The algebraic expression for the product of 9 and x is 9x. This can be expressed in steps as follows:
Step 1: Identify the values that are being multiplied together. In this case it is 9 and x.
Step 2: Write the two values side by side and place a multiplication sign between them.
Step 3: The algebraic expression for the product of 9 and x is then written as 9x.
Find the value of Tan 15 without using a table or calcutator
Answer:
Step-by-step explanation:
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PLEASE HELP!!!!!!!!!
△DEF is similar to △YZX
A) which side corresponds to ED? (this one is already answered)
B) write a proportion that you could use to find XZ
C) what is XZ?
Step-by-step explanation:
B) 20:23
C) 6,0375
hope this helps
What is the equation of the line graphed?
Answer:
The simplest possible equation for the line on the graph would be x = - 2
When a researcher wants to report the average cost of college tuition from the 1950s until present time, he or she enlists _______ statistics.a) Inferentialb) Descriptivec) Correlationald) Predictive
Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features.
When a researcher wants to report the average cost of college tuition from the 1950s until present time, descriptive statistics are the appropriate method to use. Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features. By using descriptive statistics, the researcher can calculate measures of central tendency, such as the mean, median, and mode, to determine the typical or average cost of college tuition over time. Additionally, measures of variability, such as the range and standard deviation, can be calculated to understand the spread of the data. Descriptive statistics are commonly used in many fields, including business, economics, psychology, and education, and can provide valuable insights into trends, patterns, and distributions within a dataset.
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|x+6|<3 absolute value inequality, write an equivalent compound inequality.
An equivalent cοmpοund inequality is -9 < x < -3.
What is an absοlute value inequality?An inequality with an absοlute value algebraic expressiοn and variables is knοwn as an absοlute value inequality. An expressiοn using absοlute functiοns and inequality signs is knοwn as an absοlute value inequality.
Here, we have
Given: |x+6|<3 is an absοlute value inequality.
Apply absοlute rule
if |u|<a, a>0 then -a<u<a
-3 < x+6 <3
x+6 > -3 and x+6 <3
x> -9 and x< -3
-9 < x < -3
Hence, an equivalent cοmpοund inequality is -9 < x < -3.
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Annie is concerned over a report that "a woman over age 40 has a better chance of being killed by a terrorist than of getting married." A study found that the likelihood of marriage for a never-previously-wed, 40 -year-old university-educated American woman was 2.5% . To demonstrate that this percentage is too small, Annie uses her resources at the Baltimore Sun to conduct a simple random sample of 546 never-previously-wed, university-educated, American women who were single at the beginning of their 40 s and who are now 45 . Of these women, 20 report now being married. Does this evidence support Annie’s claim, at the 0.01 level of significance, that the chances of getting married for this group is greater than 2.5% ? Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0Ha: p=0.025: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.025
Due to the directed nature of the alternative hypothesis, a one-tailed test is being used (greater than).
what is null hypothesis ?The null hypothesis, which is an assertion or assumption that there is no significant difference or association between two or more variables or populations, is used in statistical hypothesis testing. It is frequently indicated by the letter H0 and is typically the hypothesis that is tested against a competing hypothesis. The objective of the hypothesis test is to either reject or fail to reject the null hypothesis based on the evidence or data seen. The null hypothesis serves as the default or baseline assumption. If the alternative hypothesis is supported by evidence, the null hypothesis is likely to be rejected.
given
The test's null and alternate hypotheses are as follows:
H0: p 0.025 (The percentage of American women with university educations who had never previously been married at the start of their 40s and are now 45 and married is less than or equal to 2.5%)
Ha: p > 0.025 (More than 2.5% of American women with college degrees who were unmarried at the start of their 40s and are now 45 and married are never before married).
Due to the directed nature of the alternative hypothesis, a one-tailed test is being used (greater than).
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Please answer these questions correctly :)
Find the percent of each number :-
1.) 64% of 75 tiles :
[tex] \implies \sf \: \dfrac{64}{100} \times 75 \\ \\\implies \sf \:0.64 \times 75 \\ \\ \implies \sf \: 48 \\ [/tex]
Hence, 64% of 75 tiles is 48 tiles.
