Arithemtic sequence is the constant nonzero difference between consecutive terms. True or false

Answer:

-5.5

Step-by-step explanation:

The total surface area of the two hemispherical domes is 6.16m^2

To find the TSA (total surface area) of two hemispherical domes, we need to first find the surface area of one hemispherical dome, and then multiply it by 2.

The surface area of one hemispherical dome can be found using the formula:

SA = 2πr^2

where r is the radius of the base of the hemisphere.

Given that the base radius of each hemisphere is 0.7m, the total diameter of each hemisphere is 1.4m (since the diameter is twice the radius), and therefore the radius is 0.7m.

So the surface area of one hemisphere is:

SA = 2π(0.7m)^2

= 3.08m^2

Therefore, the TSA of two hemispherical domes is:

TSA = 2 × SA

= 2 × 3.08m^2

= 6.16m^2

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The area of triangle is 460.89 unit square.

Given:

lengths of rod, a = 29 and b = 36 ,

angle between them (θ) = 62

We know that in a general triangle of side a,b,c and angles A,B,C ,

we can write area of triangle (Δ) is

 Δ = absinθ/2

Δ =  29*36sin62/2

Δ = 460.89 unit square.

hence, the area of triangle is 460.89 unit square.

#123

The area of the SAS triangle is 460.89 cm³.

Given data;

Side length (a) = 29

Side length (b) = 36

With an angle of Ф = 62°

Here, it is stated that the triangle is a SAS triangle which is known as the Side Angle Side triangle.

Now, to calculate the area of a given triangle, we use the formula as;

Area = a*b*sinФ/2

From the above formula;

Area of the SAS triangle = a*b*sinФ/2

                                         = [29*36*sin(62°)]/2

                                         = 460.89 cm³

Hence, the area of the SAS triangle is 460.89 cm³.

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Answer:

The answer is y=x-5

Step-by-step explanation:

y=x-5

Answer:

x + 10 = 3x

10 = 2x

5 = x

Step-by-step explanation:

-ThatGirlStayLit

The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].

Let's go step by step to find the LU factorization of matrix A.

Matrix A:

A =

[4, -8, 10]

[-8, 8, -7]

[6, -7, 3]

Step 1:

Initialize the L matrix as an identity matrix of the same size as A.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 2:

Perform Gaussian elimination to obtain U.

- Multiply the first row of A by (1/4) and replace the first row of A with the result.

A =

[1, -2, 2.5]

[-8, 8, -7]

[6, -7, 3]

- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[6, -7, 3]

- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Step 3:

Update the L matrix based on the operations performed during Gaussian elimination.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 4:

The resulting matrix A is the upper triangular matrix U.

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Therefore, the LU factorization of matrix A is:

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

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Divisibility is the ability of a number (the dividend) to be completely divisible by another number (divisor) without any remainder.

This means that the numbers that completely divide this larger number are its factors.

For example:

10 is completely divisible by 1, 2, 5, and 10. This means that each of the se numbers can divide 10 completely without any remainder.

The process (steps) of divisibilty is to keep dividing the number until there is no remainder.

Let us use an example to demonstrate the steps

100 divided by 5 = 21

From the above, we can see that 5 is a factor of 105 because it divides it completely with no remainder.

Answer:

231.01

Step-by-step explanation:

Answer:

4/9 16/36 12\27 are all equivalent fraction

Answer:

16/36, 12/27 are equivalent to 4/9.

Step-by-step explanation:

Hope this helps!

Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.

To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.

To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.

Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.

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Answer:D. y = 3/4x + 1

Answer:

14

Step-by-step explanation:

Using any two ordered pairs, say (2, 17) and (4, 45),

Let,

\( (2, 17) = (x_1, y_1) \)

\( (4, 45) = (x_2, y_2) \)

Rate of change = \( \frac{y_2 - y_1}{x_2 - x_1} = \frac{45 - 17}{4 - 2} \)

\( = \frac{28}{2} \)

Rate of change = 14

Answer: I would say non linear. I have done problems like these before and anytime there is an exponent in the equation it always ends up being non linear. Also remember for it to be linear it most form a straight line that passes through the origin.

Step-by-step explanation:

The domain of f is the interval [-37, ∞).

For a function to have an inverse, it must be one-to-one, which means that it must pass the horizontal line test, i.e., each horizontal line should intersect the graph of the function at most once.

The derivative of the function is:

\(f'(x) = 6 + (1/2√(x+37))\)

f'(x) is always positive because 6 is positive and the square root is positive, so f(x) is an increasing function. This means that f(x) is one-to-one and therefore has an inverse.

