Complete the square for the expression.
x2 − 11x + ____
−121/2
121/2
121/4
−121/4
Answers
To complete the square for the expression x2 − 11x + ____, we need to add a constant term that will make the expression a perfect square trinomial.
We can do this by taking half of the coefficient of the x-term (-11/2) and squaring it (121/4). Thus, x2 − 11x + 121/4 can be written as (x - 11/2)2.
We can check this by expanding (x - 11/2)2:
(x - 11/2)2 = x2 - 11/2 x - 11/2 x + (121/4)
= x2 - 11x + 121/4
Therefore, the complete expression is (x - 11/2)2, which is equivalent to x2 − 11x + 121/4.
In summary, to complete the square for x2 − 11x + ____, we add the constant term 121/4. This turns the expression into a perfect square trinomial, which can be written as (x - 11/2)2.
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Related Questions
sample of 16 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 MPa and a sample standard deviation of 0.73 MPa. MPa Interpret this bound. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is than With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is theater What, if any, assumptions did you make about the distribution of proportional limit stress? We must assume that the sample observations were taken from a normally distributed population. We do not need to make any assumptions. We must assume that the sample observations were taken from a uniformly distributed population. We must assume that the sample observations were taken from a chi-square distributed population. (b) Calculate and interpret a 95\% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places. MPa
Answers
With 95% confidence, we can say that the true mean proportional limit stress of all joints of this type is within a certain range.
The assumptions made about the distribution of proportional limit stress are that the sample observations were taken from a normally distributed population.
To calculate the 95% confidence interval for the true mean proportional limit stress, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √n).
In this case, the sample mean is 8.41 MPa, the sample standard deviation is 0.73 MPa, and the sample size is 16.
The critical value can be determined based on the desired confidence level (95% in this case) and the degrees of freedom (n-1 = 15).
The critical value for a 95% confidence level with 15 degrees of freedom is approximately 2.131.
Plugging these values into the formula, we get the confidence interval: 8.41 ± (2.131 * (0.73 / √16)), which simplifies to approximately 8.41 ± 0.388. Therefore, with 95% confidence, we can say that the true mean proportional limit stress of all joints of this type is between 8.022 MPa and 8.798 MPa.
Regarding the assumptions, we assume that the sample observations were taken from a normally distributed population.
This assumption is necessary for applying the formula and calculating the confidence interval.
It implies that the underlying data follows a normal distribution, which allows us to make inferences about the population mean based on the sample mean.
Without this assumption, the validity of the confidence interval calculation may be compromised.
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Given vector u = ⟨−3,−2⟩ and v = ⟨1,−5⟩,determine the value of u - 2v in component form.
Answers
The component form of the linear combination of the two vectors is u - 2v = < -5, 20>
How to find the vector u - 2v?Here we have the two vectors: u = <-3, -2> and v = <1, -5> We want to determine the value of the linear combination:
u - 2v
To do that we just add the correspondent components, then we get:
u - 2v = <-3, -2> - 2*<1, -5>
= <-3, -2> - <2*1, 2*-5>
= <-3, -2> - <2, -10>
= < -3 - 2, -2 -(-10)>
= < -5, 20>
That is the component form of the linear combination.
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Let y = f (x) be a twice-differentiable function such that f (1) = 2 and dydx=y^3+3 . What is the value of d^2ydx^2at x = 1 ?12 66 132 165
Answers
The value of second order differentiation, that is d²y/dx² at x = 1 is 132 for function y= f(x) such that f(1) = 2 and dy/dx=y³+3 .
Hence option c is the correct answer.