2.) 20% of 70 plants.
[tex] \implies \sf \: \dfrac{20}{100} \times 70 \\ \\\implies \sf \:0.2 \times 70 \\ \\ \implies \sf \: 14 \\ [/tex]
Hence, 20% of 70 plants is 14 plants.
3.) 32% of 25 pages .
[tex] \implies \sf \: \dfrac{32}{100} \times 25 \\ \\\implies \sf \: 0.32 \times 25 \\ \\ \implies \sf \: 8 \\ [/tex]
Hence, 32% of 25 pages is 8 pages.
4.) 85% of 40 e -mails.
[tex] \implies \sf \: \dfrac{85}{100} \times 40 \\ \\\implies \sf \:0.85 \times 40 \\ \\ \implies \sf \: 34 \\ [/tex]
Hence, 85% of 40 e -mails is 34 e-mails.
5.) 72% of 350 friends.
[tex] \implies \sf \: \dfrac{72}{100} \times 350 \\ \\\implies \sf \:0.72 \times 350 \\ \\ \implies \sf \: 252 \\ [/tex]
Hence, 72% of 350 friends is 252 friends.
6.) 5% of 220 files.
[tex] \implies \sf \: \dfrac{5}{100} \times 220 \\ \\\implies \sf \:0.05 \times 220 \\ \\ \implies \sf \: 11 \\ [/tex]
Hence, 5% of 220 files is 11 files.
A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4sin4t. If the mass is pulled down 6 in and then released, determine the position of the mass at any time t. (Use g=32ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)
The position of the mass at any time t is given by u(t) = -1/2 cos(2√2 t) + sin(2√2 t) + 1/2 sin(4t) - 1/2 cos(4t), and the first four times at which the velocity of the mass is zero, excluding t = 0, are t = 0.0567, 0.283, 0.510, and 0.736.
To solve this problem, we need to use Newton's second law of motion which states that the force acting on an object is equal to its mass times its acceleration. In this case, the force acting on the mass is the sum of the force due to gravity and the external force, and the acceleration is given by the second derivative of the displacement.
Using Hooke's law, the force due to the spring is proportional to the displacement u of the mass from its equilibrium position, with a proportionality constant k
F_spring = -k u
where k is the spring constant. Since the mass is pulled down 6 in. from its equilibrium position, the initial displacement is u(0) = -0.5 ft. The spring stretches 24 in. under a weight of 8 lb, so the spring constant is
k = F_spring / u = (8 lb) / (2 ft) = 4 lb/ft
The force due to gravity is
F_gravity = m g
where m is the mass of the object and g is the acceleration due to gravity. The mass is given in pounds, so we need to convert it to slugs:
m = 8 lb / (32.2 ft/s^2) = 0.248 slugs
Thus, the force due to gravity is
F_gravity = (0.248 slugs) (32 ft/s^2) = 7.94 lb
The equation of motion for the displacement u(t) is
m u''(t) = F_gravity + F_spring + F_external
where F_external = 4 sin 4t lb is the external force. Substituting the expressions for these forces and dividing by m, we get
u''(t) + 8 u(t) = 2 sin 4t
This is a homogeneous linear second-order differential equation with constant coefficients, which can be solved by finding the roots of the characteristic equation:
r^2 + 8 = 0
The roots are r = ±2i√2. The general solution of the differential equation is then
u(t) = c1 cos(2√2 t) + c2 sin(2√2 t) + u_p(t)
where u_p(t) is a particular solution of the nonhomogeneous equation. Since the right-hand side of the equation is a sinusoidal function with frequency 4/π, we can guess a particular solution of the form
u_p(t) = A sin(4t) + B cos(4t)
Substituting this into the equation and equating coefficients, we get
16 A - 16 B + 8 A = 2, or A = 1/2
-16 A - 16 B + 8 B = 0, or B = -1/2
Therefore, the particular solution is
u_p(t) = 1/2 sin(4t) - 1/2 cos(4t)
The general solution is then
u(t) = c1 cos(2√2 t) + c2 sin(2√2 t) + 1/2 sin(4t) - 1/2 cos(4t)
We can use the initial conditions u(0) = -0.5 and u'(0) = 0 to determine the values of c1 and c2
u(0) = c1 + 1/2 = -0.5, or c1 = -1/2
u'(0) = -2√2 c1 + 2√2 c2 - 2 = 0, or c2 = 1
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The given question is incomplete, the complete question is:
A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4 sin 4t. If the mass is pulled down 6 in. and then released, determine the position of the mass at any time t. (Use g = 32 ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)
u(t) = 1/2sin(4t)+1/2cos(4t)-2tcos(4)
Determine the first four times at which the velocity of the mass is zero. (Exclude t = 0 as trivial.)
