\(\text{LHS}=\frac{\sin x}{1-\cos x}-\cot x\\\\=\frac{\sin x}{1-\cos x}-\frac{\cos x}{\sin x}\\\\=\frac{\sin^{2} x}{\sin x(1-\cos x)}-\frac{\cos x(1-\cos x)}{\sin x(1-\cos x)}\\\\=\frac{\sin^{2} x-\cos x(1-\cos x)}{\sin x(1-\cos x)}\\\\=\frac{\sin^{2} x-\cos x+\cos^{2} x}{\sin x(1-\cos x)}\\\\=\frac{(\sin^{2} x+\cos^{2} x)-\cos x}{\sin x(1-\cos x)}\\\\=\frac{1-\cos x}{\sin x(1-\cos x)}\\\\=\frac{1}[\sin x}\\\\=\csc x\\\\=\text{RHS}\)
PLEASEEEE SOMEONE HELP I GIVE AS MUCH POINTS :’( Thank you!
The approximate area of the trapezoid is determined as 13.95 unit².
What is the approximate area of the trapezoid?The approximate area of the trapezoid is calculated as follows;
Area = ¹/₂(b₁ + b₂)h
Where;
b₁ and b₂ are the lengths of the parallel sidesh is the heightThe y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;
y(3/2) = - (3/2)²/2 + 3/2 + 5
y(3/2) = -9/8 + 3/2 + 5
y(3/2) = 5.375
y(4) = -4²/2 + 4 + 5
y(4) = -8 + 9
y(4) = 1
h = 5.375 - 1 = 4.375
The approximate area of the trapezoid is calculated as;
Area = ¹/₂(5.375 + 1) x 4.375
Area = 13.95 unit²
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A rectangle pool has dimensions x and (x+6). The area of the pool is 143 square feet. What are the dimensions of the length and width of the pool?
Answer:
Step-by-step explanation:
A=length x width
143=(x)(x+6)
143=x squared +6x
X=12
the other might be 18
Can you help me solve this?
Y-intercept= 4, goes through the point (2, 3)
Please solve using y=Mx+b
Answer:
y=-1/2x+4 Is your answer
Step-by-step explanation:
y=mx+b
3=2x+4
-1=2x
x=-1/2
You already know y is 4 so y=-1/2x+4
What kind of relationship is expressed below?
5x-9>12
Answer:
Today: Tuesday, 12th January 2021
21.16 PM
\( \tt 5x - 9 > 12\)
\( \tt 5x > 12 + 9\)
\( \tt 5x > 21\)
\( {\orange{\boxed{ \red{\tt x = \frac{21}{5} }}}}\)
The given relation 5x-9>12 represents inequality. the solution of inequality is x > ( 21 / 5).
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Given inequality, the relation is 5x-9>12. The solution to inequality be done as:-
5x - 9 > 12
5x > 12 + 9
5x > 21
x > 21 / 5
Therefore, the given relation 5x-9>12 represents inequality. the solution of inequality is x > ( 21 / 5).
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Suppose a golf club company has designed a new club, which it claims will allow a professional golfer to make a hole in 120% of the time and an amateur golfer 10% of the time. Professional an amateur golfers sign up to play 5 games of 18 holes each
A professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6.
First, let's define some variables to represent the probabilities of making a hole for a professional golfer and an amateur golfer:
Let p be the probability that a professional golfer makes a hole with the new club.
Let q be the probability that an amateur golfer makes a hole with the new club.