The given function of x is, y = f(x)
y = f(x) is twice differentiable.
dy/dx = f'(x) = y³ + 3
Differentiation dy/ dx with respect to x, that is differentiating y = f(x) second time with respect to x, we get,
f''(x) = d²y / dx² = [d(dy/dx)] / dx
= d (y³ + 3) / dx
Thus by chain rule of differentiation we get,
f''(x) = d²y / dx² = 3y² (dy/dx)
= 3y² ( y³ +3)
= 3\(y^{5}\) + 9y²
Since, f(1) = 2, it implies when x=1 , then y = 2 as y = f(x)
Therefore, d²y/dx² at x = 1 or f''(1) is,
f''(1) = 3[\((2)^{5}\)] + [9(2²)]
= 96 + 36 = 132
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Dhdjcusjbcjsjxjendxhdicisnchjd
Answers
Answer:
y=x+3
Step-by-step explanation:
slope is 1
intercept is 3
4.6 yd-12 ydO 348.8 yd²532.1 yd²O 385.6 yd2O 520.9 yd²6 yd10 yd5 yd
Answers
From the statement, we have a right triangle with:
• angle θ,
,• opposite side OS = 7,
,• hypotenuse H = 12,
and we must find the value of angle θ.
We also have Tom's resolution of the problem.
(1) From the resolution, we see that Tom computes the angle θ using the following formula:
\(\cos\theta=\frac{7}{12}.\)Adding the data above the sides, we have:
\(\cos\theta=\frac{7}{12}=\frac{OS}{H}\Rightarrow\cos\theta=\frac{OS}{H}\text{ }✖\)From trigonometry, we know that this equation is wrong. The correct trigonometric relation is:
\(\sin\theta=\frac{OS}{H}.\)(2) Replacing the values OS = 7 and H = 12 in the correct trigonometric relation, we have:
\(\sin\theta=\frac{7}{12}.\)Solving for θ, we get:
\(θ=\sin^{-1}(\frac{7}{12})\cong35.7\degree.\)Answer• The mistake in Tom's resolution is that he used the incorrect trigonometric relation for the angle, the opposite side and the hypotenuse.
,• Using the correct trigonometric relation, which involves a sine function instead of the cosine, we get θ ≅ 35.7°.
What is an equation of the line that passes through the points (-3, -5) and
(-5, -3)?
Answers
Answer: y = -x-8
Step-by-step explanation:
(-3,-5) (-5,-3)
Slope (m) = (y-y)/(x-x) = (-3- -5)/(-5- -3) = (-3+5)/(-5+3) = 2/- 2 = - 1
m = - 1
Point (-3,-5)
y-y=m(x-x)
y- -5= -1(x- -3) = y+5 = -1(x+3)
y+5 = - x -3
y+5= - x - 3 (substract 5 from both sides)
y = - x - 8
Phoebe invested $5800 and after one year the investment was worth $6100. How much interest did she receive?
Answers
Answer:
Amount of interest received by Phoebe = $300
Step-by-step explanation:
Given:
Amount Phoebe invested = $5,800
Amount Phoebe received after one year = $6,100
Find:
Amount of interest received by Phoebe
Computation:
Amount of interest received by Phoebe = Amount Phoebe received after one year - Amount Phoebe invested
Amount of interest received by Phoebe = 6,100 - 5,800
Amount of interest received by Phoebe = $300
Mary mixes white paint and blue paint in the ratio 2:3. She makes a total of 20 litres of paint. How much more blue paint does she need to add to the mixture so that the ratio of white paint to blue paint becomes 1 : 7?
Answers
Answer:
7 i believe, if not then sorry. bad calculations.
Step-by-step explanation:
It is another Friday evening, and you want to have some pizza again! You have $60 in your
pocket, and a slice of pizza costs $3.
a) Draw your feasible set in terms of pizza and leftover cash and your preferred choice
point. Let’s put pizza on the x (horizontal) axis and cash on the y (vertical) axis.
b) Explain why the preferred choice point you selected above is your preferred choice.
c) Imagine you went to a Pizza place, and you find out that there is an entrance fee of $9.
Draw your new feasible set and new preferred choice.
d) Describe in words how the change in entrance fee affected your decision.
