A communications satellite is in a synchronous orbit 18,000 miles above an alien planet's surface. Points B and D in the figure are points of tangency of the satellite signal with the planet. They represent the greatest distance from the satellite at which the signal can be received directly. Point C is the center of the planet, which has a radius of 3,500 miles.

Satellite diagram with satellite at point A, planet with center c and points of tangency with A at B and D. Radius of planet is 3,500 mi and distance from edge of planet to satellite is 18,000 mi.





Find distance
. Round to the nearest mile. Show your process and explain your reasoning.
m∠BAC = 9.4°. If the circumference of the circle represents the the planet's equator, what percent of the planet's equator is within range of the satellite’s signal? Show your process and explain your reasoning.
How much longer does it take a satellite signal to reach point B than it takes to reach point E? Use 186,000 mi/sec as the speed of a satellite signal. Round your answer to the nearest hundredth. Show your process and explain your reasoning.
The satellite is in orbit above the planet's equator. Along with the point directly below it on the planet's surface, the satellite makes one complete revolution every 36 hours. How fast must it travel to complete a revolution in that time? Round your answer to the nearest whole number. Show your process and explain your reasoning.

The probability that exactly 3 customers out of 3 will complain that their cup looks dirty is 0.006 to the nearest thousandth.

The probability that exactly 3 of the customers will complain that their cup looks dirty is determined as follows:

Using the binomial distribution formula, the probability is calculated as:

P(X = k) = [tex]^{n}C_k * (p^{k}) * (1-p)^{(n-k)}[/tex]

Where:

Substituting the values:

P(X = 3) = ³C₃ * (0.18³) * ((1-0.18)³⁻³

P(X = 3) = 0.18³

P(X = 3) = 0.006

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Answer:

here is not much information

Step-by-step explanation:

To calculate Tebogo's total cost per month, we need to consider the cost of blankets, delivery fee, and rent for selling space.

Cost of blankets:

Tebogo buys blankets from the wholesaler at R60 per blanket. Since he is restricted to 50 blankets per month, the cost of blankets is calculated as follows:

Cost of blankets = R60 per blanket x 50 blankets = R3000

Monthly delivery fee:

Tebogo incurs a monthly delivery fee of R120.

Rent for selling space:

The rent for selling space is not provided in the given information. To calculate the total cost per month, we would need the specific amount for rent.

To determine the total cost per month, we can sum up the costs:

Total cost per month = Cost of blankets + Monthly delivery fee + Rent for selling space

However, since the rent for selling space is not provided, we cannot calculate the exact total cost per month without that information.

Given the current i = 6 - 3i amperes and resistance r = 7 + 8i ohms, the voltage E of the Circuit, calculated using Ohm's law, is 66 + 27i volts.

To find the voltage (E) of a circuit using Ohm's law, we can substitute the given values of current (i) and resistance (r) into the formula E = i * r.

Given:

i = 6 - 3i (amperes)

r = 7 + 8i (ohms)

Substituting these values into the formula, we have:

E = (6 - 3i) * (7 + 8i)

To multiply these complex numbers, we can use the distributive property and perform the multiplication as follows:

E = 6 * 7 + 6 * 8i - 3i * 7 - 3i * 8i

 = 42 + 48i - 21i - 24i^2

Remember that i^2 is defined as -1, so we can simplify further:

E = 42 + 48i - 21i - 24(-1)

 = 42 + 48i - 21i + 24

 = 66 + 27i

Therefore, the voltage (E) of the circuit is 66 + 27i volts.

Given the current i = 6 - 3i amperes and resistance r = 7 + 8i ohms, the voltage E of the circuit, calculated using Ohm's law, is 66 + 27i volts.

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The transformation mapping triangle ABC into triangle DEF is given as follows:

A. reflection.

Examples of transformations are given as follows:

For this problem, the biggest change is in the orientation of the figure, hence the figure was a reflection.

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The equation x - 6y = -15 does not have a unique solution without additional information or constraints. It represents a line with infinitely many solutions (x, y) that satisfy the equation.

To solve the equation x - 6y = -15, we need to isolate one variable and solve for it. Let's solve for x in terms of y:

x = -15 + 6y

Now we have an expression for x in terms of y. This means that for any given value of y, we can substitute it into the equation to find the corresponding value of x.

