-4(7j+2) = 10
Urgent question, please! How do I know I start to solve the above by distributing it, and not dividing the -4 from both sides? How do I know?
Please answer! Thank you.
Answer:
hdjeujnejsjjdjdjjdjd
Find the expected value E(X) of the following data. Round your answer to one decimal place. 1 2 3 x 4 5 P(X = x) 0.1 0.2 0.3 0.2 0.2
The expected value of the given data is 3.2.
The expected value of a discrete random variable is the weighted average of its possible values, where the weights are their respective probabilities. Thus, the expected value of X is given by
E(X) =[tex]1*0.1 + 2*0.2 + 3*0.3 + 4*0.2 + 5*0.2\\ = 0.1 + 0.4 + 0.9 + 0.8 + 1\\ = 3.2[/tex]
Therefore, the expected value of X is 3.2, rounded to one decimal place.
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can perform element by element addition, subtraction, multiplication and division when the matrices are different sizes.
No, we cannot perform element by element addition, subtraction, multiplication and division when the matrices are different sizes, because to do this the size of matrices should be same.
The Element-by-element operations, also called element-wise operations, can only be performed when two matrices have the same dimensions, meaning they have the same number of rows and columns.
In this case, the operations are applied to the corresponding elements of each matrix, resulting in a new matrix with the same dimensions as the original matrices.
When the two matrices have different sizes, element-by-element operations are not defined. In some cases, it may be possible to perform other types of operations, such as matrix multiplication or matrix addition (if the matrices have compatible dimensions).
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The given question is incomplete, the complete question is
Can your perform element by element addition, subtraction, multiplication and division when the matrices are different sizes?
hellpppppppppppp. need it for math and am just confused
Step-by-step explanation:
this is solution which is given above in photo
The table provides various values, including all zeros, of a tangent function f (x) on the interval [–2π, 2π].
Angle –2π negative 5 times pi over 3 negative 2 times pi over 3 negative pi over 2 0 pi over 3 pi over 2 2 times pi over 3 2π
f (x) 0 radical 3 negative 3 radical 3 –3 0 radical 3 3 –3 0
What is the period of the function?
4π
2π
π
pi over 2
4π is the period of the tangent function.
What does Tangent Function mean?
The tangent function, one of the primary six trigonometric functions, is typically expressed as tan x. When considering the angle in a right-angled triangle, it is the ratio of the opposite side to the adjacent side.
It is crucial to understand the tangent function in trigonometry because it is a periodic function. Using the unit circle will make understanding the tangent function the simplest possible.
a tangent function f (x) on the interval [–2π, 2π].
∵ f(-2π) and f(2π) are not defined.
∴ x = -2π and x = 2π are two closet asymptotes . { the asymptotes of
tangent function.}
∴ period = 2π - (- 2π )
= 4π
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I will mark you brainiest!
If the triangles above are reflections of each other, then BC ≅ to:
A) DE.
B) ED.
C) EF.
D) DF.
E) AC.
Answer:
D
Step-by-step explanation:
If their reflections are congruent to each other then looking at the diagram we can see a reflection just like a mirror where its flipped on the other side of the dotted line. When flipping it and aligning one triangle to the other we find that BC is congruent to DF
show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied.
The process to show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied is shown below.
We prove this using the Pigeonhole Principle, which states that if n items are placed into m containers, and n > m, then at least one container must contain more than one item.
Let us consider the 16 people seated in a row of 20 chairs. Each person occupies one chair, so there are 20 - 16 = 4 empty chairs in the row.
We assume that empty chairs as containers, and people as items that need to be placed into containers.
Since there are more items (people) than containers (empty chairs), there must be at least one group of 2 or more consecutive empty chairs.
Now, let's consider the complement of this statement: Suppose there are no groups of 4 consecutive chairs that are occupied. Then, each group of 4 consecutive chairs contains at most 3 people.
We partition the row of chairs into groups of 4 consecutive chairs.
So, there are 20 - 3 = 17 such groups. By the statement above, each of these groups contains at most 3 people. Therefore, the total number of people seated in the row is at most 17×3 = 51.
But, we know that there are actually 16 people seated in the row. This is a contradiction, since 51 < 16. Therefore, our assumption that there are no groups of 4 consecutive chairs that are occupied must be false, and we have proved that some group of 4 consecutive chairs must be occupied.