Answers
a) The feasible set can be represented as a straight line with a negative slope on a graph.
b) The preferred choice point is (15, 15).
c) With an entrance fee of $9, the new feasible set shifts vertically upwards.
d) The change in entrance fee reduced the amount of leftover cash in the feasible set.
a) The x-axis represents the number of pizza slices, and the y-axis represents the leftover cash. The line starts at the point (0, 60) and intersects the x-axis at (20, 0). This means that you can buy a maximum of 20 pizza slices with $60, and if you don't buy any pizza, you will have $60 left.
b) This point represents buying 15 slices of pizza, which costs $45, and having $15 left. It is the preferred choice because it allows for a balance between enjoying pizza and not exhausting all the cash. It provides both a substantial amount of pizza and a reasonable amount of leftover cash.
c) The line now starts at (0, 51) and intersects the x-axis at (20, 9). This means that with the entrance fee, you can buy a maximum of 20 pizza slices and have $9 left.
d) It means that you have less cash available after buying pizza slices. The new preferred choice would likely shift downwards to a point that allows for a reasonable number of pizza slices while still leaving enough money to cover the entrance fee.
The change in entrance fee makes it necessary to consider the balance between the number of pizza slices and the available cash more carefully to ensure you can afford the entrance fee and still enjoy a satisfying amount of pizza.
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The initial temperature of a cup of hot coffee is 46.8°C. After 20 minutes,the temperature of the coffee has reduced by 12.6°C. What is the temperature,in °C,of the coffee now?
Answers
Answer:
The current temperature = 34.2°C
Step-by-step explanation:
Initial temperature = 46.8°C
After 20 minutes temperature reduced by 12.6°C
Therefore, the current temperature is = 46.8°C - 12.6°C = 34.2°C
PLEASE HELP!! Due very soon!!! - The graph below represents the height of a football pass, in feet, x seconds after the ball is thrown. Which of the following best describes the interpretation of f(2)? (Attached are the multiple choice answers)
Answers
Answer:
The ball is 7 feet above the ground 2 seconds after it is thrown.
Step-by-step explanation:
As per the given statement, we are given a graph of function \(f(x)\) where 'x' is time (in seconds) in the current scenario.
Time is plotted on x axis and height of football is plotted on y axis.
\(f(x)\) is the height of football according to change in time.
Following are the few things that can be observed from the given curve:
1. Initial Height of football is ~4.8 feet i.e. at 0 seconds of time.
2. Football reaches a maximum height of ~7.2 feet at 1.5 seconds.
3. After 1.5 seconds, the height of football starts decreasing.
Here f(2) means, the height of ball at 2 seconds of time.
It is clearly visible from the given graph that height is 7 feet at 2 seconds.
Please refer to the attached answer image. Height at 2 seconds is marked as point P.
Hence, The ball is 7 feet above the ground 2 seconds after it is thrown.
Triangle XYZ has coordinates X(2, 4), Y(−3, 4), and Z(−3, 1). If the triangle is translated using the rule (x, y) → (x − 2, y + 1), what are the coordinates of Y'?
Y'(–5, 5)
Y'(0, 5)
Y'(–5, 2)
Y'(–1, 3)
Answers
Answer:
Y'(-5, 5)
Step-by-step explanation:
To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).
Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:
x' = x - 2 = -3 - 2 = -5
y' = y + 1 = 4 + 1 = 5
Therefore, the coordinates of Y' are (-5, 5).
You may need to use the appropriate appendix table or technology to answer this question The life expectancy of a particular brand of tire is normally distributed with a mean of 50,000 miles and a standard deviation of 5,000 miles. What percentage of tires will have a life of 45,000 to 55,000 miles 15.87% 31.73% 68,27% 84.13%
Answers
The percentage of tires that will have a life of 45,000 to 55,000 miles is 68.27%. So the correct option is 68.27%.
To find the percentage of tires that will have a life of 45,000 to 55,000 miles, we can use the concept of the normal distribution.
First, we calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation
For 45,000 miles:
z1 = (45,000 - 50,000) / 5,000 = -1
For 55,000 miles:
z2 = (55,000 - 50,000) / 5,000 = 1
Next, we look up the corresponding values in the standard normal distribution table. The table will provide the proportion of data within a certain range of z-scores.
The percentage of tires with a life between 45,000 and 55,000 miles is the difference between the cumulative probabilities for z2 and z1.
Looking at the standard normal distribution table, the cumulative probability for z = -1 is 0.1587, and the cumulative probability for z = 1 is 0.8413.
