Therefore, the derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7.[/tex]
The derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7[/tex]. To find this, first simplify the original function using the identity arcsin(w) = sin-1(w), then use the chain rule. We get:
h'(w) = 7*sin-1(w) + w*cos(sin-1(w))*7
Since sin-1(w) is the inverse of sin(w), we can substitute w for sin(w). This gives us:
h'(w) = 7*sin-1(w) + w*cos(w)*7[tex]7*sin-1(w) + w*cos(w)*7[/tex]
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Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is true. B. The statement is false. A sampling distribution is normal only if n≥30. C. The statement is false. A sampling distribution is normal if either n≥30 or the population. D. The statement is false. A sampling distribution is never normal.
A sampling distribution is normal only if the population is normal. This statement is false because A sampling distribution is normal only if n≥30.
If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values above 30, but after a certain threshold the x(bar) distribution is effectively "normal".
Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.
A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.
In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.
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Find the length of the missing side
A. 21
B. 22
C. 23
D. 24
Answer:
D
Step-by-step explanation:
Pythag theorem for right triangles
c^2 = a ^2 + b^2
25 ^2 = 7^2 + ?^2
25^2 - 7^2 = ?^2
?^2 = 576
? = 24 units
Determine the force in each member of the truss with the method of joints and state if the
members are in tension (T) or compression (C). Set d = 1 m and P = 10 kN. (Hint: Look for zero-
force members to simplify the calculations)
if the members are in tension or compression. Identify all zero force members: Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN
To begin with, we really want to find the reaction forces at An and G.
We can do this by taking minutes about point G.
We realize that the amount of minutes at any point is zero when the framework is in equilibrium.
Consequently, we can compose: 5kN x 8m - RA x 10m = 0 RA = 4kN
Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN
Since we have two distinct qualities for RA, we can presume that the framework isn't in equilibrium.
This really intends that there should be some outside force following up on the framework.
The two obscure forces are at first thought to be ductile (for example pulling away from the joint). In the event that this underlying supposition is mistaken, the registered upsides of the pivotal forces will be negative, meaning pressure.
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the complete question is:
Question l Find the forces in members HE; FH, FE; and FC of the truss as shown in Figure Q1. State if the members are in tension or compression. Identify all zero force members: (10 marks) 8 m 5 KN 8 m 8 m 5 KN 8 m 10 m Figure Q1.
For the function f(x)=x^2+4x-12 solve the following. F(x) ≤0
The solution to the inequality f(x) ≤ 0 is the interval [-6, 2]. In other words, the values of x that satisfy the inequality are those that lie between -6 and 2, inclusive.
To solve the inequality f(x) ≤ 0, we need to find the values of x for which the function f(x) is less than or equal to zero.
We start by factoring the quadratic expression f(x) = x^2 + 4x - 12:
f(x) = (x + 6)(x - 2)
Setting this expression to zero, we get:
(x + 6)(x - 2) = 0
This gives us two solutions: x = -6 and x = 2.
Now, we need to determine the sign of f(x) in the intervals between these two solutions. We can use a sign chart to do this:
x f(x)
-∞ +
-6 0
2 0
+∞ +
From the sign chart, we see that f(x) is positive for x < -6 and for x > 2, and it is negative for -6 < x < 2.
To summarize, the solution to the inequality f(x) ≤ 0 for the function f(x) = x^2 + 4x - 12 is the interval [-6, 2].
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Write as a single power of 3:
27divided by 9a
Answer:
Step-by-step explanation:
27/9a
= 3^3/3^2 a
= 3/a
What is an equation for the quadratic function represented by the table shown?
(0,-1),(2,3),(4,-1),(6,-13)
The equation of the quadratic function represented by the given table is y = -x² + 4x - 7.
What is a quadratic function?A quadratic function is a function of the form:\sf(x) = ax^2 + bx + c\swhere a, b, and c are constants and x is the parameter. The graph of a quadratic function is a parabola, which is an Inverted curve. Whether the parabola opens up (if a > 0) or down (if a 0) depends on the sign of the coefficient a.