According to the company's claims, we know that:
p = 1.2q (since the professional golfer makes a hole 120% of the time, which is 1.2 times the probability of the amateur golfer making a hole)
Next, we need to determine the probability of each golfer making a hole during one round of golf, which consists of 18 holes. Let's assume that each hole is independent of the others, meaning that the outcome of one hole does not affect the outcome of another. In that case, the probability of making at least one hole in a round can be calculated using the complement rule:
The probability that a professional golfer makes at least one hole in a round is 1 minus the probability that the golfer misses every hole: \(1 - (1-p)^{18} .\)
The probability that an amateur golfer makes at least one hole in a round is\(1 - (1-q)^{18} .\)
Now, let's use these probabilities to calculate the expected number of holes each golfer will make in 5 rounds of golf:
The expected number of holes made by a professional golfer in 5 rounds is 5 times the expected number of holes made in one round, which is \((1 - (1-p)^{18} )\times18.\)
The expected number of holes made by an amateur golfer in 5 rounds is 5 times the expected number of holes made in one round, which is \((1 - (1-q)^{18} )\times18.\)
We can simplify these expressions using the relationship between p and q:
The expected number of holes made by a professional golfer in 5 rounds is \(518(1 - (1-1.2q)^{18} ).\)
The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-q)^{18} ).\)
We can now evaluate these expressions using the values of p and q:
\(p = 1.2q, so q = p/1.2\)
Substituting this into the expressions above, we get:
The expected number of holes made by a professional golfer in 5 rounds is\(518(1 - (1-1.2(p/1.2))^{18} ) = 518(1 - (1-p)^{18} ).\)
The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-p/1.2)^{18} ).\)
Finally, we can evaluate these expressions using the given probabilities:
The expected number of holes made by a professional golfer in 5 rounds is\(518(1 - (1-1.2q)^{18} ) = 518(1 - (1-1.2(0.1))^{18} ) = 40.7.\)
The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-q)^{18} ) = 518(1 - (1-0.1/1.2)^{18} ) = 1.6.\)
So according to these calculations, we would expect a professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6
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surface area of a cube if the sides are 0.7
Answer:
\(SA = 2.94 \, \textrm{units}^2\)
Step-by-step explanation:
The surface area of a regular 3D figure can be represented as:
\(SA = A_{\textrm{\,1 side}} \cdot (\# \textrm{ of sides})\).
Therefore, the surface area of a cube is:
\(SA = s^2 \cdot 6\)
where \(s\) is the length of a side.
To solve this problem, simply input the given side length into the above formula:
\(SA = 0.7^2 \cdot 6\)
and simplify.
\(SA = 0.49 \cdot 6\)
\(SA = 2.94 \, \textrm{units}^2\)
what is the HCF of 9a² -6ax
Answer:
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the mean of a distribution is defined as the data value where 50% of the data is above and 50% is below. group of answer choices true false
FALSE, it is not the mean but the median of a distribution which is defined as the data value where 50% of the data is above and 50% is below.
The median denotes the point at which 50% of data values are higher and 50% are lower. As a result, it is the data's midpoint. In a symmetrical distribution, the median is always the midpoint, resulting in a mirror image with the median in the center.
The median is the number in the middle of a sorted, ascending or descending list of numbers, and it might be more descriptive of the data set than the average.
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Help
A tank can be filled in 10 hours by pump "A" working alone. Working together, it takes pump "A" and pump "B" 6 hours to do the same job. How long would it take pump "B" to fill the tank by itself?
Let's assume that the tank has a capacity of 1 unit (you can use any unit of measurement).
If pump "A" can fill the tank in 10 hours, then in 1 hour, pump "A" can fill 1/10th (1/10) of the tank.
If pump "A" and pump "B" working together can fill the tank in 6 hours, then in 1 hour, their combined rate is 1/6th (1/6) of the tank.
Let's denote the rate at which pump "B" fills the tank by "x" (in units per hour).
So, the rate at which pump "A" fills the tank is 1/10 and the combined rate of pump "A" and pump "B" is 1/6.
The combined rate of pump "A" and pump "B" can be expressed as the sum of their individual rates:
1/10 + x = 1/6
Now, let's solve this equation to find the value of "x," which represents the rate of pump "B."
1/10 + x = 1/6
Multiply both sides by 60 (the least common denominator of 10 and 6) to eliminate the fractions:
6 + 60x = 10
Subtract 6 from both sides:
60x = 4
Divide both sides by 60:
x = 4/60
Simplifying the fraction:
x = 1/15
Therefore, pump "B" can fill the tank at a rate of 1/15th (1/15) of the tank per hour.
To find the time it would take for pump "B" to fill the tank by itself, we can calculate the reciprocal of its rate:
1 / (1/15) = 15
So, pump "B" would take 15 hours to fill the tank by itself.
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A ____________ can be used to help us determine the extent of how much an outcome is achieved.
A metric can be used to help us determine the extent of how much an outcome is achieved.
