Answer:
-7/3
Step-by-step explanation:
The first step is to combine like numbers. Although there are several different ways to go about doing this, I started by adding 2y to both sides which left me with -8-6y=6. I then added 8 to both sides and got 6y=14. Now divide 6 on both sides to get "y" by itself which left me with y = -14/6. When you simplify the answer you get -7/3.
An _________ is a figure formed by two rays with a common ________?
Answer:
1: Angle
2:endpoint
Step-by-step explanation:
Hey there!
An angle is a figure formed by two rays with a common endpoint.
Hope it helps and have a good day!
Wanda has three times more shirts than her brother, Will. The equation a = 3b, where a represents the number of shirts Wanda has, and b represents the number of shirts Will has, shows this relationship. If Wanda has 24 shirts, how many shirts does Will have?
Answer:
8 shirts
Step-by-step explanation:
Given the equation a = 3b, where
a = the number of shirts Wanda has
b = the number of shirts Wanda's brother (Will) has
Hence if Wanda has 24 shirts then
24 = 3b
Divide both sides by 3
24/3 = b
b = 8 shirts
Will has 8 shirts.
Answer:
8 shirts
Step-by-step explanation:
Phoebe wants to buy 65 swimming lessons that cost £30 each, but she only has £1400. What percentage (%) of the total cost of the lessons does phoebe have? Round your answer to 1 decimal place,
Phoebe has 71.8 percentage of the total cost of the swimming lessons.
Define percentageA number can be expressed as a fraction of 100 using a percentage. It is often represented by the symbol "%". Percentages are commonly used to express a proportion or rate of change, particularly in business, finance, and science. For example, if a student scores 90 out of 100 on an exam, their percentage score is 90%.
The total cost of 65 swimming lessons at £30 each is:
65 x £30 = £1950
Percentage = (Amount / Total) x 100
where "Amount" is the amount that Phoebe has, and "Total" is the total cost of the swimming lessons.
Plugging in the numbers, we get:
Percentage = (1400 / 1950) x 100
Percentage = 0.7179487 x 100
Percentage = 71.8 (rounded to 1 decimal place)
Therefore, Phoebe has 71.8% of the total cost of the swimming lessons.
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Identify the correct slope and y-intercept for this equation: -6y + 8x + 2y = 24
Answer:Slope: 2 and the y-intercept: (0,−6)
Step-by-step explanation:
Step-by-step explanation:
Sorry I don't know if u actually put -6 or just 6 But any ways I will solve both of them for you
6y + 8x + 2y = 24
6y+2y+8x=24
8y+8x=24
8y=-8x+24
according to this formula (y=mx+c) the slope is -8 while the intercept is 24
or if not that
-6y+8x+2y=24
-6y+2y+8x=24
-2y+8x=24
-2y=-8x+24
according to the formula (y=mx+c) the slope is -8 while the y intercept is 24
a tour bus normally leaves for its destination at 5 : 00 p.m. for a 350 mile trip. this week however, the bus leaves at 6 : 10 p.m. to arrive on time, the driver drives 10 miles per hour faster than usual. what is the bus` usual speed? the bus' usual speed is miles an hour.
The usual speed of the bus is 60 km/hr.
Define speed.Speed is the rate of change in location of an item, expressed in meters per second.
Given,
Let x be the usual speed.
Speed = Distance/ Time
Time = Distance/Speed
Bus usually travels 350 miles.
It takes time for it to get there = 350/x h
The bus departs this week at 6:10, though.
The 70-minute bus delay = 70/60 = 7/6 h
The bus's current speed is (x+10) miles per hour.
The new window of time for getting there is \(\frac{350}{x+10}\)
\(\frac{350}{x}\) + \(\frac{350}{x+10}\) = \(\frac{7}{6}\)
350(\(\frac{x+10-x}{x(x+10)}\) ) = \(\frac{7}{6}\)
350 ( \(\frac{10}{x^{2} +10x}\) )= \(\frac{7}{6}\)
7(x² +10x) = 6(350)(10)
x² + 10x = 3000
x² + 10x - 3000 = 0
x² -60x + 50x - 3000 = 0
x( x - 60) + 50(x - 60) = 0
(x + 50)(x - 60) = 0
x = -50 , x = 60
The usual speed of the bus is 60 km/hr.
