The average rate of change from 2009 to 201 is $1.00/year, and If the trend from 2009 to 2018 continues, the cost of gas in 2025 will be $6.00.
What is the average rate of change?
It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
The average rate of change from 2009 to 2018 is $1.00/year.
The cost of gas in 2025 can be computed by using the average rate of change from 2009 to 2018.
If the trend from 2009 to 2018 continues, the cost of gas in 2025 will be $6.00.
This is calculated by taking the starting price of $3.00 in 2018 and adding on the average rate of change of $1.00/year for 7 years.
$3.00 + 7*$1.00 = $6.00.
Hence, the average rate of change from 2009 to 201 is $1.00/year, and If the trend from 2009 to 2018 continues, the cost of gas in 2025 will be $6.00.
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Ramón makes nectar for a hummingbird feeder by mixing 8 cups of water with 2 cups of sugar. Tiffany makes nectar by mixing 9 cups of water with 3 cups of sugar. Whose nectar is more sugary? Explain.
Answer: Tiffany
Step-by-step explanation: Ramon Ratio 8:2 can be reduced to 1 cup of sugar every 4 cups of water. Tiffany Ration is 9:3 which is reduced to 1 cup of sugar every 3 cups of water.
4 Describe at least two different transformations or sequences of transformations that
transform square A to square B.
The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).
Does the order of transformations matter in functions?
Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.
The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.
ABCD can be transformed to A'B'C'D' by ...
rotation 90° CCW about the point (-1, -1)
Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...
reflection across the line y=x
reflection across the line x=-1
Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.
b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
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By rounding to 1 significant figure, estimate
101
×
52
The significant figure by multiplying 101 with 52 is 5000.
What is significant figures?The number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value is referred to as significant figures. At the first non-zero digit, we begin counting significant figures.A number's first significant figure is the first digit that is not zero.To round to the nearest one, ten, hundred, thousand, and so on, change all digits to the right of the rounding digit to zeroes.Here given,
101 x 52
Round 101 to 100 and 52 to 50, then multiply together to get 5000.
Significant Figures: 1
Decimals: 0
The significant notation: 5e+3
Therefore the significant notation is 5000.
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CHALLENGE:
Combine like terms:
3y + 4xy + x + 2y + 2xy + x + 10 + 1
Answer: 2x+6xy+5y+11
Step-by-step explanation:
Which tatement i not true?
B. All counting number are rational number. D. Zero i not a rational number. C. A mixed number i a rational number. A. The et of rational number include the et of integer
Answer: D. Zero is not a rational number
Step-by-step explanation:
[tex]0=\frac{0}{1}[/tex]. Thus, by definition, zero is rational.
Please help me with this
meghan and sara are on their way to disneyland. they travel 65 mph (miles/hour) for 2.2 hours and then stop for a 45-minute lunch break. after lunch they travel 55 mph for another 3.8 hours until they reach disneyland. what is their average speed, in miles/hour, for the entire duration of the trip? (round your answer to the nearest whole number. d
The average speed for the entire duration of trip is 52 mph.
The total distance traveled by an object in a given time frame is defined as its average speed. It is computed by dividing the entire distance traveled by the total amount of time spent.
Given,
S1 = 65 mph , T1 = 2.2 hours
S2= 0 mph (during lunch break) , T2 = 45 min = 45 / 60 hour
=0.75 hour
S3= 55mph , T3 = 3.8 hours
Therefore, S avg =(S1T1 + S2T2 + S3T3)/(T1 + T2 + T3)
=(65×2.2 + 0 ×0.75 + 55×3.8)/(2.2 + 0.75 + 3.8)
= 52.148 mph
The average speed for the entire duration of trip is 52 mph.
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Please help
The linear combination method gives a solution of (-4,2) for which a of these systems of linear equations?
A) 3x+13y=14
6x+11y=-2
B)4x+5y=12
8x+3y=-4
C) 5x+4y=12
7x+8y=12
D) 10x+3y=8
17x+6y=10
Please show your work
Using the provided points, Applying the substitution of the points in these system of linear equations. The equations which satisfies the points are the required answer. The answer is A) 3x+13y =14 and 6x+11y=-2
What is a equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What do you mean by system of linear equation?The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.
point = (-4,2)
for option A) 3*-4 +13*2 =14
14=14
and 6*-4 + 11*2 = -2
-2 = -2
For other options these equality doesn't holds.