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A invested Rs 4500 for 3 years at the rate of 8% annual compound interest and B invested the
same amount for same time at the rate of per month per rupee I paisa simple interest. Calculate
(i) The interest received by A. (ii) The interest received by B.
The calculation of the interest received by Investor A and Investor B is as follows:
Investor A = $1,168.70 (Compound)Investor B = $1,620 (Simple).What is the difference between compound and simple interest?Compound interest is based on the system of charging interest on accumulated interest and principal for each period.
Simple interest is charged on only the principal for each period.
A's Investment at 8% Annual Compound Interest:N (# of periods) = 3 years
I/Y (Interest per year) = 8%
PV (Present Value) = $4,500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $5,668.70
Total Interest = $1,168.70
B's Investment at Paisa 1 per R1.00 Monthly Simple Interest:N (# of periods) = 3 years
r = 1 paisa per rupee per month
= 1÷100*100 = 1%
Annually rate =1%*12 = 12%
PV (Present Value) = $4,500
Results:
Total Interest = $1,620 (R4,500 x 12% x 3)
Future Value (FV) = $6,120.
Thus, while Investor A receives $1,168.70 at the end of 3 years, Investor B receives $1,620.
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Which of the columns in the table below is categorical data? Name Position Goals Bob Goal 0 Cindy Wing 5 Maurice Center 10 Luke Center 15 A. Name B. Goals C. Position
The categorical data in the table is column C, Position.
What is table?In mathematics and statistics, a table is a way of presenting data in a structured manner, typically with columns and rows. Tables are commonly used to organize and present large amounts of data in a clear and concise way, making it easier to read and analyze. Tables can be used to display numerical data, as well as categorical data, such as names, dates, and labels. They can also be used to summarize data and display relationships between different variables. Tables are often used in scientific research, business, finance, and other fields where data analysis is important.
Here,
In the table given, the only column that contains categories or groups is the "Position" column. It contains categorical data as it lists the positions of the players - Goal, Wing, and Center. On the other hand, "Name" and "Goals" columns contain individual values and numerical data, respectively, and are not considered categorical data.
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a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
In response to the stated question, we may state that As a result, the function journey lasted 5.1875 hours.
What is the role of function in maths?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range).
In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y.
A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
a) Because time cannot be negative, the domain of the function g(t) is the set of all non-negative real numbers. As a result, the domain is [0, ].
Because the amount of gas in the tank cannot be negative or more than the tank's capacity. The range of the function g(t) is the set of all non-negative real numbers less than or equal to 23 (the maximum capacity of the tank).
We can graph the function g(t) by plotting points for different values of t and connecting them with a line. For instance, if we pick t = 0, g(0) = 23, we plot the point (0, 23). We plot the point if we select t = 1 and g(1) = 19.8. (1, 19.8).
c) We are informed that there are 6.4 gallons remaining at the end of the journey. As a result, g(t) = 6.4. We can solve for t by plugging this number into the equation for g(t):
[tex]6.4 = 23–3.2t 3.2t = 16.6 t = 5.1875 g(t) = 23–3.2t[/tex]
Therefore, the journey lasted 5.1875 hours.
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simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.
Simplifying remex's works the same way we simplify fractions. In fractions, a rational number is considered to be a simplified form when its numerator and denominator have no other common factors than 1.
Regular expressions are fractions with variables. In rational expressions, the numerator and denominator are polynomials. That is, it is of the form p(x)/q(x), where q(x) ≠ 0 and p(x) and q(x) are polynomials. Because regular expressions are nothing but fractions, we treat them as if they were fractions.
It is not possible to divide a number by 0. Check what 1/0 is with your calculator, it will return an error. Therefore, no regular expression is defined for variable values with a denominator of 0 (because it is a fraction). For example, in the expression x / (x + 2), the denominator becomes zero when x = -2, so it is called the limit of the rational expression x / (x + 2). In other words, we say x / (x + 2) for all values of x but x ≠ -2.
Simplifying a regular expression means reducing the value of a regular expression to its lowest term or simplified form. Simplifying regexps works the same way we simplify fractions. In fractions, a rational number is considered a simplified form when its numerator and denominator have no other common factors than 1. The same works for simplified rational expressions, but the only difference is that there are polynomials in the fraction. Let's see the steps to follow to simplify a regular expression.
Step 1: Factor each numerator and each denominator by taking the common factor.
Step 2: Cancel the common factor.
Step 3: Write the remaining terms in the numerator and denominator.
Step 4: Indicate limits, if any. Note that a constraint is any value that makes the denominator equal 0, including terms canceled during simplification.
