This sketch represents Terry on horizontal ground, flying a kite K. an imaginary right
angled triangle TKZ can be drawn. The string TK is 18.2m long and makes an angle of
72 with the horizontal TZ.
Work out the value of

The coordinate vector [x]B of the vector x relative to the given basis B is [-2] [2] that is option C.

To find the coordinate vector [x]B of the vector x relative to the basis B, we need to express x as a linear combination of the basis vectors b1 and b2.

Given:

b1 = [5]

[-1]

b2 = [-11]

[1]

x = [-6]

[-19]

To find the coefficients of the linear combination, we solve the system of equations:

x = c1 * b1 + c2 * b2

where c1 and c2 are the coefficients.

Substituting the given values, we have:

[-6]

[-19] = c1 * [5] + c2 * [-11]

[4]

Solving this system of equations, we find that c1 = -2 and c2 = 2.

Therefore, the coordinate vector [x]B of the vector x relative to the basis B is:

[x]B = [-2]

[2]

To know more about vector,

https://brainly.com/question/31427002

#SPJ11

Answer:

J

Step-by-step explanation:

Using the cofunction identity

cosθ = sin(\(\frac{\pi }{2}\) - θ )

Then

\(\frac{1}{sin(\frac{\pi }{2}-0) }\)

= \(\frac{1}{cos0}\)

= \(\frac{1}{0.8}\)

= 1.25 → J

The value of 1/sin(\(\frac{\pi }{2}\) - θ) is 1.25.

The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown. Angles in the third quadrant, for example, lie between 180 degrees and 270 degrees.

Given

1/cosθ = 0.8

1/sin(\(\frac{\pi }{2}\) - θ) =?

By using quadrants in trigonometry

we know that sin(\(\frac{\pi }{2}\) - θ) = cosθ

= 1/sin(\(\frac{\pi }{2}\) - θ)

= 1/cosθ

= 1/0.8

= 1.25

1/sin(\(\frac{\pi }{2}\) - θ) = 1.25

Hence, the value of 1/sin(\(\frac{\pi }{2}\) - θ) is 1.25.

Learn more about four quadrants of trigonometry here

https://brainly.com/question/21864197

#SPJ2

Answer:

3.89

Step-by-step explanation:

To find the price per quart of the window cleaner, we need to first determine how many quarts the 3-gallon container contains. We can do this by converting the number of gallons to quarts using the conversion factor that 1 gallon is equal to 4 quarts.

3 gallons * 4 quarts/gallon = 12 quarts

Next, we need to divide the total cost of the window cleaner, $46.68, by the number of quarts to find the price per quart.

Price per quart = $46.68 / 12 quarts = $3.89/quart

Therefore, the price per quart of the window cleaner is $3.89.

Answer:

1/3

Step-by-step explanation:

3x3= 9

Make 3/9 a fraction and simplify it and it would give you 1/3

The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

Know more about the Maclaurin series here :

https://brainly.com/question/31683608

#SPJ11

The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

The complete question is

A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.

Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?

It is defined as the margin by which the values calculated will differ from the real values .

Let the chosen number is 95  %

95% Confidence Interval ,

\(\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\\)

Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043

The margin of error is given by  0.4043-0.3329

= 0.0357

Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

To know more about Margin of Error

https://brainly.com/question/10501147

#SPJ1

The number of different orders of top-three finishers in the free throw contest depends on the total number of participants. The specific number of participants is not provided in the given information.

To determine the number of different orders of top-three finishers, we need to know the total number of participants in the free throw contest. The order of finishers can be calculated using the concept of permutations, where the order matters.

If there are "n" participants, the number of different orders of top-three finishers can be calculated using the formula nP3, which represents the number of permutations of "n" objects taken 3 at a time. However, since the total number of participants is not provided in the given information, we cannot determine the exact number of different orders of top-three finishers.

To learn more about permutations click here:

brainly.com/question/29990226

#SPJ11

Hey there!

The answer is D

We solve this by multiplying the exponents, and we get 15:

3 x 5 = 15

So, the answer is 2^15

Hope it helps and have a great day!

