]\begin{gathered} m=\frac{1-2}{2-4} \\ \\ m=-\frac{1}{-2} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]Final Answer
Hence , the slope of line is m = 1/2
After the expression (x10)^3/5 Is simplified as much as possible, x is raised to what exponent?
The exponent of x in the expression (x¹⁰)³⁺⁵ is 6.
What is an exponent?Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These rules can help simplify formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.
The mathematical process known as an exponent often indicates the power of a variable.
As of right now, we are aware that under the scenario of
[tex](x^{a})^{b} = x^{ab}[/tex]
Therefore, solve the power by multiplying 10 by 3/5, and we get
10 × (3/5)
=6
Thus, the expression simplified as
(x¹⁰)³⁺⁵ = x⁶
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The dot plot shows predictions for the winning time in the 200-meter sprint. The winner finished the race in 22.3 seconds. What is the greatest percent error among the predictions?
2.69%, is the required maximum percent error among the predictions.
Given,
The predicted winning time in 200 meter sprint shows in the dot plot
The winner finished the race in 22.3 seconds
We have to find the greatest percent error among the predictions;
Here,
The actual time to complete is 22.3 seconds.
22.9 seconds is the prediction that is the most off.
The difference is, 22.9 - 22.3 = 0.6 seconds
To obtain a prediction, divide this by the actual time value.
= 0.6/22.3 = 0.0269 = 2.69
Therefore, 2.69%, is the required maximum percent error among the predictions.
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Is the function positive or negative over the interval (–8, –6)?
Answer:negative
Step-by-step explanation:
Because it should be on the bottom left corner if you are using a graph it is different in each corners of the graph. There is four sides for the graph.
Airfare from Atlanta, GA to Nashville, TN was decreased from $250 to $180. By what percentage did the cost of the airfare change
this is junior high math
Step-by-step explanation:
100% = $250
1% = 100%/100 = 250/100 = $2.50
the price decreased by
250 - 180 = $70
how many % are $70 ?
as many as how many times 1% ($2.50) fits into $70 :
70 / 2.50 = 28%
it changed (decreased) by 28%.
hassan is cooking some rice.
the recipe says he needs 450 granms of rice for 6 people
how many kilograms of rice would he need for 18 people
Answer:
Round 1350 to decimal form and your answer should be 1.35 kg.
the half-life of carbon 14 is 5715 years. an artifact has been located such that only 10% of the original amount of carbon 14 remains in the item. Rounded to the nearest year, how old is the artifact?
The age of the radioactive artifact is approximately 19029.6 years old
RadioactivityRadioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.
To solve this problem, we have to find the disintegration constant and we can use the formula of half-life of the sample to do that.
The half-life of a sample is given as;
[tex]T_\frac{1}{2}=\frac{ln}{\lambda}\\T_\frac{1}{2} =\frac{ln}{5715} \\ T_\frac{1}{2} = 0.000121\\[/tex]
The formula of radioactivity is given as
[tex]N = N_oe^(^-^\lambda ^t)[/tex]
Substituting the values into the equation
[tex]N = N_oe^(^-^\lambda ^t)\\\frac{N}{N_o} = e^-^(^\lambda ^t)\\0.1 = e^-^(^0^.^0^0^0^1^2^1^*^t^)\\t = 19029.6 years[/tex]
The artifact is approximately 19029.6 years.
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Write a simplified explession for the perimeter of the triangle.
[tex]p =( 1.5x - 3) + (1.5x - 3) + (0.75x - 1) \\ = 1.5x + 1.5x + 0.75x - 3 - 3 - 1 \\ p= 3.75x - 7[/tex]
ABOVE IS THE SIMPLIFIED PERIMETER OF THE TRIANGLE.
What is the average speed of a walker who walks 600hm in 20 seconds
Answer:
30 km/s
Explanation:
Formula for average speed = Total distance/total time
From the question,
Total distance = 600 km, Total time = 20 seconds
∴ Average speed = 600 km/20 seconds
Average speed = 30 km/s
provide an appropriate response. the owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. the daily revenue totals for the next 30 days will be monitored. what is the probability that the mean daily revenue for the next 30 days will be less than $7000?