Complete Question:
Simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.
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What are the zeros of the function f(x)= 240x -2x^2
Answer:
What are the zeros of the function f(x)= 240x -2x^2
Step-by-step explanation:
To find the zeros of the function f(x) = 240x - 2x^2, we need to set f(x) equal to zero and solve for x:
240x - 2x^2 = 0
We can factor out 2x from the left side:
2x(120 - x) = 0
So either 2x = 0 or 120 - x = 0. Solving for x in each case gives:
2x = 0 => x = 0
120 - x = 0 => x = 120
Therefore, the zeros of the function are x = 0 and x = 120.
Solve for w.
74=171-w
Answer:
w = 97
Step-by-step explanation:
Solve for w.
74=171-w
74 = 171 - w
w = 171 - 74
w = 97
----------------------
check
74 = 171 - 97
74 = 74
the answer is good
Find the largest interval which includes x = 0 for which the given initial value problem has a unique solution.(x−4)y′′+2y=x, y(0)=0, y′(0)=1.
The largest interval which includes x=0 for which the given initial value problem has a unique solution is (-∞,4).
The Differential Equation is : (x-4)y'' + 2y = x,
Now, we convert the differential-equation into the standard form,
We get,
⇒ y'' + 2y/(x-4) = x/(x-4) ...equation(1)
We know that second order differential-equation is :
⇒ ay'' + by' + cy = R ...equation(2),
Now, On comparing equation(2) with equation(1),
we get,
The values are : a = 1, b = 0 and c = 2/(x-4), R = x/(x-4),
The Values of "c" , "R" are continuous except at the value "4" because on substituting 4 in x of c and x of R the values of c and R approaches to ∞.
Therefore, The largest-interval which includes x=0 is (-∞,4).
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Subtract: ? 5/6 - 4/6
Answer:
1/6
Step-by-step explanation:
5/6 - 4/6 = 1/6
Answer:
Step-by-step explanation:
To subtract these fractions, we need to have a common denominator. In this case, the denominators 5 and 6 do not match, so we have to find the least common multiple (LCM) of 5 and 6, which is 30.
Then, we can convert both fractions so that they have a denominator of 30:
5/6 = 25/30
4/6 = 20/30
Now we can subtract the numerators:
25/30 - 20/30 = 5/30
Simplifying the result to its lowest terms, we have:
5/30 = 1/6
Therefore, 5/6 - 4/6 = 1/6.
Converging duct flow (Fig. P4–16) is modeled by the steady, two-dimensional velocity field of Prob. 4–16. Is this flow field rotational or irrotational? Show all your work.
V=(u,v)=(U0+bx)i−(by)j
The flow field is rotational because the curl of the velocity field is non-zero, which is calculated as (-b)k, where k is the unit vector in the z direction.
The velocity field V can be expressed as:
V = (u,v) = (U0+bx)i - (by)j
The flow is rotational if the curl of the velocity field is non-zero, i.e.:
∇ x V ≠ 0
Using the curl operator:
∇ x V = (∂v/∂x - ∂u/∂y)k
where k is the unit vector in the z direction.
Evaluating the partial derivatives:
∂v/∂x = 0, since v does not depend on x
∂u/∂y = -b, since the derivative of by with respect to y is -b
Therefore, the curl of the velocity field is:
∇ x V = (-b)k
Since the curl is non-zero, the flow field is rotational.
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universe gas law state that the volume (VM³) of a given mass of an ideal gas varies directly with it absolute temperature (TK) an inversely with it pressure (pM/ m²). A certain mass of gas at an absolute temperature 275K and pressure 10 N/ m² has volume 0.0224m³. find the formula that connect p, V, and T
The formula for the temperature (T), number of gas molecules (n), volume (V), and pressure (P) is found as: nR = 0.224 / 275.
Explain about the universe gas law?While dealing with gas, a popular equation was utilized to relate the various components necessary to solve a gas problem. This same Ideal Gas Equation is the name given to this formula. We have always understood that there is no such thing as an ideal. Two well-known presumptions must have been made in this case in advance:
the particles also had no forces acting among them, and these particles do not start taking up any space, implying their atomic volume is entirely ignored.Those four gas variables are: temperature (T), number of gas molecules (n), volume (V), and pressure (P) . Last but not least, the following equation's constant, R, or the gas constant, will be covered in more detail later:
PV = nRT
PV/T = nR
Given data:
absolute temperature 275Kpressure 10 N/ m² volume 0.0224 m³Putting the value;
nR = PV/T
nR = 10*0.0224 / 275
nR = 0.224 / 275
Thus, the formula for the temperature (T), number of gas molecules (n), volume (V), and pressure (P) is found as: nR = 0.224 / 275.
