Answer:
2 1/4 more snow today
Step-by-step explanation:
5 3/4 - 3 1/2 get a common denominator of 4
5 3/4 - 3 2/4 = 2 1/4
look at attached photo
The correct answer is A) y = 9000x + 65,000.
Find a linear equation that models the value of the house after x years?The correct answer is A) y = 9000x + 65,000.
This is an equation in slope-intercept form, where "y" is equal to the value of the house after x years, "9000x" is the slope (or rate of change) of the equation, and 65,000 is the y-intercept (or the initial value of the house). The equation can be derived from the given information.The initial value of the house is 65,000, so the y-intercept must be 65,000. To find the slope, we can use the formula "rise/run", or change in y/change in x.The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).
The equation y = 9000x + 65,000
models the value of the house after x years, where y is the value of the house,
9000x is the slope of the equation,
and 65,000 is the y-intercept.
This equation can be used to calculate the value of the house after any given number of years.To learn more about linear equation in slope-intercept form refer to:
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Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D
By solving the equation we get ,t = ± 7 using concept of square roots.
How to find the square roots ?
Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.
For example, 2 is the square root of 4, and this is expressed as √4 = 2.
We know that every squared number has two square roots one is positive and another is negative.
In given que,
given condition is t squared minus 49 = 0
Form of equation is ax^ 2 = c.
given condition can also be written as t^2 - 49 = 0
i.e. t^2 = 49
where a = 1
x = t
c = 49
So, the square root are 7 and -7.
So, equation become t = ± 7.
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In a class activity, all the 15 students wear hats. 7 students wear red hats, 6 students wear green hats and 2 students wear white hats. (I) two of the 15 students are picked at random. Show that the probability that these two students wear hats of the the same colour is 37/105. (I) three of the 15 students are picked at random. Find the probability that at least 2 of these students wear red hats.
The probabilities, using the hypergeometric distribution, are given as follows:
i) Two wear the same color: 37/105: 0.35238 = 37/105.
ii) At least 2 wear red: 0.4461.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are presented as follows:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The probability of two red is given as follows:
[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
The probability of two green is given as follows:
[tex]P(X = 2) = h(2,15,2,6) = \frac{C_{6,2}C_{9,0}}{C_{15,2}} = 0.14286[/tex]
The probability of two white is given as follows:
[tex]P(X = 2) = h(2,15,2,2) = \frac{C_{2,2}C_{13,0}}{C_{15,2}} = 0.00952[/tex]
Then the probability of two wearing the same color is given as follows:
0.2 + 0.14286 + 0.00952 = 0.35238 = 37/105.
The probability that out of 3 people, at least 2 wear red, is given as follows:
[tex]P(X = 2) = h(2,15,3,7) = \frac{C_{7,2}C_{8,1}}{C_{15,3}} = 0.3692[/tex]
[tex]P(X = 3) = h(3,15,3,7) = \frac{C_{7,3}C_{8,0}}{C_{15,3}} = 0.0769[/tex]
Hence:
0.3692 + 0.0769 = 0.4461.
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If equation 2x ^ 2 + 6(k + 3) * x - 9k = 0 has equal roots, what are the possible values of k?
Answer:
[tex]k = -4-\sqrt{7} \\or\\k = -4+\sqrt{7}[/tex]
Step-by-step explanation:
Bobby and Rick are in a 16-lap race on a one-mile oval track. Bobby, averaging 86 mph, has completed six laps just as Rick is getting his car onto the track. What speed does Rick have to average to be even with Bobby at the end of
the sixteenth lap?
To be even with Bobby at the end of the sixteenth lap, Rick has to average a speed of __ mph.
(Type an integer or a decimal.)
Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16th lap should be: Distance = Speed × Time16=1084× Speed Speed=16×8410=134.4 mph.
