From the checks and calculation the tractor is not operating correctly.
What is standard deviation?Standard deviation refers to by how how much the data varies from the mean
How to determine if the tractor is not operating correctlyGiven data form the question
1% level of significance
variance was found to be 68mm2
A sample of 31 planting lines
a maximum variance of 55mm2
Definition of variables
1% level of significance is equivalent to 99% confidence interval
mean sample, μ = ?
standard deviation, SD = √variance = √68 = 8.246
Z score, Z = 2.576
from z table z score of 99%confidence interval = 2.576sample size, n = 31
maximum variance, X = 55mm2
The formula in term s of Z is
Z = ( X - μ ) / SD
2.576 = (55 - μ) / 8.246
(55 - μ) = 2.576 * 8.246
55 - μ = 21.242
μ = 55 - 21.242
μ = 33.758 mm²
For the tractor to be working correctly the difference between the mean and 2 * SD should not be more than the maximum variance which is 55mm²
55mm² ≥ mean ± 2 * SD
55mm² ≥ 33.758 mm² ± 2 * 8.246
55mm² ≥ 50.25
Since 50.25 is less than the maximum variance the tractor is operating correctly
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1. The sliders for y = ax + b have been set to create the following graph. What are possible values for a and b?
The slope of the line is m = 2 and the y-intercept b = 2
Therefore, the equation for the graph is
[tex]y=-2|x|+2[/tex]meaning a = -2 and b = 2.
(The negative sign in front of the absolute value drags the graph below the y = 0 )
two systems of equations are given below. for each system, choose the best description of its solution. if applicable, give the solution.
Let:
[tex]\begin{gathered} x-4y=8_{\text{ }}(1) \\ -x-4y=8_{\text{ }}(2) \\ \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (1)+(2) \\ x+(-x)+(-4y)+(-4y)=8+8 \\ -8y=16 \\ y=\frac{16}{-8} \\ y=-2 \end{gathered}[/tex]Replace the value of y into (1):
[tex]\begin{gathered} x-4(-2)=8 \\ x+8=8 \\ x=8-8 \\ x=0 \end{gathered}[/tex]The system has unique solution:
[tex](x,y)=(0,-2)[/tex]Identify the value for C in the following equation that would make theconic section a hyperbola: 2x2 + y2 + 3x + 5y + 1 = 0
ANSWER:
C = -1
STEP-BY-STEP EXPLANATION:
We know that the general formula of hyperbola is the following
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Which means that the sign must have y must be negative for it to be a hyperbola.
Therefore y must be equal to -1.
[tex]2x^2-1y^2+3x+5y+1=0[/tex]the ratio of men to woman working for a company is 5 to 4. if there is 225 employees total how many women work for the company
Given:
The ratio of men to women = 5: 4
Total number of employees = 225
The total ratio is:
[tex]\begin{gathered} =\text{ 5 + 4} \\ =\text{ 9} \end{gathered}[/tex]The number of women is the ratio of women to the total ratio times the number of employees
[tex]\begin{gathered} =\frac{4}{9}\times225 \\ =\text{ 100} \end{gathered}[/tex]Answer:
100 women
Find the value of x. Round tothe nearest tenth.27°Х34°11=x = [?]Law of Sines: sin AAsin Bbsin CIIaС
Using the law of Sines
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]Consider the given triangle
Let A = 27°, the a = 11
Let B = 34°, the b = x
Substitute the values into the sine rule formula
This gives
[tex]\frac{\sin27}{11}=\frac{\sin 34}{x}[/tex]Cross multiply
[tex]x\times\sin 27=11\times\sin 34[/tex]Divide both sides by sin 27
This gives
[tex]x=\frac{11\times\sin 34}{\sin 27}[/tex]Solve for x
[tex]\begin{gathered} x=\frac{11\times0.5592}{0.4540} \\ x=\frac{6.1512}{0.4540} \\ x=13.55 \end{gathered}[/tex]Therefore, the value of x is approximately 13.55
hello im stuck on this hw problem and need help ty
The amount of money that Abdul is going to donate to the City Youth Fund is denoted by x, and the amount of money that Abdul is going to donate to the Educational Growth Foundation is denoted by y.
Since Abdul will donate up to $500, the sum of those amounts must be less or equal to 500.
[tex]x+y\leq500[/tex]It is not possible to donate less than zero, therefore, we also have the following constrains
[tex]\begin{gathered} x\geq0 \\ y\geq0 \end{gathered}[/tex]Abdul wants the amount of money donated to the Educational Growth Foundation to be at least 4 times the amount of money donated to the City Youth Fund, therefore, we have our final constrain
[tex]4x\leq y[/tex]Combining those four regions, the solution is their interception, which is
Look at triangles A through F shown in the rectangles below.Which triangles are acute triangles?