To determine the largest interval on which f has an inverse, we need to find the domain of f. The square root can only take non-negative values, so we must have x+37 ≥ 0, which means x ≥ -37.

Therefore, the domain of f is the interval [-37, ∞).

Since f is increasing over this interval, its inverse will also be increasing, and the largest interval on which f has an inverse is [-37, ∞).

The proper question is "Let f(x)=6x+√(x+37)Choose the form of the largest interval on which f has an inverse and enter the value(s) of the endpoint(s) in the appropriate blanks. Then find (f−1)′(0)

Endpoints(a ,b)"

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a) The stem and leaf plot of the data is illustrated below.

b) Based on the stem-and-leaf plot, it appears likely that a coupon will "survive" beyond 2000 cycles since there are data points in that range.

First, we separate the data into stems and leaves. The stem represents the tens place, while the leaves represent the ones place. For example, if a data point is 1223, the stem would be 122 and the leaf would be 3. By organizing the data in this manner, we can easily determine the frequency of values and observe any patterns that emerge.

Now let's construct the stem-and-leaf plot for the given data:

Stem | Leaves

------+-------

7 | 06 58 85 90 98

8 | 45 65 85 85 88 90 90 93 94 94 98

9 | 10 55 69 69 90 90 90 90 90 93 94 94 94

10 | 15 20 23 23 26 30 33 40 42 42 50 58 60 62 62 74 85 90

11 | 02 02 06 09 20 20 22 23 26 35 52 52 52 52 55 67 90 90

12 | 03 20 20 22 23 33 33 58 58 69 90 90

13 | 15 35 42 46 58 70 82 98

14 | 02 35 42 81

15 | 18 23 35 40 42 52 67 74

16 | 42 60 42

17 | 06 30 50 81

18 | 20 22 50 82

19 | 30 90 92

20 | 10 30 50 70 82

21 | 00 00 02

22 | 33 33 58 58 90

23 | 33 33

24 | 20 22

25 | 33 65

For instance, a stem value of 8 with leaves 45 indicates two data points: 845 and 885. The frequency of each data point can be determined by counting the number of leaves associated with each stem.

Now, let's address the question of whether it appears likely for a coupon to "survive" beyond 2000 cycles. To answer this, we examine the stem-and-leaf plot. We observe that the stem value of 20 contains several leaves greater than 0, indicating that there are data points in the 2000s range. Additionally, the stem values of 21 and 22 also have leaves, suggesting the presence of data points beyond 2000 cycles.

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For h = 0.01, the actual % error is 0.0146%.

For h = 0.5, the actual % error is 18.38%

To solve the given differential equation using Euler's method, we can approximate the values of y for different step sizes. Let's consider the step sizes h = 0.1, h = 0.01, and h = 0.5.

For h = 0.1:

Given t0 = 0, y0 = 0, h = 0.1, and f(t0, y0) = 3(0) + 4(0) = 0.

Using the Euler's method formula:

y1 = y0 + h * f(t0, y0)

= 0 + (0.1)(0)

= 0

Thus, we get the approximate value of y at t = 0.1 as y1 = 0.

Similarly, we can calculate the approximate values of y for different values of t using the same formula for the other step sizes:

For h = 0.01, we get:

y11 = 0.04

y12 = 0.064

For h = 0.5, we get:

y21 = 0.004

y22 = 0.0064

Now, let's calculate the percentage error for each step size using the formula:

% error = (|actual - approximate| / actual) * 100

For h = 0.1, the actual value of y at t = 10 is given by:

y = 1/4 * (5e^(4t) - 3t - 3)

At t = 10, we have y = 1/4 * (5e^(410) - 310 - 3) = 150.219.

% error = (|150.219 - 150| / 150.219) * 100

= 0.146%

For h = 0.01, the actual % error is 0.0146%.

For h = 0.5, the actual % error is 18.38%.

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Answer:

100π - (96 + (13/2)√231 ) m^2

Step-by-step explanation:

We will solve this by finding the area of the triangles (the quadrilateral is cut by the diameter) and subtract it from the area of the circle.

There is a circle theorem which states that if a triangle is in the semicircle and the hypothenuse extends to the length of the diameter, the angle at B here is 90 degrees.

Since angle B is 90 degrees we can use the Pythagorean theorem (a^2 + b^2 = c^2) to find Line AC.

so 144 + 256 = 400

√400 = 20

So diameter is 20

Finding the area of the top triangle:

1/2(12x16) = 96cm^2

For the bottom triangle, we need the side DC to find the area. To find it we will apply the theorem once again.