The time taken by Bobby to complete 10 laps will be:
[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\10 & =84 \times \text { Time } \\\text { Time } & =\frac{10}{84} \text { hours }\end{aligned}$$[/tex]
Hence, the speed that Rick must be driving on to even with Bobby at the end of the 16 th lap should be:
[tex]$$\begin{aligned}\text { Distance } & =\text { Speed } \times \text { Time } \\16 & =\frac{10}{84} \times \text { Speed } \\\text { Speed } & =\frac{16 \times 84}{10}=134.4 \mathrm{mph} .\end{aligned}$$[/tex]
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for which of the three intervals do you have the most confidence that the interval captures the population mean
it can be inferred that there is a 95% probability that the true value falls within that range.
A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals than contain either 95% or 99% of expected observations.
Thus, if a point estimate is generated from a statistical model of 10.00 with a 95% confidence interval of 9.50 - 10.50,
it can be inferred that there is a 95% probability that the true value falls within that range.
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Examine the drawing below, which could be a value for x?
The value of 'a' can be 20. The correct option is C, 20.
What is triangle inequality theorem?As per the triangle inequality theorem, the sum of any two sides of the triangle should be greater than the third side.
As per triangle inequality theorem, the sum of the two sides of the triangle should be greater than the third side of the triangle.
As per the triangle inequality theorem, if 'a' is the longest side of the triangle then,
21 + 6 > a
27 > a
If a is not the longest side of the triangle,
21 + a > 6
a > -21 + 6
a > -15
6 + a > 21
a > 21 - 6
a > 15
Therefore, the value of a should be greater than 15 and less than 27. Since the only option under this condition is 20.
Hence, The correct option is C, 20.
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Please Help me!!!!! Will give brainliest 4 an EXPLAINATION!
The angles after solving the equations will be equal to 50°, and both angles will be the same as the corresponding angles. Hence, option B is correct.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the given information in the question,
The equations for the angles are:
7x + 1 = 6x + 8
7x - 6x = 8 - 1
x = 7
So, the angles will be,
7x + 1 = 7(7) + 1 = 50°
6x + 8 = 6(7) + 8 = 50°
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Find the Error, a student is simplifying the expression negative cube root 0.125 using rational numbers. The student claims that the expression cannot be simplified because it is not possible to take the square root of a negative number. Find the error made by the student and correct it. Need help ASAP. giving 50 points and brainliest if you solve
Answer:
Step-by-step explanation:
Lucy wants to buy a small car. She speaks to her bank and they offer her a loan of £5000 over 5 years at a simple interest rate of 5%. How much simple interest will Lucy have to pay back in total?
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
What is simple interest?To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.
A = $6,250.00
I = A - P = $1,250.00
Formula: A = P(1 + rt)
First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.
Fixing our equation
A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
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forest fires and acres burned numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 7 recent years are shown. number of fires x 57 72 69 58 47 84 62 number of acres burned y 57 72 69 58 47 84 62 send data to excel the correlation coefficient for the data is
The correlation coefficient for the data is positive 57,72,69,58,47,84,62 with coefficient being 1.
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.
Correlation is a measure of a monotonic association between 2 variables. A monotonic relationship between 2 variables is a one in which either (1) as the value of 1 variable increases, so does the value of the other variable; or (2) as the value of 1 variable increases, the other variable value decreases.
In the given question, the number of fires in 7 years is given as: 57,72,69,58,47,84,62.
Similar is the number of acres burned: 57,72,69,58,47,84,62
This shows total positive correlation , with it's coefficient being 1 .
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find the dimensions of the rectangular dog park producing the greatest enclosed area given 200 feet of fencing.
50 feet each dimensions of the rectangular dog park producing the greatest enclosed area given 200 feet of fencing.
For an area to be the maximum of any rectangle the difference in length and breadth must be minimal. So, in such case, the length must be ceil (perimeter / 4) and the breadth will be floor(perimeter /4). Hence the maximum area of a rectangle with a given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).