Pls help! Due tmrrww!!
Answer:
1. basement: 1,4,7,10,13
middle : 2,5,8,11,14
top: 3,6,9,12,15
2. you just need to skip count ten times then we will have 30. so she lives in apartment 30.
Step-by-step explanation:
2 cities are 210 miles apart. If the distance on the map is 3 1/4 inches, find the scale of the map
The scale of the map = 682.5.
How would you define distance in one sentence?We kept a safe distance and followed them. She perceives a separation between her and her brother that wasn't there before. Although they were previously close friends, there was now a great deal of gap between them.
We must calculate the ratio of the distance shown on the map to the real distance between the cities in order to ascertain the scale of the map.
We are aware that there are 210 miles separating the two cities. Let x represent the precise location of this distance on the map. From that, we may establish the ratio:
Actual distance / Map Distance = 210 / x
The distance on the map is indicated as 3 1/4 inches, which is also known as 13/4 inches. When we enter this into the percentage, we obtain:
Actual distance divided by (13/4) = 210 / x
We can cross-multiply and simplify to find x's value:
Actual distance: 682.5 = x * 210 x = 3.25 when 210 * (13/4) Equals x.
Consequently, 3.25 inches on the map represent the actual distance between the cities. We can write: To determine the map's scale:
Actual distance divided by 1 inch on the chart equals 210 miles.
When we replace the values we discovered earlier, we obtain:
1 / 210 = 3.25 / scale
If we solve for the scale, we obtain:
scale = 682.5.
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Solve for the short leg of the 30-60-90 triangle.
Answer:
2
Step-by-step explanation:
The basic 30-60-90 triangle ratio is:
Side opposite the 30° angle: x
Side opposite the 60° angle: x√3
Side opposite the 90° angle: 2x
Here, the side opposite the 90° angle is 4.
This means that 2x = 4 and, thus, x = 2.
Since b is the side opposite the 30° angle, b = x, so it is 2.
find all real numbers k for which there exists a nonzero 2 dimensional vector bold v such that begin bmatrix 2
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The point on the parabola y=x^2 that is closest to the point (1,0) is (_______,_______). The distance between the two points is ________.
you can use Newtons's Method or Bisection to help but you don't have to.
Answer:Approximately
(0.58975,0.34781)
Step-by-step explanation:
If (x,y) is a point on the parabola, then the distance between (x,y) and (1,0) is:
√(x−1)2+(y−0)2=√x4+x2−2x+1
To minimize this, we want to minimize
f(x)=x4+x2−2x+1
The minimum will occur at a zero of:
f'(x)=4x3+2x−2=2(2x3+x−1)
graph{2x^3+x-1 [-10, 10, -5, 5]}
Using Cardano's method, find
x=3√14+√8736+3√14−√8736≅0.58975
y=x2≅0.34781
There are two coins. One of them is a biased coin such that P (head): P (tail) is 1 : 3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.
Answer:
Step-by-step explanation:
Let B be the event that the selected coin is biased, and F be the event that the selected coin is fair. Let H be the event that the coin toss shows a head.