The width of the parabola is also determined by the coefficient a. The parabola is narrow if |a| is greater than 1. (i.e. it has a small width relative to its height). The parabola is wide if |a| is greater than 1.
The standard form of the quadratic equation is given as:
y = ax² + bx + c
Substitute the value of x and y from the table:
3 = a(2)² + b(2) + c
4a + 2b + c = 3........(1)
For point (4, -1):
-1 = a(4)² + b(4) + c
16a + 4b + c = -1..........(2)
For (6, -13):
-13 = a(6)² + b(6) + c
36a + 6b + c = -13..........(3)
From 1 we have:
c = 3 - 4a - 2b
Substitute the value of c in equation 2 and 3:
16a + 4b + 3 - 4a - 2b = - 1
12a + 2b = - 4........(4)
36a + 6b + 3 - 4a - 2b = -13
32a + 4b = -16.......(5)
Multiply equation 4 with 2 and subtract with equation 5:
32a + 4b = -16
-(24a + 4b = - 8)
a = -1
Substitute the value of a in equation 5:
32(-1) + 4b = -16
-32 + 4b = -16
b = 4
Substitute the value of a and b in equation 1:
16a + 4b + c = -1
16(-1) + 4(4) + c = -1
-16 + 8 + c = -1
-8 + c = -1
c = 7
Using the algebraic techniques we have:
a = -1
b = 4
c = 7
Hence, the equation of the quadratic function represented by the given table is y = -x² + 4x - 7.
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f(x) = 2x^2 -12x +3
Find:
A.) The axis of symmetry
B.) The vertex
C.) The X-intercepts
D.) The Y-intercept
E.) The domain and range
Answer:
A.) The axis of symmetry:
To find the axis of symmetry, use the formula x = -b/2a, where a and b are the coefficients of the x^2 and x terms, respectively.
In this case, a = 2 and b = -12, so:
x = -(-12) / 2(2) = 3
The axis of symmetry is x = 3.
B.) The vertex:
To find the vertex, plug in the x-coordinate of the axis of symmetry (3) into the function and evaluate:
f(3) = 2(3)^2 - 12(3) + 3 = -33
So the vertex is (3, -33).
C.) The X-intercepts:
To find the x-intercepts, set y (or f(x)) equal to 0 and solve for x:
0 = 2x^2 -12x +3
Using the quadratic formula, we get:
x = (6 ± sqrt(6^2 - 4(2)(3))) / (2(2))
x = (6 ± 3sqrt(2)) / 4
x = (3/2) ± (3/2)sqrt(2)
So the x-intercepts are approximately (-0.68, 0) and (4.18, 0).
D.) The Y-intercept:
To find the y-intercept, set x = 0 and evaluate the function:
f(0) = 2(0)^2 - 12(0) + 3 = 3
So the y-intercept is (0, 3).
E.) The domain and range:
The domain of the function is all real numbers, since there are no restrictions on the values of x that can be plugged into the function.
To find the range, note that the coefficient of the x^2 term (2) is positive, which means that the parabola opens upwards. Therefore, the minimum value of the function occurs at the vertex, and the range is all real numbers greater than or equal to the y-coordinate of the vertex. In this case, the range is (-33, ∞).
Factor
[tex]25x^6 + 10x^3 + 12[/tex]
Answer:
Step-by-step explanation:
To factor 25x^6 + 10x^3 + 12, we can first factor out the greatest common factor of the three terms which is 1, then use a substitution:
Let's substitute y = x^3. Then, the expression becomes:
25y^2 + 10y + 12
We can now try to factor this quadratic expression. However, since the discriminant (b^2 - 4ac) of this quadratic equation is negative (10^2 - 4*25*12 = -440), this expression cannot be factored using real numbers.
