Consider a political discussion group consisting of 6 Democrats, 4 Republicans, and 6 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting and then .
The probability of selecting a Democrat and then an Independent is (6/16) * (6/15) = 3/40. The probability of selecting two Republicans with replacement is (4/16) * (4/16) = 1/16.
What is probability ?
Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. It is the ratio of the number of favorable outcomes to the total number of possible outcomes in a given situation. Probability is used in many fields, such as mathematics, statistics, science, engineering, economics, and social sciences, to model and analyze uncertain situations and make predictions about the future based on available data.
(a) selecting a Democrat and then an Independent without replacement.
The probability of selecting a Democrat on the first draw is 6/16, and the probability of selecting an Independent on the second draw, without replacement, is 6/15. So the probability of selecting a Democrat and then an Independent is:
(6/16) * (6/15) = 3/40
(b) selecting two Republicans with replacement.
The probability of selecting a Republican on the first draw is 4/16, and with replacement, the probability of selecting another Republican on the second draw is also 4/16. So the probability of selecting two Republicans with replacement is:
(4/16) * (4/16) = 1/16
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A verbal description of a linear function h is given. Express the function h in the form
h(x) = ax + b.
The graph of the linear function h has slope
8
9
and y-intercept 3.
h(x) =
The graph of the linear function h has slope the function h in the form
h(x) = 8x + 9.
What is a linear function?Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.
What does the described linear function look like?As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.
Since f(x) = axe + b is the typical slope-intercept form of a linear function,
an is the slope (rate of change), and b is the y-intercept (initial value).
g = -12x + 100 is the necessary linear function, which is what has been presented.
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Which number is the larger one in the decimal system?
3 x 102 or 1100
What can be said about the vertices of an equilateral triangle drawn in Poincaré's system?
a. Each of the angles formed at the vertices equals 60 degrees.
b. The vertices are equidistant from the center of the circle.
c. The vertices always lie on the circle.
d. none of these
Please select the best answer from the choices provided
OB
OD
Mark this and return
Next
Submit
Answer:
Step-by-step explanation:
The correct answer is C: The vertices always lie on the circle.
In Poincaré's system, an equilateral triangle is a unique type of triangle in which all three sides are equal in length and all three angles are equal to 60 degrees. Since the vertices of an equilateral triangle lie on the circumference of a circle, it can be said that the vertices always lie on the circle.
The other options, A and B, are also true for equilateral triangles in Poincaré's system, but option C is the best answer because it directly addresses the question of where the vertices lie.
In Poincaré's system, a geometric model of non-Euclidean geometry, the vertices of an equilateral triangle are points that lie on the circumference of a circle.
Here's how this can be demonstrated step by step:
Draw a circle with a center point and a circumference.
Choose three points on the circumference of the circle and connect them with lines to form an equilateral triangle.
Measure the angles at each vertex using a protractor or by counting the number of degrees along the circumference of the circle. In an equilateral triangle, all three angles will be equal to 60 degrees.
Measure the sides of the triangle. In an equilateral triangle, all three sides will be equal in length.
Since the vertices of the triangle are points on the circumference of the circle, it can be concluded that the vertices always lie on the circle.
It is important to note that in Poincaré's system, the relationships between the vertices, sides, and angles of a triangle are different from those in Euclidean geometry. However, an equilateral triangle in Poincaré's system still follows the basic definition of an equilateral triangle, with all sides equal in length and all angles equal to 60 degrees.
Is 4^3.5 halfway between 4^3 and 4^4? If not, explain why. If it is, do you believe that it is
generally true that x^3.5 is halfway between x^3! and x^4? Check out a couple of values to see what you can determine if there is a pattern here. You need to present some
explanation of your observations here.
No, [tex]4^{3}[/tex]. 5 is not equal distance away from both [tex]4^{3}[/tex] and [tex]4^{4}[/tex]. However, when x is a perfect square, it is halfway between [tex]x^{3}[/tex] and [tex]x^{4}[/tex]. 5 is halfway between [tex]9^{3}[/tex] and [tex]9^{4}[/tex].
What is a perfect square?A perfect square is an integer that is the result of multiplying an integer by itself. In other words, it is a number that can be expressed as the product of two equal integers. For example, the number 16 is a perfect square because it can be written as 4 • 4.