We want to find P(B|H), the probability that the selected coin is biased given that the coin toss shows a head. By Bayes' theorem, we have:
P(B|H) = P(H|B) * P(B) / P(H)
We know that P(H|B) = 1/4 (since the biased coin has a probability of 1/4 of showing a head), and that P(B) = 1/2 (since there are two coins, one of which is biased).
To find P(H), we can use the law of total probability:
P(H) = P(H|B) * P(B) + P(H|F) * P(F)
P(H) = (1/4) * (1/2) + (1/2) * (1/2)
P(H) = 3/8
Putting it all together:
P(B|H) = P(H|B) * P(B) / P(H)
P(B|H) = (1/4) * (1/2) / (3/8)
P(B|H) = 1/3
Therefore, the probability that the selected coin is biased given that the coin toss shows a head is 1/3.
true/false. all of the following are things you can do when faced with any ethical dilemma as a managerial accountant except: always contact the board of directors first.
The statement " all of the following are things you can do when faced with any ethical dilemma as a managerial accountant except: always contact the board of directors first" is false because contacting the board of directors is not always necessary or appropriate when faced with an ethical dilemma as a managerial accountant
Contacting the board of directors is not always necessary or appropriate when faced with an ethical dilemma as a managerial accountant. While the board of directors may need to be informed in some situations, there are other steps that can be taken depending on the specific circumstances. For example, seeking guidance from a supervisor, consulting with a professional organization, or seeking legal advice may be more appropriate in some cases. The appropriate course of action will depend on the specific situation and ethical principles involved.
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The breadth of a rectangular playground is 5m shorter than its length. If its perimeter is 130m,find ids length and breadth.
Answer:
Length is 35 m and breadth is 30 mStep-by-step explanation:
Given,
The breadth of a rectangular playground is 5m shorter than its length.Perimeter is 130 mLet length be x and breadth (x - 5).
Perimeter of rectangle is calculated by :
[tex] \: \: \boxed{ \pmb{ \sf{Perimeter_{(rectangle)} = 2(l + b)}}} \\ [/tex]
On substituting the values we get :
[tex]\dashrightarrow \: \: 130 = 2(x + x - 5) \\ [/tex]
[tex]\dashrightarrow \: \: 130 = 2(2x - 5) \\ [/tex]
[tex]\dashrightarrow \: \dfrac{130}{2} = (2x - 5) \\ [/tex]
[tex]\dashrightarrow \: \: 65 = 2x - 5 \\ [/tex]
[tex]\dashrightarrow \: \: 65 + 5 = 2x \\ [/tex]
[tex]\dashrightarrow \: \: 70 = 2x \\ [/tex]
[tex]\dashrightarrow \: \: \frac{70}{2} = x \\ [/tex]
[tex]\dashrightarrow \: \: 35 = x \\ [/tex]
Hence,
Length = x = 35 m.Breadth = x -5 = (35 -5) = 30 mWhat is the probability that someone who does not take vitamins is a female? Round to three decimal places.
Female
Male
Total
(1 point)
O 0.374
O 0.139
O 0.080
O 0.626
Takes vitamins
248
145
193
Does not take vitamins
40
67
107
Total
288
212
500
Answer:
A) 0.374
Step-by-step explanation:
Let event A be that the person is female.
Let event B be that the person does not take vitamins.
[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Therefore, from the given table:
[tex]\sf P(A) = \dfrac{288}{500}=0.576[/tex]
[tex]\sf P(B) = \dfrac{107}{500}=0.214[/tex]
[tex]\sf P(A \cap B)=\dfrac{40}{500}=0.08[/tex]
To calculate the probability that someone is female (Event A), given that they do not take vitamins (Event B), use the conditional probability formula for A given B:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\A given B:\\\\$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$\\\end{minipage}}[/tex]
[tex]\sf \implies P(A|B)=\dfrac{0.08}{0.214}=0.374\;(3\;s.f.)[/tex]
Bret needs to put a logo on a business card. He prints the logo the wrong way up by mistake. Bret needs to turn the logo the correct way up. What fraction does Bret need to turn the logo?
