Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 9x – 1702 – 20, 13x2 – 8x + 18 and 5x – 9x2 – 11.
a. The dimension of the subspace H is________
b. Is {9x - 17x2 - 20,13x2 - 8x +18,5x -9x2 -11} a basis for P2?________ Be sure you can explain and justify your answer.
c. A basis for the subspace H is {____________}. Enter a polynominal or a comma separated list of polynomials.

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:Domain = [-3, 1)\)

\(\qquad \tt \rightarrow \:Range = [-5 , 4]\)

____________________________________

\( \large \tt Solution \: : \)

Domain = All possible values of x for which f(x) is defined

[ generally the extension of function in x - direction ]

Range = All possible values of f(x)

[ generally the extension of function in y - direction ]

\( \large\textsf{For the given graph : } \)

\(\qquad \tt \rightarrow \: domain = [ -3, 1)\)

\(\qquad \tt \rightarrow \: range= [ -5,4]\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The perimeter of a shape is the measurement around its edge and it is 101.36 in.

We must sum up the lengths of the quadrilateral four sides to determine its perimeter. Since there are two of each side measurement, it is easy to accomplish this by simply adding the length and width and multiplying the result by two.

Perimeter of given shape = 18 + 27 +27 + perimeter of the arc

the perimeter of the arc = Perimeter of the semicircle = \(\pi r\)

Therefore the perimeter of the shape = 72 + 3.14 * 9 = 101.36 in.

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The distance the golfer has to originally hit the ball for it to go directly to the same position on the green is (B) d ≈ 313.087 yards.

The given parameters are:

Required:

To calculate the distance between the two locations:

According to cosine law, we have:

Where,

It gives,

Therefore, the distance the golfer has to originally hit the ball for it to go directly to the same position on the green is (B) d ≈ 313.087 yards.

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The complete question is given below:
On a dogleg golf hole, one golfer hits the ball 250 yards and then another 150 yards to reach the green. The angle between the two hits is equal to 100 degrees. How far would the golfer have to originally hit the ball for it to go directly to the same position on the green?

(A) 98,023.613 yards

(B) 313.087 yards

(C) 142.570 yards

(D) 105.543 yards

The actual question is this:
Lines AC and BD intersect at point O.

Lines AC and BD intersect at point O.

If m∠AOD = (7x − 5)° and m∠BOC = (3x + 15)°, what is m∠BOC?


The answer is 30°

Hope that helps!

The measure of angle BOC is 30 degrees.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

Given the angle, AOD and BOC are opposite angles.

Since opposite angles are the same

So,

∠BOC = ∠AOD

3x + 15 = 7x - 5

7x - 3x = 15 + 5

4x = 20

x = 5

Now,

∠BOC = 3(5) + 15 = 30

Hence "The measure of angle BOC is 30 degrees".

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Given question is incomplete the complete question with the figure is ;

Lines AC and BD intersect at point O.

If m∠AOD = (7x − 5)° and m∠BOC = (3x + 15)°, what is m∠BOC?

In the given public good provision game, player 1's expected payoff for contributing and not contributing depends on player 2's cutoff point (C*₂). When player 1 contributes, their payoff is v - C₁ if C₁ < C*₂, and 0 if C₁ ≥ C*₂. When player 1 does not contribute, their payoff is always 0.

In this public good provision game, player 1's decision to contribute or not contribute depends on their private cost, C₁, and player 2's cutoff point, C*₂. If player 1 contributes, they incur a cost of C₁ but gain access to the public good valued at v dollars. However, if C₁ is greater than or equal to C*₂, player 1's expected payoff for contributing would be 0 since player 2 would not contribute.

On the other hand, if player 1 does not contribute, their expected payoff is always 0, as they neither incur any cost nor receive any benefit from the public good. Therefore, player 1's expected payoff for not contributing is constant, irrespective of the cutoff point.

To determine player 1's expected payoff for contributing, we consider the case when C₁ is less than C*₂. In this scenario, player 2 contributes to the public good, allowing both players to consume it. Player 1's payoff would then be v - C₁, which represents the value of the public good minus their cost of contribution. However, if C₁ is greater than or equal to C*₂, player 1's contribution would be futile, as player 2 would not contribute. In this case, player 1's expected payoff for contributing would be 0, as they would not gain access to the public good.