The probabilities and the expected values are calculated below

Next cereal box wll contain blue or yellow

Here, we have

Yellow or blue = 15 + 5 = 20

Total = 50

So, we have

P(Yellow or blue) = 20/50

P(Yellow or blue) = 2/5

Arrival time before 7:30 am

Here, we have

Arrival time before 7:30 am = 7

Total time = 20

So, we have

P(Arrival time before 7:30 am) = 7/20

Team least likely

Convert the probabilities to decimal

So, we have

Nets = 0.67

Rockets = 0.5

Bucks = 0.8

Warriors = 0.375

This means that the team least likely to play in the championship game is 0.375

Section 7 in the game

Here, we have

P(7) = 35/250

In 150 times, we have

n(7) = 35/250 * 150

n(7) = 21

So, the number of times is 21

Expected students to eat chicken nuggets

Here, we have

P(Chicken) = 14/40

In 840 students, we have

n(Chicken) = 14/40 * 840

n(Chicken) = 294

Hence, the expected number of students to eat chicken nuggets is 294

Read more about probabilities at

https://brainly.com/question/251701

#SPJ1

Answer:

Because they can help with understanding

Answer:

When given a verbal or written word problem, it is important to be able to translate the words to a numerical expression so you can solve the problem.

Step-by-step explanation:

used a search engine

Answer:

8

Step-by-step explanation:

Answer:

what do you need to do?

Step-by-step explanation:

what is the Question

A) The measure of central tendency that best describes the data for time spent on the internet (min/day) is the median.

The median is the middle value in a set of data when the data is arranged in numerical order. In this case, the data arranged in numerical order is 38, 43, 48, 52, 65, 75, 120. The median value is 52, which is the middle value in the data set.

B) The measure of central tendency that best describes the data for the weight of books (oz) is the mode. The mode is the value that occurs most frequently in a data set. In this case, the data is 12, 10, 9, 15, 16, 10. The mode is 10, as it occurs twice in the data set and is the most frequent value.

Read more aboutarea of statistics here:https://brainly.com/question/29093686

#SPJ11

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

To learn more about logarithm click here: brainly.com/question/30226560

#SPJ11

Answer:

$178.50

Step-by-step explanation:

Big brain go thinky-think.

A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

___________________________

Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

5:2 means that it is divided into 7, and we do not move two positions from (7,7)

X axis

7- (-7) = 14

14/7 = 2

7-2*2 = 3

Y axis

7-(-6)= 13

13/7 =

7 - 2* (13/7) = 49/7 - 26/ 7 = 23/7 = 3 2/7

______________________________

Answer

(3, 3 2/7)

Answer:

I believe the answer is 103.

Step-by-step explanation:

Since line a is parallel to line b, angle m1 = angle m3.

Supposedly, angle m4 + angle m5 = 180 degrees, since it's a line. That also means that angle m3 + angle m4 = 180 degrees too.

That means:

angle m4 + angle m5 = angle m3 + angle m4

Subtract angle m4 from both sides of the equation.

You get,

angle m5 = angle m3.

Angle m5 is 103, and as we stated earlier, angle m3 = angle m1.

Thus, angle m1 = 103 degrees.

Except than x = 1, all real numbers fall within the function's domain.

Since there are no limitations on what we can substitute for x, the domain of a function, f(x), is all real numbers because any real numbers would make f(x) a defined function. As a result, when this is not the case, the domain of a function, f(x), is not all real numbers.

The rational function r(x) = 2x/(x-1) is defined as follows.

So, we set the denominator to zero and solve for x in order to determine the domain of r(x):

x - 1 = 0

x = 1

Hence, x = 1 is the only value of x that causes the denominator to equal 0. R(x) therefore has a domain of all real numbers other than x = 1.

We can express the domain as follows in interval notation:

(-∞, 1) U (1, ∞)

Except than x = 1, all real numbers fall within the function's domain.

To know more about function visit:-

https://brainly.com/question/14830166

#SPJ1

Question:

Which of the following correctly describes the domain of the function shown below?

r(x) = 2x x-1

A. {x:x0}

B. {x: x = 1}

c. x all .real .numbers}

D. xx1}

Answer:

1. x=14

2. x = -2

3.y=3

4.w=2

5.r=5

6. y = 6

7. x = -1

8. y = 1

Answer:

- 4

Step-by-step explanation:

Step 1:

5m = - 20

Step 2:

m = - 20 ÷ 5

Answer:

m = - 4

Hope This Helps :)

The given statement "The General Law of Multiplication is used to calculate the probability of the union of two events" is false because the General Law of Multiplication, also known as the Product Rule, is used to calculate the probability of the intersection of two events, not the union.

To calculate the probability of the union of two events, we use the Addition Rule, which states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection, if they are not mutually exclusive. If the events are mutually exclusive, then we can simply add their probabilities.

Therefore, it is important to understand the difference between the union and intersection of events and which rules to use for each type of probability calculation.