The acute triangles are those whose all 3 angles have a measure less than 90 degrees.
We need to follow the next image:
Let us check each triangle.
Triangle A:
It has a right angle, hence, it can not be an acute triangle.
Triangle B:
All three sides are less than 90 degrees. Hence, it is an acute triangle
Triangle C:
It has an angle with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle D
All three sides are less than 90 degrees. Hence, it is an acute triangle.
Triangle E
It has a side with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle F
It has a right angle, hence, it can not be an acute triangle.
Hence, the correct answer is H. B and D
13. slove for x so the [tex]f(x) = 5[/tex]
Solution
We have the following function given:
f(x) = -3x+5
And we need to do the following:
5= -3x+5
And if we subtract 5 in both sides we got:
0 =-3x
Dividing both sides by -3 we got:
[tex]\frac{0}{-3}=\frac{-3x}{-3}[/tex]And finally we got:
x= 0
Problem 17
17) f(-2)= 3
18) f(0)= 3
19) f(1)= 0
20) f(-1)= 5.2
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Problem
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Solution
For this case we can find the real price with this operation:
95+265= 360
And the rate of discount can be founded as:
(95/265)*100= 35.85%
Rounded to the nearest percent would be 36%
Mr. Garcia gave his students a biology test last week.Here are the test scores for each of the fifteen students.Test scores938398899791838692908884858291(b) Construct a histogram for the data.(a) Complete the grouped frequency distribution forthe data. (Note that the class width is 5.)FrequencyTest scores7-6+79 to 835+84 to 88Frequency0.0043+89 to 932+1194 to 980-79 1083941 98844 to 58 89 to 93Test scoresx5?
Test scores: 93 83 98 89 97 91 83 86 92 90 88 84 85 82 91
organizing the data: 82,83,83,84,85,86,88,89,90,91,91,92,93,97,98
(a) Complete the grouped frequency distribution for the data.
79 to 83 -> 3
84 to 88 -> 4
89 to 93 -> 6
94 to 98 -> 2
(b) Construct a histogram for the data.
the histogram can be constructed using the information obtained in point (a)
Hello! Need help with this, please explain in an easy way I am in year 9
Let's factor the trinomial step by step:
1. Multiply and divide the whole trinomial by the leading coefficient. For the middle term, leave it expressed:
[tex]3x^2-20x+12\rightarrow\frac{9x^2-20(3x)+36}{3}[/tex]2. We'll factor just like a regular x^2+bx+c trinomial:
• Open two sets of parenthesis and put the square root of the first term on each one
[tex]\frac{(3x)(3x)}{3}[/tex]• Put the sign of the second term of the trinomial in the first set of parenthesis, and the result of multiplying the sign of the second term by the sign of the third term on the second set:
[tex]\frac{(3x)(3x)}{3}\rightarrow\frac{(3x-)(3x-)}{3}[/tex]• Find two numbers whose product is 36 and whose sum is 20
[tex]\begin{gathered} 18\cdot2=36 \\ 18+2=20 \\ \\ \rightarrow18,2 \end{gathered}[/tex]• Fill both sets with such numbers, in ascending order:
[tex]\frac{(3x-)(3x-)}{3}\rightarrow\frac{(3x-18)(3x-2)}{3}[/tex]3. Simplify one of the terms with the denominator:
[tex]\frac{(3x-18)(3x-2)}{3}\rightarrow\frac{3(x-6)(3x-2)}{3}\rightarrow(x-6)(3x-2)[/tex]Therefore, the factorization of our trinomial is:
[tex](x-6)(3x-2)[/tex]Hello hope all is well can you tell me what am doing wrong for number 6
We have the next data
70,89,75,36,80
First we will calculate the mean
(70+89+75+36+80)/5=70
mean=70
Then we will calculate the Median
36,70,75,80,89
median =75
Then we will calculate the mode because any value is repeated all the values given are the mode
mode:70,89,75,36,80
Range
89-36=53
Range =53
Leila wrote an equation to represent the revenue of a parking lot for one day. She let x represent the number of cars that paid to park and y represent the number of trucks that paid to park. If a car costs $8 per day, a truck costs $10 per day, and the total revenue for the day was $830, which equation could Leila use to represent the number of cars and trucks that paid to park that day?
8 x + 10 y = 1,660
10 x + 8 y = 1,660
8 x + 10 y = 830
The equation that Leila can use to represent the number of cars and trucks that paid to park that day is C. 8 x + 10 y = 830
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 the scenario
Let x represent the number of cars that paid to park.
