Find the indicated angle using trigonometry

The equation of the transmission boundary for all three towers are  x^2 + y^2 = 3^2, (x - 5)^2 + (y - 3)^2 = 2.5^2 and  (x - 2)^2 + (y - 5)^2 = 2^2 respectively

To write the equations of the transmission boundaries for all three towers, we can use the equation of a circle.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

For Tower A:

Center: (0, 0)

Radius: 3 miles

Equation: x^2 + y^2 = 3^2

For Tower B:

Center: (5, 3)

Radius: 2.5 miles

Equation: (x - 5)^2 + (y - 3)^2 = 2.5^2

For Tower C:

Center: (2, 5)

Radius: 2 miles

Equation: (x - 2)^2 + (y - 5)^2 = 2^2

These three equations represent the transmission boundaries of the respective towers.

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Answer:

-5x=35

Step-by-step explanation:

The product= an answer to a multiplication problem, so product means multiply

A number= a variable, an unknown integer(number)

So, therefore, a number multiplied by -5 = -5x

x= the variable, the variable being multiplied should go right after the known number.

so, -5x=35

solved= divide -5 by 35 which equals -7

a negative number and a positive number being multiplied make the product a negative number.

Please mark brainliest, I hope this helps!!

Answer:

6/6 or one foot.

Step-by-step explanation:

If one of the fish tanks is 5/6 of a foot wide, and the other is 1/6, add them together.

5/6+1/6=6/6 or 1 foot wide. 6/6 means a whole number.

The total width of the two fish tanks as per the given relation is equal to 1 foot.

To find the total width of the two fish tanks when placed next to each other, add their widths.

The widths are given as fractions of a foot, so add them directly:

Width of the first fish tank = 1/6 foot

Width of the second fish tank = 5/6 foot

Total width of the two fish tanks = (1/6) + (5/6)

To add fractions, they need to have the same denominator.

Here, both fractions already have the same denominator (6),

So, simply add their numerators:

Total width = (1 + 5)/6

Total width = 6/6

Now, 6/6 is equal to 1.

Therefore, the total width of the two fish tanks is 1 foot.

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A simple random sampling of 5 observations from a population containing 400 elements was taken. Then, the point estimate of the population means is 18.

You have a simple random sample of 5 observations from a population containing 400 elements, and the observed values are 12, 18, 19, 20, and 21.

To calculate the point estimate of the population mean, we simply take the average of the sample values.

Point estimate of population mean = (12 + 18 + 19 + 20 + 21)/5 = 18

Therefore, the point estimate of the population means is 18.

To clarify the terms used in the question, a "random sample" is a sample that is selected randomly from the population, meaning that every element in the population has an equal chance of being included in the sample. In this case, a simple random sample of 5 observations was taken. "Elements" refers to the individual units or objects within the population that is being studied. In this case, there were 400 elements in the population.

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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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The right answers are

1. C, 1

2. B, an+1 = an x 3, a1 =5

3. C, an = -6 x 0.5^n-1

4. D, an + 2/3 x (1/2)^n-1

5. D, an+1 = an x (-2), a1 = 5

I just took the test and got 100% so these should be correct

Answer:

Yes, Frank does have enough, he has 250 metal and only has 228 surface area.

Step-by-step explanation:

You take all the triangles (4) and multipy 4 x 6 (24) then divide that by 2 (12) so now you know all the triangles are equal to 12. Then the squares, you multiply 6 x 6 (36) now you know all the squres are equal to 36 and then you add 12 + 12+12+12+36+36+36+36+36 and then you get 228.

Therefore, H(t) is increasing on the intervals (-∞, -1/\(\sqrt7\)) and (\(1/\sqrt7\), ∞) and decreasing on the interval (\(-1/\sqrt7\), \(1/\sqrt7\)).and There are no local or absolute maximum values for H(t).

To find the intervals on which the function H(t) is increasing or decreasing, we need to take the first derivative of H(t) and find its critical points.

a.) First derivative of H(t):

\(H'(t) = 12t^11 - 84/7t^13\)

\(= 12t^11(1 - 7t^2)/7t^2\)

The critical points are where H'(t) = 0 or H'(t) is undefined.

So, setting H'(t) = 0, we get:

\(12t^11(1 - 7t^2)/7t^2 = 0\)

\(t = 0\) or t = ±(\(1/\sqrt7\))

H'(t) is undefined at t = 0.