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This graph shows fuel consumption for a car during a test run. Three of the statements are true. Which is NOT?
Line graph. X axis labeled miles; y axis labeled gallons. Line with upward arrow extends from point where X and Y axes connect (0, 0) with one marked coordinate (73.5, 3.5).
The car used 312 gallons of gas to go nearly 75 miles.
The car used 70 gallons of gas to go 3 miles.
The car used gas at a unit rate of 21 miles per gallon.
At this rate, it would take 4 gallons of gas to travel 84 miles.
In the graph showing fuel consumption for a car during a test run the correct statement is
At this rate, it would take 4 gallons of gas to travel 84 miles.How to find the correct statementThe information given in the problem will help to find the equation of the graph in the form
y = mx + c
definition of variable to suit the problem
y = output variable = number of gallons
m = slope
x = input variable = number of miles
c = y intercept
The slope
= (3.5 - 0) / (73.5 - 0)
= 0.05
the y intercept is 0
the equation of the line is y = 0.05x
Only option the last option fits the equation as shown
number of gallons = 0.05 * number of miles
= 0.05 * 84 miles
= 4.2 gallons
= 4 gallons
hence the last option is the correct choice
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Which of the following equations represent linear functions?Select all that apply
y = 7²,y + (1/2)x = 9 and 2.3 = y - 5.8x are the linear function thus option (A),(D) and (F) are correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear function is a line in a coordinate plane with a constant slope and can be written in form of y = mx + c.
Thus the degree of x and y will be 1.
For example, y = 7² can be written as, y = 0(x) + 7² so it will be a linear line.
Another y + (1/2)x = 9 and 2.3 = y - 5.8x are can be written as y = mx + c so they will be linear functions.
Hence "the functions y = 7²,y + (1/2)x = 9 and 2.3 = y - 5.8x are the linear function".
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If 400 m long fencing wire is required to surround a square flower garden 2 times, find length of the garden. -Maths Links Book 6 Approved by CD
Answer:
garden=400/2
=200
4× side = perimeter=200
So, =200/4
=50 m.
Step-by-step explanation:
Answer:
Length of garden is 50 m.
Step-by-step explanation:
Fence required for 1 time,
→ 400 ÷ 2
→ 200 m
Perimeter of square formula is,
→ P = 4 × L
Now length of the garden will be,
→ P = 4 × L
→ 200 = 4L
→ 4L = 200
→ L = 200/4
→ [ L = 50 m ]
Hence, length of garden is 50 m.
Salma finds some nickels and pennies
under the couch cushions. How much
money (in dollars) does she have if she
has 100 nickels and 150 pennies? How
much money (in dollars) does she have if
she has a nickels and y pennies?
Total value, 100 nickels and 150
pennies (dollars):
Total value, x nickels and y pennies
(dollars):
Answer:
$6.50
0.05x + 0.01y
Step-by-step explanation:
There are 100 pennies in a dollar. So each penny is 1/100 = $0.01
Each nickel is worth 5 pennies. So there are 20 nickels per dollar and therefore each nickel is worth 20/100 = $0.05
If you have 100 nickels, this works out to 0.05 x 100 = $5.00
If you have 150 pennies this works out to 0.01 x 150 = $1.50
Total value = 5 + 1.50 = $6.50
If you have x nickels and y pennies then that, inn dollar amount, would work out to
0.05x + 0.01y
The bottom of a ladder must be placed 5 feet from a wall. The ladder is x ft long. The ladder touches the wall 10 ft from the ground. How tall is the ladder? Round to the nearest whole number. 18 ft
Using Pythagoras theorem, the length of the ladder is 11 feet
Pythagoras TheoremThe Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle xyz, in which we have x² = y² +z². Here, y is the base, z is the altitude (height), and x is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
Data;
x = hypothenuse = length of laddery = 5 feetz = 10 feetUsing Pythagoras theorem;
x = 5² + 10²
x = 25 + 100
x = 125
x = √25
x = 11ft
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Complete the equation of the line whose yyy-intercept is (0,-1)(0,−1)left parenthesis, 0, comma, minus, 1, right parenthesis and slope is 444.