Every perfect square has an ending of 1, 4, 5, 6, 9 or 00. (i.e. Even number of zeros). A number that finishes in 2, 3, or 7 is not a perfect square, and so is 8. In essence, a perfect square is the result of multiplying two equal numbers by one another. As a result of multiplying two equal integers (5 and 5) by one another, the number 25 is a perfect square.
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There are vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%.
Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
Red
Total
Question content area bottom
Part 1
Complete the table.
Row Relative Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
enter your response here%
enter your response here%
100%
Red
enter your response here%
enter your response here%
100%
Total
enter your response here%
enter your response here%
100%
Answer:
you su ck hah lol
Step-by-step explanation:
ez
A couch and coffee table cost a total of $1128. The cost of the couch is three times the cost of the coffee table. Find the cost of each item.
cost of couch :
cost of coffee table:
Answer:
cost of couch: $846
cost of coffee table: $282
Step-by-step explanation:
A positive number a or the same number a decreased by 50% and then increased by 50% of the result
Answer:
75a%
or
3/4a
or
0.75a
Step-by-step explanation:
A positive number a or the same number a decreased by 50% and then increased by 50% of the result
I answer for what I understand, a number a is reduced by 50% and the result increased by 50%
decreasea - 50% = 50% or 1/2 or 0.5
2. increase
50 + 50% = 75% or 3/4 or 0.75
Help me it’s Quadratic Functions
The graph of the quadratic function y = -2x² + 1 is given by the image presented at the end of the answer.
How to obtain the graph of the quadratic function?The parent quadratic function is given as follows:
y = x².
The transformed quadratic function is given as follows:
y = -2x² + 1.
The transformations are given as follows:
Multiplication by the negative number: reflected over the x-axis,Multiplication of x by the number with an absolute value of 2: horizontal compression by a factor of 2.Addition by 1: translation up one unit.More can be learned about quadratic functions at https://brainly.com/question/1214333
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Describe a single transformation of △ABC that is a composition of the following pair of transformations:
T<−5,−3>(ABC) followed by T<−4,−2> (A'B'C).
A. T<−1,−5>(ABC)
B. T<−9,−5>(ABC)
C. T<−9,−1>(ABC)
D. T<−1,−1>(ABC)
The required overall translation is T<−9,−5>(ABC). The correct answer would be option B.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Starting with triangle ABC, we first apply the transformation T<−5,−3>, which means each vertex of the triangle is shifted 5 units to the left and 3 units down. So the triangle becomes A'B'C'.
Next, we apply the transformation T<−4,−2> to triangle A'B'C', meaning that each vertex is shifted 4 units to the left and 2 units down.
To find the overall effect of these two transformations, we can think of the second transformation as shifting the entire triangle produced by the first transformation.
In other words, we're combining the effects of the two transformations by adding the translations together.
So, the overall translation is T<−5 + −4, −3 + −2> = T<−9,−5>,
Thus, the correct answer would be option B: T<−9,−5>(ABC).
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(5^-4)^2 using only positive exponents
Hi there, here's your answer:
Given the question:
[tex](5^{-4})^{2}[/tex]
We know that a number [tex]x[/tex] raised to the power of a negative integer [tex]-y[/tex] is evaluates as [tex]\frac{1}{x^{y} }[/tex]
Hence, on evaluating this expression we get:
[tex](\frac{1}{5^{4} })^{2}[/tex] = [tex](\frac{1}{625} )^2 = \frac{1}{390625}[/tex]
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What is the slope between the two points
(-10,50) and (-4,20)
Answer:
Below
Step-by-step explanation:
Slope = rise / run = change in y / change in x = -30 / 6 = -5
Answer: -5
Step-by-step explanation:
Start with the slope formula
m = (y2 - y1) / (x2 - x1)
Substitute point values in the formula
m = (20 - 50) / (-4 - -10)
Simplify the fraction
m = (20 - 50) / (-4 - -10) = -30 / 6
Solve for slope (m)
m = -5
porfavor me ayudarian es urgente
Answer: no exact answer
Step-by-step explanation:
The result of fraction multiplication are:
2/3 x 2/5 = 4/15
4/2 x 6/3 = 4
2/4 x 3/6 = 1/4
2/3 x 6/3 = 4/3
Given that, simplify the following:
2/3 x 2/5
4/2 x 6/3
2/4 x 3/6
2/3 x 6/3
For the expression 2/3 x 2/5:
To multiply fractions, we multiply the numerators together and the denominators together.
So, (2 x 2)/(3 x 5) = 4/15.