The fraction Bret needs to turn the logo is 1 / 2.
How to find the fraction Bret needs to turn the logo?Bret needs to put a logo on a business card. He prints the logo the wrong way up by mistake. Bret needs to turn the logo the correct way up.
Therefore, the fraction he needs to turn the logo can be represented as follows:
For a complete turning, it will be 360 degrees. according to the diagram he has already turned the logo 180 degrees.
Therefore, for Bret to turn the logo correctly, he needs to turn it 180 degrees.
Hence, the fraction he needs to turn the logo is as follows:
180 / 360 = 18 /36 = 1 / 2
Hence, Bret needs to turn the logo half way(1 / 2)up.
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9x+6=24
8x-4=28
-18-x=57
-4-8x=8
3x+0.7=4
Answer:
Step-by-step explanation:
To solve each of these equations, we need to isolate the variable (x) on one side of the equation. Here are the steps to solve each equation:
9x + 6 = 24
Subtract 6 from both sides:
9x = 18
Divide both sides by 9:
x = 2
Therefore, the solution to the equation is x = 2.
8x - 4 = 28
Add 4 to both sides:
8x = 32
Divide both sides by 8:
x = 4
Therefore, the solution to the equation is x = 4.
-18 - x = 57
Add 18 to both sides:
-x = 75
Multiply both sides by -1:
x = -75
Therefore, the solution to the equation is x = -75.
-4 - 8x = 8
Add 4 to both sides:
-8x = 12
Divide both sides by -8:
x = -1.5
Therefore, the solution to the equation is x = -1.5.
3x + 0.7 = 4
Subtract 0.7 from both sides:
3x = 3.3
Divide both sides by 3:
x = 1.1
Therefore, the solution to the equation is x = 1.1.
Which of the ten basic functions in
our toolkit have all real numbers for
their range?
The functions that have all real numbers for their range are the ones in the option B.
Which set of ten basic functions has all real numbers for their range?Remember that for a function y = f(x), we define the range as the set of possible outputs of the function, that is, possible values of y.
Here we can see a lot of functions, first, the option with the absolute value function can be discarded because we know that:
|x| ≥ 0
So it never takes negative values.
We also can discardthe option with the sine and cosine, because the range of these two functions is [-1, 1].
The only remaining option is B, and the range of these 3 functions is (-∞, ∞), so that is the correct option in this case.
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find an ordered pair (x, y) that is a solution to the equation. -x+6y=7
Step-by-step explanation:
(-1, 1) is a solution.
because
-(-1) + 6×1 = 7
1 + 6 = 7
7 = 7
correct.
every ordered pair of x and y values that make the equation true is a solution.
(5, 2) would be another solution. and so on.
WILL GIVE BRAINLIEST NEED ANSWERS FAST!!!
Find the missing length indicated
Step-by-step explanation:
4)
based on similar triangles and the common ratio for all pairs of corresponding sides we know
LE/LM = LD/LK = DE/EM
because E and D are the midpoints of the longer sides, all of these ratios are 1/2.
1/2 = DE/8
8/2 = 4 = DE
5)
same principle as for 4)
BQ/BA = BR/BC = QR/AC
again, Q and R are the midpoints, so all these ratios are 1/2.
1/2 = QR/10
QR = 10/2 = 5
A rectangular fish tank 60 cm x 15 cm x 34 cm is 13 full of water. Find the volume of water needed to fill the tank completely.
Step-by-step explanation:
The volume of the rectangular fish tank is:
V = l x w x h = 60 cm x 15 cm x 34 cm = 30,600 cm³
Since the tank is 1/3 full, the volume of water in the tank is:
V_water = (1/3) x V = (1/3) x 30,600 cm³ = 10,200 cm³
To find the volume of water needed to fill the tank completely, we can subtract the volume of water already in the tank from the total volume of the tank:
V_needed = V - V_water = 30,600 cm³ - 10,200 cm³ = 20,400 cm³
Therefore, 20,400 cm³ of water is needed to fill the tank completely.
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.