Let y represent the number of trucks that paid to park.
Therefore, the equation will be:
= (8 × x) + (10 × y) = 830
8x + 10y = 830
In conclusion, the correct option is C.
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Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
A) f(x) = (x − 8)2
B) f(x) = (x − 4)2 − 13
C) f(x) = (x − 4)2 + 3
D) f(x) = (x − 4)2 + 16
By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.
The vertex form of a quadratic equation.In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
f(x) = x² − 8x + 3
f(x) = x² − 8x + (8/2)² - 13
f(x) = x² − 8x + (4)² - 13
f(x) = x² − 8x + 16 - 13
f(x) = (x² − 8x + 16) - 13
f(x) = (x − 4)² − 13
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f(n) = -11 + 22(n - 1)Complete the recursive formula of f(n).f(1) = f(n) = f(n - 1) +
F(n) = -11 + 22(n-1)
[tex]\begin{gathered} f(1)\text{ implies that n=1} \\ F(1)\text{ = -11+22(1-1)} \\ f(1)=-11 \end{gathered}[/tex]Hence F(1) = -11
[tex]\begin{gathered} f(n-1)\text{ implies n=n-1} \\ f(n-1)=-11\text{ +22(n-1-1)} \\ f(n-1)=-11+22(n-2)_{} \\ =\text{ -11+22n-44} \\ f(n-1)=22n-55 \end{gathered}[/tex][tex]\begin{gathered} f(n)=\text{ -11+22(n-1)} \\ =-11+22n-22 \\ 22n-33 \\ \end{gathered}[/tex]
let An = F(n) -F(n-1)
[tex]\begin{gathered} 22n-33\text{ - (22n-55)} \\ 22n\text{ - 33-22n+55} \\ =-33+55 \\ =22 \end{gathered}[/tex]Hence F(n)= f(n-1) +22
For each ordered pair, determine whether it is a solution.
To determine which ordered pair is a solution to the equation we shall substitute the values of x and y in the ordered pair.
Taking the first ordered pair;
[tex]\begin{gathered} \text{For;} \\ 3x-5y=-13 \\ \text{Where;} \\ (x,y)\Rightarrow(9,8) \\ 3(9)-5(8)=-13 \\ 27-40=-13 \\ -13=-13 \end{gathered}[/tex]This means the ordered pair (9, 8) is a solution.
We can also solve this graphically a follows;
Observe from the graph attached that the solution to the equation shown above is indicated at the point where x = 9 and y = 8.
The other ordered pairs in the answer options cannot be found on the line which simply mean they are not solutions to the equation given.
ANSWER:
The ordered pair (9, 8) is a solution to the equation 3x - 5y = -13
What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
An example of situation involving quantitative variables is given by:
The gameplan of an NFL coach.
What are qualitative and quantitative variables?The variables are classified as follows:
Qualitative variables are variables that assumes labels or ranks, such as good/bad, yes/no and so on.Quantitative variables are variables that Assume numerical values.In the context of this problem, we want to use quantitative variables, that is, numbers.
Multiple examples of this are given by the gameplan of NFL coaches, as the following example:
How often to blitz? The coach has to analyze the opposing offense statistics against the blitz or against standard pressure. For example, Patrick Mahomes is known to be a blitz killer, hence a coach should visualize the statistics and conclude that he has a better chance of stopping Mahomes playing standard coverage than blitzing.
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Task 2: Interest in Finance
Interest is a concept familiar to most people: every credit card in existence has a term called annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a credit card that has a minimum payment each month equal to the interest owed. Can you figure out how much the interest rate is based on this amount?
The formula for simple interest is where I is the amount you will pay in interest, r is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the number of times the interest is applied.
2
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2
To solve for the interest rate of your credit card, you need to understand which variables in the above formula you have. If your minimum monthly payment is $22 on the $1,000 credit card bill, which variables do you know the values of?
Type your response here: rate= interest/$1000
Manipulate the formula so it will calculate the interest rate you are paying instead of the amount of money you are paying.
Type your response here:
Now that you have a formula that will give you the interest rate, plug in the values for the problem and solve for that interest rate. Interest rates are usually represented for a time period: over what time period does this rate apply? What would the interest rate be if it were a yearly rate?
Type your response here:
Now consider a different situation. Payday loans are a type of loan where you can get money for a future paycheck, typically two weeks in advance. A typical payday loan service might charge $15 for a loan against a paycheck you will receive in two weeks. The interest rate is 10% of the paycheck over that two-week period. Given this information, which variables in the interest formula are known? Develop a formula that will solve for the unknown variable.