For the expression 4/2 x 6/3:
Again, we multiply the numerators together and the denominators together.
Thus, (4 x 6)/(2 x 3) = 24/6 = 4.
For the expression 2/4 x 3/6:
Following the same process, we multiply the numerators and denominators.
Therefore, (2 x 3)/(4 x 6) = 6/24 = 1/4.
Lastly, for the expression 2/3 x 6/3:
Similarly, we multiply the numerators and denominators together.
Hence, (2 x 6)/(3 x 3) = 12/9 = 4/3.
Therefore, the result of fraction multiplication are:
2/3 x 2/5 = 4/15
4/2 x 6/3 = 4
2/4 x 3/6 = 1/4
2/3 x 6/3 = 4/3
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Ava goes out to lunch. The bill, before tax and tip, was $10. A sales tax of 6% was added on. Ava tipped 24% on the amount after the sales tax was added. How much was the sales tax ? Round to the nearest cent.
Answer:
0.60
Step-by-step explanation:
sales tax=
\,\,\text{6\% of \color{blue}{bill}}
6% of bill
=
=
\,\,0.06\times\color{blue}{\$10}
0.06×$10
6% = 0.06
=
=
\,\,\color{green}{\$0.60}
$0.60
\text{The sales tax was \$0.60.}
The sales tax was $0.60.
The mail carrier has to deliver three boxes The first Box has the mass of 80 kg the second Box has the mass of 40 kgs third box has a mass of 60 kg what is the total mass of all three boxes in grams?
The total mass of all three boxes to be delivered by the mail carrier is 180,000 grams.
What is the total mass of all three boxes in grams?Given the data in the question;
Mass of the boxes carried by the mail carrier.
Mass of first box = 80kg
Mass of second box = 40kg
Mass of third box = 60kg
First, we convert from kilograms to grams.
Note: 1 kg = 1000g
Hence;
Mass of first box = 80kg = ( 80 × 1000 )g = 80000g
Mass of second box = 40kg = ( 40 × 1000 )g = 40000g
Mass of third box = 60kg = ( 60 × 1000 )g = 60000g
Now, we add the mass of the boxes in gram.
80000g + 40000g + 60000g
180,000 grams
Therefore, the total mass is 180,000 grams.
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A circular walkway is to be built around a monument, with the monument as the center. The distance from the monument to any point on the inner boundary of the walkway is 30 feet.
The equation of the inner boundary of the circular walkway around the monument is x² + y² = 900.
The equation of the outer boundary of the circular walkway around the monument is x² + y² = 1369.
What is the equation of a circle?A circle is a conic section whenever the plane cuts the cone parallel to its base. Every point of the circumference lies at the same distance from its center. The equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
a.
According to the diagram, the radius of the inner boundary is 30 feet and the center is (0, 0).
Substitute h = 0, k = 0, and r = 30 into the equation of circle (x-h)² + (y-k)² = r².
(x-0)² + (y-0)² = 30²
x² + y² = 900
Therefore, the obtained answer is x² + y² = 900.
b.
According to the diagram, the radius of the outer boundary is 37 feet (30 feet + 7 feet) and the center is (0, 0).
Substitute h = 0, k = 0, and r = 37 into the equation of circle (x-h)² + (y-k)² = r².
(x-0)² + (y-0)² = 37²
x² + y² = 1369
Therefore, the obtained answer is x² + y² = 1369.
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The complete question is mentioned in the image below.
the sides of quadrilateral measure 12cm, 9cm, 16cm, and 20cm.tee longest sides of a similar quadrilateral measure 8cm.find the measure of the remaining sides of a quadrilateral ?
The measure of the remaining sides of a quadrilateral will be 4.8 cm, 3.6 cm, and 6.4 cm.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The sides of the quadrilateral measure 12cm, 9cm, 16cm, and 20cm. The longest sides of a similar quadrilateral measure 8cm. Then the scale factor is given as,
SF = 8 / 20
SF = 0.40
Then the other sides of the quadrilateral are given as,
⇒ 0.40 x 12
⇒ 4.8 cm
⇒ 0.40 x 9
⇒ 3.6 cm
⇒ 0.40 x 16
⇒ 6.4 cm
The measure of the remaining sides of a quadrilateral will be 4.8 cm, 3.6 cm, and 6.4 cm.
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Please help me find the answer!!!
Answer:
270 square units
Step-by-step explanation:
The area of a regular hexagon is given by the equation:
A = (1/2)(a · P)
where a is the hexagon's apothem and P is its perimeter.