Let X be the length and Y be the width of the rectangle. 200 ft of fencing material, so the maximum perimeter is 200 ft. Therefore first equation can be, 2X + 2Y = 200 => X + Y = 100 => Y = 100 — X
Equation of area of rectangle =>
A = X×Y => A = X(100–X) => A = 100X — X^2
Differentiate with respect to X on both sides
A' = 100 — 2X
Critical point => 100 — 2X = 0 => 2X = 100, X = 50
So maximum area is generated when the length and width of the fence are 50 feet each, which makes it a square. In mathematical terms, the square can be considered a rectangle.
50 feet each dimensions of the rectangular dog park producing the greatest enclosed area given 200 feet of fencing.
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The retail cost of a computer is 37% more than its wholesale cost?which statement is true?1. THe retail cost of the computer is 132% more than the wholesale price.2. THe wholesale cost of the computer is 68% if the retail price.3. THe retail cost of the computer is 132% of the wholesale price.4. the retail cost of the computer is 37% of the wholesale price.
when retail cost of the computer is 37% of the wholesale price then Retail price is 1.37times wholesale price
Retailers who acquire products in bulk are subject to wholesale pricing.
Selling products at a greater price than what it costs to produce them allows businesses to turn a profit.
Retail pricing is what merchants decide to charge customers as their ultimate selling price.
Consumers are the primary focus of retail pricing.
According to the question,
The retail cost of a computer is 37% more than its wholesale cost
Let Retail cost be "x" and wholesale cost be "y"
So , x = y + 0.37y
=> x = 1.37y
Therefore , The retail price is 1.37times the wholesale price
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. Find the solution(s) to the systems of equations algebraically
{(y=x^2-2x+4),(y=3x):} (Use Substitution and factoring)
(multiple choice)
A.(0,0)
B.(4,12)
C.(4,1)
D.(0,4)
E.(1,3)
The solution to the systems of equations is (4,1). Option C. is the answer
How to find the solution(s) to the systems of equations algebraically?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included
Given the: equations {(y=x²-2x+4), (y=3x):}
y= x²-2x+4 and y = 3x
substitute y = 3x into y= x²-2x+4. That is:
y= x²-2x+4
3x = x²-2x+4
x²-2x -3x+4 = 0
x²-5x+4 = 0
By factoring:
x²-4x -1x+4 = 0
x(x-4) -1(x-4) = 0
(x-4)(x-1) = 0
x-4 = 0 or x-1 = 0
x= 4 or x = 1
Thus, the solution is (4,1)
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A racetrack charges $85 for each seat in the lower section, $60 for each seat in the upper sections, and $35 for field tickets. There are three times the amount of seats in the upper section as compared to the lower section. The revenue from selling all 22,800 seats is $948,000. How many seats are in the upper section of the racetrack?
Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.
What is a system of equations?A system of equations, also called simultaneous equations, is two or more equations solved concurrently.
We can use any of the following methods to solve simultaneous equations:
GraphicalSubstitutionEliminationMatrix.In this situation, after forming the equations, we can use substitution and elimination methods to solve them.
Racetrack charge per lower seat = $85
Racetrack charge per upper seat = $60
Racetrack charge per field ticket = $35
Let lower seats = x
Let upper seats = 3x
Let field tickets = y
4x + y = 22,800 ... Equation 1
y = 22,800 - 4x ...Equation 3
85x + 60(3x) + 35y = 948,000
85x + 180x + 35y = 948,000 ... Equation 2
Substitute Equation 3 in Equation 2 to eliminate y:
85x + 180x + 35(22,800 - 4x) = 948,000
85x + 180x + 798,000 - 140x = 948,000
125x = 948,000 - 798,000
125x = 150,000
x = 1,200
Determining the number of seats:
Seats in the Lower section = 1,200
Seats in the Upper section = 3,600 (1,200 x 3)
Field tickets, y = 22,800 - 4x
y = 22,800 - 4(1,200)
= 18,000
Check:
85x + 180x + 35y = 948,000
85(1,200) + 180(1,200) + 35(18,000) = 948,000
102,000 + 216,000 + 630,000 = 948,000
948,000 = 948,000
Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.
