The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b
Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b
Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.
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express 0,2:0,15 as a ratio between whole numbers, in its simplest form
Answer:
yes it is in simpleat form
In the number 40.9113, how does the value of the 1 in the hundredths place compare to the value of the 1 in the thousandths place?
Drag and drop a fraction into the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The value of the 1 in the hundredths place is Response area the value of the 1 in the thousandths place
Answer:
The 1 in the hundredths place is ten times bigger in value than the 1 in the thousandths place. They are also both behind the decimals.
Step-by-step explanation:
1/100 = 1/1000 x 10
A peron buy 5 cup of coffee at a kiok in the mall. The bill i under $20. 0. What i the cot of each cup?
The cost of each cup of coffee at a kiosk is $ 4.
Let the cost of each cup of coffee is $ x.
A person buys 5 cup of coffee at a kiosk in the mall.
This question is related to unitary method problems.
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Then, the cost of 5 cup of coffee is 5x.
Given that bill is under $20.
So the cost of 5 cup of coffee will be $20.
5x=20
x=20/5
x=4
Therefore, the cost of each cup of coffee is $4.
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help i need to pass
From 8 apples and 5 peaches, the probability for the first apple then peach fruit is 40/156.
What is probability?
Probability is defined as a number between zero to one for the analysis of random phenomena.
Given that there are 8 apples and 5 peaches in a basket.
Total Fruits = 13
For the first event, the probability of getting an apple is,
p1=8/13
Now, Total Fruits = 12
For the second event, the probability of getting peach is,
p2=5/12
The probability for both events is given below.
p=p1*p2 = (8/13)*(5/12) = 40/156
Hence we can conclude that the probability for the first apple then peach fruit is 40/156.
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do the table and the equation represent the same function y=110+32(x) yes no
Answer:
Yes
Step-by-step explanation:
y = 110 + 32x
Let x = each value in the table and calculate the corresponding value of y.
You get the following.
x = 0; y = 110
x = 2; y = 174
x = 4; y = 238
x = 6; y = 302
x = 8l y = 366
Since every value from evaluating the function gives the same value as the table, then the answer is yes, the table and the equation represent the same function.
Why is one side and all angles equal the other two sides are not equal?.
It is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles.
What is Pythagorean theorem?
The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This is the basis for the Pythagorean identities, which relate the sine, cosine, and tangent of an angle to the ratios of the sides of a right triangle.
In a right triangle, one angle is a right angle (90 degrees) and the side opposite the right angle is called the hypotenuse. It is the longest side of the triangle and is always opposite the right angle. The other two sides are called the legs of the triangle, and are referred to as the opposite side and the adjacent side.
The reason that one side is equal to all angles while the other two sides are not, is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles. In a right triangle, the hypotenuse is opposite the right angle and has a unique relationship with the legs, which are the opposite and adjacent sides. This is the foundation of the theorem and identities.
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It is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles.
What is Pythagorean theorem?
The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This is the basis for the Pythagorean identities, which relate the sine, cosine, and tangent of an angle to the ratios of the sides of a right triangle.
In a right triangle, one angle is a right angle (90 degrees) and the side opposite the right angle is called the hypotenuse. It is the longest side of the triangle and is always opposite the right angle. The other two sides are called the legs of the triangle, and are referred to as the opposite side and the adjacent side.
The reason that one side is equal to all angles while the other two sides are not, is because the Pythagorean theorem and the Pythagorean identities are based on the properties of right triangles. In a right triangle, the hypotenuse is opposite the right angle and has a unique relationship with the legs, which are the opposite and adjacent sides. This is the foundation of the theorem and identities.
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In a class of 40 students the number who studied French is 10 more than the number who studied History if 8 studied both French and History find using a venn diagram the number who Studied [1] History [2] French only
Answer:
11 students studied history
21 students studied French
8 students studied both
Step-by-step explanation:
first you have to subtract the number of students who studied both classes.
40-8=32
this leaves you with 32 students to study either history or French.
we know 10 more students studied French than history so subtract that from the 32 students because we already know where they go.
32-10=22
we're left with 22 students that can be equally split between the 2 classes.
22/2=11
so there are 11 more students in each history and French.
but don't forget to add the 10 more students that we already knew were in the French class.
11+10=21
What is the area of the front side of the fifty-cent piece? Use 3.14 for π. Round to the nearest hundredth if necessary.
30.61mm
The area of the front side of the fifty-cent piece is 48.06 mm².
