The geometric mean of a number and nine times the number is 30. What is the number?

The function you're referring to is likely a periodic function, as Fourier series expansions are typically used for periodic functions.

The convergence of the Fourier series expansion depends on the properties of the function, such as its continuity and differentiability.

If the function is continuous and piecewise smooth, then the Fourier series will converge to the function itself.

However, if the function is not continuous or not piecewise smooth, then the Fourier series may not converge uniformly.

In some cases, the Fourier series may converge to a different function altogether, known as a Fourier series of the function.

Therefore, to determine the value at which the Fourier series converges, you would need to analyze the properties of the function itself.

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Answer:

True

Step-by-step explanation:

8 + 5 = 13 + 5 = 18 + 5 = 23.

139.49

Step-by-step explanation:

using trig ratios.

tan=o/a

tan74°=n/40

40tan74°=n

use calculator to solve

=139.49

hope this helped :)

We will solve it using trigonometry formulas:

\(\boxed{ \begin{minipage}{5 cm} {Formulae:} \\ \\ $\bigstar\:\:\sin\theta\:=\:\frac{Opposite}{Hypotenuse} \\ \\ \bigstar\:\:\cos\theta\:=\:\frac{Adjacent}{Hypotenuse} \\ \\ \bigstar\:\:\tan\theta\:=\:\frac{Opposite}{Adjacent}$ \end{minipage} }\)

\(\rule{190pt}{2pt}\)

\(\bold{\ttt{Given,}}\\\)

\(\sf{Adjacent=40}\\ \sf{Opposite=n}\\ \sf{\theta=74\°\)

\(\bold{\ttt{Solution,}}\\\)

\({\tan\theta\:=\:\frac{Opposite}{Adjacent}}}\)

\({\sf{\tan74\:=\:\frac{n}{40}\)

\({\sf{\tan74\:x\:40\:=\:n\)

\({\sf{139.49\:=\:n\)

\({\sf{n\:\approx139.5\)

\(\boxed{\sf{n\:=\:139.5}}\)

Given

LM = 9, MN = 6x, and LN = 9x

Find

LN

Explanation

as we see LN = LM + MN

so ,

so , LN = 9x = 9 * 3 = 27

Final Answer

Therefore , the length of LN is 27

Step-by-step explanation:

To find the slope between two given points you use the equation:

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

(8,10) are \((x_{1},y_{1})\)

(16,24) are \((x_{2},y_{2})\)

After that you just plug in:

\(m=\frac{24-10}{16-8}\)

\(m=\frac{14}{8}\)

Simplify:

Answer:

The slope is \(\frac{7}{4}\) for #1

The parent function g(x) = |x| has the following graph:

then, given the function f(x) = -3 |x-2| + 4, we have to make a stretch and a reflection, with a traslation of 2 units to the right and 4 units up, to get the following graph:

Answer:

65 mph

Step-by-step explanation:

520/8 is 65

The term that refers to the fact that the distance between two or more points is equal is "equidistant".

In geometry, the concept of equidistance is important when dealing with circles, which are sets of points that are equidistant from a single point called the center. This property is what allows circles to be defined in terms of their radius, which is the distance between the center and any point on the circle.

Equidistance is also important in other areas of mathematics and science. For example, in physics, equidistant points can be used to define a plane or surface that is perpendicular to a given line or axis. This is useful in many applications, such as designing electronic circuit boards or constructing buildings.

The concept of equidistance is not limited to mathematics and science, however. It can also be applied in everyday life. For instance, if you are planning a road trip and want to visit several destinations that are equidistant from your starting point, you can use this information to help plan your route and estimate your travel time.

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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer:

Step-by-step explanation:

They have the same amount

The z-score for a 34-minute wait time in the cpt-memorial distribution is 1.1.

The z-score is a measure of how many standard deviations away from the mean a particular value falls. It is calculated by subtracting the mean from the value of interest and then dividing by the standard deviation.
In this case, we want to find the z-score for a 34 minute wait when the mean is 23 minutes and the standard deviation is 10 minutes.
z = (34 - 23) / 10
z = 1.1
So the z-score for a 34 minute wait is 1.1. This means that a 34 minute wait is 1.1 standard deviations above the mean wait time for cpt-memorial.
We can use this z-score to determine the percentage of wait times that fall below or above 34 minutes by using a standard normal distribution table. For example, a z-score of 1.1 indicates that approximately 86.42% of wait times are below 34 minutes, while 13.58% of wait times are above 34 minutes.
Overall, the z-score is a useful tool for understanding how a particular value relates to the distribution of a dataset.

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Answer:

C≈81.68cm is the answer.

Option b. f(x) = (x + 3)² - 1 represents the given graph based on its matching shape, vertex, and direction of opening.