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AA contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answer:
Model D) a spinner with 6 equal sections can be used to simulate the contestant's chances of winning.
Step-by-step explanation:
A spinner with 6 equal sections represents the possible outcomes of the game show, where each section represents a possible win or loss. Since the contestant has a 1 in 6 chance of winning, the spinner would have one section representing a win and five sections representing a loss. Each spin of the spinner would represent one try at the game show, and the probability of winning can be determined by calculating the theoretical probability of landing on the win section.
Find the mass of the solid bounded by the xy-plane, yz-plane, xz-plane, and the plane (x/2)+(y/3)+(z/6)=1, if the density of the solid is given by δ(x,y,z)=x+4y.
mass=?
The mass of the solid is approximately 17.333 units.
To find the mass of the solid bounded by the given planes, we need to integrate the density function δ(x,y,z) over the volume of the solid. We can express the volume of the solid as the region enclosed by the planes
0 ≤ x ≤ 2, 0 ≤ y ≤ 3, 0 ≤ z ≤ 6-3x-2y
So, the mass of the solid is given by the triple integral
M = ∭ δ(x,y,z) dV
= ∫₀² ∫₀³ ∫₀^(6-3x-2y) (x+4y) dz dy dx
= ∫₀² ∫₀³ [(x+4y)(6-3x-2y)] dy dx
= ∫₀² [(6x-3x²)⁄2 + 8xy - 4y²] dy
= ∫₀² [(6x-3x²)⁄2 + 12x - 36] dx
= [3x³/2 - x⁴/4 + 6x² - 36x]₀²
= (12 - 8/3 + 24 - 72) - (0 - 0 + 0 - 0)
= 17.333 units
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A joined in a partnership with B after 3 months by investing Rs. 27000. The profit of A is 3/5th of B's share at the end of one year. What was the amount invested by B?
Thus, A’s share is Rs. 2,40,000 and B’s share is Rs. 2,61,000.
What is profit and loss?A profit and loss statement (P&L) is a financial statement that summarizes income, expenses, and expenses incurred during a specified period of time.
Along with the balance sheet and cash flow statement, the income statement is one of the three financial statements issued quarterly and annually by all publicly traded companies.
When used together, the Income Statement, Balance Sheet, and Cash Flow Statement provide detailed insight into the company's overall financial performance.
Accounting is created using the cash method or the accrual method of accounting.
Changes over time are more important than the numbers themselves, so it's important to compare income statements from different accounting periods.
According to our question-
Ratio of their share in profit = Ratio of their investments
Ratio of their share in profit = Ratio of their investments
⇒ 27000 × 5 + 23000 × 15 ∶ 36000 × 9 + 33000 × 6 ∶ 50000 × 6
Thus, ratio of their investments = 480000 ∶ 522000 ∶ 300000 = 480 ∶ 522 ∶ 300 = 80 ∶ 87 ∶ 50
Profit earned after a year = Rs. 6,51,000
A’s share = (80/217) × 651000 = Rs. 240000
B’s share = (87/217) × 651000 = Rs. 261000
Hence, Thus, A’s share is Rs. 2,40,000 and B’s share is Rs. 2,61,000.
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f the determinant of a matrix is , and the matrix is obtained from by swapping the third and fourth columns, then
If the determinant of a 5 times 5 matrix A, swapping two columns in a matrix changes the sign of the determinant. Thus, det(C) = -det(A) = -(9) = -9. Determinant of a 4 times 4 matrix A is det (A) = 6, multiplying a column of a matrix by a scalar k multiplies the determinant by k. Thus, det(B) = 5det(A) = 5(6) = 30.
To evaluate det(C) given that det(A) = 9 and C is obtained by swapping the third and fourth columns of A, we can use the fact that swapping two columns of a matrix multiplies its determinant by -1. Thus, det(C) = -det(A) = -9.
To evaluate det(B) given that det(A) = 6 and B is obtained by multiplying the second column of A by 5, we can use the fact that multiplying a column of a matrix by a scalar multiplies its determinant by that scalar. Thus, det(B) = 5(det(A)) = 5(6) = 30.