Alternatively, if you have another equation involving x and y, we can substitute the expression for x into that equation to solve for y.

However, if we're only given the equation x - 6y = -15 without any additional information or constraints, we cannot find unique values for x and y. This equation represents a straight line in the coordinate plane, and there are infinitely many points (x, y) that satisfy this equation.

To illustrate this, let's plot the equation x - 6y = -15 on a graph:

We can rearrange the equation to the slope-intercept form y = (1/6)x + (15/6). From this form, we can see that the coefficient of x is the slope of the line, which is 1/6, and the y-intercept is (0, 15/6).

Using this information, we can plot the line and see that it extends infinitely in both directions.

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Each salesperson will receive $36 as their bonus. None of the option is Correct. Option E

To calculate the bonus amount for each salesperson, we need to follow the given instructions. We have six months of sales data represented in the graph, and we need to find the average of the four middle monthly sales values.

Looking at the graph, we can identify the four middle monthly sales values by ignoring the highest and lowest values. Based on the graph, the four middle monthly sales values are $1,800, $1,600, $1,400, and $1,200.

Now, we need to calculate the average of these four values. Adding them up and dividing by four, we get:

(1,800 + 1,600 + 1,400 + 1,200) / 4 = 6,000 / 4 = 1,500

The average of the four middle monthly sales values is $1,500.

Next, we need to take 12% of this average. To calculate the bonus amount, we multiply the average by 0.12:

1,500 * 0.12 = 180

The bonus amount is $180.

Finally, we need to split the bonus evenly among the five salespeople. To find the amount each salesperson will receive, we divide the bonus amount by the number of salespeople:

180 / 5 = 36

Each salesperson will receive $36 as their bonus.

Since we need to round the answer to the nearest dollar, the final answer is $36. None of the options provided in the answer choices match the correct amount, so the question may be flawed or there may be an error in the provided answer options. Option E noe of these.

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The probability for this event is 0.44

All the balls have the same probability of being selected at random, then the probability that the ball chosen at random is either green or blue, is equal to the quotient between the number of balls green or blue and the total number.

The total number is 27.

9 are green.

3 are blue.

Then the probability is:

P = (9 + 3)/27

P = 12/27

P = 0.44

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The angle of elevation is 44.4°

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. The angle of elevation is calculated by using trigonometry ratio.

Example is a man that is looking at a mango on the mango tree by an angle. This angle is angle of elevation.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

The opposite to the angle of elevation is the height of the house and the hypotenuse is the length of the dollar.

sinθ = 14/20

sinθ = 0.7

θ = 44.4°

therefore the angle of elevation is 44.4°

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Loan 1 would require more money over the time of the loan.

When you borrow money, the lender assesses interest as compensation for letting you use their resources. The principal, or the amount borrowed initially, and the length of time it takes to repay the loan are used to compute interest. Interest must accumulate over a longer length of time the longer the repayment duration.

The number of interest accrual periods rises as a result of extending the payback period, which raises the total amount of interest paid. The total interest paid over a longer term will be larger than over a shorter period even if the interest rate stays the same.

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Answer:

Step-by-step explanation:

[tex]\textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y-2)^2}{16}-\cfrac{(x+1)^2}{144}=1\implies \cfrac{(y-2)^2}{4^2}-\cfrac{( ~~ x-(-1) ~~ )^2}{12^2}=1[/tex]

now, since the positive fraction is the one with the "y" in it, that means the traverse axis is running over the y-axis in short the hyperbola is opening up and down.

From the same equation above, we can see the center is at (-1 , 2) and the conjugate axis has a half which is "b" or namely b = 12, since that's half of the conjugate axis, then the conjugate axis must be 2b or 24.

Answer: [tex]5\sqrt 5[/tex]

Step-by-step explanation:

Sol [tex]\sqrt 125[/tex] = [tex]\sqrt{25.5}[/tex]

= [tex]\sqrt{25}[/tex]  x  [tex]\sqrt{5}[/tex]

[tex]5 \sqrt{5}[/tex]

Group B has lower range.

Group A shows variability.

Mean is the best to make concussion about age of Salsa students.

Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.

This inference is supported by the observation that the majority of data points in Group B are concentrated around younger ages.

In contrast, Group A exhibits a more dispersed distribution of data points across a wider range of ages, including higher.

So, Group B has lower range.

and, Group A shows variability.

Lastly, Mean is the best to make concussion about age of Salsa students.

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Answer:

y = - 1/2 x + 2

Step-by-step explanation:

Main concepts:

1. Slope intercept form of Equation for a line

2. ordered pairs

3. Finding the y-intercept

4. Finding slope

5. Finding the equation for our line

1. Slope intercept form of Equation for a line

For any non-vertical line, the equation can be written in "slope-intercept" form: [tex]y=mx+b[/tex] where b is the y-coordinate of the y-intercept of the line, m is the "slope" of the line, and x & y are the (x,y) coordinates of any point you choose on the line.

2. ordered pairs

Any point on the coordinate system (whether on the line or not) is defined by an (x,y) coordinate pair.  All points are measured starting from the origin (0,0).

The "x-coordinate" is the distance to the left or right of the origin, and the "y-coordinate" is the distance above or below the origin.

3. Finding the y-intercept

The y-intercept of a line is the place where the line crosses the "y-axis" (the vertical axis).  Notice that the blue line crosses the y-axis at a height of 2, so the y-intercept is (0,2), and [tex]b=2[/tex]

4. Finding slope

The slope of any non-vertical line can be found from two known points  [tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex] using the following formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Both to minimize error to to work with "nicer" numbers, try to choose points that are crossing through the intersection of grid lines (but any two points will work).  Two points that are fairly easy to identify on this line are (0,2) and (4,0).  (these two points are the y-intercept that we already identified, and the place where the blue line crosses the horizontal axis -- called the x-intercept).

Substituting into the formula:

[tex]m=\dfrac{(0)-(2)}{(4)-(0)}[/tex]

[tex]m=\dfrac{-2}{4}[/tex]

[tex]m=-\frac{1}{2}[/tex]

5. Finding the equation for our line

Knowing both the y-intercept and the slope, we can now substitute the values into the equation and get the equation for this line:

[tex]y=- \frac{1}{2}x+2[/tex]

The greatest common factor of  25x⁵  - 15x² - 20x is 5x.

The greatest common factor (GCF) of a set of numbers is the largest factor \that all the numbers share.

In other words, the greatest common factor (GCF) of a set of whole numbers or polynomial is the largest positive integer that divides evenly into all numbers with zero .

Therefore, let's find the greatest common factor of 25x⁵  - 15x² - 20x.

Hence,

25x⁵  - 15x² - 20x = 5x(5x⁴ - 3x - 4x)

Therefore, the greatest common factor is 5x.

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The graph of equation is shown in figure.

We have to given that,

The equation is,

⇒ y = - 2x² + 12x - 17

Now, We have the given equation is a quadratic equation.

Hence, We can simplify as,

⇒ y = - 2x² + 12x - 17

⇒ y = - 2 (x² + 6x) - 17

⇒ y = - 2 (x² - 6x + 3² - 3²) - 17

⇒ y = - 2 (x - 3)² + 18 - 17

⇒ y = - 2 (x - 3)² + 1

Hence, This represent the equation of parabola with vertex (3, 1).

Thus, The graph of equation is shown in figure.

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Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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The probability that Pablo goes jogging on that day is 0.57 or 57%.

Given that,

The probability of rain on a particular day is 0.4.

When it rains, the probability that Pablo goes jogging is 0.15.

And, it does not rain, the probability that he goes jogging is 0.85.

Now, The probability for Pablo goes jogging on that day is find as,

The probability that it rains and Pablo goes jogging,

0.4 x 0.15 = 0.06

And, The probability that it does not rain and Pablo goes jogging,

0.6 x 0.85 = 0.51

Therefore, the total probability that Pablo goes jogging on that day is:

0.06 + 0.51 = 0.57

Thus, the probability that Pablo goes jogging on that day is 0.57 or 57%.

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Answer:

3/4 there are 4 lines indicating the numbers and it is on the 3rd.