Therefore, the percentage of tires that will have a life of 45,000 to 55,000 miles is:
0.8413 - 0.1587 = 0.6826
Converting this to a percentage, we get:
0.6826 * 100 = 68.26%
So the correct answer is 68.27%.
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Put the numbers in order least to greatest!
0.9
-2.4
-0.8
1.6
0.2
Thanks to anyone who answers it always helps!
Have a great day!
Answers
Answer:
-2.4
-0.8
0.2
0.9
1.6
Step-by-step explanation:
I just know.
-0.8
0.2
0.9
1.6
I’m so smart
the different between two possitive nymbers is 48. the lesser number is 1/3 of the greater number. what are the two positive numbers
Answers
Let's call the greater number "x" and the lesser number "y". According to the problem, we know that:
x - y = 48 (since the difference between the two numbers is 48)
y = (1/3)x (since the lesser number is one third of the greater number)
Now we can substitute the second equation into the first equation:
x - (1/3)x = 48
Simplifying this equation, we get:
(2/3)x = 48
Multiplying both sides by 3/2, we get:
x = 72
Now that we know x, we can use the second equation to find y:
y = (1/3)x = (1/3)(72) = 24
So the two positive numbers are 72 and 24.
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A-which temperature is warmer, -2 degrees Celsius or, -5 degrees Celsius B-Write and inequality to express the relationship between -2 and -5
Answers
Answer:
Step-by-step explanation:
On a number line, -2 appears to the right of -5, and therefore -2 is warmer than -5. (Answer A)
The difference between -2 and -5 is -2 - (-5) = 5 - 2 = 3 degrees C (Answer B)
In other words, -2 is 3 degrees C warmer than -5 degrees C.
Tony bought a pair of jeans for $168, a shirt for $35, and two packages of socks for $15 each. What will Tony's total be, including a tax of 8%?
Answers
Answer:
251.64
Explanation:
168 + 35 + 30 = 233.
Where did i get that random thirty from? Two packages of socks that both cost 15 would just be 15 x 2 which equals 30. Simple.
2b x b
is this answer only 2b ^ 2 or is there any other answer without using exponentiation
Answers
The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.
Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.
So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.
The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.
The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.
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Evaluate (4/5) to the third power
Answers
Answer:
ie (4/5)^3
= 64/125
Step-by-step explanation:
please mark as brainliest
PLEASE HELP!!!!!!!! its for geometry and im so confused
Answers
Answer:
a
Step-by-step explanation:
as the step by step is named you would calculate the radius and how long the diamitor and the add that all together and your awnser is a
Please answer in detail Determine whether the following statement is True, False, or Uncertain, and explain your answer. Statement: Flexible exchange rates ...
Answers
The statement "Flexible exchange rates ..." is incomplete, and without further clarification, it is uncertain to determine whether it is true or false. A complete statement is required to provide a clear context for discussing the nature and implications of flexible exchange rates.
Flexible exchange rates refer to a system in which currency exchange rates are determined by market forces, such as supply and demand. Under this system, exchange rates fluctuate freely based on various economic factors, including inflation rates, interest rates, trade balances, and investor sentiment.
Flexible exchange rates offer advantages such as the ability to adjust to changing economic conditions and promote trade balance adjustments. They can also help absorb external shocks and enhance monetary policy autonomy. However, they may also introduce volatility and uncertainty in international trade and investment. To assess the accuracy of the statement, additional information or context is needed.
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Provide reasons for the statements.
Given: ∠1 and ∠3 are vertical angles.
Prove: ∠1 ≅ ∠3
(See image for more details on the equation, please.)
Answers
The reasons for the statement about the angles include:
3. Definition of linear pair.
4. Definition of supplementary angles.
5. Substitution.
6. Subtraction property of equality.
7. Definition of congruence.
How to illustrate the information?The angles are supplementary because the angles 1 and 2, 2 and 3 form a linear pair and thus because of the definition of linear pair, they are supplementary angles.