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If the triangles above are reflections of each other, then ∠D ≅ to:
A) ∠F.
B) ∠E.
C) ∠C.
D) ∠A.
E) ∠B.
Answer:
D I believe
Step-by-step explanation:
consider the funciton f given by f(t)=log49(t7). find values for a and b such that f(t)=a+logb(t).
The values for a and b such that f(t) = a + logb(t) are,
a = log(1/log(49))
b = 49
Therefor
We can start by simplifying the expression for f(t)
f(t) = log49(t7)
f(t) = log(t7)/log(49) [Using the change of base formula]
Now we can rewrite f(t) as:
f(t) = log(t)/log(b) + a [Using the logarithmic properties log(ab) = log(a) + log(b)]
Comparing this expression with f(t) = a + logb(t), we can see that:
a = log(1/log(49)) [since log(b) = 1/log(49)]
b = t
Therefore, we have
f(t) = log(t7)/log(49) = log(t)/log(b) + log(1/log(49))
= log(t)/log(49) + log(1/log(49))
= log(1/log(49)) + log(t)/log(49)
So, a = log(1/log(49)) and b = 49.
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each of the cars on the left has th esame solution as on of the card ont the right find the cards with macthing solutions to coplete the sentece below.[tex]6x - 72 = -18[/tex]
Answer:
x=9
Step-by-step explanation:
this is solved by using cover and cancel so we can isolate the x variable
1) first add 72 to both sides.
6x=54
2) second divide both sides by 6
3) x=9
5. Which of these statistics is used in basketball as an all-in-one rating of how well a player performs per minute they play?
O A. Wins above replacement (WAR)
O B. Field goal percentage (FG%)
O C. Double doubles (DD2)
OD. Player efficiency rating (PER)
Answer:
Player Efficiency Rating (PER)
Step-by-step explanation:
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is Player Efficiency Rating (PER).
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is the Player Efficiency Rating (PER). So, correct option is D.
PER is a widely used metric that quantifies a player's overall performance by taking into account various statistical categories and normalizing them based on playing time.
PER evaluates a player's contributions in areas such as points, rebounds, assists, steals, blocks, and turnovers. It considers both positive and negative statistical events and provides a single numerical value that represents a player's efficiency on the court. A higher PER indicates a more productive player.
On the other hand, Wins Above Replacement (WAR) is a metric commonly used in baseball to estimate the number of wins a player contributes to their team compared to a replacement-level player.
Field Goal Percentage (FG%) measures the accuracy of a player's shooting by calculating the percentage of successful field goal attempts. Double doubles (DD2) count the number of games in which a player achieves double-digit totals in two statistical categories.
Among the options listed, Player Efficiency Rating (PER) is specifically designed to assess a player's overall performance per minute played in basketball.
So, correct option is D.
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Find the measures of angles 1 through 5 in the figure shown !
Answer:
55 degrees angles on a rights angle triangle. 1 and 3 they are equal cause they are vertical opp angles 55 degrees
Let V be a 3 dimensional vector space with A and B its subspace of dimension 2 and 1 respectively if A
∩
B
=
0
then A
V=A-B
B
V=A+B
C
V=AB
D
none of the above
The 3-dimensional vector space represented in the form subspace dimensions A and B is given by option B. V = A + B.
V be 3-dimensional vector space.
Subspace of dimensions of A and B are 2 and 1 respectively.
And A ∩ B = 0.
It follows that every vector in A is linearly independent of every vector in B.
This implies,
Any vector v in V can be expressed uniquely as a sum of a vector in A and a vector in B.
Let v be an arbitrary vector in V.
A has dimension 2, it has a basis of two linearly independent vectors.
Let {a1, a2} be such a basis.
B has dimension 1, it has a basis consisting of a single nonzero vector b.
Then, any vector v in V can be expressed uniquely as
v = c1a1 + c2a2 + cb,
where c1, c2, and c are scalars.
Thus,
V = A + B.
Therefore, the correct answer to represents 3 dimensional vector space V as option(B). V = A + B.
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