In summary, player 1's expected payoff for contributing is v - C₁ if C₁ < C*₂, and 0 if C₁ ≥ C*₂. On the other hand, player 1's expected payoff for not contributing is always 0. Therefore, when C₁ is low, player 1 would prefer to contribute, as long as the cost of contribution is less than player 2's cutoff point.

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Answer: Slope intercept form

Step-by-step explanation:

m=slope

b=y-intercept

Answer:

Slope: 6

Y-intercept: 4

Equation: y=6x+4

Step-by-step explanation:

For slope you do change in y over change in x so its 10-4/1-0 in this case which gets you 6/1 or 6 for your slope

It crosses the y-axis at (0,4) so your y-intercept is 4

The base equation is y=mx+b m is slope b is y-intercept so you plug in your values and get y=6x+4

Answer:

6 in

Step-by-step explanation:

The angle bisector divides the opposite side into segments that are proportional to the other 2 sides.

let the third side of the triangle be x , then

\(\frac{9}{x}\) = \(\frac{6}{4}\) ( cross- multiply )

6x = 36 ( divide both sides by 6 )

x = 6

The third side of the triangle is 6 in

Answer: 1/10 is literally only one out of 10. the fraction to a decimal is 0.1 so, 3 x 0.1 is 0.3 and 3 x 10 is 30.

0.3 is less than 30.

Step-by-step explanation:

Answer:

The identity property of multiplication, also called the multiplication property of one says that a number does not change when that number is multiplied by 1. Ex. 12x1=12

Answer:

Identity property of multiplication: The product of 1 and any number is that number. For example, 7 × 1 = 7 7 \times 1 = 7 7×1=77, times, 1, equals, 7.

Step-by-step explanation:

PLZZ MARK AS BRAINLIEST!!!!

Answer:

The perimeter of the rectangle is 70 cm

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ Two sides of a rectangle are in the ratio 3 : 4

→ Let the width is the shorter side and the length is the longer side

∴ The ratio between the width and the length is 3 : 4

∵ The longer side is 20 cm

∴ The length of the rectangle = 20 cm

→ By using the ratio method

→  width  :  length

→  3          :  4

→  w         :  20

→ By using cross multiplication

∵ w × 4 = 3 × 20

∴ 4w = 60

→ Divide both sides by 4

∴ w = 15

∴ The width of the rectangle = 15 cm

∵ The perimeter of the rectangle = 2(length + width)

∴ The perimeter of the rectangle = 2(20 + 15)

∴ The perimeter of the rectangle = 2(35)

∴ The perimeter of the rectangle = 70 cm

∴ The perimeter of the rectangle is 70 cm

Answer:

A

Step-by-step explanation:

Using the Sine rule in Δ ABC

∠ B = 180° - (30 + 50)° = 180° - 80° = 100° ( sum of angles in triangle ) , then

\(\frac{13}{sin100}\) = \(\frac{BC}{sin30}\) ( cross- multiply )

BC × sin100° = 13 × sin30° ( divide both sides by sin100° )

BC = \(\frac{13sin30}{sin100}\) ≈ 6.6 ( to the nearest tenth )

The minimum number of coin tosses required to have more than a 50% chance of getting at least one head is two.

The possible outcomes of flipping a coin:

If the coin is flipped more than once, there are only two possible outcomes: H or T, whereby each outcome has a 50% chance of occurring.

So let us say that the coin is flipped twice, we have four possible outcomes:

In this case, the only outcome that do not have at least one head is TT.

In conclusion,  the probability of getting at least one head is 1 - (1/2 x 1/2) = 3/4, or 75% which is greater than 50%

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Write a function which accepts a nested list of integers and returns the count of all the integers greater than 0. This can be done in a recursive manner by first flattening the nested list and then counting all the integers that are greater than 0.The function can be implemented using any programming language such as Python, Java, or C++.