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6.1 Colby bought a laptop worth Rx for his university studies. The value of the laptop decreased at r% per annum using the reducing balance method. After 4 years, the value of the laptop was worth 31 of its original price. Calculate r, the rate of depreciation.
6.2 On 1 February 2014 , Ncominkosi took a loan from a bank to buy a car. His first payment for the loan was due on 31 July 2014 . Once he started paying the loan, it took him 6 years to fully pay the loan at an interest rate of 9,5% p.a. compounded monthly. In total, he paid the bank R596 458,10.
6.2.1 How much was his monthly instalment?
6.2.2 How much money did he borrow from the bank? Write down your answer to the nearest rand.
6.1). the rate of depreciation, r, is approximately 10.77%.
6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.
6.2.2). Ncominkosi borrowed approximately R 377,510.83 from the bank.
6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.
Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.
Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.
Therefore, the rate of depreciation, r, is approximately 10.77%.
6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:
\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)
Where:
P = Monthly payment
PV = Loan principal amount
r = Monthly interest rate
n = Total number of monthly payments
Let's calculate the monthly installment amount for Ncominkosi's loan:
Loan amount = Total amount paid to the bank - Interest
Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)
Number of monthly payments = 6 years * 12 months/year = 72 months
Using the formula mentioned above:
\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)
Substituting the values:
\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)
Calculating the value:
P≈R10,505.29
Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.
6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.
Total amount paid to the bank: R 596,458.10
Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.
Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:
\(A=P(1+r/n)(n*t)\)
Where:
A = Total amount paid
P = Loan principal amount
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years
We can rearrange the formula to solve for the loan principal:
\(P=\frac{A}{(1+r/n)(n*t)}\)
Substituting the values:
Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)
Calculating the value:
Loan principal (P) ≈ R 377,510.83
Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.
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Write an equation to find the amount of simple interest, A, earned on a $970 investment after 2 years the semi-annual (6-month) interest rate is 2%. Show the third read below & solve.
1R: what is the problem about?
2R: what is the question asking you to find?
3'R: show work
help
The amount of simple interest earned on a $970 investment after 2 years at a semi-annual interest rate of 2% is $19.40.
How is simple interest determined?We may use the simple interest formula, which is: to determine how much simple interest was gained on a $970 investment after two years at a 2% semi-annual interest rate.
I = P * r * t
where I equals interest accrued
Principal (P) (the initial investment)
r = annual interest rate (in decimal form)
T is the duration in years.
As the interest rate is stated as a semi-annual rate, we must double the time period by two and divide the interest rate by two to convert them to years.
When we enter the specified values into the formula, we obtain:
I = $970 * 0.02/2 * 2 = $19.40
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Andrea is three times Nick's age. In 10 years, Andrea will be twelve years older than Nick.
What are their ages now?
Answer:
Nick is 6
Andrea is 18
Step-by-step explanation:
Sounds like a system of equations
Letting...
a = Andrea
n = Nick
Since she's 3 times the age, the first equation will be
a = 3n
Since in 10 years, Andrea will be 12 years older than Nick, we can write
a = n + 12
Since we have two a = ,we can set them equal to each other
3n = n + 12
Subtracting n
3n - n = 12
Now combining the n's (n is the same as 1n)
2n = 12
And last but not least, we can divide by 2
n = 6... so Nick is 6 right now.
Going back to our first equation of a = 3n, if we plug 6 in
a = 6(3) = 18.
Making Andrea 18 right now
Let Pij = the production of product i in period j. To specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units, we need to add which pair of constraints?
P52-P42 <= 80; P42-P52 <= 80
None of the other above.
P24 - P25 <= 80; P25-P24 >= 80
O P24 - P25 >= 80; P25-P24 >= 80
P24 - P25 <= 80; P25-P24 <= 80
The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.
Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.
Therefore, we can write the following inequalities:
P24 - P25 <= 80
This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.
P25-P24 <= 80
This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.
Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.