The complete equation in the slope-intercept form is y = 4x-1.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
So, the equation is,
y - y₁ = m (x - x₁)
And the standard form of the slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
From the question, we have
m = 4 and coordinates of b is (0, -1).
So, the equation is,
y + 1 = 4 (x - 0)
y +1 = 4x
y = 4x-1
Therefore, the equation is y = 4x-1.
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suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked. (i) define the random variable of interest and state how the variable is distributed. (ii) determine the expected value of the random variable and interpret the expected value in context.
i) The random variable is the number of suspicious transmissions reviewed until finding the first blocked one and the random variable is distributed usinng geometric distribution
ii) The expected value of the random variable: 2.5 which means the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.
In this question we have been given a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history.
Based on past history, the specialist blocks 40 percent of the suspicious transactions.
so, p = 0.40
i. Let X represent the number of suspicious transmissions reviewed until finding the first blocked one.
We will use a geometric distribution to model the first transmission.
ii. We know that according to the geometric model the expected value of the random variable would be.
E(X) = 1/p ,
= 1/0.4
= 2.5
This means, the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.
Therefore, i) the random variable: the number of suspicious transmissions reviewed until finding the first blocked one.
ii) the expected value of the random variable: 2.5
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The complete question is:
At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions.
Suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked.
(i) Define the random variable of interest and state how the variable is distributed.
(ii) Determine the expected value of the random variable and interpret the expected value in context.
miguel is mixing up a salad dressing. regardless of the number of servings, the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
44 is the proportion of the botched dressing will be olive oil.
Given, Miguel is mixing up a salad dressing. regardless of the number of servings,
the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if he accidentally doubles the vinegar and forgets the sugar altogether,
we have to find the proportion of the botched dressing that will be olive oil.
first we will find the amount of the even mixture of salt, pepper and sugar.
as, olive oil + vinegar + even mixture of salt, pepper and sugar = 100
58 + 14 + mixture of salt, pepper and sugar = 100
mixture of salt, pepper and sugar = 100 - 72
mixture of salt, pepper and sugar = 28
if he mixed doubles of the vinegar i.e. 28 then olive oil be,
x + 28 + 28 = 100
x = 100 - 56
x = 44
Hence, 44 is the proportion of the botched dressing will be olive oil.
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A photo is 16in long and 126cm wide.what is the approximate area of the picture in square feet?
The picture has the dimension of a rectangle and will have the area of 66.166 in square feet.
How to calculate for the areaWe have to convert the length and width to be in same unit, before calculating for the area by multiplying the length by the width, and then convert the result to be in square feet.
1 cm = 0.394 inches
126 cm = 126 × 0.394 inches
126 cm = 49.644 inches
So the picture has length 16 inches and width 49.644 inches
area of picture = 16 inches × 49.644 inches
area of picture = 794.304 square inches
1 inch = 0.0833 feet
794.304 square inches = 794.304 × 0.0833 square feet
794.304 square inches = 66.166 square feet.
In conclusion, the picture has an area of 66.166 square feet.
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PLEASE HELP ME!!!!!! THIS IS DUE ON FRIDAY!!!!!! (There is another part)
Answer:
it's c trust me I had the same problem
Elijah bought stock in a company two years ago that was worth a dollars. During the
first year that he owned the stock, it increased by 35%. During the second year the
value of the stock increased by 11%. Write an expression in terms of a that represents
the value of the stock after the two years have passed.
Answer:
x + .35X - .11(x - .35x)
Step-by-step explanation:
Let x = the original price of the stock.
x + .35x This is first year
-.11( x + .35x) is the second year
x + .35X - .11(x - .35x)
Help meee please !!!???
Answer:
Step-by-step explanation:
it is c
Which ordered pair is a solution of the
equation?
-3x + 5y = 2x + 3y
Answer:
Solve the equation for [tex]{y}[/tex].