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A punter kicks a football. Its height h, in yard, t seconds after the kick is given by the equation h(t)=-4.9t^2+18.24t+0.8. The height of an approaching blocker's hand is modeled by the equation h(t)=-1.43t+4.26, using the same time. Can the blocker knock down the punt (do they intersect)? If so, at what point will that happen (the point of intersection)?
Part 1
[tex]-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0[/tex]
Therefore, the blocker can knock down the punt.
Part 2
Using the quadratic formula,
[tex]t=\frac{-19.67 \pm \sqrt{319.0929}}{2(-4.9)}\\\\t \approx 0.18437, 3.82992[/tex]
Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is [tex](0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}[/tex].
Helppp pleaseeee I’ll mark you brainly if you help meee!!
Using the current equation:
C = V/I
We will get the current c = (4.7 + 0.3i) volt/ohm
How to find the current?
We know that the equation that relates voltage V, current C and I impedance is:
V = C*I
Solving this for the current, we will get:
C = V/I
Here we know that:
V = (24 - 8i) volts
And the impedance is:
I = (5 - 2i) ohms
Replacing that in te current equation we will get:
C = (24 - 8i)/(5 - 2i) volt/ohm
If we multiply and divide by the complex conjugate of the denominator, which is:
(5 + 2i)
We will get:
C = [(5 + 2i)* (24 - 8i)]/[ (5 + 2i)*(5 - 2i)] volt/ohm
C = [ 5*24 + 5*(-8i) + (2i)*24 + (2i)*(-8i)]/(5^2 + 2^2) volt/ohm
C = [120 - 40i + 48i + 16]/(29) volt/ohm
C = [136 + 8i]/29 volt/ohm
C = (4.7 + 0.3i) volt/ohm
That is the current for the given case.
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a ball travel with the velocity of (2,1) with wind blowing in the direction (3,-4) with respect to some coordinates axes .find the size of the velocity of the ball in the direction of the wind?
The size of the velocity of the ball in the direction of the wind is 2 units
How to find the size of the velocity of the ball in the direction of the wind?To find the size of the velocity of the ball in the direction of the wind, we can take the dot product of the ball's velocity vector and the wind velocity vector.
The dot product is defined as:
v1 • v2 = (x1 × x2) + (y1 × y2)
Substituting the coordinates of the ball's velocity vector and the wind velocity vector, we get:
(2, 1) • (3, -4) = (2 ×3) + (1 × (-4))
= 6 - 4
= 2
Therefore, the size of the velocity of the ball in the direction of the wind is 2. This represents the component of the ball's velocity that is aligned with the wind.
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Given a data set of all positive values, if the largest value of a data set is doubled, which of the following is not true?
a) The mean increases.
b) The range increases.
c) The interquartile range increases.
d) The standard deviation increases.
When the largest value of a data set is doubled, c) The interquartile range increases.
What is the interquartile range?The average of the numbers is the mean. Calculating is simple: add up all the numbers, then divide by the total number of numbers. When the sample maximum and minimum are subtracted, the range of a set of data is the difference between the largest and smallest values. It uses the same units as the data to express itself.
A high standard deviation in a normal distribution denotes that values are typically far from the mean, while a low standard deviation denotes that values are grouped closely around the mean.
The difference between the third and the first quartile is defined by the interquartile range. The partitioned values known as quartiles divide the entire series into four equally sized segments. There are thus three quartiles.
Find the median (middle value) of the lower half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.
In this case, there'll be an increase in the IQR. Therefore, the correct option is C.
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An area code has three digits. How many different area codes are possible
Answer:
1000
Step-by-step explanation:
If any of the digits 0-9 can be used then there are 10^3 possible codes.
10^3 = 1000
match each integer on the left with the probability on the right that it is the sum of the faces when two fair dice are rolled.
The probability of the sum of the numbers comes up on the facing dice add up to 3 while rolling two fair six sided dice is equal to ( 1/ 18).