The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm

Given are the circles and the circular items we need to find their circumference,

Circumference of a circle = 2π × radius = Diameter × π

4. a) Circumference = 5 × 3.14 = 15.7 cm

b) Circumference = 8.36 × 3.14 = 26.25 m

5. a) Circumference = 41 × 3.14 = 128.74 cm

b) Circumference = 13 × 3.14 = 40.82 mm

c) Circumference = 14.3 × 3.14 = 45 cm

6.

The perimeter of the cloth = circumference of the circular ends plus length in the middle,

= 76 × 2 × 3.14 + 150 × 2

= 477.28 + 300

= 777.28 cm

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The function is odd, and the graph would be shifted downward. option(2)

The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.

Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.

This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units.

The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.

Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.

This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units. Option(2)

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1) The chart for the above data is attached accordingly.

2) The type of chart chosen is a line chart. This is because it is able to display the undulations in each of the data given.

A line chart is a graphical depiction of an asset's historical price activity in which a sequence of data points are connected by a continuous line.

This is the most basic sort of chart used in finance, and it generally merely shows the closing prices of a securities over time.

Line charts may be used for any timescale, however they are most commonly used for tracking day-to-day price fluctuations.

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Answer:

-7

Step-by-step explanation:

The significance of sample size in statistical experiments cannot be overstated. A larger Sample size enhances the reliability and generalizability of the results, reducing sampling errors and increasing statistical power.

Sample size is a critical aspect of statistical experiments that significantly impacts the reliability of the results. It represents the number of individuals, observations, or data points included in a study. Understanding the significance of sample size is essential for ensuring the validity and generalizability of statistical findings.

The size of the sample directly influences the precision and accuracy of the estimates or conclusions drawn from the data. A larger sample size generally leads to more reliable results by reducing sampling errors and increasing the representativeness of the population under study. With a larger sample, the estimates are likely to be closer to the true values, providing greater confidence in the findings.

When the sample size is small, the variability in the data may be magnified, making it challenging to draw accurate conclusions. Results obtained from a small sample may not adequately capture the diversity or complexity of the population, leading to biased or misleading findings. This is known as sampling error, where the sample does not fully reflect the characteristics of the larger population.

Moreover, the statistical power of an experiment is directly related to the sample size. Statistical power refers to the ability of a study to detect true effects or relationships between variables. A larger sample size increases the power of the analysis, allowing researchers to identify smaller, yet meaningful, differences or associations. In contrast, a small sample size may result in low statistical power, making it difficult to detect significant effects even if they exist.

It is important to note that sample size requirements can vary depending on the research design, objectives, and the anticipated effect size. Complex studies or analyses involving rare events or small effect sizes may require larger sample sizes to achieve sufficient power and precision.

In conclusion, the significance of sample size in statistical experiments cannot be overstated. A larger sample size enhances the reliability and generalizability of the results, reducing sampling errors and increasing statistical power. Researchers should carefully consider sample size calculations to ensure their studies yield robust and trustworthy conclusions.

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The most appropriate chart to depict US energy consumption would be a pie chart since a pie chart helps to see the composition of different proportions representing total consumption.

Chart A is not appropriate because a line graph is used to depict information to analyze changes over time or over a period. However, to show the energy consumption, the line graph is not an accurate depiction since the type of energy source is a categorical variable.

Chart B is also appropriate because it is a column graph and such type of graphs are used to represent categorical variables. The US energy consumption can be represented well through a column graph as it well depicts the highest consumption source and the lowest consumption source.

Yes more than one kind of display would therefore be acceptable as we can use to show the information through both a pie chart and a column graph.

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Answer:

Step-by-step explanation:

From this parabola,  we are able to identify that:

To distinguish the focus, directrix, and axis of symmetry of the parabola modeled by the condition 3x² - 6y = 0, ready to revamp the condition in standard shape, which is (x - h)² = 4p(y - k).

Comparing this standard frame with the given condition, we have:

3x² - 6y =

Isolating the condition by 3, we get:

x² - 2y =

Presently, we are able to rework it within the standard frame by completing the square:

(x - 0)² = 2(y - 0)

(x - 0)² = 2y

Subsequently, the focus is (0, 1/2), the directrix is y = -1/2, and the axis of symmetry is x = for the parabola modeled by the condition 3x² - 6y = 0.

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