[tex]y=\frac{5x}{2}[/tex]
Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.
Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(0,0)}[/tex]
Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex](1,\frac{5}{2})[/tex]
Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(2,5)}[/tex]
These are three possible solutions to the equation.
[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]
miley believes that listening to white noise can enhance verbal exam performance. she takes a random sample of college students and randomly assigns each student to one of two groups-the quiet group and the white noise group. the quiet group is asked to take a verbal exam in a completely silent classroom. the white noise group is asked to take the same exam in a classroom in which white noise is playing in the background. all students have one hour to complete the exam. miley will then compare the mean exam score for the two groups. suppose miley makes a type i error. in terms of the scenario, what would this mean?
A Type I error in this scenario would mean that Miley would conclude that the noise impacts the students when in fact it doesn't.
What are Type I errors and Type II errors?The definitions of Type I errors and Type II errors are presented as follows:
Type I: Rejection of a true null hypothesis, meaning that the null hypothesis is true, but a sample gives you enough evidence to reject it.Type II: Non-rejection of a false null hypothesis, meaning that the null hypothesis is false, but the sample does not give you enough evidence to reject it.The hypotheses tested in this problem are given as follows:
Null hypothesis: not enough evidence to conclude that there are differences in the exam scores.Alternative hypothesis: enough evidence to conclude that there are differences in the exam scores.A Type I error would mean that she rejected a true null hypothesis, meaning that Miley would conclude that the noise impacts the students when in fact it doesn't.
(rejected null hypothesis means that there is enough evidence to conclude that there are differences).
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there are 498 identical plastic chips numbered 1 through 498 in a box. what is the probability of reaching into the box and randomly drawing a chip number that is greater than 315? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of reaching into the box and randomly drawing a chip number that is greater than 3150 is 0.3675
In this question we have been given there are 498 identical plastic chips numbered 1 through 498 in a box.
We need to find the probability of reaching into the box and randomly drawing a chip number that is greater than 315
Total number of chips = 498
so, n(S) = 498
Let event A: drawing a chip number that is greater than 315
The number of chips greater than 315:
498 - 315 = 183
So, n(A) = 183
The probability of reaching into the box and randomly drawing a chip number that is greater than 315 using the formula of probability,
p(A) = n(A)/n(S)
p(A) = 183/498
p(A) = 0.3675
Therefore, the required probability is 0.3675
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(HELP-)
On the day of the test, the teacher instructed the students to take out at least 3 pencils from their backpacks.
Determine which inequality represents this scenario.
3 < p
3 > p
3 ≥ p
3 ≤ p
Chad purchased a new dirt bike for a competition. The salesperson recommended that the tires maintain an air pressure of at least 12psi for good traction on the riding surface.
Determine which inequality represents the salesperson's recommendation.
number line with open circle on the number 12 and line shaded to the left
number line with closed circle on the number 12 and line shaded to the left
number line with closed circle on the number 12 and line shaded to the right
number line with open circle on the number 12 and line shaded to the right
Ms. Rumble's history class conducted interviews with their grandparents for a class project. The grandparents at least 89 years old knew that Amelia Earhart was the first woman to fly solo across the Atlantic Ocean.
Determine the graph to represent this scenario.
number line with open circle on the number 89 and line shaded to the right
number line with closed circle on the number 89 and line shaded to the right
number line with closed circle on the number 89 and line shaded to the left
number line with open circle on the number 89 and line shaded to the left
Wyatt had to climb the stairs to ride the waterslide. The top of the waterslide was more than 56 feet from the ground. Which graph represents this inequality?
number line with open circle on the number 56 and line shaded to the left
number line with closed circle on the number 56 and line shaded to the left
number line with a open circle on the number 56 and line shaded to the right
number line with an closed circle on the number 56 and line shaded to the right
Zan took her dog, Simba, to the dog park on Saturday afternoon. There were more than 20 dogs running around the park when they arrived.
Determine which inequality describes the dogs at the park.
d < 20
d > 20
d ≥ 20
d ≤ 20
The inequality which can represent the above scenario is 3 ≤ p
What is Inequality ?