A nested list is a list that contains other lists. It is a common data structure used in programming languages such as Python, LISP, and Scheme. The task at hand is to write a function that accepts a nested list of integers and returns the count of all the integers greater than 0. To accomplish this task, we can use a recursive approach. The first step is to flatten the nested list into a single list. This can be done by recursively iterating through the list and adding each element to a new list.

Once we have a single list, we can count all the integers that are greater than 0 using a loop or list comprehension. Finally, we return the count as the output of the function. Here is an implementation of the function in Python: def count_positive(lst): flat_list = [] for i in lst: if type(i) == list: flat_list. extend(count _ positive(i)) else: flat _ list. append(i) return len([x for x in flat_list if x > 0])The above function takes a nested list as an argument and returns the count of all the integers greater than 0.

The function first flattens the list and then counts all the integers that are greater than 0 using a list comprehension. The function can be tested using the example given in the question:>>> count_positive([[6,[-3,[1]]],[4,-1,[[0],5]]])5In the above example, there are five integers greater than 0 in the nested list. Therefore, the output of the function is 5.

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a. The formula B = 703w/h^2 can be solved for w by rearranging the equation as w = B * h^2 / 703.
b. For a person who is 64 inches tall and has a body mass index of 21.45, the weight can be calculated by substituting the values into the formula w = B * h^2 / 703, where B is 21.45 and h is 64 inches.

a. To solve the formula B = 703w/h^2 for w, we can rearrange the equation to isolate w on one side of the equation. Multiply both sides of the equation by h^2, then divide both sides by 703. The resulting equation is w = B * h^2 / 703.
b. To find the weight of a person who is 64 inches tall and has a body mass index of 21.45, we can substitute the values into the formula w = B * h^2 / 703. In this case, B is 21.45 and h is 64 inches. Plugging these values into the equation, we get w = 21.45 * 64^2 / 703. Evaluating this expression will give us the weight in pounds.

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do you mean

6+(-5-7)/2-8(3)?

-5-7= -12

6+-12/2-8(3)

8(3)=24

6+-12/2-24

-12/2=-6

6+-6-24

6+-6=0

0-24= 24

Answer:

Subtract 7 from –5.

Step-by-step explanation:

7 is an outlier.

Data:

7, 58, 62, 68, 65, 86, 72, 76, 74

Let us rearrange the data

7, 58, 62, 65, 68, 72, 74, 76, 86

To know if a number is an outlier, it is usually either:

1. Lower Outlier Threshold = Less than Q1 + 1.5 x IQR

2. Higher Outlier Threshold = Greater than Q3 - 1.5 x IQR

where IQR is the interquartile range

Q1 is the First Quartile

Q3 is the Third Quartile.

Now we have to find Q1, Q3, and IQR.

The formulas are given below:

n = 9 (according to the question)

Thus, with these formulas, we can find the Q1, Q3, and IQR

Therefore, the first Quartile Q1 is in the third position in the arranged data:

7, 58, 62, 65, 68, 72, 74, 76, 86

Q1 = 62.

Now we solve for Q3:

Therefore, the third Quartile Q3, is in the 8th position in the arranged data:

7, 58, 62, 65, 68, 72, 74, 76, 86

Q3 = 76

Now, we can calculate IQR as:

Q3 - Q1 = 76 - 62 = 14

Thus, IQR = 14

Now we can test which values are outliers.

We have a value of 7 which is much lower than the Lower Outlier threshold value.

Thus 7 is an outlier.

Now let us check for the HIgher Outlier:

We have no value from the dataset that is greater than 97, thus there is no upper outlier

Therefore, the final answer is = 7

Answer:

Step-by-step explanation:

it woulkd be 200 gallons

Answer:

The current of the circuit at t = 0 is equal to 0.

If we take the limit as t approaches infinity, the current is equal to ε/R or V/R.