The sum of angles of 1 and 2, 2 and 3 is equal to 180 because these pair of angles are supplementary angles. Supplementary angles are those angles whose sum is 180 degrees.
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You have a plate of 40 cookies. Ten have chocolate chips and 15 have pecans. Of the cookies mentioned in the preceding sentence, two have both chocolate chips and pecans. You select a cookie at random. What is the probability that your cookie has chocolate chips or pecans ?
Answers
Answer:
see below
Step-by-step explanation:
23 out of the 40 have cc or pecans
23/40
Which of the following is an expression
A. 7x = 4
B. 7 = x = 4
C. 7 - x
D. 7n - 3 = 32
Answers
Answer:
c 7-x
Step-by-step explanation:
Data where the difference between data values has meaning but there is no defined starting point
Answers
Examples of such data include stock prices, economic indicators, and meteorological data such as temperature, wind speed, and barometric pressure.
These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.
1. Data where the difference between data values has meaning but there is no defined starting point can be defined as data that is not linearly dependent.
2. Examples of such data include stock prices, economic indicators, and meteorological data. These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.
3. Stock prices, economic indicators, and meteorological data all have different scales and can move in different directions, making it difficult to track the exact difference between data points.
4. Despite this, these types of data still allow for meaningful analysis and can be used to make predictions and draw conclusions.
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A forester shows the accompanying histogram of tree diameters he used in analyzing 27 trees in a large woods that was for sale. Was he justified in using a Normal model to analyze the woods? Explain, citing some specific concerns
Choose the correct answer below
A. Yes, because the histogram is unimodal and symmetric.
B. No, because while the histogram is unimodal, it is not symmetric
C. No, because the histogram is not unimodal or symmetric.
D. No, because while the histogram is symmetric, it is not unimodal
Answers
Yes, the forester was justified in using a Normal model to analyze the woods, because the histogram is unimodal and symmetric. So option A is correct.
A histogram is a type of graph that uses vertical bars to show the distribution of a set of data. This particular histogram is unimodal, meaning that it has one peak which is an indication that the data is distributed normally. Additionally, the histogram is symmetric, which is another indication that the data is normally distributed.
Using a Normal model to analyze the woods is a valid approach because it allows the forester to identify the average diameter of the trees, as well as the spread of the data. It also allows him to check for any outliers, or points that fall outside the normal range. With this information, the forester can determine if the woods is suitable for sale, or if the buyer should be aware of any unexpected features.
Overall, the histogram is an effective way for the forester to analyze the data and determine if a Normal model is appropriate. By noting the unimodal and symmetric nature of the histogram, the forester can be sure that a Normal model will accurately represent the data, allowing him to make an informed decision about the woods.
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If anyone can help I would really appreciate it!
Answers
Answer: y= 2/5 * x - 6
Step-by-step explanation:
y intercept
y= 2/5 x+b putting in the point 5,4
y=2/5 5+ b
4=10+b
b= -6
Factored to Standard Form
Mar 21, 11:20:07 AM
Watch help video
Re-write the quadratic function below in Standard Form
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=
y=
−
4
(
�
−
1
)
(
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+
2
)
−4(x−1)(x+2)
Answers
Which angle in the figure is a right angle?
1: ∠STU
2: ∠TSR
3: ∠TUS
4: I don't know.
Answers
Answer:
TUS
Step-by-step explanation:
The angle parallel has the square that indicates its a right angle - parallel angles have the same number
Answer:
3: ∠TUS
Step-by-step explanation:
line measures 180°
so < U + <TUS =180°................ < U = 90°
< U + <TUS =180°................ < U = 90° 90° + <TUS = 180°
< U + <TUS =180°................ < U = 90° 90° + <TUS = 180° <TUS = 90°
For each type of effect listedâmain effects, two-way interactions, and three-way interactionsâidentify the maximum number of possible effects that could be tested in a 2 Ã 2 Ã 2 factorial design. - 3 main effects- 1 three- way interaction- 3 two-way interactions
Answers
The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.
In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:
There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.
Two-way interactions:
There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.
These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:
There is 1 possible three-way interaction that can be tested in this design: AxBxC.
This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.
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