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
Given, The front side of a circular area fifty-cent piece has a diameter of 30.61 mm.
We know, Radius is half of the diameter which is, (30.61/2) mm.
= 15.305 mm.
We also know the area of a circle is πr².
Therefore, The area of the front side of the fifty-cent piece is,
= π(15.305)² mm².
= 48.0577 mm².
= 48.06 mm².
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Find the area of a rhombus whose diagonals are 9.6cm and 6.0cm long.
Answer:
A = 28.8cm²
Step-by-step explanation:
multiply 9.6 by 6.0
= 57.6
divide 57.6 by 2
= 28.8
Kendrick i packing crate that can hold 8 pear, and Nick i packing crate that hold 4 pear. If they mut pack the ame total number of pear, what i the minimum number of pear each mut pack?
The minimum number of pears that each must pack is x = 12 pears.
We can start by using algebra to represent the problem.
Let x be the number of pears that Kendrick and Nick must pack.
We know that the total number of pear that Kendrick packs is 8 pear per crate * the number of crates he packs = 8x. Similarly, the total number of pears that Nick packs is 4 pears per crate * the number of crates he packs = 4x.
Therefore, the total number of pears that Kendrick and Nick must pack is 8x + 4x = 12x. We are given that they must pack the same total number of pears, so we can set this equal to x. Therefore, we have:
12x = x
So the minimum number of pears that each must pack is x = 12 pears. This means that Kendrick must pack 12 pears in 8 crates and Nick must pack 12 pears in 4 crates.
It could be also represented as:
Kendrick: 8 pear/crate * C crates = 12 pear
Nick: 4 pear/crate * C crates = 12 pear
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A jewelry salesperson earns 10 2/5 % commission on all sales. Today she sold $6,090 in jewelry. What is total commission earned?
The total commission the salesperson earned is $ blank
(Round to the nearest cent as needed.)
Answer:
$633.36
Step-by-step explanation:
10 2/5 % = 10.4% = 0.104
10 2/5 % of $6090 = 0.104 × $6090 = $633.36
The organizers of a concert are preparing for the arrival of 50,000 people in a field. Each person is alloted 5 square ft of space, so the organizers rope off a circular area big enough to account for 5 square feet per person. Find the radius of this region, rounding to the nearest foot.
To find the radius of the circular area, the organizers must divide 50,000 by pi and then multiply by 5. The result of this calculation is the amount of area needed, which can then be divided by pi to find the radius of the circular region, rounding to the nearest foot.
To find the radius of the circular area, the organizers should first calculate the amount of area needed to accommodate each person in the field. This is done by dividing the total number of people (50,000) by pi and then multiplying by 5, which represents the 5 square feet of space allotted to each person. The result of this calculation is the amount of area needed to fit all 50,000 people. Next, the organizers should divide this area by pi to calculate the radius of the circular region. Finally, they should round the result to the nearest foot. This will give them the radius of the circular area that is needed to fit all 50,000 people in the field.
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What are the 4 parts of division?.
There are four types of division are:
DividendDivisorQuotientRemainderNow, According to the question:
Division is one of the four basic math operations with addition, subtraction, and multiplication. Division is an important operation because it is common in everyday life and helps people understand multiplication better. Division is splitting a group into equal parts. Division is used to split up a class into equal groups for a game or activity or even split a pizza into equal portions between a group of friends.
Dividend: The dividend is the number that is being divided in the division process. Divisor: The number by which the dividend is being divided by is called the divisor. Quotient: The quotient is a result obtained in the division process. Remainder: Sometimes, we cannot divide things exactly.
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Is 37 a perfect square?.
What is the fastest way to find the distance between two points?.
The fastest way to find the distance between two points in a plane is to use the distance formula.
The distance formula is a mathematical expression that gives the distance between two points in a plane, given their coordinates. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them.
This formula uses the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
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How much data is within 4 standard deviations of the mean?.
99.9% of the population is within 4 standard deviations of the mean.
In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.
Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.
The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.
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The absolute value of the difference between 4x and 2 is less than or equal to 2
The inequality form of the statement is: |4x - 2| ≤ 2. And the lowest value of x that makes this inequality true is x = -1.