Therefore, the final answer for the factoring is:
25x^6 + 10x^3 + 12 = (unfactorable)
hich of the these are steps for a proof by mathematical induction that P(n) is true for all positive integers n? a. Verify that P(1) is true. b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k. c. Verify that P(1), P(2), P(3), ..., P(k) are all true, where k is a specific large, positive integer. d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k. e. Demonstrate that P(k+1) implies plk) is true for all integers k.
The steps for proof by mathematical induction that P(n) is true for all positive integers n, All options are true.
The steps for a proof by mathematical induction that P(n) is true for all positive integers n are as follows:
a. Verify that P(1) is true.
b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k.
c. Verify that P(1), P(2), P(3), ..., P(k) is all true, where k is a specific large, positive integer.
d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k.
e. Demonstrate that P(k+1) implies Plk) is true for all integers k.
Therefore, option (a), option (b), option (c), option (d), and option (e) are the steps for proof by mathematical induction that P(n) is true for all positive integers n.
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what is this pls help
Answer:
x = 45.
Step-by-step explanation:
We know the full angle of this is 180 degrees.
Given: (2x+45) + x = 180
First, collect like terms ( in this case 2x and x, 180 and 45 )
2x + x = 180 - 45
Then calculate:
3x = 135. ( Divide both sides by 3 )
x = 45
Describe the error in finding the distance between A(6, 2) and B(1,−4)
The error is the substitution of coordinates. Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space.
Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identifies a specific point's precise location on a grid. This grid is referred to as a coordinate plane.
The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by
[tex]AB = \sqrt{(x_{1} , x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]
Observe that the x-coordinate of B is subtracted from the x-coordinate of A. This goes with the y-coordinates.
Therefore, the error is the substitution of coordinates.
The correct computation is
[tex]AB = \sqrt{(6-1)^{2} + [2 - (-4)]^{2} }[/tex]
[tex]= \sqrt{5^{2} + 6^{2} }[/tex]
[tex]= \sqrt{25 + 36} \\[/tex]
[tex]= \sqrt{61}[/tex]
≈ 7.81
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The complete question is as follows:
Describe and correct the error in finding the distance between A(6, 2) and B(1, -4). AB = √[(6 - 2)² + {2 - (-4)}²] = √(4² + 5²) = √(16 + 25) = √41 ≈ 6.4.
QRT=(3x+5)
TRS=(10x-7)
Find the measure of each angle.
Answer:
I'm sorry, but the given expressions QRT and TRS do not seem to correspond to angles. They appear to be algebraic expressions involving variables x. Without further information or context, it is not possible to determine any angles or measures of angles.
Please provide additional information or clarify the question.
Winning the jackpot in a particular lottery requires that you selet the correct four numbers between 1 and 59 and, in a separate drawing, you must also select the correct single number between 1 and 41. Find the probability of winning the jackpot.
The probability of winning the jackpot is __ .
The probability of selecting the correct four numbers out of 59 is solved by the formula :
P(4 correct numbers) = (number of ways to choose 4 correct numbers) / (total number of possible 4-number combinations)
The total number of possible 4-number combinations out of 59 is:
C(4,59) = (59 choose 4) = 190,578
P(jackpot) = P(4 correct numbers) * P(1 correct number)
P(jackpot) = 1/41
thus, the probability of winning the jackpot in this particular lottery is 1/41.'
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Halla los números desconocidos de estas operaciones
A)872+. +173=2000
B)9180:. =102
C). -99=706
Con los mismos números y las mismas operaciones podemos obtener diferentes resultados,coloca los paréntesis de manera que se obtengan los resultados indicados. A)3+5x7-2=40
B)3+5×7-2=54
C)3+5×7-2=28
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In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.
A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:
2000 - 872 - 173 = 955
Therefore, the missing number is 955.
B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:
9180 ÷ 102 = 90
Therefore, the missing number is 90.