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____The given question is incomplete, the complete question is given below:
If the determinant of a 5 times 5 matrix A is det (A) = 9= and the matrix C is obtained from A by swapping the third and fourth columns, then det C = If the determinant of a 4 times 4 matrix A is det (A) = 6, and the matrix B is obtained from A by multiplying the second column by 5 then det (B) =
Use the Pythagorean theorem to find the distance between points P and Q
The distance between the points P and Q is 10 units using the Pythagorean theorem.
What is Pythagoras Theorem?The right-angled triangle's three sides are related in accordance with the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of the other two sides. According to the Pythagoras theorem, if a triangle has a right angle, the hypotenuse's square is equal to the sum of the squares of the other two sides.
The coordinates of the point P and Q are (3, 2) and (9, 10).
Using the Pythagoras theorem:
c² = (x2 - x1)² + (y2 - y1)²
Substitute the values:
c² = (9 - 3)² + (10 - 2)²
c² = 36 + 64
c² = 100
c = 10 units.
Hence, the distance between the points P and Q is 10 units using the Pythagorean theorem.
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If p is a positive integer, then p(p + 1)(p − 1) is always divisible by
F. 7
G. 5
H. 4
J. 3
K. None of these
We can see that p(p + 1)(p − 1) is not always divisible by 7, but it is always divisible by 5, 4, and 3. Thus, the correct answer is (G) 5.
What is positive integer?A positive integer is a whole number greater than zero. In other words, it is a number that can be written without any fractional or decimal components, and is larger than zero. Positive integers are commonly denoted by the symbol "N" or "Z+".
What is negative integers?A negative integer is a whole number less than zero. In other words, it is a number that can be written without any fractional or decimal components, and is smaller than zero. Negative integers are commonly denoted by the symbol "Z−".
In the given question,
We can simplify p(p + 1)(p − 1) as follows:
p(p + 1)(p − 1) = p(p² - 1) = p³- p
Now, we can consider the remainders when p is divided by each of the answer choices:
F. 7: If p = 7, then p³- p = 7³ - 7 = 342, which is not divisible by 7.
G. 5: If p = 5, then p³ - p = 5³ - 5 = 120, which is divisible by 5.
H. 4: If p = 4, then p³ - p = 4³ - 4 = 60, which is divisible by 4.
J. 3: If p = 3, then p³ - p = 3³ - 3 = 24, which is divisible by 3.
Therefore, we can see that p(p + 1)(p − 1) is not always divisible by 7, but it is always divisible by 5, 4, and 3.
Thus, the correct answer is (G) 5.
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HELP ME ASAP YOU WILL BE BRAINLIEST!!!
Answer:
0.2162 (21.62%)
Step-by-step explanation:
Notice the total time of students is 407. (this is 83+79+88+72+85)
So the probability of having a 3 is:
[tex]P(3)= \frac{88}{407} =0.2162[/tex]
This is 21.62%
Find the closed formula for each of the following sequences by relating them to a well known sequence. Assume the first term given is a1.
(a) 2, 5, 10, 17, 26, . . .
(b) 0, 2, 5, 9, 14, 20, . . .
(c) 8, 12, 17, 23, 30, . . .
(d) 1, 5, 23, 119, 719, . . .
The final closed formula answers for each part,
(a) an = n^2 + 1
(b) an = n(n + 1)(n + 2)/6
(c) an = 2n + 6
(d) an = n! + (n-1)! + ... + 2! + 1!
(a) The given sequence can be seen as the sequence of partial sums of the sequence of odd numbers: 1, 3, 5, 7, 9, . . . . That is, the nth term of the given sequence is the sum of the first n odd numbers, which is n^2. Therefore, the closed formula for the given sequence is an = n^2 + 1.
(b) The given sequence can be seen as the sequence of partial sums of the sequence of triangular numbers: 1, 3, 6, 10, 15, . . . . That is, the nth term of the given sequence is the sum of the first n triangular numbers, which is n(n + 1)(n + 2)/6. Therefore, the closed formula for the given sequence is an = n(n + 1)(n + 2)/6.
(c) The given sequence can be seen as the sequence of differences between consecutive squares: 1, 5, 9, 16, 21, . . . . That is, the nth term of the given sequence is the difference between the (n+1)th square and the nth square, which is (n + 1)^2 - n^2 = 2n + 1. Therefore, the closed formula for the given sequence is an = 2n + 6.