Based on the options provided, the function that represents the graph above is b. f(x)=(x+3)²-1.

To determine the correct option, let's analyze the given graph. We observe that the graph is a parabola that opens upward and has its vertex at the point (-3, -1).

This vertex represents the lowest point on the graph.

The general form of a quadratic function (parabola) is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Comparing the graph to the options provided:

a. f(x) = -(x + 3)² - 1:

This option is incorrect because it has a negative sign in front of the squared term, which would result in a downward opening parabola. However, the given graph shows an upward opening parabola.

b. f(x) = (x + 3)² - 1: This option is correct because it matches the form of the graph, with the squared term (x + 3)² resulting in an upward opening parabola.

The vertex form of this function is f(x) = a(x - h)² + k, where (h, k) represents the coordinates of the vertex. In this case, (h, k) = (-3, -1).

c. f(x) = (x - 3)² - 1: This option is incorrect because it has a different value for the x-coordinate of the vertex.

The given graph shows the vertex at (-3, -1), not (3, -1).

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Answer:

Sine Formula or Sine Rule :

BC / sinA = AC / sinB

60 / sinA = 84.95 / sin(115°)

60 / sinA = 84.95 / 0.91

60 / sinA = 93.7

sinA = 60 / 93.7

sinA = 0.64

A = arc(sin0.64)

A = 39°48'30"

A ≈ 40°

Hence, the value of angle BAC is 40°

Answer:

-88

Step-by-step explanation:

If a=2, we can say that -\(a^{2}\) would be -4.

Secondly, if a=2 and b=-6 we can assume that 4ab would become -48.

Finally, if b=-6 we can say that -\(b^{2}\) would become -36.

Adding all of those up gives you -88, your answer.

Answer:

they will ring together at 7:50 am

Step-by-step explanation:

then again at 8:10,8:30,8:50 ect

Answer:

at 7:50 because after 10 min it will be 7:40 after more 10 min both clock's will ring as it is 7:50

explenation:

10 min from 7:30= 7:40. after more 10 min 7:40=7:50

20 min from 7:30 =7:50

thats my understanding

The area of the region is  rectangles

The given curves are y = x2 and y = 2 − x2. They intersect at x = 1, y = 1. See the graph below. The shaded region enclosed by the curves is the region whose area we wish to find.To find the area of the shaded region,

The left part of the region is the part bounded by the x-axis, the curve y = x2, and the line x = 1. This region is shown below. To find the area of this region, we integrate with respect to y from y = 0 to y = 1. Along the curve y = x2, the values of x are ± y1/2. So we have to integrate from x = −y1/2 to x = 1.

Thus the area of the right part of the region isThus the total area of the shaded region is Approximating rectangle The area of each approximating rectangle is given by height times width. Since we are dividing the region into two parts we

A typical rectangle is shown below. The value of x corresponding to the lower end of the rectangle is x = −y1/2 and the value of x corresponding to the upper end of the rectangle is x = 1. So the height of the rectangle is x2 and the width is Δy = 1/n. Therefore, the area of the rectangle isSince the rectangle is located below the curve, this approximation underestimates the true area of the region.

 Therefore, the area of the rectangle is Since the rectangle is located above the curve, this approximation overestimates the true area of the region. By computing the sum of the areas of all the approximating rectangles and taking the limit as n approaches infinity, we can find the exact area of the region.

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The standard error of the mean is 1.6

The confidence interval provides us a range in which an unknown population parameter is likely to fall. Generally, we use a 95% confidence level to calculate such a range. Also, a large sample size gives us the most accurate confidence intervals, however, it may not be suitable due to the cost and difficulty of taking numerous samples.

The information available is :

Mean (μ) = 40.75

Standard deviation (σ) = $7.00

Zα/2 = 1.96

Sample size (n) = 75

The margin of error is:

E = \(Z_\alpha /2*(\sigma/\sqrt{n} )\)

Plug all the values in above formula:

E = 1.96 × (7/\(\sqrt{75}\))

E = 1.5842

E ≅ 1.6

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==================================================

Work Shown:

4x^3 - 4

4(x^3 - 1)

4(x - 1)(x^2 + x + 1)

In the last step, I used the difference of cubes factoring formula which is

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Answer:

1) 2400 sq feet

2) $93.75

3) A (first answer)

Step-by-step explanation:

1) replace the 6 inches with 60 feet and 4 inches with 40 feet. We do this bc 1 inch = 10 feet. Then multiply 60 x 40 to get 2400 sq feet

2) we know that 25% off of 100 is 75. Then to add 25% back to 75 we find 25% of 75. 25% of 75 is 18.75. So we add 18.75 + 75 to get $93.75

3)

hope this helps <3

Answer:

The square root of 37 is approximately 6.0827. To determine which two integers it lies between, we can find the integers that are closest to the square root of 37.