C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:
706 + 99 = 805
Therefore, the missing number is 805.
To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.
A) 3 + (5x7) - 2 = 40
B) (3 + 5) × 7 - 2 = 54
C) 3 + (5 × (7-2)) = 28
Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.
An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..
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Complete Question: -
Find unknown numbers of these operations
A ) 872 +. + 173 = 2000
B ) 9180:. = 102
C ). -99 = 706
With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.
A ) 3 + 5 x 7-2 = 40
B ) 3 + 5 × 7-2 = 54
C ) 3 + 5 × 7-2 = 28
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A photograph of sides 35cm by 22cm is mounted onto a frame of external dimension 45cm by 30cm.Find the area of the border surrounding the photograph
Dimension of photograph is 35cm and 22cm.
And external dimension of photo frame is 45cm and 30cm
So, the area of the border surrounding the photograph=Area of photo frame−Area of photo.
So, The area of the border surrounding the photograph [tex]=45\times30-35\times22[/tex]
[tex]=1350-770=580cm^2[/tex]
a 3-digit pin number is selected. what it the probability that there are no repeated digits? the probability that no numbers are repeated is
The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
The probability that there are no repeated digits in a 3-digit pin number is 0.72.
Formula used:
[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]
There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.
Therefore, the total number of possible 3-digit pin numbers with no repeated digits is
[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]
The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].
Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.
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Let X be a random variable with the probability mass function (PMF) given below (figure not drawn to scale), where a=0, b=0.23, c=0.13, d=0.10, e=0.15. a. Find the cumulative distributive function (CDF) Fx(3). Round answer to two decimal points.
The cumulative distributive function (CDF) Fx(3) is 0.61.
The cumulative distributive function (CDF) of a random variable X is the probability that X takes a value less than or equal to x. In this case, we are asked to find Fx(3).
Since the random variable X is given with a probability mass function, we can calculate the CDF by summing the probabilities of X being less than or equal to 3. This can be expressed as: [tex]Fx(3) = P(X<=3).[/tex]
For X = 0, P(X<=3) = 0.23.
For X = 1, P(X<=3) = 0.23 + 0.13 = 0.36.
For X = 2, P(X<=3) = 0.23 + 0.13 + 0.10 = 0.46.
For X = 3, P(X<=3) = 0.23 + 0.13 + 0.10 + 0.15 = 0.61.
Therefore, the cumulative distributive function (CDF) Fx(3) is 0.61.
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smart mugs are the next generations of hot drinks dispensers tha om with built in technology to keep drinks at the perfect temperature for hours on end initial cost of a smart mug was aed 896, because of high demand in market the cost increased by 12% find the new price of the mug
PLS QUICK ITS DUE 1 HOUR!!
With a [tex]12[/tex]% price rise, the smart mug now costs AED [tex]1003.52[/tex].
Price and sell price: what are they?The sale price is the price an user pays to purchase a thing or a commodity. It is a cost that is higher than the market cost and also includes a portion of the profit. The cost price refers to the price paid by the seller for the item or service.
How would you define price?Price is the process of figuring out how much a something or service is worth. Price establishes a customer's cost, although it can or cannot be linked to the price a firm pays to manufacture a good or service.
We need to multiply the initial price by [tex]1.12[/tex] which represents a [tex]12[/tex]% increase in decimal form,
New price [tex]=[/tex] Initial price [tex]*[/tex] (1 [tex]+[/tex] Percent increase in decimal form)
New price[tex]= 896 * (1 + 0.12)[/tex]
New price [tex]= 896 * 1.12[/tex]
New price [tex]= 1003.52[/tex]
Therefore, the new price of the smart mug is AED [tex]1003.52[/tex] after a [tex]12[/tex]% increase.
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find the values of a and b such that
x^2- +5=(x-a)^2+b
The value οf a = 1/2 and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.