Now, we can use the first derivative test to determine the intervals on which H(t) is increasing or decreasing. We can do this by choosing test points between the critical points and checking whether the derivative is positive or negative at those points.

Test point: -1

\(H'(-1) = 12(-1)^11(1 - 7(-1)^2)/7(-1)^2 = -12/7 < 0\)

Test point: (-1/√7)

\(H'(-1/\sqrt7) = 12(-1/\sqrt7)^11(1 - 7(-1/\sqrt7)^2)/7(-1/\sqrt7)^2 = 12/7\sqrt7 > 0\)

Test point: (1/√7)

\(H'(1/\sqrt7) = 12(1/\sqrt7)^11(1 - 7(1/\sqrt7)^2)/7(1/\sqrt7)^2 = -12/7\sqrt7 < 0\)

Test point: 1

\(H'(1) = 12(1)^11(1 - 7(1)^2)/7(1)^2 = 5/7 > 0\)

Therefore, H(t) is increasing on the intervals (-∞, -1/√7) and (1/√7, ∞) and decreasing on the interval (-1/√7, 1/√7).

b.) To find the local and absolute extreme values of H(t), we need to check the critical points and the endpoints of the intervals.

Critical points:

\(H(-1/\sqrt7) \approx -0.3497\)

\(H(0) = 0\)

\(H(1/\sqrt7) \approx-0.3497\)

Endpoints:

H (-∞) = -∞

H (∞) = ∞

Since H (-∞) is negative and H (∞) is positive, there must be a global minimum at some point between -1/√7 and 1/√7. The function is symmetric about the y-axis, so the global minimum occurs at t = 0, which is also a local minimum. Therefore, the absolute minimum of H(t) is 0, which occurs at t = 0.

There are no local or absolute maximum values for H(t).

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The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.

When charged electrons (current) are forced through a conducting loop by the weight of an electrical raceway power source, they can perform tasks like lighting a lamp. In a nutshell, voltage equals pressure and is expressed in volts (V).

Here,

The voltage generated by the uv spectrophotometer is inversely proportionate to the amount of light present and linearly proportional to the sample's absorbance.

This indicates that as the sample's absorbance rises, so does the energy the colorimeter generates.

Similar to this, the voltage generated by the colorimeter rises as light strength falls.

The Beer-Lambert Law, which says that a sample's absorbance is directly proportional to its concentration of the absorbing substance and its path length and inversely proportional to incident light intensity, describes this connection.

The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.

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Answer:

A) Events A and B

Step-by-step explanation:

event a : 3

event b : 2,4,6,8

event c : 3, 6

event d : 3, 4, 5, 6, 7, 8, 9

Events A and B are disjoint

Answer:

9s-3s10s or 3-10s

Step-by-step explanation:

10s+s-3s10s+s-3s

first of all, we collect like terms

10s+s+s-3s-3s10s

=9s-3s10s

it could also be equal to

9s/3s-(3s10s/3s)

3-10s

when we divide through by 3s

The culture starts out with 39 members.

Given that;

After 20 minutes and 40 minutes, a bacteria culture had an 800 and 1700 count, respectively.

To get exponential growth;

We can get growth with an exponential function,

F(t) = A₀\(e^k^t\)

Here, k is the growth constant and A₀ is the initial amount of bacteria.

Let;

800 = A₀\(e^2^0^k\)  → (I)

1700 = A₀\(e^4^0^k\) → (II)

From (I) and (II);

1700 / 800 =  A₀\(e^4^0^k\) / A₀\(e^2^0^k\)

17/8 = \(e^2^0^k\)

For the above equation take the natural log on both sides;

ln(17/8) = ln \(e^2^0^k\)

ln(17/8) = 20k

k = ln(17/8) / 20

To get the initial size of the culture;

From (I),

800 = A₀\(e^2^0^k\)

800 = A₀e⁰°⁰³⁷⁶ ˣ ²⁰

A₀ = 800 / 20.76

A₀ = 38.53 ≅ 39

Therefore, the initial size of the culture is 39.

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Answer:

a. 120 meters

b.5 seconds

c. 5 seconds

d. 40 meters

e. 2 seconds

Step-by-step explanation:

I hope this helps!