The probability that the mean daily revenue for the next 30 days will be less than $7000 IS 0.7333
Standard deviation of the sample is equal to the population's Standard Deviation divided by the square root of the sample's item count.
Standard Deviation of the sample = [tex]1200/\sqrt{30} = 219.09[/tex]
SD of the sample is equal to the population's Standard Deviation divided by the square root of the sample's item count.
To reach a result of 300, divide 7500 by the mean of 7200. 300 divided by the sample's SD (219.09) yields a result of 1.37. A z-table search for +1.37 returns a result of 0.9147. Accordingly, there is a 0.9147 percent chance that the average daily revenue over the following 30 days will be less than $7500.
To get a result of -200, divide 7000 by the mean of 7200. Divide -200 by the sample's standard deviation (219.09), and you'll get -0.91. search for -0.91 in a z-table receive a score of 0.1814. The likelihood that the mean daily revenue for the following 30 days would be less than $7000 is therefore 0.1814.
Simply subtract the likelihood that the mean daily revenue is less than $7000 (0.1814) from the likelihood that the mean daily revenue is less than $7500 (0.9147) to arrive at the probability that the mean daily revenue for the upcoming 30 days will be between $7000 and $7500. This yields a result of 0.7333.
There is a 73.33% chance that the average daily income over the following 30 days will be less than $7000.
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3×10^9
---------
3×10^-7
Answer:
1 x 10^16
Step-by-step explanation:
find the ratio of the shaded pattern to the total area of the figure.
We are given a rectangle with the following dimensions;
[tex]\begin{gathered} l=(x+3) \\ w=(x+1) \end{gathered}[/tex]Also, placed inside the large rectangle, is a smaller shaded rectangle which has the dimensions;
[tex]\begin{gathered} l=(x+1) \\ w=x \end{gathered}[/tex]The ratio of both figures can be expressed as follows;
[tex]\text{Ratio}=a\colon b=\frac{a}{b}[/tex]Substituting for the values of both figures, we now have;
[tex]undefined[/tex]PLEASE HELP
Question
A function f(x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
f(x)=
The graphed function in the slope-intercept form can be written as:
y = -4*x - 2
How to get the linear function?
A general linear function in the slope-intercept form is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
On the graph, we can see that our line intercepts the y-axis at y = -2, so the y-intercept is b = -2, replacing that we get:
y = m*x - 2
We also can see that the line passes through (-1, 2), replacing these values on the linear equation we get:
2 = m*(-1) - 2
m = -2 - 2
m = -4
Thus, the linear function in the graph is:
y = -4*x - 2
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PLEASE HELP IF YOU KNOW AP STATS OR HAVE TAKEN THIS QUIZ!! THANK U
The data set for the average height of men at a ballgame compared to their shoe size is represented by the table.
Table with two columns titled men's shoe size (U. S. ) and height (inches). Data values 7 and 64, 10 and 69, 12 and 72, 8 and 67, 9. 5 and 69, 10 and 70, 11. 5 and 75, 12. 5 and 73, 13. 5 and 71, 10 and 68.
Part A: What is the equation of the least-squares regression line? (3 points)
Part B: Carlos wears a size 9 and is 71 inches tall. What is the residual for Carlos's data? Show your work. (4 points)
Part C: Interpret the meaning of the residual from part B. (3 points)
An equation for the line of best fit for a men's height, y, based on her shoe size, x is; y = 0.25x + 66.6
What is a line of best fit?A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the men's shoe size would be plotted on the x-axis of the scatter plot while her height would be plotted on the y-axis.
By critically observing the scatter plot (see attachment) which models the data, we can reasonably deduce that an equation for the line of best fit is given by:
y = 0.25x + 66.6
Interpret the meaning of the residual from part B is given below.
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(2x-3)²=4x solved using the equator formula
After solving the given equation using quadratic formula we gat solutions as 0.83 and 0.169
What is quadratic formula?