In mathematical expressions, inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. The symbols we will use in this instead of equals to are Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs.
≤ - less than or equal to
≥ - greater than or equal to
≠ - Not equal
Main Body:
Given:
On the day of the test, the teacher instructed the students to take out at least 3 pencils from their backpacks.
To find:
Determine which inequality represents this scenario.
Let us know about Inequality
In the given scenario,
The teacher asked the to take out at least 3 pencils from their backpacks. which the students can take out 3 pencils or 2 or 1 pencil (which is less than 3) but not greater than 3.
Therefore,The inequality which can represent the above scenario is 3 ≤ p
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O
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 0≤x≤ 4.
x
0
1
2
32
4
5
3
6
12
24
48
96
The average rate of change of the function at the interval 0 ≤ x ≤ 4 is 11.25
How to determine the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
x 0 1 2 3 4 5
y 3 6 12 24 48 96
The interval is given as
0 ≤ x ≤ 4
On the table, we have
x = 0 and y = 3
x = 4 and y = 48
This means that
f(0) = 3 and f(4) = 48
The average rate of change is then calculated as
Average rate of change = [f(4) - f(0)]/[4 - 0]
Substitute the known values in the above equation, so, we have the following representation
Average rate of change = [48 - 3]/[4 - 0]
Evaluate
Average rate of change = 11.25
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What is the answer to 21≥3(a−7)+9
Brendan deposited $3,967 in an account earning 5% interest compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
The interest earned in 5 years is $1096.
What is interest?Interest is the fee a business pays a lender (creditor) to borrow money.
Given that, Brendan deposited $3,967 in an account earning 5% interest compounded annually.
A = P(1+r/100)ⁿ
n = 5, r = 5% = 0.05, P = 3967 and a = amount earned
A = 3967(1+0.05)⁵
A = 3967(1.05)⁵
A = 5063
Interest earned = amount - principal
Interest = 5063-3967
Interest = $1096
Hence, Brendan earned $1096 as interest.
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Answer:
$1096.01
Step-by-step explanation:
five adults and five children randomly sit in ten seats that are equally spaced around a circle, such that one person sits in each seat. what is the probability that there is at least one diameter of the circle with two adults sitting on opposite ends of the diameter?
The probability is [tex]\frac{2}{5}[/tex] ,that there is at least one diameter of the circle with two adults sitting on opposite ends of the diameter.
What is probability ?
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Have given,
Five adults and five children,
Total seats are available 10
P(an adults apposite of a children) = [tex]\frac{2}{10}[/tex]
P(a children apposite of a children) = [tex]\frac{2}{5}[/tex]
We know that ,
P(True) = 1 - P(Not True)
P(True) = [tex]1 - (\frac{2}{10} + \frac{2}{5} )[/tex]
P(True) = [tex]\frac{2}{5}[/tex]
The probability is [tex]\frac{2}{5}[/tex] ,that there is at least one diameter of the circle with two adults sitting on opposite ends of the diameter.
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2
Write the answer in each blank.
Of these numbers
745 281 578 170
is the smallest
is the largest
Answer:
170 is the smallest
745 is the largest
Step-by-step explanation:
It is what it is
please help me I don’t get this
The operations between functions are:
a) h(f(3)) = 5
b) (f×g)(4) = -8
c) f( g(h(0))) -1
How to operate with functions?
The first thing we want to find is a composition, we want to find:
h(f(3))
That means that we need to evaluate h(x) in f(3), look at the graph and you can see that f(3) = -4
Replacing that we get:
h(f(3)) = h(-4)
And on the graph, we can see that h(-4) = 5
then h(f(3)) = 5
b) Now we have the product:
(f×g)(4) = f(4)*g(4)
Again, looking at the graph:
f(4) = -4
g(4) = 2
Then:
(f×g)(4) = f(4)*f(4)
(f×g)(4) = -4*2
(f×g)(4) = -8
c) Finally we have other composition:
f( g(h(0)))
So we have 2 compositions, first we find:
h(0) = 5
f( g(h(0))) = f(g(5))
Then:
g(5) = 0
f( g(5)) = f(0)
Finally, look at the graph and you can see that f(0) = -1
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