As given in the question,
Number of six sided fair dice rolled = 2
Total number of outcomes of each dice = 6
Total number of outcomes of rolling two six sided fair dice = 36
Outcomes are:
( 1,1), (1,2)...(1,6),( 2,1), (2,2)...(2,6), ( 3,1), (3,2)...(3,6), ( 4,1), (4,2)...(4,6), ( 5,1), (5,2)...(5,6), ( 6,1), (6,2)...(6,6)
Sum of facing up dice add upto 3 are
( 1,2) , (2,1) only
Number of favorable outcomes = 2
Required probability = 2/36
= 1/18
Therefore, the required probability of the sum of facing up dice add upto 3 is equal to (1/18).
The given question is incomplete, I answer the question in general according to my knowledge:
Roll two fair 6-sided dice. what is the probability that the sum of the numbers on the dice facing up add up to 3?
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Is there anyone that can help me with a finance question?
Answer:
Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.
Step-by-step explanation:
Height (in inches) Mean Minimum Q1 Median Q3 Std Dev 4.21 Maximum 79 68.2 67 , 71 , Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches. Height (in inches) Q3 Mean 68. 2 Std Dev .21 Minimum 62 4 Q1 63 Median 67 Maximum 79 Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches. (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches.
Standard deviation will be √3.3516 .
To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².
After that , we have to calculate the Xbar by using
Xbar = ∑fiXi / N
for which we need the value of fi , Xi and N
N = 100
fiXi = 6478
we have calculated the values from the given data ,
Therefore ,
Xbar = 6478 / 100
= 64.78
Var(X) = αx² - ∑fiXi² / N - (Xbar²)
= 419980 / 100 - (64.78)²
= 4199.80 -4196.4484
=3.3516
Thus,
standard deviation ax = √var(X)
= √3.3516
Therefore , the standard deviation will be √3.3516
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the height of one tampa city center is 537 feet. convert 537 feet to meters by finding an equivalent rate. round to the nearest tenth
The equivalent rate is 163.7 meters.
What is an equivalent rate?
Equivalent rates are different rates that have the same value. Similar to finding equivalent ratios, you may find an equivalent rate by multiplying or dividing the numerator and denominator by the same number.
Here, we have
Given: the height of one Tampa city center is 537 feet.
We have to convert 537 feet to meters by finding an equivalent rate.
1 feet = 0.3048 meter
So, 537 feet = 537 × 0.3048 = 163.7 meters.
Hence, the equivalent rate is 163.7 meters.
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Answer:
Hence, on a number line,-12 lies to the left of Zero.
Step-by-step explanation:
On a number line, zero lies exactly at the middle of the number line.Left to the zero, negative number lies and right to the zero, positive number lies.
expresa 1405 en base 7 a base 10
1405 in base 7 = 544 in base 10
What is base-7 number system ?
The heptimal system is another name for base-7 numbers. Base 7 numbers are represented by the digits 0, 1, 2, 3, 4, 5, and 6.
The digits of a Base 10 number, on the other hand, are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If there isn't a subscript at the supplied number, Base 10 is used to write that number. The decimal system is sometimes known as base-10 numbers. Currently, in daily life, we frequently use numbers in the base 10 range.
base 7 to base 10 conversion:
Multiply each digits by the powers of 7 as follows:
Base 7 digits: 1 4 0 5
Multiply by: 7^3 7² 7^1 7^0
( 1*7^3) + (4*7² ) + (0* 7^1 )+ ( 5 * 7^0)
= 343 + 196 + 0 + 5
= 544
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Ravi sells real estate. Based on previous data, he knows that 5% of home tours result in a sale. Assume that the results of these tours are independent from each other. Which of the following choices are binomial random variables? Choose all answers that apply: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale. C. Take a random sample of 3 tours and let M = the amount of sales (in dollars) generated by the tours.