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b±√(b²-4ac))/(2a).
On simplifying the given equation we get,
(2x-3)²=4x
4x²+9-12x = 4x
4x²-16x+9 = 0
Comparing with ax²+bx+c = 0
a = 4, b = -16, c = 9
Quadratic formula is:
[tex]\frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]
putting the values from question we get,
[tex]\frac{16 +- \sqrt{16^2-4(4)(9)} }{216}[/tex]
[tex]\frac{16 +- \sqrt{256-144} }{32}[/tex]
[tex]\frac{16 +- \sqrt{112} }{32}[/tex]
[tex]Solution 1 = \frac{ 16+ 10.58 }{32} = 0.83[/tex]
[tex]Solution 2 = \frac{16 - 10.58}{32} = 0.169[/tex]
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Complete question
(2x-3)²=4x solve using quadratic formula
The Kansas City Chiefs are trying to figure out if there is a relationship between the number of passes thrown by Quarterback Patrick Mahomes and the total passing yards earned in each game.
Using your graphing calculator, analyze their data and then answer the 2 questions below.
Passes Thrown, [39] [35] [35] [37] and [40
Total Passing Yards [360] [235] [262] [249] [338]
• What is the linear regression equation that represents this data? Round to the nearest whole number. (worth 2 points)
Using your equation, calculate the number of passing yards the Chiefs can expect if Mahomes throws 38 passes in a game. (worth 2 points)
Explain how you calculated your answer for the expected passing yards if 38 passes are thrown. (worth 2 points)
The linear regression equation that represents this data is given as follows: y = 22x - 518.
Using this equation, when 38 passes are thrown, the expected yardage is of 318 yards.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
In the context of this problem, the input and output are given as follows:
Input: number of passes thrown by Patrick Mahomes.Output: number of passing yards obtaining by Mahomes/KC.The points to be inserted in the calculator are given as follows:
(39, 360), (35, 235), (35, 262), (37, 249), (40, 338).
Hence the equation is given by:
y = 22x - 518.
With 38 passes, the expected yardage is calculated as follows:
y = 22(38) - 518 = 318 yards.
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Find the pairs (LOTS OF POINTS!)
1. The pairs for each tent, based on common factors of 40, are given as follows (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2), and (40, 1).
2. Matching the number of tents with the number of boys is as follows:
Number of Tents Number of Boys1 40
2 20
3 No match
4 10
5 8
6 No match
7 No match
What are the factors?The factors of a number are the numbers that can divide it exactly or without a remainder.
For instance, the factors of the number, 40, are 1, 2, 4, 5, 8, 10, 20, and 40.
Thus, there are 8 ways that the tents can be arranged to accommodate the campers (boys) based on the factors of 40.
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There are 10 books are arranged on a shelf. If 4 books you are choosing are in alphabetical order,how many different groups of books could be chosen? Determine if it is permutation orcombination then solve.A). 24B). 210C). 3,628,800D). 5040
The problem says you have 10 books arranged on a shelf and then you are choosing 4 books in alphabetical order.
Given that you are choosing books with an order (alphabetical) it means the order does matter, then it is a permutation (which is an ordered combination).
In this case, no repetitions are allowed because you can't repeat a book in the selection, they'll be 4 different books from the shelf, the formula you have to use is:
[tex]\frac{n!}{(n-r)!}\begin{cases}n=\text{total number of books} \\ r=\text{ number of books you are choosing}\end{cases}[/tex]Then n=10 and r=4, replace these values:
[tex]\frac{10!}{(10-4)!}=\frac{3628800}{720}=5040[/tex]Then, can be chosen 5040 different groups of books.
The answer is option D.
2) At age 22, Joseph places $4,500 in a retirement account with a fixed annual interest rate 7%,compounded continuously. He never places any additional money in the account. What will hisbalance be at age 55 ?
lets remember what it means compound continuously,
the interest never stopped, the balance is earning interest at all time
Joseph is 22 and he wants to know how much money he will have at 55
55-22=33
his balance will gain interest for 33 years, this is our time
there is a 7% rate
the formula is
P(t)= P(0) e ^rt
our t is 33
rate=7%
Joseph will have a balance at age 55, 45,334.99 dollars
What is the degree of the polynomial above?