The integer that is smaller than 6.0827 is 6, and the integer that is larger than 6.0827 is 7.

Therefore, the square root of 37 is between the integers 6 and 7.

The magnitude of the projection of f1 onto the line of action of f2 is 5.55.

The magnitude of the projection of f1 onto the line of action of f2 can be calculated using the dot product of the two vectors. The dot product is given by the formula:

f1 • f2 = |f1| |f2| cos θ

Where f1 • f2 is the dot product of f1 and f2, |f1| and |f2| are the magnitudes of f1 and f2 respectively, and θ is the angle between the two vectors.

To find the magnitude of the projection, we need to find the dot product of f1 and f2 and divide it by the magnitude of f2. The magnitude of the projection is given by:

Magnitude of the projection = (f1 • f2) / |f2|

Let's calculate it step by step:

Step 1: Calculate the dot product of f1 and f2:
f1 • f2 = (3.8 * 9.3) + (6.3 * 3.0) = 35.34 + 18.9 = 54.24

Step 2: Calculate the magnitude of f2:
|f2| = √(9.3^2 + 3.0^2) = √(86.49 + 9) = √95.49 = 9.772

Step 3: Calculate the magnitude of the projection:
Magnitude of the projection = (f1 • f2) / |f2| = 54.24 / 9.772 = 5.55

Therefore, the magnitude of the projection of f1 onto the line of action of f2 is 5.55.

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Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

Answer/Step-by-step explanation:

To complete the table, substitute the value of n into c = 10n + 19 to get its corresponding value.

Thus:

When n = 6,

c = 10(6) + 19

c = 60 + 19

c = 79

When n = 7

c = 10(7) + 19

c = 70 + 19

c = 89

When n = 9,

c = 10(9) + 19

c = 90 + 19

c = 109

This type of blinding is used to prevent a potential source of bias in the experiment. By keeping the subjects unaware of the treatment they are receiving, the researchers can eliminate the possibility of any psychological effects influencing the outcome of the study. This is particularly important in cases where a treatment is being evaluated for subjective outcomes such as pain, anxiety, or depression, as the subjects' expectations and beliefs can influence their perception of the treatment's effectiveness. By keeping the subjects blinded to their treatment, researchers can ensure that the results of the study are as unbiased as possible.

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(a) For the sequence x1[n], the conjugate symmetric part (xs[n]) is {-2.5 + j4, 2.5 - j6, 4, 2.5 + j6, -1.5 - j2}, and the conjugate antisymmetric part (xa[n]) is {0, -j7, 0, j7, 0}.

(b) For the sequence x2[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

(c) For the sequence x3[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

To determine the conjugate symmetric and conjugate antisymmetric parts of a sequence, we need to perform the following calculations:

(a) For the sequence x1[n] = {-1+j3, 2-j7, 4-j5, 3+j5, -2-j}, -2 ≤ n ≤ 2:

The conjugate symmetric part (xs[n]) can be calculated as:

xs[n] = (x[n] + x*[-n])/2

The conjugate antisymmetric part (xa[n]) can be calculated as:

xa[n] = (x[n] - x*[-n])/2j

Let's calculate them step by step:

For n = -2:

xs[-2] = (x[-2] + x*[2])/2 = (-1+j3 - 4+j5)/2 = (-5 + j8)/2 = -2.5 + j4

xa[-2] = (x[-2] - x*[2])/2j = (-1+j3 - 4+j5)/(2j) = (j2 - j2)/2 = 0

For n = -1:

xs[-1] = (x[-1] + x*[1])/2 = (2-j7 + 3-j5)/2 = (5 - j12)/2 = 2.5 - j6

xa[-1] = (x[-1] - x*[1])/2j = (2-j7 - 3+j5)/(2j) = (-j2 - j12)/2 = -j7

For n = 0:

xs[0] = (x[0] + x*[0])/2 = (4-j5 + 4+j5)/2 = 4

xa[0] = (x[0] - x*[0])/2j = (4-j5 - 4+j5)/(2j) = 0

For n = 1:

xs[1] = (x[1] + x*[-1])/2 = (3+j5 + 2+j7)/2 = (5 + j12)/2 = 2.5 + j6

xa[1] = (x[1] - x*[-1])/2j = (3+j5 - 2-j7)/(2j) = (j2 + j12)/2 = j7

For n = 2:

xs[2] = (x[2] + x*[-2])/2 = (-2-j + -1-j3)/2 = (-3 - j4)/2 = -1.5 - j2

xa[2] = (x[2] - x*[-2])/2j = (-2-j - -1+j3)/(2j) = (-j2 + j2)/2 = 0

Therefore, for the sequence x1[n], we have:

Conjugate symmetric part (xs[n]) = {-2.5 + j4, 2.5 - j6, 4, 2.5 + j6, -1.5 - j2}

Conjugate antisymmetric part (xa[n]) = {0, -j7, 0, j7, 0}

(b) For the sequence x2[n] = ej2πn/5 + ejπn/3:

Since this sequence is a complex exponential sequence, it does not contain any conjugate symmetric or conjugate antisymmetric parts. In other words, both xs[n] and xa[n] will be empty sets.