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Need help! Similarity of triangles
Answer:
x = 12
Step-by-step explanation:
Comparing corresponding sides of the 2 similar Δ 's inside the larger, then
\(\frac{x}{6}\) = \(\frac{6}{3}\) ( cross- multiply )
3x = 36 ( divide both sides by 3 )
x = 12
6. In OA, find CE if BA = 20.
The length of CE from the given circle above would be = 40.
What is a diameter of a circle?The diameter of a circle is defined as the distance the passes through the centre of a circle from a point to another.
From the circle given above;
The diameter of the circle = CE
But radius (BA) = 20
And 2×radius = diameter
Therefore,the diameter of the circle (CE) = 20×2 = 40
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1. An initial population of 10 cats triples every year. How many cats will there be in 5 years? Make a table and
graph your results.
Answer:
150
Step-by-step explanation:
file is graph
What is the growth factor when something is decreasing by:
15.7%
0.12%
When something decreases by 15.7%, the growth factor is about 1.182 and when something decreases by 0.12%, the growth factor is about 1.00012.
In math, what is the definition of multiplying?
Multiplication is a mathematical process that shows the amount of times a number has been added to itself. It is represented by the multiplication symbols (x) or (*). Division is a mathematical process that shows how many equal amounts add up to a given quantity.
If something decreases by 15.7%, the increase in the factor is 100 / (100 - 15.7) Equals 1.182.
As a result, when something decreases by 15.7%, the growth factor is about 1.182.
When something falls by 0.12%, the expansion factor is 100 / (100 - 0.12) = 1.00012.
As a result, when something decreases by 0.12%, the growth factor is about 1.00012.
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After watching baking shows on T.V., Latrell signs up for a cake-decorating class. To practice
his new skills, he decorates a batch of cupcakes with sugar flowers. Latrell puts 4 sugar
flowers on each cupcake. In all, Latrell puts 32 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Latrell decorates?
An economy is described by the following model:
Z≡C+I+G
Y
d
≡Y−T
C=100+0.5(Y−T)
I=100+0.1Y
Y=Z
How many identities does this model have? How many behavioural equations does this model have? How many equilibrium conditions does this model have? How many variables does this model have? Question 17: In March 2022 there were 2826000 employed and 94000 unemployed. Please calculate the size of the labour force and the unemployment rate (round to the nearest 2 decimal places).
The given economic model has four identities, two behavioral equations, three equilibrium conditions, and four variables. The size of the labor force is 2,920,000 and the unemployment rate is 3.22%.
The identities in the model are:
Z ≡ C + I + G: This identity states that total spending (Z) is equal to consumption (C), investment (I), and government spending (G).
Yd ≡ Y - T: This identity defines disposable income (Yd) as total income (Y) minus taxes (T).
C = 100 + 0.5(Yd): This identity represents consumption (C) as a function of disposable income (Yd), with a consumption function that has an intercept of 100 and a marginal propensity to consume of 0.5.
I = 100 + 0.1Y: This identity represents investment (I) as a function of total income (Y), with an investment function that has an intercept of 100 and a marginal propensity to invest of 0.1.
The behavioral equations in the model are equations (3) and (4) above, which represent the consumption and investment functions, respectively.
The equilibrium conditions in the model are:
Y = Z: This condition states that total income (Y) is equal to total spending (Z) in the economy.
Yd = C + I: This condition ensures that disposable income (Yd) is equal to consumption (C) plus investment (I).
Y = Yd: This condition implies that total income (Y) is equal to disposable income (Yd).
The model has four variables: Z (total spending), Y (total income), Yd (disposable income), and T (taxes).
To calculate the size of the labor force and the unemployment rate, we need to know the total labor force and the number of unemployed individuals. The labor force is the sum of employed and unemployed individuals. In this case, the labor force is 2,826,000 (employed) + 94,000 (unemployed) = 2,920,000.
The unemployment rate can be calculated by dividing the number of unemployed individuals by the labor force and multiplying by 100 to get a percentage. In this case, the unemployment rate is (94,000 / 2,920,000) * 100 ≈ 3.22%.
Therefore, the size of the labor force is 2,920,000 and the unemployment rate is approximately 3.22%.
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If the allele frequency of the dominant allele is 0.4, what value is used for the term p^2 in the equation p^2+ 2pq + q^2 = 1?
The value is used for the term p^2 in the equation p^2+ 2pq + q^2 = 1 is 0.16.