To solve for the lowest value of x that makes this inequality true, we need to consider two cases:
If 4x - 2 ≥ 0, then |4x - 2| = 4x - 2, so the equation becomes:
4x - 2 ≤ 2
Adding 2 to both sides, we get:
4x ≤ 4
Dividing both sides by 4, we get:
x ≤ 1
If 4x - 2 < 0, then |4x - 2| = -(4x - 2), so the equation becomes:
-(4x - 2) ≤ 2
Adding 2 to both sides, we get:
-4x + 4 ≤ 4
Dividing both sides by -4, we get:
x ≥ -1
So, the solution to the inequality is -1 ≤ x ≤ 1. This means that any value of x that lies between -1 and 1, inclusive, satisfies the inequality.
So, the lowest value of x that makes this inequality true is x = -1.
"
Complete question
The absolute value of the difference between 4x and 2 is less than or equal to 2.
Write the statement as an inequality, then solve for the lowest value of x that makes this inequality true. Lowest value _____
"
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Find the equation of the linear function represented by the table below in slope intercept form
Answer:
y=-2x+5
Step-by-step explanation:
What is the resulting transformation of: RX=1ο RX=3?
The graph transformations are discussed below.
What is graph transformation?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
Given is the transformation of a graph.
A function transformation either "moves" or "resizes" or "reflects" the graph of the parent function. There are mainly three types of function transformations:
TranslationDilationReflectionTransformation Function Changes in Position/Size
Translation moves the curve Change in position
Dilation Stretches or shrinks the curve Change in the size
Reflection Flips the curve Change in position
and produces the mirror image.
Therefore, the graph transformations are discussed above.
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Graph the system of equations on your graph paper to anwser the question.
Y=-x+3
Y=x+5
Whats the solution for this system of equations?
Enter your anwser in the boxes.
Answer:
The solution is: (-1,4)
Step-by-step explanation:
I used an online graph but you can replicate it onto paper
Purple is Y=-x+3
Black is Y=x+5
12) A function f(x) = x² is given. Answer the following question for the function i) What is the algebraic nature of the function? ii) Write the name of the locus of the curve. iii) Write the vertex of the function. iv) Write any one property for sketching the curve. v) Write the domain of the function.
Given that f(x) is the square of x, there are no negative values in its range, which ranges from 0 to.
What is the algebraic nature of the function?The answer to a polynomial equation with polynomial coefficients is a function, and that function is an algebraic function.
Linear, quadratic, cubic, polynomial, rational, and radical algebraic functions are some examples of the several types of algebraic functions.
The range of the function f(x) = x2 is higher than or equal to zero, and the domain of the function is the set of all real numbers (x can be anything).
A function that represents an upward-facing parabola is f(x) = x2.
Its range from - to - is its domain.
Given that f(x) is the square of x, there are no negative values in its range, which ranges from 0 to.
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Engineer want to deign eat in commercial aircraft o that they are wide enough to fit 95% of all male. (Accommodating 100% of male would require very wide eat that would be much too expenive. ) Men have hip breadth that are normally ditributed with a mean of 14. 8 in. And a tandard deviation of 0. 9 in. Find P95. That i, find the hip breadth for men that eparate the mallet % from the larget %
The hip breadth of 95% of all male is 16.2 inches, which is greater than the mean of 14.8 inches with a standard deviation of 0.9 inches.
1. Calculate the Z-score for 95th percentile:
Z = (P95 - mean)/standard deviation
= (16.2 - 14.8)/0.9
= 2.44
2. Look up the Z-score in a Z-table to find the corresponding percentile:
95th percentile = 2.44
The hip breadth of 95% of all male can be calculated using the normal distribution. First, we must find the Z-score for the 95th percentile, which is calculated by subtracting the mean (14.8 inches) from the desired percentile (16.2 inches) and dividing by the standard deviation (0.9 inches). This gives us a Z-score of 2.44. We can then look this up in a Z-table to find the corresponding percentile, which is 95th percentile. Therefore, the hip breadth of 95% of all male is 16.2 inches.
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For what value of k for which the roots of the quadratic equation 9x² 3kx +K 0 has real and equal roots?.
The roots of the quadratic equation 9 x 2 - 3 k x + k = 0 are equivalent. As a result, the needed values of k are 0 and 4.
Any equation featuring one condition that involves the unknown is cubed and no term in which it has been increased to a greater number is a quadratic equation.
This has the equation ax2 + bx + c = 0, where a = 9, b = -3k, and c = k.
If D=0, the solution will be implemented and will have real and equivalent roots.