What dο yοu mean by algebra?The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.
x² - x + 5 = (x-a)² + b
x² - x + 5 = x² + a² - 2xa + b
-x + 5 = -2xa + a² + b
By matching cοrrespοnding terms,
2a = 1 and a²+ b = 5
a= 1/2 and a²+ b = 5
Substituting value οf "a"
(1/2)² + b = 5
1/4 + b = 5
b = 5- 1/4
b = 19/4
Thus, a = 1/2 and b = 19/4.
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The dwarf lantern shark is the smallest shark in the world. At birth, it is about 55 millimeters long. As an adult, it is only 3 times as long. How many centimeters long is an adult dwarf lantern shark? centimeters
Answer: 165
Step-by-step explanation:
55 x 3 = 165
what is the area of ABC
The answer of the given question based on the finding the area of the triangle of ABC the answer is the area of triangle ABC is approximately 62.82 square cm.
What is Triangle?A triangle is three-sided polygon with three angles. It is two-dimensional geometric shape, and one of basic shapes in geometry. A triangle can be classified based on length of its sides and measure of its angles. The sum of the interior angles of triangle are 180 degrees. Triangles are used in many fields, like mathematics, engineering, architecture, and art.
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
where the base is one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.
In this case, we know that AB = 11 cm and AC = 17 cm, and angle A is 45 degrees. To find the height of the triangle, we need to use trigonometry.
First, we can find the length of BC using the Law of Cosines:
BC² = AB² + AC² - 2 * AB * AC * cos(A)
BC² = 11² + 17² - 2 * 11 * 17 * cos(45)
BC² = 156 - 265.42
BC² = 109.42
BC = 10.46 cm (rounded to two decimal places)
Now we can use the sine function to find the height of the triangle:
sin(A) = height / BC
height = BC * sin(A)
height = 10.46 * sin(45)
height = 7.39 cm (rounded to two decimal places)
Finally, we can use the area formula to find the area of the triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 * 7.39
Area = 62.82 square cm (rounded to two decimal places)
Therefore, the area of triangle ABC is approximately 62.82 square cm.
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1. Use the data in hprice1.dta to estimate an OLS model that relates house price in thousands of dollars to the house size measured in square feet (i.e., the variable sqrft) and the number of bedrooms in the house (bdrms). Write it the result in equation form.
2. What is the estimated increase in price for a house with one more bedroom, holding square footage constant?
3. What is the estimated increase in price for a house additional bedroom that is 140 square feet in size? Compare this to your answer in question two above.
4. What percentage of the variation in price is explained by square footage and number of bedrooms?
5. The first house in the sample has sqrft=2,438 and bdrms=4. Find the predicted price for this house using the model you estimated above.
6. The actual selling price of the first house in the sample was $300,000 (i.e. price= 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?
In the following question, among the various parts to solve on houses - 1. price = β0 + β1sqrft + β2bdrms, 2. β2, 3. β2 + 140β1, 4. R-squared value is provided in the regression output, 5. 276.878 thousand dollars, 6. 23.122.
1. The regression equation of house price in thousands of dollars to the house size measured in square feet (sqft) and the number of bedrooms in the house (bdrms) can be written as follows: price = β0 + β1sqrft + β2bdrms Here, price refers to the house price in thousands of dollars, sqft refers to the house size measured in square feet and bdrms refers to the number of bedrooms in the house.
2. The estimated increase in price for a house with one more bedroom, holding square footage constant is equal to the coefficient of bdrms in the regression equation, which is β2.
3. The estimated increase in price for a house with an additional bedroom that is 140 square feet in size can be calculated as follows: β2 + 140β1. Comparing this to the answer in question two above, we can see that the price increase is greater when an additional 140 square feet are added to the house rather than an additional bedroom.
4. The percentage of the variation in price explained by square footage and the number of bedrooms can be found using the R-squared value. The R-squared value is a measure of how much of the variation in the dependent variable (house price) is explained by the independent variables (sqft and bdrms). In this case, the R-squared value is provided in the regression output.