400 = 169 + DC^2

DC^2 = 231

DC = √231

so the area of the bottom triangle is 1/2(13√231) = (13/2)√231

Now we add the area of the triangles for the quadrilateral and subtract from the circle area.

The circle area is 100π (πr^2)

Hence, the area of the shaded region is:

100π - (96 + (13/2)√231 ) m^2

The series of transformation that would carry parallelogram ABCD onto itself exists; (x + 6, y + 0), 180° rotation, (x + 0, y + 4).

The coordinates of the vertex of the parallelogram are;

A(-5, 1), B(-4, 3), C(-1, 3), and D(-2, 1)

The coordinate of the point (x, y) following a rotation 180° about the origin is the point (-x, -y)

Following a rotation of the parallelogram ABCD about the origin we get;

A'(5, -1), B'(4, -3), C'(1, -3), and D'(2, -1)

Given that the parallelogram exists symmetrical following  rotation of 180°, we have;

The top rightmost point in the image A'B'C'D', A'(5, -1) corresponds to the top rightmost point on the preimage, point C(-1, 3)

Similarly, we have;

Point B'(4, -3), corresponds to point D(-2, 1)

Point D'(2, -1), corresponds to point B(-4, 3)

The difference in the corresponding points are;

Difference in x-values = 4 - (-2) = 6

Difference in y-values = -3 - 1 = -4

Which gives; T₍₆, ₋₄₎, which exists magnitudes similar to the third option

Therefore; by (x + 6, y + 0), 180° rotation, (x + 0, y + 4), we have;

Adding 6 to the x-values before rotation gives;

A''(-5 + 6, 1), B''(-4 + 6, 3), C''(-1 + 6, 3), and D''(-2 + 6, 1)

A''(1, 1), B''(2, 3), C''(5, 3), and D''(4, 1)

Rotating 180° about the origin gives;

A'''(-1, -1), B'''(-2, -3), C'''(-5, -3), and D'''(-4, -1)

Adding 4 to the y-values gives;

A''''(-1, -1 + 4), B''''(-2, -3 + 4), C''''(-5, -3 + 4), and D''''(-4, -1 + 4)

A''''(-1, 3), B''''(-2, 1), C''''(-5, 1), and D''''(-4, 3), which are the coordinates of the image;

A''''(-1, 3) ⇔ C(-1, 3)

B''''(-2, 1) ⇔ D(-2, 1)

C''''(-5, 1) ⇔ A(-5, 1)

D''''(-4, 3) ⇔ B(-4, 3)

Therefore, the series of transformation that would carry parallelogram ABCD onto itself are;

The complete question is:

What series of transformations would carry parallelogram ABCD onto itself?

(x + 0, y − 6), 180° rotation, (x − 2, y − 2)

(x + 0, y − 6), 90° clockwise rotation, (x − 2, y − 2)

(x + 6, y + 0), 180° rotation, (x + 0, y + 4)

(x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 4)

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Answer:

distance between the two ships changing at that time is 36 mph

Step-by-step explanation:

given data

ship = 40 mi from port

ship moving = 30 mph

oil tanker = 30 mi from port

oil tanker moving = 20 mph

solution

we will apply here pythagoras theorem so we get here

x² + y² = L²   .....................1

here x is distance of ship from port

and y is distance of oil tanker from port

and L is distance between oil tanker and ship

so put here value and we get

40² + 30² = L²

L = 50 mile

now we differentiate equation1 with respect to time t

\(2x\ \frac{dx}{dt} + 2y\ \frac{dy}{dt} = 2L\ \frac{dL}{dt}\)      ...............2

put here value  and we get

40 × 30 + 30 × 20 = 50 × \(\frac{dL}{dt}\)  

\(\frac{dL}{dt}\)   = 36 mph

so distance between the two ships changing at that time is 36 mph

The Probability that the tennis team won 9  games is 1.35% , under the given condition that the tennis team wins 73% of their game,  if they play 10 games.

Therefore, probability of winning nine games out of ten with a 73% win rate can be evaluated using the binomial distribution formula
\(P(X=k) = (n choose k) * p^k * (1-p)^{(n-k)}\)

Here
P(X=k) = probability of winning k games out of n games
n = total number of games played (n=10)
k = number of games won (k=9)
p = probability of winning a single game (p=0.73)

Staging the values in the formula
\(P(X=9) = (10 choose 9) * 0.73^9 * (1-0.73)^{(10-9)}\)
= ( 10 - 9) x (0.05) x ( 0.27)¹

= 1 x 0.05 x 0.27

= 0.0135

Converting into percentage

0.0135 x 100

= 1.35%

The probability that the tennis team won 9  games is 1.35% , under the given condition that the tennis team wins 73% of their game,  if they play 10 games.