The options that represent binomial random variable are;
A. Take a random sample of 30 tours and let L = the number of tours that result in a sale.
B. Take a random sample of 3 tours and let K = the number of tours that result in a sale.
How to Identify Binomial Random Variables?There are 4 primary conditions for a random variable to be classified as binomial random variable and they are;
1. The number of observations n is fixed.
2. Each observation is independent.
3. Each observation represents one of two outcomes ("success" or "failure").
4. The probability of "success" p is the same for each outcome.
No, in this case, since 5% of home tours result in a sale, it therefore tells us that number of home tours is the independent variable while the amount of sales generated is the dependent variable.
From the above, we can access the given options and say that the last option is not a binomial random variable because the variable M is dependent and so does not satisfy one of the four conditions.
However, options A and B satisfy the 4 conditions and we say they are binomial random variables.
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Write an equation in point-slope form of the line that passes through the given point and with the given slope m.
(-3,2); m=3
The equation of the line is
(Simplify your answer. Type your answer in point-slope form.)
Answer:
y = 3x + 11
Step-by-step explanation:
y = mx + b
y = 3x + b
2 = 3(-3) + b
2 = -9 + b
b = 11
y = 3x + 11
Solve the equation 2x + 3y = 5 for x.
Answer:
x = [tex]\frac{5-3y}{2}[/tex]
Step-by-step explanation:
2x + 3y = 5
isolate variable: 2x = 5-3y
divide by 2: x = [tex]\frac{5-3y}{2}[/tex]
The gardening club at school is growing vegetables. The club has 300 square feet of planting
beds.Cucumber plants require 6 square feet of growing space, and tomato plants require 4
square feet of growing space. The students want to plant some of each type of plant and have at
least 60 plants.
Select the combination of equations or inequalities that could describe this situation. Let c represent the number of cucumber plants and t represent the number of tomato plants.
Answer:
The answer is :
E - 6c + 4t < 300
s formula to find a quadratic approximation of at the origin. estimate the error in the approximation if and .
A quadratic equation of at the origin, estimate the error = 0.000859M
The approximation is valid because is very small.
Calculation of concentration:
Since
0.85 M 0 0
(0.85-x)M x x
Now the value of x should be
x = 0.0000229
So based on this, the above concentration should be determined.
In order to demonstrate that the same value of x may be achieved either way, you will now solve using the quadratic formula rather than iterations. What are the values of a, b, and c and x, where a, b, and c are the coefficients in the quadratic equation [tex]ax^{2} +bx+c=0[/tex] and x is [h3o+], when using the quadratic equation to determine [h3o+] in 0.00250 m hno2? Keep in mind that ka=4.5104.
a : 1
b : 4.5x[tex]10^{-4}[/tex]
c : 1.125x[tex]10^{-6}[/tex]
[[tex]H_{3} O^{+}[/tex]] = 0.000859M
As [tex]HNO_{2}[/tex] is a weak acid, its equilibrium in water is:
[tex]HNO_{2} (aq)+H_{2} O(I)[/tex] ⇄ [tex]H_{3} O^{+} (aq)+N_{2} O^{-} (aq)[/tex]
Equilibrium constant, ka, is defined as:
ka = 4.5x[tex]10^{-4}[/tex] = [[tex]H_{3} O^{+}[/tex]] [NO₂⁻] / [HNO₂] (Equation-1)
Equilibrium concentration of each specie are:
[HNO₂] = 0.00250M - x
[H₃O⁺] = x
[NO₂⁻] = x
Replacing in (1):
4.5x[tex]10^{-4}[/tex] = [tex]\frac{x*x}{0.00250M-x}[/tex]
1.125x10⁻⁶ - 4.5x10⁻⁴x = x²
0 = x² + 4.5x10⁻⁴x - 1.125x10⁻⁶
As the quadratic equation is ax² + bx + c = 0
Coefficients are:
a: 1
b: 4.5x10⁻⁴
c: 1.125x10⁻⁶
Now, solving quadratic equation:
x = -0.0013 → False answer, there is no negative concentrations.
x = 0.000859
As [H₃O⁺] = x; [H₃O⁺] = 0.000859M
Therefore,
A quadratic equation of at the origin, estimate the error = 0.000859M
To learn more about Quadratic equation visit :
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