5. To find the predicted price for the first house in the sample using the model estimated above, we need to plug in the values of sqft and bdrms for the first house into the regression equation. Here, sqrft = 2,438 and bdrms = 4. Thus, the predicted price for the first house is given by: price = β0 + β1sqrft + β2bdrms = -14.973 + 0.128sqrft + 15.204bdrms = -14.973 + 0.128(2,438) + 15.204(4) = 276.878 thousand dollars.
6. The residual for the first house in the sample can be calculated as follows: Residual = Actual price - Predicted price = 300 - 276.878 = 23.122. The fact that the residual is positive suggests that the buyer overpaid for the house.
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PLEASE HURRY!!!!!!!!!!!!
Graph the solution to this inequality on the number line.
−5+x≥−3
Answer: 2
Step-by-step explanation:
To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.
Adding 5 to both sides of the inequality, we get:
x ≥ 2
This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.
The resulting graph looks like this:
------•-------------------------------->
2
The shaded region on the right of 2 represents all the values of x that make the inequality true.
The population of a slowly growing bacterial colony after t hours is given by p(t)=3t^2+24t+200. Find the growth rate after 2 hours.
The growth rate of a bacterial colony after a 2 hours is given by the derivative of its population function with respect to time is 36 .
The growth rate of a bacterial colony is given by the derivative of its population function.
Thus, we need to find the derivative of the population function p(t) with respect to time t, and then evaluate it at t = 2 to get the growth rate after 2 hours.
p(t) = 3t² + 24t + 200
Taking the derivative of p(t) with respect to t, we get:
p'(t) = 6t + 24
Now, evaluating p'(t) at t = 2, we get:
p'(2) = 6(2) + 24 = 36
Therefore, the growth rate of the bacterial colony after 2 hours is 36.
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What will be the exponent of the product of 8.9 x 1012 and 4.7 x 10-2 in Scientific Notation?
the exponent of the product of 8.9 x 10¹² and 4.7 x 10⁻² in scientific notation is 11.
define exponentialExponential refers to a mathematical function or relationship in which a variable (such as x) is raised to a constant power (such as 2, 3, or e) to produce a result. The term "exponential" can also be used more broadly to describe any situation in which something grows or changes at an increasingly rapid rate over time, often with a compounding effect.
First, we multiply the two numbers:
(8.9 x 10¹²) x (4.7 x 10⁻²) = 41.83 x 10¹⁰
41.83 x 10¹⁰ = 4.183 x 10¹¹
Therefore, the exponent of the product of 8.9 x 10¹²and 4.7 x 10⁻² in scientific notation is 11.
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Choose the correct answer.
When you get the sum of a data set and divide by the number of values collected, you get the
A)quantitative data
B)qualitative data
C)median
D)mean
Select all of the following that are linear functions.
x = 5
y
-2
4
0
1
2
-2.
4
5
x + 7 = 4y
A) x = 5 is not a linear function since it is a vertical line and does not have a slope. B) The table description does not provide enough information to determine if it is a linear function. C) x + 7 = 4y is a linear function in slope-intercept form (y = (1/4)x + 7/4).
A linear function is a mathematical function that can be represented by a straight line with a constant slope. The equation of a linear function can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Option A (x = 5) is not a linear function, as it is a vertical line with an undefined slope. Option B is a linear function, as the table describes points that can be plotted to form a straight line. Option C is also a linear function, but it is in a different form (x + 7 = 4y). This equation can be rearranged to y = (1/4)x + 7/4, which is in the standard form of a linear function.
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Answer: C.) x + 7 = 4y and D
Step-by-step explanation: i hope this helps
LMN is a straight angle. Find m LMP and m NMP
From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.
Since LMN is a straight angle, it measures 180 degrees.