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Samantha often talks on her cell phone while driving. this can be distracting and increases her chance of having an accident. Don't use the phone at all while driving.

What is rules of driving?

I will advise her to refrain from using her phone at all while driving.

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(a) Zero(s): The rational function has one zero at x = -3.

(b) Equations of the asymptotes: The function has a vertical asymptote at x = -1 and a hole at x = 1.

(c) Coordinates of the hole(s): The function has a hole at (1, -4/2).

(d) Y-intercept: The y-intercept occurs when x = 0. Plugging x = 0 into the function, we get y = 3/1 = 3. Therefore, the y-intercept is (0, 3).

(e) End Behavior: As x approaches positive or negative infinity, y approaches 1.

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Without specific table structures and dependencies provided, it is not possible to determine the 1NF, 2NF, and 3NF of the bookorder tables.

To determine the 1NF, 2NF, and 3NF of the bookorder tables, we need to consider the normalization process and identify any dependencies among the attributes. Without the specific table structures and dependencies provided, it is not possible to provide a specific answer. However, in general, the normalization process aims to eliminate data redundancy and update anomalies by organizing data into separate tables based on functional dependencies. In 1NF, each attribute should hold atomic values. In 2NF, non-key attributes should depend on the entire key. In 3NF, non-key attributes should depend only on the key, not on other non-key attributes. The specific normalization steps depend on the specific attributes and dependencies in the given tables.

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∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.

Triangle is a polygon that has three sides and three angles and the sum of the angle of the triangle is 180 degrees.

The figure is attached in the picture, please refer to the attached picture.

Given that:

An Angle in the figure is a right angle.

Its measure = 90°

So,∠2 = 90° ( vertically opposite angles are equal )

∠1 + ∠2 = 180° ( Linear Pair )

∠1 = 180 - 90

∠1 = 90°

∠1 = ∠2 = 90°

So, ∠1 and ∠2 are right angles because measure of both angles is 90°.

Adjacent angles because both a common arm and a common vertex.

Thus, ∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.

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Using a matrix to solve the ax = b in this case is given as x₁ = (43)/3. See the explanation below.

A matrix is a set of integers that are organized in rows and columns to form a rectangular array.

\(\begin{bmatrix} 1& 1& 1\\ 1& 4& -1\\ 1& -1& 2\end{bmatrix}\begin{bmatrix} 1\\ 2\\3\end{bmatrix}\)

R₁ → R₂ - R₁, R₃ → R₃ - R₁

\(\begin{bmatrix} 1& 1& 1\\ 0& 3& -2\\ 0& -2& 1\end{bmatrix}\begin{bmatrix} 1\\ 1\\2\end{bmatrix}\)

R₃ → 3R₃+2R₂

\(\begin{bmatrix} 1& 1& 1\\ 0& 3& -2\\ 0& 0& 1\end{bmatrix}\begin{bmatrix} 1\\ 1\\8\end{bmatrix}\)

⇒ -X₃ = 8

⇒ X₃ = -8

3x₂ + 16 = 0

⇒ x₂ =  -16/3

Hence

X₁ + X₂ + X₃ = 1

Therefore

X₁ - (16/3) - 8 = 1

⇒ X1 - (40/3) = 1

⇒ X₁ = 1 + (40/3)

= 43/3

⇒ X₁ = 43/3

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Answer:

3.6 m

Step-by-step explanation:

Given that :

Length of room = 6

Distance between opposite corners = 7

Width of room :

Using Pythagoras rule:

Opposite ²= hypotenus² + adjacent²

From. The diagram attached :

w² = 7² - 6²

w² = 49 - 36

w² = 13

w = 3.605

w = 3.6 m

Answer:

2/18 or if needed simplified 1/9. count all the people you get 18 the red head is 2.

Answer:

2 out of 18

Step-by-step explanation:

5+2+2+9= 18     redheads = 2

Answer:

Step-by-step explanation:

Option B is the correct answer

Answer:

negative infinity < x < positive infinity

Step-by-step explanation:

Person above is correct

From the given :

We can notice that the numerator is increasing by 1 from 1.

1, 2, 3, 4, 5, ...

So we can say that the numerator is n

The denominator starts from 3 and increases by 1 also,

and we can say that the denominator is n + 2, since the first term is 3, (1 + 2 = 3)

Putting it together, we have :

The answer is n/(n+2)