Answer:

hhhkkljooopjbhhhgiiijnnbbbb

Answer:

a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. The effect of multiplying a given matrix by an identity matrix is to leave the given matrix unchanged.

Note that :

n! = n(n-1)(n-2)(n-3)...(2)(1)

Example :

3! = 3(2)(1) = 6

4! = 4(3)(2)(1) = 24

5! = 5(4)(3)(2)(1) = 120

From a. :

which is obviously not equal to 3! = 3 x 2 x 1 = 6

So, "a" is false

From b :

which is also obvious that it is not equal to 9! = 9 x 8 x 7 x ... x 1

So, "b" is also false

From c :

Since the result is equal to 126, therefore c. is TRUE

The cancel symbol, it is used when the numerator and the denominator has the same value.

For example :

ab/b will result to a

Lets try an example :

when a = 2

b = 3

It is the same as :

It is like multiplying 2 x (3/3) = 2 x (1) = 2

The percentage of tires that will have a life of 45,000 to 55,000 miles is  68.27%. So the correct option is 68.27%.

To find the percentage of tires that will have a life of 45,000 to 55,000 miles, we can use the concept of the normal distribution.

First, we calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation

For 45,000 miles:
z1 = (45,000 - 50,000) / 5,000 = -1

For 55,000 miles:
z2 = (55,000 - 50,000) / 5,000 = 1

Next, we look up the corresponding values in the standard normal distribution table. The table will provide the proportion of data within a certain range of z-scores.

The percentage of tires with a life between 45,000 and 55,000 miles is the difference between the cumulative probabilities for z2 and z1.

Looking at the standard normal distribution table, the cumulative probability for z = -1 is 0.1587, and the cumulative probability for z = 1 is 0.8413.

Therefore, the percentage of tires that will have a life of 45,000 to 55,000 miles is:
0.8413 - 0.1587 = 0.6826

Converting this to a percentage, we get:
0.6826 * 100 = 68.26%

So the correct answer is 68.27%.

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The size of one sigma is approximately 0.027 inches. The quality level of the process is 4 sigma. The process does not meet the definition of true 6 Sigma quality. The change to the process control chart values has increased the quality of the process.

The process capability ratio is calculated by dividing the tolerance range (2 * 0.28 ounces) by 6 times the process standard deviation (6 * 0.13 ounces), resulting in a value of 0.62. This ratio indicates that the process is capable of meeting the specifications.

The process capability index is calculated by dividing the tolerance range (2 * 0.28 ounces) by 6 times the standard deviation (6 * 0.13 ounces), resulting in a value of 0.92. This index suggests that the process is close to meeting the specifications.

Based on the given options, the actual process quality level is currently less than 3σ Quality, but a shift in location could increase it to better than 3σ Quality. This means that the process has room for improvement but has the potential to meet higher quality standards with adjustments.

For the length of a component, the process meets the traditional definition of a "Capable" process as the average falls within the control limits (LCL = 5.673", UCL = 5.727").

The size of one sigma is approximately the process standard deviation, which is 0.13 inches.

The quality level of the process can be calculated by subtracting the process average from the upper specification limit (USL) and dividing it by 3 times the process standard deviation. In this case, \(\frac{(USL - process average) }{(3 * standard deviation)}\) = \(\frac{(5.727 - 5.700) }{(3 * 0.13) }\) ≈ \(\frac{0.077}{0.39}\)≈ 0.20. Rounded to 1 significant digit past the decimal, the quality level is 0.2 sigma or 4 sigmas.

The process does not meet the definition of true 6 Sigma quality, as it falls short of the required quality level.

The change to the process control chart values has increased the quality of the process. The new values of x, LCL, and UCL are still within control limits, indicating an improvement in process stability.

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Answer:

Step-by-step explanation:

Question= 8(3x-5)

To solve this, we have to use the distribution property. In this method, we multiply the 8 with 3x and -5 in this example.

Solving we get:

Area=24x-40

Hope this helps!

It takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles. This is determined by calculating the harmonic mean of their individual running speeds.

To determine how many hours it takes for Alex, Bethany, and Carol to collectively run a total of 26 miles, we need to consider their individual running speeds. Alex runs at a rate of 26 miles in 6 hours, Bethany runs at a rate of 26 miles in 5 hours, and Carol runs at a rate of 26 miles in 4 hours.