(A.) 1
(B.) 2
(C.) 3
(D.) 4
Answer:
The answer is B.
Step-by-step explanation:
I remember this question.
Answer:
c
Step-by-step explanation:
Can someone help me answer this question about area of trapezium
Answer:
x = 11
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 4 , b₁ = x , b₂ = 6 and A = 34 , then
[tex]\frac{1}{2}[/tex] × 4 × (x + 6) = 34
2(x + 6) = 34 ( divide both sides by 2 )
x + 6 = 17 ( subtract 6 from both sides )
x = 11
shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound
The number of pounds when company A and B have same amount is 16 pounds.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.
In this case, shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound.
Let each pound be represented by p.
Company A will be 7 + 0.50p
Company B will be 11 + 0.25p
We will equate both equations.
7 + 0.50p = 11 + 0.25p
Collect like terms
0.50p - 0.25p = 11 - 7
0.25p = 4
Divide
p = 4 / 0.25
p = 16
The number of pounds is 16 pounds.
The complete information is given below.
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shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound. How many pounds will give an equal amount?
Which of the following rational functions is graphed below?
Which fraction is closest to 1/2?
a. 1/6
b.3/8
c.3/4
d.-1/2
Answer:
A. 1/6 would be the answer I think
For 10 weeks Dolly wrote down everything she ate as well as weighed herself each morning. For two separate weeks during the 10-week period when her car was broken down and she was walking to work, she was running late each day so she did not have a chance to write down what she ate.
At the end of the 10 weeks, she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight. She concluded that for this experiment NOT writing down what she ate would help her lose weight.
Which mistake did Dolly have in her conclusion?
Responses
Her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks. That her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks.
B Confusing an experiment with an observational study. Confusing an experiment with an observational study.
C Confusing causation with correlation.Confusing causation with correlation.
D She did not make any mistakes in her conclusion.
The mistake that Dolly have in her conclusion is A. Her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks. That her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks.
How to illustrate the information?An experiment is carried out in order to get more information about a particular thing.
In this case, at the end of the 10 weeks, she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight.
Therefore, this caused the mistake that was noticed.
In conclusion, the correct option is A.
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what is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x + 8) ?A) shifted upB) shifted leftC) shifted right D) shifted down
Solution
- The rule for this transformation is given below:
[tex]\begin{gathered} f(x)\to f(x+h) \\ when\text{ h is positive, then, the graph is shifted left} \\ when\text{ h is negative, then, the graph is shifted right} \end{gathered}[/tex]- Based on this rule, f(x + 8) will shift the graph 8 units to the left
Final Answer
Shifted left (OPTION B)
The length of a rectangle is twice its width. If the area of the rectangle is 162in^2, find its perimeter.
We know that the length of a rectangle is twice its width. Then:
The area of a rectangle is the product of its width and length. Then:
[tex]A=2x\cdot x=2x^2[/tex]Additionally, we know that the area is 162 in². Using the expression above we can obtain the value of x:
[tex]\begin{gathered} 162=2x^2 \\ 81=x^2 \\ x=9\text{ in} \end{gathered}[/tex]Finally, the perimeter (2P) is just twice the sum of the width and the length of the rectangle:
[tex]2P=2\cdot(2x+x)=6x=6\cdot9=54\text{ in}[/tex]if 63 Naira is shared in the ratio 4 ratio 5 what is the larger share
Answer:
35
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide 63 by 9 to find the value of 1 part of the ratio
63 ÷ 9 = 7 , then
4 parts = 4 × 7 = 28
5 parts = 5 × 7 = 35 ← larger share
What is the quotient in simplest form?
12/7 divided by 3
A. 7/36
B. 4/7
C. 1 3/4
D. 5 1/7
Answer:
Step-by-step explanation:
the answer would be the second option