Type your response here:
Solve for the value of the unknown variable.
Type your response here:
1. One cannot figure out how much the interest rate is based on the amount charged to the credit card unless other variables are supplied.
2. We know the values of the following variables now:
The interest amountThe principal amount.3. The interest rate is 2.2% per month.
4. The period that this interest rate applies is monthly, called the MPR.
5. The annual interest rate (APR) is 26.4%.
6. The known variables about this payday loan are the interest amount, the interest rate, and the period.
7. A formula to solve for the unknown variable, principal/credit amount, is P = I / (RT), where I = interest, R = rate, and T = time period.
8. The solution for the value of the unknown variable, Principal, is $3,900.
Minimum monthly payment = interest amount = $22
Credit card bill = $1,000
Rate = interest/$1,000
Rate = $22/$1,000 = 0.022
= 2.2%
MPR = 2.2%
APR = 26.4% (2.2% x 12)
Payday Loans:The service charge for a 2-week loan = $15
Interest rate = 10%
Principal/Payloan = $3,900 ($15 / (10% x 2/52)
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Find du and v. Treat a and n as constants.
Stated that;
[tex]u=x^n[/tex]Then, differentiating u with respect to x using the power rule where n is a constant is;
[tex]\begin{gathered} du=(n\times1)x^{n-1} \\ du=nx^{n-1} \end{gathered}[/tex]Also,
[tex]dv=e^{ax}[/tex]Then, we can find v by integrating, we have;
[tex]\begin{gathered} \int dv=\int e^{ax}dx \\ v=\frac{1}{a}e^{ax} \\ \end{gathered}[/tex]
need help with math
The y intercept is when x = 0.Therefore,
[tex]\begin{gathered} \text{when} \\ x=0 \\ y=0 \end{gathered}[/tex]The vertex can be found below
What is the area of the shaded region if the radius of the circle is 6 in.
Then, the area of 1/4 of the circle is:
[tex]\begin{gathered} A=\text{ }\frac{\theta}{360}\text{ x }\pi r^2 \\ A=\text{ }\frac{90}{360}\text{ x }\pi r^2 \\ A\text{ = }\frac{1}{4}\pi\text{ 6}^2 \\ A=\text{ 9}\pi \\ \\ \end{gathered}[/tex]The area of the triangle is:
[tex]\begin{gathered} A=\text{ }\frac{b\text{ x h }}{2} \\ A\text{ = }\frac{6\text{ x 6}}{2} \\ A=\text{ 18in}^2 \end{gathered}[/tex]The area of the shaded region is the area of 1/4 of the circle minus the area of the triangle:
[tex]\begin{gathered} A\text{ = 9}\pi\text{ - 18 in}^2 \\ A=\text{ 28.27in}^2\text{ - 18in}^2 \\ A=\text{ 10.27in}^2 \end{gathered}[/tex]18. The table below gives the population of a town (in thousands) from the year 2000 to the year 2008. Year '00 '01 '02 03 04 '05 06 '07 '08 Population 87 84 83 80 77 76 78 81 85 (thousands) What was the average rate of change of population: a. between 2002 and 2004? b. between 2002 and 2006?
a . Average rate of change between 2002 and 2004 can be calculated below
[tex]\begin{gathered} average\text{ rate of change=}\frac{chang\text{e in y}}{\text{change in x}} \\ average\text{ rate of change = }\frac{77-83}{2004-2002} \\ average\text{ rate of change}=\frac{-6}{2}=-3(thousand) \end{gathered}[/tex]b. Average rate of change between 2002 and 2006 is
[tex]\begin{gathered} \text{average rate of change = }\frac{78-83}{2006-2002} \\ average\text{ rate of change}=\frac{-5}{4}=-\frac{5}{4}(thousand) \end{gathered}[/tex]This is very hard for me I need to know how to do it
The zeros of a function are the values of x that make the function be equal to zero.
When graphing a quadratic equation, the graph is a parabola, and the zeros of the function are the x-intercepts of the graph, which are the points where the graph intersects the x-axis.
So, if the zeros of this function are x = -8 and x = 2, that means the parabola crosses the x-axis at x = -8 and x = 2.
Therefore the correct option is the first one.
Which decimal represents 8 X 1,000 + 4 X 100 + 7 X7 16 +31,0001,0A 8,004.073C 8,400.703B 8,040.073D 8,400.730
The given expression:
[tex]8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}[/tex]Simplify the expression:
[tex]\begin{gathered} 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8000+400+0.7+0.003 \\ 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8400.703 \end{gathered}[/tex]Answer : c) 8400.703
Simplify 6+ √-80.