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:

\(\displaystyle (cu)' = cu'\)

Derivative Property [Addition/Subtraction]:

\(\displaystyle (u + v)' = u' + v'\)

Derivative Rule [Basic Power Rule]:

Slope Fields

Integration

Integration Rule [Reverse Power Rule]:

\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Rule [Fundamental Theorem of Calculus 1]:

\(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:

\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Method: U-Substitution

Electricity

Ohm's Law: V = IR

Circuits

Step-by-step explanation:

*Note:

In the given equation, our variable of differentiation is x. I will rewrite this as current I for physics notation purposes.

Step 1: Define

Identify given.

\(\displaystyle L \frac{dI}{dt} + RI = V\)

[Assuming switch S is closed] Recall that an inductor is used in a circuit to resist change. After a long period of time, when it hits steady-state equilibrium, we expect to see the inductor act like a wire.

Step 2: Find Current Expression Pt. 1

Step 3: Find Current Expression Pt. 2

Identify variables for u-substitution.

Step 4: Find Current Expression Pt. 3

Recall that our initial condition is when t = 0, denoted as u₀, and we go to whatever position u we are trying to find. Also recall that time t always ranges from t = 0 (time can't be negative) and to whatever t we are trying to find.

Recall that our initial condition u₀ (derived from Ohm's Law) contains only the voltage across resistor R, where voltage is supplied by the given battery. This is because the current is stopped once it reaches the inductor in the circuit since it resists change.

Step 5: Solve

If we are trying to find the strength of the electrical current I at t = 0, we simply substitute t = 0 into our current function:

\(\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\I(0) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(0)} \\& = \boxed{\bold{0}}\end{aligned}\)

If we are taking the limit as t approaches infinity of the current function I(t), we are simply just trying to find the current after a long period of time, which then would just be steady-state equilibrium:

\(\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\\lim_{t \to \infty} I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(\infty)} \\& = \boxed{\bold{\frac{\mathcal E}{R}}}\end{aligned}\)

∴ we have found the current I at t = 0 and the current I after a long period of time and proved that an inductor resists current running through it in the beginning and acts like a wire when in electrical equilibrium.

---

Topic: AP Physics C - EMAG

Unit: Induction

Answer:

b

Step-by-step explanation:

Totals to 77 minutes after 9:00 am.

answer:

c. just after 10:30 am

explanation:

add 15 + 15

30

+ 8 x 4

30

add 10

30 + 32 + 10 = 72 minutes

plus 5 min with coach

78 minutes

which is just past 10:00 am and to be exact it is 10:18 am

then it takes 15 minutes to get home

so milo gets home just after 10:30 am!

hope this helped <3 also if wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)

Answer:

4th option

Step-by-step explanation:

given

sinΘ = \(\frac{5}{13}\) and cosΘ = \(\frac{12}{13}\) , then

( \(\frac{5}{13}\) )² + ( \(\frac{12}{13}\) )²

= \(\frac{25}{169}\) + \(\frac{144}{169}\)

= \(\frac{25+144}{169}\)

= \(\frac{169}{169}\)

= 1

showing sin²Θ + cos²Θ = 1

The correct relationship between Student's t-distribution and the standard normal distribution is option B: as the sample size approaches infinity, the Student's t-distribution approaches the standard normal distribution.

The sample mean's estimation of the population mean is less precise and the sample mean's distribution is more erratic when the sample size is small. Because the distribution of t-values is more skewed as a result, the student's t-distribution has thicker tails than the traditional normal distribution.

The sample mean's distribution, however, narrows as sample size increases, making it a more precise reflection of the population mean. The student's t-distribution resembles the traditional normal distribution as a result of the narrowing of the t-value distribution.

For the ordinary normal distribution to accurately approximate the student's t-distribution in practice, a sample size of 30 or more is frequently thought to be sufficient.

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Correct question:

what is the relationship between student's t distribution and the standard normal distribution?

student's t will approach to standard normal distribution as the sample size approachs 0.

student's t will approach to standard normal distribution as the sample size approachs infinite

standard normal distribution will approach to student's t distribution as the sample size approachs 0

standard normal distribution will approach to student's t distribution as the sample size approachs infinite.