According to the statement
we have given that the allele frequency of the dominant allele is 0.4, and we have to find that the value of p^2 in the equation p^2+ 2pq + q^2 = 1.
So, For this purpose, we know that the
The allele frequency represents the incidence of a gene variant in a population. Alleles are variant forms of a gene that are located at the same position, or genetic locus, on a chromosome.
And here
allele frequency is the 0.4 and represent the value of P.
So, The value of p is 0.4 and the
Then p^2 = (0.4)^2
so, the value becomes
p^2 = (0.4)^2
p^2 = 0.16.
So, The value is used for the term p^2 in the equation p^2+ 2pq + q^2 = 1 is 0.16.
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a pole that is 2.8m tall casts a shadow that is 1.49m long. at the same time, a nearby building casts a shadow that is 37.5m long. how tall is the building? round your answer to the nearest meter.
The height of the building is 71 meters.
We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:
(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)
Substituting the given values:
2.8 / 1.49 = (height of building) / 37.5
To find the height of the building, we can cross-multiply and solve for it:
(2.8 * 37.5) / 1.49 = height of building
Calculating the expression on the right side:
(2.8 * 37.5) / 1.49 ≈ 70.7013
Rounding to the nearest meter, the height of the building is approximately 71 meters.
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807 x 491
AND THEM ESTIMATE THE ANSWER
Answer:
396237 / Estimation would be 396000 I believe.
Step-by-step explanation
Answer:
396000
Step-by-step explanation:
Write an equation for each translation. x²+y²=25 ; right 2 units and down 4 units
The translated equation would be: (x - 2)² + (y - 4)² = 25
To translate the equation x² + y² = 25 right 2 units and down 4 units, we need to adjust the coordinates of the equation.
First, let's break down the translation process. Moving right 2 units means we need to subtract 2 from the x-coordinate of every point on the graph. Moving down 4 units means we need to subtract 4 from the y-coordinate of every point on the graph.
The translated equation would be: (x - 2)² + (y - 4)² = 25
In this equation, the x-coordinate has been shifted 2 units to the right, and the y-coordinate has been shifted 4 units down.
The overall effect is a translation of the original graph to the right and downward by the specified amounts.
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given the triangle below what is the value of x?
Answer:
x = -8
Step-by-step explanation:
all the angles in a triangle add up to 180 degrees
55 + 70 + x + 63 = 180
188 + x = 180
x = -8
What is the value of X?
Answer:
X=9
Step-by-step explanation:
A circle adds up to 360°
63+89+73= 225
360-225= 135
Since 15x
135÷15=9
x=9
Complete the point-slope equation of the line through (1,3)(1,3)left parenthesis, 1, comma, 3, right parenthesis and (5,1)(5,1)left parenthesis, 5, comma, 1, right parenthesis.
Answer: dang that's tough but like look it up
Step-by-step explanation: give brainlyiest
The vertices of a square are located at (0, 2), (2, 0), (0, -2), and (-2, 0).
Select all transformations that will carry this square onto itself.
A reflection across the line y = x
B reflection across the line y = -X
C reflection across the x-axis
D 45° rotation about the origin
E 90° rotation about the origin
Answer:
Step-by-step explanation:
A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.
A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.
However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.
A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.
Therefore, the correct answers are C, D, and E.
> A person places $479 in an investment account earning an annual rate of 8.2%, compounded continuously. Using the formula V = Pert, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 12 years. help please
Answer:
$1281.39
Step-by-step explanation:
use formula given
If a property is valued at $487,500 and assessed for 50% of its value, what are the annual taxes if the tax rate is 4.80 per $100 of assessed valuation?
$11,700.00 is are the annual taxes.
What is the meaning of annual tax?
Annual Tax is the real property tax assessed on a property for a fiscal year, as determined after deducting any amounts from which the property is exempt or whose assessment has been reduced in accordance with applicable law.
a property is valued = $487,500
$487,500 /2 = $243750
"per $100 of valuation" tax units = $243750 / 100 = $2437.5
Total tax = $2437.5 * 4.80 = $11,700.
Therefore, the $4.80 rate for a total tax of $11,700.