To find the total time it takes for them to finish 26 miles together, we can calculate the harmonic mean of their individual running speeds. The harmonic mean is used because it accounts for the different rates at which they run.

The formula for the harmonic mean is given by:

Harmonic Mean = Total Distance / (1 / Speed1 + 1 / Speed2 + 1 / Speed3)

Substituting the values, we have:

Harmonic Mean = 26 / (1 / 6 + 1 / 5 + 1 / 4)

To simplify the equation, we find the common denominator:

Harmonic Mean = 26 / ((5 + 6 + 7) / 60)

Harmonic Mean = 26 / (18 / 60)

Harmonic Mean = 26 / (3 / 10)

Harmonic Mean = 26 * (10 / 3)

Harmonic Mean ≈ 86.67

Therefore, it takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles.

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Answer:

(3,2)

Step-by-step explanation:

So like the last one we just have to find the distances between x on point a and x on point x and the distances between y on point a and y on point b. 4+2=6 and 3+3=6 and since we are trying to find the point that is 1/6 of the distance from a we do 6/6 and 6/6 which is 1 and 1. Then we subtract 1 from the x and y values of A. So the coordinates 1/6 of the way is (3,2)

The probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John is 0.60 or 60%

We can find the probability that a person does not believe Marilyn Monroe had an affair with John F Kennedy by dividing the number of people who responded "no" by the total number of people who responded to the survey:

Probability of "no" = Number of "no" responses / Total number of responses

Total number of responses = Number of "yes" responses + Number of "no" responses

Total number of responses = 110 + 163 = 273

Probability of "no" = 163 / 273

Simplifying the fraction, we get:

Probability of "no" = 0.5967 or approximately 0.60

So, the probability that if a person is chosen at random, he does not believe Marilyn Monroe had an affair with John F Kennedy is approximately 0.60, or 60%.

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Since f(14) = 19, it follows that f⁻¹(19) = 14. Thus, the inverse function f⁻¹ maps the output value 19 back to the input value 14.

To find f⁻¹(19), we need to find the input value that maps to 19 under the function f. Since f is one-to-one, each output value corresponds to a unique input value.

Since f(14) = 19, we know that the input value 14 maps to the output value 19 under the function f. In a one-to-one function, the inverse function f⁻¹ "undoes" the mapping of f. Therefore, f⁻¹(19) will be the input value that maps to 19 under the inverse function f⁻¹.

In this case, f⁻¹(19) will be equal to the value that, when plugged into f, yields 19 as the output. Since f(14) = 19, it follows that f⁻¹(19) = 14. Thus, the inverse function f⁻¹ maps the output value 19 back to the input value 14.

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The number of phones sold is 15 and the number of accessories sold is 24, and the graph is attached below.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given:

Samir earns an $8 commission for every phone he sells and a $4 commission for every accessory he sells,

Total money earned = $216,

Total number of phones  and accessories sold = 39

Write the equation of the above statement as shown below,

8x + 4y = 216,

x + y = 39

Assume the number of phones sold is x and the number of accessories sold is y,

Solve the equation by elimination as shown below

x = 15,

y = 39 - 15 = 24

The graph is also attached below,

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Answer:

x+ x=?

Step-by-step explanation:

Workers in an office of 40 staff were asked their favourite type of take- away.1/9 bit of a person is one degree.

What's Fraction?

An element of a total is a bit. The number is represented mathematically as a quotient, where the numerator and denominator are resolve. Both are integers in a simple bit. A bit appears in the numerator or denominator of a complex bit. The numerator of a proper bit is lower than the denominator.

The magnitude of an angle is measured using a unit of dimension. In magnitude, 1 degree is original to1/360 of a full gyration.

Degree 1 – direct.

Degree 2 – quadratic.

Degree 3 – boxy.

Degree 4 – quartic( or, if all terms have indeed degree, biquadratic)

Given that;

total workers = 40

Bit of a person = 1 degree

we know that 360 ° = 40 person

so for 1 degree = 40/360 = 1/9

Hence,1/9 bit of a person is one degree.

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Answer:

The number of ways in which the digits can be assigned in the color wheel can be determined by the permutation of 8 taken 4 since it is in circular formation and whichever comes first is not important.

number of ways = 9P4 = 3024 ways