Conjugate symmetric part (xs[n]) = {}

Conjugate antisymmetric part (xa[n]) = {}

(c) For the sequence x3[n] = jcos(2πn/7) - sin(2πn/4):

Similarly, since this sequence is a combination of cosine and sine functions, it does not have any conjugate symmetric or conjugate antisymmetric parts.

Conjugate symmetric part (xs[n]) = {}

Conjugate antisymmetric part (xa[n]) = {}

In conclusion:

(a) For the sequence x1[n], the conjugate symmetric part (xs[n]) is {-2.5 + j4, 2.5 - j6, 4, 2.5 + j6, -1.5 - j2}, and the conjugate antisymmetric part (xa[n]) is {0, -j7, 0, j7, 0}.

(b) For the sequence x2[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

(c) For the sequence x3[n], both the conjugate symmetric part (xs[n]) and conjugate antisymmetric part (xa[n]) are empty sets.

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Answer:

ABC = 30

Step-by-step explanation:

The two angles are complementary so they add to 90 degrees

2x+14  + x+7  = 90

Combine like terms

3x+21 = 90

Subtract 21 from each side

3x+21-21 = 90-21

3x = 69

Divide by 3

3x/3 = 69/3

x = 23

ABC = x+7 = 23+7 = 30

Answer: used plot graph

Step-by-step explanation: sourced it with plot

The way to plot the graph is to find both x-intercept and y-intercept. (Unless if it's a polynomial function which you need to find vertexes. But this one is linear so no vertex.)

(1) - Find x-intercept, substitute y = 0

\(y=3x+1\\0=3x+1\\-1=3x\\3x=-1\\x=-\frac{1}{3}\)

Therefore, the graph intercepts x-axis at (-1/3, 0)

(2) - Find y-intercept, substitute x = 0

\(y=3x+1\\y=0+1\\y=1\)

Therefore, the graph intercepts y-axis at (0,1)

The graph's picture is below

1. The area between z=0 and z=0.68 is: 0.7517 - 0.5000 = 0.2517.

2.  The area between z=-0.46 and z=0 is: 0.5000 - 0.3222 = 0.1778.

3. The area between z=-0.34 and z=0.68 is: 0.7517 - 0.3669 = 0.3848.

To find the area under the standard normal curve using the z-table, you need to locate the corresponding z-scores and subtract the areas.

Between z=0 and z=0.68:

From the z-table, the area to the left of z=0 is 0.5000, and the area to the left of z=0.68 is 0.7517.

Therefore, the area between z=0 and z=0.68 is: 0.7517 - 0.5000 = 0.2517.

Between z=-0.46 and z=0:

From the z-table, the area to the left of z=-0.46 is 0.3222, and the area to the left of z=0 is 0.5000.

Therefore, the area between z=-0.46 and z=0 is: 0.5000 - 0.3222 = 0.1778.

Between z=-0.34 and z=0.68:

From the z-table, the area to the left of z=-0.34 is 0.3669, and the area to the left of z=0.68 is 0.7517.

Therefore, the area between z=-0.34 and z=0.68 is: 0.7517 - 0.3669 = 0.3848.

Note: The z-table provides the area to the left of the given z-score. To find the area between two z-scores, you need to subtract the areas corresponding to those z-scores.

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The lower confidence interval for the mean life of the new type of LED at a 95% confidence level is [5084.7,∞ )

To calculate the lower confidence interval for the mean life of the new type of LED, we can use the formula:

Lower confidence limit = sample mean - (critical value) x (standard error)

where the standard error is the standard deviation of the sample mean, given by:

standard error = sample standard deviation / √sample size

The critical value depends on the confidence level and the degrees of freedom, which for a sample of size 9 is 8 (n-1).

For a 95% confidence level, the critical value with 8 degrees of freedom is 2.306. Substituting the given values into the formula, we get:

Lower confidence limit = 5200 - 2.306 x (150 /√9 )

= 5200 - 115.3

= 5084.7

Therefore, the lower confidence interval for the mean life of the new type of LED at a 95% confidence level is [5084.7,∞ )

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