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suppose 88% of all batteries from a supplier have acceptable voltages. a certain type of flashlight requires two d batteries, and the flashlight will work only if both its batteries have acceptable voltages. treat all batteries and flashlights as independent of one another. in 20 randomly selected batteries, what is the probability that either 19 or 20 have acceptable voltages?
The probability that either 19 or 20 of the randomly selected batteries have acceptable voltages is 0.4399.
First, we have to understand that there are 2 batteries required for the flashlight to work. And for the flashlight to work, both batteries must have acceptable voltages.
To solve this, you can use the binomial probability formula:
P(x) = nCx * p^x * (1 - p)^(n-x)
Where n is the number of trials, x is the number of successes, and p is the probability of success.
For this problem, n = 20, p = 0.88, and x is either 19 or 20.
P(19) = 20C19 * 0.88^19 * (1 - 0.88)^(20 - 19) = 0.0239
P(20) = 20C20 * 0.88^20 * (1 - 0.88)^(20 - 20) = 0.4160
P(19) + P(20) = 0.0239 + 0.4160 = 0.4399
Therefore, the probability that either 19 or 20 of the batteries have acceptable voltages is 0.4399.
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a college's soccer team will play 18 games next fall. each game can result in one of 3 outcomes: a win, a loss, or a tie. find the total possible number of outcomes for the season record.
The total possible number of outcomes for the season record is 3¹⁸, or 387,420,489. This is because there are three possible outcomes for each of the 18 games: win, loss, or tie.
To find the total number of outcomes, you can use the fundamental counting principle, which states that the total number of outcomes is equal to the product of the number of outcomes for each event. For example, if you flip a coin twice, there are two possible outcomes for each flip: heads or tails. Using the fundamental counting principle, you can find the total number of outcomes by multiplying the number of outcomes for each event:2 x 2 = 4So there are four possible outcomes for flipping a coin twice: heads-heads, heads-tails, tails-heads, or tails-tails. Using the same logic, you can find the total number of outcomes for the soccer team's season record by multiplying the number of outcomes for each game:3 x 3 x 3 x ... (18 times)= 3¹⁸= 387,420,489So there are 387,420,489 possible outcomes for the soccer team's season record.
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An equation is shown.
23x = 24
What value of x makes the equation true?
Answer:
all of them are right answers
\(x = \frac{24}{23 \\ } \)
or
\(x = 1.04\)
or
\(x = 1 \frac{1}{23} \)
Thirty samples of size 4 of the customer waiting time at a call center for a health insurance company resulted in an overall mean of 10.4 minutes and average range of 0.9 minutes . Compute the control limits for x and r charts.
the control limits for the x-bar chart are 9.7439 minutes (LCL) and 11.0561 minutes (UCL), and the control limits for the R chart are 0 minutes (LCL) and 2.0529 minutes (UCL).
To compute the control limits for the x-bar (mean) and R (range) charts, we'll use the following formulas:
For the x-bar chart:
Upper Control Limit (UCL) for x-bar = x-double-bar + A2 * R-bar
Lower Control Limit (LCL) for x-bar = x-double-bar - A2 * R-bar
For the R chart:
Upper Control Limit (UCL) for R = D4 * R-bar
Lower Control Limit (LCL) for R = D3 * R-bar
Where:
x-double-bar = Overall mean of the sample means
R-bar = Overall mean of the sample ranges
A2 = Constant from the control chart constants table
D4 = Constant from the control chart constants table
D3 = Constant from the control chart constants table
For sample sizes of 4, the control chart constants are as follows:
A2 = 0.729
D4 = 2.281
D3 = 0
Given the information you provided:
Overall mean (x-double-bar) = 10.4 minutes
Average range (R-bar) = 0.9 minutes
Let's calculate the control limits:
For the x-bar chart:
UCL for x-bar = 10.4 + 0.729 * 0.9
= 10.4 + 0.6561
= 11.0561 minutes
LCL for x-bar = 10.4 - 0.729 * 0.9
= 10.4 - 0.6561
= 9.7439 minutes
For the R chart:
UCL for R = 2.281 * 0.9
= 2.0529 minutes
LCL for R = 0
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Factorise 9x2+49y2-42xy-30xz+70yz
the equation can not be factored ^