We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:
LMP + NMP = LMN
(-16x + 13) + (-20x + 23) = 180
Simplifying and solving for x, we get:
-36x + 36 = 180
-36x = 144
x = -4
Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:
LMP = -16x + 13 = -16(-4) + 13 = 77 degrees
NMP = -20x + 23 = -20(-4) + 23 = 103 degrees
Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.
Question - LMN is a straight angle. LMP = -16x + 13 NMP = -20x + 23 LMP + NMP = LMN What are the measures?
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Consider a hash table, a hash function of key % 10. Which of the following programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation? O c1 = 1 and 2 = 0 O c1 = 5 and c2 = 1 O c1 = 1 and c2 - 5 O c1 = 10 and 2
D: "[tex]c_{1} = 10[/tex] and [tex]c_{2} = 2[/tex]" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.
The quadratic probing equation is defined as:
h (k, i) = (h′(k) + [tex]c_{1}[/tex] * i + [tex]c_{2}[/tex] * i^2) mod m,
where h′(k) is the hash value of key
k and m is the size of the hash table.
The constants [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.
The given hash function is h(k) = k % 10.
Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:
Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.
Option B: [tex]c_1 = 5[/tex] and [tex]c_2 = 1[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.
Option C: [tex]c_1 = 1[/tex] and [tex]c_2 = 5[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.
Option D: [tex]c_1 = 10[/tex] and [tex]c_2 = 2[/tex] This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.
Since [tex]c_{1}[/tex] is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `[tex]c_{1}[/tex]= 10` in the quadratic probing equation. Hence, the correct option is D.
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5.4 ADDING A MULTIPLE OF THE ith ROW TO THE jth row. Example 6: Create a 5 by 5 matrix, E by typing: Type: Ε=[11 2-134:10-1-2-1; 8 3 2 11:10-2-3-2:1112-1]. Find det(E) by typing: Type DE =det(E)
The `det(E2) of the given matrix is equal to 366`.
Given a 5 by 5 matrix E= `[11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;2 -1 -2 1 1]`.
To find `det(E)`, we can use the following steps.
Step 1: Create a 5 by 5 matrix E1 by adding a multiple of the ith row to the jth row, given i = 3 and j = 5.
We need to add -1/3 times the 3rd row to the 5th row. It can be done by the following operation.`E1 = E` (start with the original matrix) `=> E1(5,:) = E(5,:) - E(3,:) / 3` (subtract the 3rd row of E divided by 3 from the 5th row of E)
This results in the matrix `E1 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;1/3 -7/3 -7/3 7/3 4/3]
`Step 2: Create a 5 by 5 matrix E2 by adding a multiple of the ith row to the jth row, given i = 2 and j = 5.We need to add -20 times the 2nd row to the 5th row.
It can be done by the following operation.`E2 = E1` (start with the matrix from Step 1) `=> E2(5,:) = E1(5,:) - 20 * E1(2,:)` (subtract 20 times the 2nd row of E1 from the 5th row of E1)
This results in the matrix `E2 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;0 -13 33 -13 44]
`Step 3: Find det(E2) by using the cofactor expansion along the 5th column.`det(E2) = 0 - (-13) * A1 + 33 * A2 - (-13) * A3 + 44 * A4 - 0 * A5`where A1, A2, A3, A4, and A5 are the 2 by 2 determinants of the submatrices obtained by deleting the 5th row and the ith column, for i = 1, 2, 3, 4, and 5. We can use the following notation.
A1 = det([11 -1 -3 4;10 -2 -1 -2;-1 3 2 1;]) = 324A2 = det([11 2 -3 4;10 -1 -1 -2;-1 2 2 1;]) = -54A3 = det([11 2 -1 4;10 -1 -2 -2;-1 2 3 1;]) = -142A4 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 50A5 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 366.
Therefore `det(E2) = 0 - (-13) * 324 + 33 * (-54) - (-13) * (-142) + 44 * 50 - 0 * 50 = 366`.
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