06+16√5i
06+4√5
06+16/ √5
06+4√ √5i
Answer:
6 + 4[tex]\sqrt{5}[/tex]i
Step-by-step explanation:
The prime factorization of 80 is 2x2x2x2x5
6 + [tex]\sqrt{-2x2x2x2x5}[/tex] We can take out 2 pairs of 2 which would be 4 and [tex]\sqrt{-1}[/tex] is i
6 + 4[tex]\sqrt{5}[/tex] i
Tony will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60and costs an additional $0.50per mile driven
The second plan has noinitial fee and costs an additional $0.70per mile driven
E
For what amount of driving do the two plans cost the
Same
Plan 1:
Initial (fixed) fee: $60
Variable fee: $0.50 per mile
Plan 2:
Initial (fixed) fee: $0
Variable fee: $0.70 per mile
If we call x to the number of miles driven by Tony, then the cost of Plan 1 is:
P1 = 60 + 0.5x
The cost of Plan 2 is:
P2 = 0.7x
It's required to find the number of miles Tony should drive for both plans to cost the same, that is:
60 + 0.5x = 0.7x
Subtracting 0.5x:
60 = 0.7x - 0.5x
Operating:
60 = 0.2x
Dividing by 0.2:
x = 60 / 0.2
x = 300
Tony should drive 300 miles for both plans to cost the same.
Under that condition, both plans cost the same. Plan 1 cost:
P1 = 60 + 0.5*300
P1 = 60 + 150
P1 = $210
Plan 2 cost:
P2 = 0.7*300
P2 = $210
Both costs are equal
c. Where would the line y = - 2x + 1 lie? Again, justify your prediction and add the graph of this lineto your graph from part (b).
Given:
b) First the two lines are graphed,
[tex]\begin{gathered} y=2x+3 \\ y=2x-2 \end{gathered}[/tex]Now, yoshi wants to add one more equation,
[tex]y=2x+1[/tex]The graph is represented as,
In the above graph the green line represents the y=2x+1 and it lies between the line y= 2x+3 and y= 2x-2.
c) The graph of the line y = -2x +1
It is observed that the green line y= -2x+1 intersects both the lines y= 2x+3 and y= 2x-2.
Use appropriate identities to rewrite the following expression in terms containing only first powers ofsine.4tanx1 + tan2x
The given question is
[tex]\frac{4\tan x}{1+\tan ^2x}[/tex]Use the identity
[tex]1+\tan ^2x=\sec ^2x[/tex]Then replace the denominator by sec^2 (x)
[tex]\frac{4\tan x}{\sec ^2x}[/tex]Since sec is the reciprocal of cos, then
[tex]\sec ^2x=\frac{1}{\cos ^2x}[/tex]Replce sec^2(x) by 1/cos^2(x)
[tex]\frac{4\tan x}{\frac{1}{\cos ^2x}}[/tex]Since denominator of denominator will be a numerator
[tex]4\tan x\times\cos ^2x[/tex]Use the value of tan
[tex]\tan x=\frac{\sin x}{\cos x}[/tex]Replace tan by sin/cos
[tex]4\times\frac{\sin x}{\cos x}\times\cos ^2x[/tex]Reduce cos(x) up with cos(x) down
[tex]\begin{gathered} 4\times\sin x\times\cos x= \\ 4\sin x\cos x \end{gathered}[/tex]Use the identity
[tex]\sin (2x)=2\sin x\cos x[/tex][tex]4\sin x\cos x=2(2\sin x\cos x)[/tex]Replace 2 sin(x)cos(x) by sin(2x)
[tex]2(2\sin x\cos x)=2\sin 2x[/tex]The answer is
2 sin(2x)
which number is 5 more than 8009998
A number which is 5 more than 8009998 is 8010003
In this question we need to find a number which is 5 more than 8009998.
Let x be a number which is 5 more than 8009998.
We get the required number by adding 5 to 8009998.
so, we write it down as:
x = 8009998 + 5
x = 8010003
Therefore, a number which is 5 more than 8009998 is 8010003
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Steve has been training for a 5-mile race. Before the race, he predicts he will finish in 42minutes. He actually finishes the race in 40 minutes. What is the percent error for hisprediction?
To find the percent error
percent error = | (actual - expected)/ actual| * 100 %
The actual is 40 and the expected is 42
percent error = | ( 40 - 42) / 40 | * 100 %
= | -2/40| * 100%
= .05 * 100 %
= 5%