Answer:

m<HJF = \(56^{o}\)

Step-by-step explanation:

From the given diagram, ΔFHJ is similar to ΔFEG. So that;

m<HJF = m<EGJ

⇒ 10x + 36 = 6x + 44

10x - 6x = -36 + 44

4x = 8

x = \(\frac{8}{4}\)

x = 2

Substitute the value of x in the expression for m<HJF to have,

m<HJF = 10x + 36

           = 10(2) + 36

           = 20 + 36

m<HJF = \(56^{o}\)

The measure of angle HJF is \(56^{o}\).

There is no value for which the missing place should be filled in order to have exactly one solution.

A Linear equation may be defined as the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Since the equation only has one variable that is x then the linear equation will be rightly called as linear equation in one variable. We are given the equation -2(2x - _) + 1 = 17 - 4x. We solve the equation further which results as

-4x - _ + 1 = 17 - 4x

As we can see that there is -4 in both the right-hand side as well as the left-hand side both of them gets cancelled out.

- _ +1 = 17

As we can see that there is no variable left in order to find the value so any value of missing space will not be able to give any solution.

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To find the probability distribution for Y, the number of errors detected by the auditor, we can use the binomial distribution formula. The binomial distribution is used when there are only two possible outcomes, success or failure, and each trial is independent.

In this case, the probability of success (detecting an error) is 5% or 0.05, and the probability of failure (not detecting an error) is 1 - 0.05 = 0.95.

a. To find the probability distribution for Y, we can use the formula for the binomial distribution:

P(Y = y) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (3 in this case), k is the number of successes (errors detected), p is the probability of success (0.05), and (nCk) is the combination formula.

For y = 0:
P(Y = 0) = (3C0) * (0.05)^0 * (0.95)^(3-0) = (1) * (1) * (0.95)^3 = 0.857375

For y = 1:
P(Y = 1) = (3C1) * (0.05)^1 * (0.95)^(3-1) = (3) * (0.05) * (0.95)^2 = 0.135375

For y = 2:
P(Y = 2) = (3C2) * (0.05)^2 * (0.95)^(3-2) = (3) * (0.05)^2 * (0.95)^1 = 0.007125

For y = 3:
P(Y = 3) = (3C3) * (0.05)^3 * (0.95)^(3-3) = (1) * (0.05)^3 * (0.95)^0 = 0.000125

So the probability distribution for Y is:
Y = 0 with probability 0.857375
Y = 1 with probability 0.135375
Y = 2 with probability 0.007125
Y = 3 with probability 0.000125

b. To construct a probability histogram for p(y), you can create a bar graph where the x-axis represents the number of errors detected (Y) and the y-axis represents the probability (P(Y = y)). Each bar will have a height corresponding to the probability.

c. To find the probability that the auditor will detect more than one error, we need to calculate the sum of the probabilities for Y = 2 and Y = 3:

P(Y > 1) = P(Y = 2) + P(Y = 3) = 0.007125 + 0.000125 = 0.00725

Therefore, the probability that the auditor will detect more than one error is 0.00725.

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To determine if the experimental probability for getting a 6 is close to the theoretical probability, we need to compare the observed frequency of rolling a 6 to the expected probability based on a fair six-sided die.

In the given list of rolls, we have a total of 20 rolls. To calculate the experimental probability of rolling a 6, we count the number of times a 6 appears and divide it by the total number of rolls.

From the list, we can see that a 6 appears 6 times. Therefore, the experimental probability of rolling a 6 is:

Experimental probability = Number of 6's / Total number of rolls = 6/20 = 0.3

Now let's compare this experimental probability to the theoretical probability. In a fair six-sided die, each face has an equal chance of occurring, so the theoretical probability of rolling a 6 is 1/6 ≈ 0.1667.

Comparing the experimental probability of 0.3 to the theoretical probability of 0.1667, we can see that the experimental probability is higher than the theoretical probability for rolling a 6.

Therefore, the statement "the experimental probability for getting a 6 is close to the theoretical probability" is false. The experimental probability is higher than the theoretical probability in this case.

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Answer: 14 degree decrease

Step-by-step explanation:

8-14= -6

Answer: Only A and B

Step-by-step explanation:

opposite vertical angles are made by two intersecting lines