Most typically, the quadratic equation is represented as ax2 + bx + c = 0. The coefficients are the recognized numbers a, b, and c, while x represents the undetermined.
Quadratic equations must be employed whether directly or indirectly in any field where speed, area, or profit must be calculated.
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If the simple interest on 5,000 for 2 years is $500, then what is the interest rate?
Answer:
5%
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
I = $500P = $5,000t = 2 yearsSubstitute the given values into the simple interest formula and solve for r:
[tex]\implies 500=5000 \cdot r \cdot 2[/tex]
[tex]\implies 500=10000r[/tex]
[tex]\implies r=\dfrac{500}{10000}[/tex]
[tex]\implies r=0.05[/tex]
[tex]\implies r=5\%[/tex]
Therefore, the interest rate is 5%.
Answer:
Interest rate = 5% (or) 0.05
Step-by-step explanation:
Now we have to,
→ find the required interest rate.
Formula we use,
→ I = P × R × T
→ PRT = I
→ R = I/PT
Then the interest rate will be,
→ R = I/PT
→ R = $500 ÷ ($5000 × 2 years)
→ R = 500/(5000 × 2)
→ R = 500/10000
→ R = 0.05 × (100)
→ [ R = 5% ]
Hence, the interest rate is 5%.
Tessa did 3/5 of her homework problems on Saturday. On Sunday she did 1/3 of what was left plus the last 4 problems. How many problems did Tessa do over the weekend.
The total problems assigned over the weekend are 15.
What are fractions?In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.
Let us suppose the total number of problems assigned = x.
Given that the problems solved on Saturday is 3/5 of her total questions. This is represented as:
(3/5) x
The remaining problems are:
1 - (3/5) x = (2/5) x
On, Sunday the problems solved are 1/3 of the remaining. This is represented as:
(1/3) (2/5) x
(2/15) x
The remaining problems are:
(1 - 1/3)(2/5 x) = (2/3) * (2/5) x = 4/15 x
Given that the final number of problems remaining are 4, that is:
(4/15) x = 4
x = 4 (15/4)
x = 15
Hence, the total problems assigned over the weekend are 15.
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a texy car draiver ran away frome police but their was a passanger in the car than what should passanger doo
Answer:
he should do nothing because he is just a passenger.
Given f(x) =2x+2,find f(-10)
Using the conversion 8km/h = 5mph convert 28m/s to mph.
If your answer is a decimal, give it to 1d.p
Miles per hour and meters per second are formally known as mph and m/s, respectively.
Kilometers per hour 28 km/h
Miles per hour 62.6342
What is mph to m/s Formula?Let's first review the metric conversions for a mile and an hour. Speed is the distance traveled in a given amount of time.
Miles per hour and meters per second are formally known as mph and m/s, respectively. If so, converting mph to m/s will be simple. We are cognizant of:
A mile is equal to 1.60934 kilometers or 1609.34 meters.
3600 seconds make up 1 hour, which is equal to 60 minutes, 60 minutes, and 60 seconds.
With the help of these conversions, let's create the mph to m/s formula.
mph to m/s Formula
1 mph = 1 mile per hour
=1 mile / 1 hour
=1609.34 meters/3600 seconds
0.447 meter / seconds
=0.447 m/s
So, multiplying by 0.447 is required to change mph to m/s.
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What is the formula for coordinate plane?.
The coordinate plane's formula is (x, y), where x denotes the x-axis and y denotes the y-axis.
A linear equation is a two-variable equation with a line as the graph.
A collection of points in the coordinate plane that are all solutions to the equation make up the graph of the linear equation.
If every variable has a real value, the equation can be graphed by placing enough points on the graph to identify a pattern, then connecting those points to include all of the points.
A linear equation must have at least two points in order to be graphed, however it's usually a good idea to utilize more.
Try to include zero as well as both positive and negative numbers when selecting your points.
The term "x-intercept" refers to the point where the graph crosses the x-axis, and the term "y-intercept" refers to the point where the graph crosses the y-axis.
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zhen borrows $1,200.she borrows the money for 2 years and owes $180 in simple interest.what is the yearly simple interest rate on zhen's loan?
r = annual interest rate
F = final value (amount owed including interest)
P = principal (initial amount borrowed)
n = number of years the loan is taken out for
Plugging in the given values:
r = (1300 - 1200) / 1200 * 2
r = 0.15 or 15%
This formula also gives the same result, that the annual simple interest rate on Zhen's loan is 15%.