(d) The given sequence can be seen as the sequence of partial sums of the sequence defined recursively by a1 = 1 and an+1 = an(n + 1) for n ≥ 1. That is, the nth term of the given sequence is the sum of the first n terms of the recursive sequence. It can be shown that the nth term of the recursive sequence is n! (n factorial), and therefore the nth term of the given sequence is the sum of the first n factorials. That is, an = 1 + 1! + 2! + ... + (n-1)! + n!. Therefore, the closed formula for the given sequence is an = n! + (n-1)! + ... + 2! + 1!.
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PLEASE HELLP IM AWARDING 100 POINTS FOR THIS What is the scale factor, or constant of proportionality from Figure 1 to Figure 2?
Enter your answer as a decimal in the box.
Answer:
4:9
Step-by-step explanation:
Answer:
Scale factor = 2.25
Step-by-step explanation:
To find the scale factor between two similar shapes, we need to compare the corresponding sides of the shapes.
The scale factor is the ratio of the length of any side of one shape to the length of the corresponding side on the other shape.
From inspection of the given diagram, the ratio of the corresponding sides of the two similar figures is:
⇒ Figure 1 : Figure 2 = 8 : 18
Therefore, to find the scale factor from Figure 1 to Figure 2, divide the side length of Figure 2 by the corresponding side length of Figure 1:
[tex]\implies \sf Scale\;factor=\dfrac{18}{8}=2.25[/tex]
Let f(x) = x? - 6x + 8 and g (x) = x - 5.
Find (f + g) (x) and (f - g) (x) .
In the diagram of right triangle ABC shown below, AB= 14 and AC = 9.
What is the measure of ZA, to the nearest degree?
1) 33
2) 40
3) 50
4) 57
The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a given a right angle triangle in the picture
It is required to find the measure of angle A
Applying cos ratio to find the measure of the angle A:
cosA = 9/14
cosA = 0.642
A = 49.99 ≈ 50 degree
Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
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T/F. Research shows that sketch artists almost always produce more-accurate facial images than technicians using other methods.
The given statement " Research shows that sketch artists almost always produce more-accurate facial images than technicians using other methods." is True. Because sketch artists are able to capture more nuanced details of face
Research suggests that trained sketch artists can produce more accurate facial images compared to other methods such as facial recognition software or composite imaging software. This is because sketch artists can capture more details and variations in the facial features of a suspect or witness.
They can also work with the witness to create a likeness that accurately reflects their memory of the individual. Additionally, sketch artists are able to adjust and refine the image as the witness provides more information or corrections, leading to a more accurate final image.
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Evaluate the following integral using three different orders of integration. (xz − y^3) dV, E where E = (x, y, z) | −1 ≤ x ≤ 3, 0 ≤ y ≤ 2, 0 ≤ z ≤ 6
The value of the integral is (81/2) for method 1, (95/2) for method 2, and (375/2) for method 3.
To evaluate the integral (xz − y^3) dV over the region E = {(x, y, z) : −1 ≤ x ≤ 3, 0 ≤ y ≤ 2, 0 ≤ z ≤ 6}, we can use three different orders of integration
Method 1
Integrating with respect to x first
In this method, we integrate with respect to x first, then with respect to y, and finally with respect to z.
∫∫∫ (xz − y^3) dV = ∫0^6 ∫0^2 ∫−1^3 (xz − y^3) dx dy dz
= ∫0^6 ∫0^2 [(1/2)x^2z − xy^3]∣−1^3 dy dz
= ∫0^6 [4z − (27/2)z] dz
= (3/2) ∫0^6 z dz
= (81/2)
Method 2
Integrating with respect to y first
In this method, we integrate with respect to y first, then with respect to x, and finally with respect to z.
∫∫∫ (xz − y^3) dV = ∫0^6 ∫−1^3 ∫0^2 (xz − y^3) dy dx dz
= ∫0^6 ∫−1^3 [(1/2)xz y^2 − (1/4)y^4]∣0^2 dx dz
= ∫0^6 [(8/3)xz − (81/4)] dz
= (95/2)
Method 3
Integrating with respect to z first
In this method, we integrate with respect to z first, then with respect to x, and finally with respect to y.
∫∫∫ (xz − y^3) dV = ∫−1^3 ∫0^2 ∫0^6 (xz − y^3) dz dy dx
= ∫−1^3 ∫0^2 [(1/2)xz^2 − y^3z]∣0^6 dy dx
= ∫−1^3 [(54/2)x − (32/3)] dx
= (375/2)
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