1. We can first solve for the hexagon's perimeter by multiplying its side length (given as 15) by 6, since there are 6 sides.
P = 15 · 6 = 90
2. Now, we can plug that perimeter value into the formula for the area of a regular hexagon (above).
A = (1/2)(90 · 6)
A = (1/2)(540)
A = 270 square units
The hypotenuse of a right triangle measures 7cm and one of its legs measures 2m. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer: 6.7
Step-by-step explanation: 7^2-2^2=45
square 45 =6.7
Mr. Harrison is going to offer tutoring after school. He is going to charge each student a $35 fee and then $15.50 per hour of tutoring. Which equation represents the total cost for each student to attend Mr. Harrison's tutoring session, if the student spend x number of hours in tutoring.
The student spends x hours tutoring, so y = 15.50x + 35, where x is the number of hours of tutoring and y is the total cost. Therefore, the total cost for a student who receives tutoring for two hours is $66.
What do you mean by tutoring?According to the dictionary definition, a tutor is a person who provides one-on-one or occasionally small-group teaching. The goal of tutoring is to enable students to help themselves, or to support or mentor them until they reach the point at which they are self-sufficient learners and no longer require a tutor.
Tutoring – a teacher's job?Tutors have the ability to, and frequently do, teach students new things. However, when comparing tutoring with teaching, what is being taught is the main difference. Teachers are meant to teach students new content, and tutors teach students how to learn new content.
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How long does it take jim to mow lawn alone?
The time Jim takes alone to mow the lawn is 10 hours.
How to find the number of hours Jim take to mow?Jim and Craig, working together can mow the lawn in 8 hours. Working alone, Craig take 4 times as long as Jim.
Therefore, the time it takes Jim to mow the lawn alone can be calculated as follows:
let
x = time use by Jim to mow the lawn
Therefore,
time Craig use to mow the lawn = 4x
Hence,
1 / 8 = 1 / 4x + 1 / x
1 / 8 = 1 + 4/ 4x
1 / 8 = 5 / 4x
cross multiply
4x = 40
x = 40 / 4
x = 10
Therefore,
time Jim takes alone to mow the lawn = 10 hours.
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Find the value of x that will make L||m
The value of x that will make L||m is 9.
How to find the value of x that will make L||m?
Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life
The angle (4x²- 324)° is equal to 90°. That is:
(4x²- 324)° = 90°
4x²- 324 = 90
4x² = 90 + 324
4x² = 324
x² = 324/4
x² = 81
x = √81
x = 9
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Need help with this problem quick!!!! <3
The product of a, b, and c would be, 9/8
What is Expression?
An expression, often known as a mathematical expression, is a finite combination of symbols that is well-formed according to context-dependent principles.
First, let's simplify the expression:
[tex]\frac{6 x^y^{-1} }{\sqrt[{4} ]{(16x^5y^2)}}\\\\\ = \frac{(6x^2y^{-1} )}{4x^{\frac{5}{4} } y^{\frac{1}{2} } } \\\\[/tex]
We can simplify further by dividing both the numerator and denominator by x²:
[tex]\frac{6x^{2} y^{-1} }{4x^{\frac{5}{4} } y^{\frac{1}{2} }} \\\\= \frac{6y^{-1} }{4x\frac{3}{4} y^{\frac{1}{2} } } \\\\= \frac{\frac{6}{4} *x^{2} y^{-1} }{x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\=\frac{3}{2x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\[/tex]
So, a = 3, b = -3/4, and c = -1/2.
The product of a, b, and c is 3 * -3/4 * -1/2 = 9/8.
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Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model mathematically his motion and starts her stopwatch. Let t be the number of seconds the stopwatch reads and let y be the number of meters Tarzan is from the riverbank. Assume that y varies sinusoidally with t, and that y is positive when Tarzan is over water and negative when he is over land. Jane finds that when t = 2, Tarzan is at one end of his swing, where y = -23. She finds when t = 5 he reaches the other end of his swing and y = 17.
We can represent the sinusoidal function for Tarzan's motion as given below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model mathematically his motion and starts her stopwatch.
Assume the sinusoidal equation to be -
y = Asin(ωt)
We can represent the coordinates as -
For {t} = 2, {y} = -23. So -
- 23 = Asin(2ω) ... { 1 }
For {t} = 5, {y} = 17. So -
17 = Asin(5ω) ... { 2 }
Therefore, we can represent the sinusoidal function for Tarzan's motion as given above.