To know more about probability refer to-

https://brainly.com/question/30034780

#SPJ11

The number of pairs of parallel sides the rotated figure have is 2

Parallel sides or lengths are line segments or lines in the same plane that extend on both sides without intersecting

The shape is given as:

Shape = Rhombus

Rotation= 90 degrees counterclockwise rotation about the vertex G

The rotation transformation is a rigid transformation

This means that when a shape is rotated by 90 degrees counterclockwise about a vertex (in this case, the vertex G), the image of the rotation would have the same properties as the preimage

A rhombus has 2 pairs of parallel sides

This means that the number of pairs of parallel sides the rotated figure have will also be 2 (same as the original shape)

Hence, the number of pairs of parallel sides the rotated figure have is 2

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.

According to the question,

The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)²  = r².

        (x-0)² + (y-0)²  = -(√41)². This is not possible.

Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.

Learn more about circle here

https://brainly.com/question/14338946

#SPJ1

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

for similar questions on triangles.

https://brainly.com/question/1058720

#SPJ8

The solution for \( X \) is \( X = (A - D C)^{-1} D B \).

Assume \( A, B, C, D \), and \( X \) are \( n \times n \) matrices, and assume invertibility of matrices wherever needed. Then, the equation \( A X(B+C X)^{-1}=D \) can be solved for \( X \) by following these steps:

Step 1: Multiply both sides of the equation by \( (B+C X) \) to get rid of the inverse:
\( A X = D(B+C X) \)

Step 2: Distribute the \( D \) on the right side of the equation:
\( A X = D B + D C X \)

Step 3: Rearrange the equation to isolate \( X \) on one side:
\( A X - D C X = D B \)

Step 4: Factor out \( X \) on the left side of the equation:
\( (A - D C) X = D B \)

Step 5: Multiply both sides of the equation by the inverse of \( (A - D C) \) to solve for \( X \):
\( X = (A - D C)^{-1} D B \)

Therefore, the solution for \( X \) is \( X = (A - D C)^{-1} D B \).

Learn more about Invertibility of matrices

brainly.com/question/30453255

#SPJ11

Answer:

B.

Step-by-step explanation:

The first pattern is red, blue, and red, so the next one would be blue.

Next, we can see that the angles are 45 and then 90 degrees.

This means that the only reasonable answer is B.

Upon calculating the sum up to the appropriate term, we find that the sum is approximately 0.0713. So, the correct answer is a. 0.0713

It seems like there is a typo in the series notation. I assume the series you are referring to is ∑(2(-1)^n-1)/(12n^2 + 1) from n=1 to infinity. In this case, we can determine the sum using a well-known function and round the answer to four decimal places. Since the given series is an alternating series, we can use the Alternating Series Estimation Theorem to determine an approximation for the sum. The theorem states that if the absolute difference between consecutive terms is decreasing and the limit of the terms as n approaches infinity is zero, the approximation for the sum is accurate up to the first term that is less than or equal to the desired error bound (in this case, 0.0001). For this series, we can see that the absolute difference between consecutive terms decreases as n increases and the limit as n approaches infinity is zero. So, we can find the smallest value of n for which the term is less than or equal to 0.0001 and calculate the sum up to that term.

Learn more about sum here

https://brainly.com/question/29275646

#SPJ11

Answer:

B

Step-by-step explanation:

26% is close to 25%, which is equal to 1/4th.

You're adding to the number and removing from the percentage so it balances it out.

The estimation of 26% of 91 is  1/4 x 92.

The correct option is (B).

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

26% of 91

Now solving the above Quantity

= 26 /100 x 91

Now, We take 1 from 26 make it 25 and add that 1 to 91 make 92.

Then, 25 / 100 x 92

= 1/4 x 92

Hence, the estimation is 1/4 x 952.

Learn more about Percentage here:

https://brainly.com/question/29306119

#SPJ2  

8+8=16

-8 + (-8)= - 16

8+ (-8)=0

-8 + 0 = - 8

have a wonderful day

Hailey lee

Answer -8

Step-by-step explanation:

The total number of people who take the elevator is 19.

Based on the given two-way table, the number of people who take the elevator is found in the "Elevator" column, which includes both athletes and non-athletes.

Looking at the "Elevator" column, we can see that the number of athletes who take the elevator is 3, and the number of non-athletes who take the elevator is 16.

To find the total number of people who take the elevator, we add the number of athletes and non-athletes who take the elevator:

3 (athletes) + 16 (non-athletes) = 19

To learn more about elevator visit;

https://brainly.com/question/2076153

#SPJ11