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A distribution is given as X~ U(0, 12).What is the theoretical mean?
The theoretical mean of the uniform distribution between 0 and 12 is given as follows:
6.
What is the uniform probability distribution?It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
The bounds for this problem are given as follows:
a = 0 and b = 12.
As each outcome is equally as likely, the mean of the distribution is equals to the mean of the bounds, hence:
(0 + 12)/2 = 6.
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Colin’s mean mark over three exams was 83%. His mean mark for the first two exams was 76%. What was Colin’s score in the final exam?
Answer: 97%
Step-by-step explanation:
If for the 3 exams, the mean was 83% and the first two were 76%, that means..
76 + 76 = 152 (divided by two = 76%/current mean)
In order to get an average of 83%, Colin has to have a score that is higher than 76% and somewhat closer to above 90%.
By doing trial and error (testing different percents between 76% and 80%), you can come to the conclusion that, 76% + 76% + 97% = 249 / 3 = 83
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude,
in feet, of the airplane and x represents the number of minutes the plane has been descending:
y=-1025x + 30,750
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and
describe what is happening to the airplane at these time intervals.
Part A:
Look at photo
Part B:
After 5 minutes, the altitude of the airplane is 20,500 feet. This means that the airplane has been descending for 5 minutes and has lost an altitude of 10,250 feet.
After 30 minutes, the altitude of the airplane is -29,250 feet. This means that the airplane has been descending for 30 minutes and has lost an altitude of 60,000 feet. The negative value of the altitude indicates that the airplane has landed or is close to landing.
At both 5 minutes and 30 minutes, the airplane is descending. The rate of descent is constant, as represented by the slope of the equation, and is equal to -1025 feet per minute. At 5 minutes, the airplane is still at a high altitude, while at 30 minutes the airplane has landed or is close to landing, as indicated by the negative value of the altitude.
Answer:
Step-by-step explanation:
Part A:
x | y | Equation
0 | 30,750 | y = -1025*0 + 30,750
5 | 27,250 | y = -1025*5 + 30,750
8 | 23,750 | y = -1025*8 + 30,750
10 | 20,250 | y = -1025*10 + 30,750
30 | -20,250 | y = -1025*30 + 30,750
Part B:
After 5 minutes, the altitude is 27,250 feet. This means that the airplane has been descending steadily for 5 minutes and is now at a lower altitude than when it started.
After 30 minutes, the altitude is -20,250 feet. This means that the airplane has been descending steadily for 30 minutes and is now much lower than when it started. The airplane is close to the ground and about to land.
What is 22/22X22-22+22? Then 33/33X33-33+33? Then Divide both answers by 5?
Answer:
22/22X22-22+22= 22÷5 =4.5
33/33X33-33+33=33÷5=6.6
Verify the Identity.
Step-by-step explanation:
[tex] \frac{ \tan( \alpha ) }{1 + \sec( \alpha ) } = - \cot( \alpha ) + \csc( \alpha ) [/tex]
Multiply by 1-sec(a)
[tex] \frac{ \tan( \alpha ) (1 - \sec( \alpha ) }{(1 + \sec( \alpha ) )(1 - \sec( \alpha ) )} [/tex]
[tex] \frac{ \tan( \alpha ) - \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]
[tex] \frac{ \tan( \alpha ) }{1 - \sec {}^{2} ( \\ \alpha ) } - \frac{ \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]
[tex] \frac{ \tan( \alpha ) }{ - \tan {}^{2} ( \alpha ) } + \frac{ \tan( \alpha ) \sec( \alpha ) }{ \tan {}^{2} ( \alpha ) } [/tex]
[tex] - \frac{1}{ \tan( \alpha ) } + \frac{ \sec( \alpha ) }{ \tan( \alpha ) } [/tex]
[tex] - \cot( \alpha ) + \frac{ \frac{1}{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } [/tex]
[tex] - \cot( \alpha ) + \frac{1}{ \sin( \alpha ) } [/tex]
[tex] - \cot( \alpha ) + \csc( \alpha ) [/tex]
9 Mr Karim had 2740 sacks of rice at first Mr Dani had 3560 sacks of rice at first. Mr Karim gave some sacks of rice to Mr Dani. In the end, Mr Dani had 4 times as many sacks of rice as Mr Karim. How many sacks of rice did Mr Karim have in the end?
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