What is metric?A metric is a quantifiable gauge that is employed to assess, scrutinize, and appraise diverse facets of a system, procedure, or outcome. It furnishes a standardized and unbiased approach to gauge and monitor performance or advancement towards particular objectives or goals. Metrics are commonly formulated based on precise criteria or prerequisites and can manifest as numerical or qualitative in essence.
They find application in various domains such as commerce, finance, science, engineering, and myriad others to evaluate performance, facilitate well-informed decisions, and oversee progress over time.
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analyze the following for freedom fireworks: requirement 1:a-1. calculate the debt to equity ratio.
To calculate the debt to equity ratio, you need to determine the total debt and total equity of Freedom Fireworks.
The formula for the debt to equity ratio is:
Debt to Equity Ratio = Total Debt / Total Equity
First, you need to determine the total debt of Freedom Fireworks. This includes any long-term and short-term liabilities or debts owed by the company. Obtain this information from the company's financial statements or records.
Next, calculate the total equity of Freedom Fireworks. This includes the owner's equity or shareholders' equity, which represents the residual interest in the assets of the company after deducting liabilities.
Once you have the values for total debt and total equity, plug them into the formula to calculate the debt to equity ratio.
For example, if the total debt of Freedom Fireworks is $500,000 and the total equity is $1,000,000, the debt to equity ratio would be:
Debt to Equity Ratio = $500,000 / $1,000,000 = 0.5
This means that for every dollar of equity, Freedom Fireworks has $0.50 of debt.
Note: It's important to ensure that the values for debt and equity are consistent and represent the same accounting period.
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Which of the following choices evaluates -2x2 + 4x, when x = -2?
Answer:
x = -2
-2(-2^2) + 4(-2)
-2(4) + -8
-8 + -8Answer = -16 is the answer.What are the coordinates of point A of the pre-image? (-1, 1) (-1, 2) (-9, 6) (-9, 18)
Answer:(-1,2)
Step-by-step explanation:
The line passing through points (5,) and (2,−3) is parallel to a line with a slope of 4/3. What is the value of y?
Answer:
Step-by-step explanation:
Parallel lines have same slope
Slope = \(\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
\(\dfrac{-3-y}{2-5}=\dfrac{4}{3}\\\\\\\dfrac{-3-y}{-3}=\dfrac{4}{3}\\\\\\-3-y=\dfrac{4}{3}*(-3)\\\\\\\)
-3-y = 4*(-1)
-3 - y = -4
- y = - 4 + 3
-y = -1
Divide both sides by (-1)
y = 1
NO LINKS PLEASE
EXPLANATION REQUIRED
I WILL GIVE BRAINLIEST
DONT MINF MY PRO CROPPING. DEFF.
ALSO ITS NOT C
Answer:
B is the correct answer
Step-by-step explanation:
Subtract area of triangle from total area: 30 - 14 = 16Since the figure is a square, all the sides are equal. Therefore, we need to find the square root of 16: √16 = 4All the sides of the square are 4 cm longTo check, reverse application:4 x 4 = 1616 + 14 = 30The percentage of measurements that are above the 39th percentile is.
The percentage of measurements that are above the 39th percentile is 61%.
To calculate the percentage of measurements above the 39th percentile, we need to find the complement of the percentile value. The 39th percentile represents the value below which 39% of the measurements fall. Therefore, the complement of the 39th percentile is the percentage of measurements above that value. Since the total percentage adds up to 100%, subtracting 39% from 100% gives us the percentage of measurements above the 39th percentile, which is 61%.
In summary, the percentage of measurements that are above the 39th percentile is 61%. This means that 61% of the measurements are higher than the value corresponding to the 39th percentile.
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What is the percentage of measurements that fall above the 39th percentile?
PLZ HELP, 20 POINTS, WILL GIVE YOU BRAINLIEST!!!
1. Li bought five lip balms. Each lip balm costs the same amount. She spent a total of $7.25.
(a) Write an equation that represents the situation. Use c to represent the cost of each lip balm.
(b) Represent the equation with a model.
(c) Solve and justify your solution.
Answer:
5×c=7.25.
c+c+c+c+c= 7.25
Step-by-step explanation:
5÷7.25=c
c=1.45
so 5×1.45=7.25
Assume double[][] x = new double[4][5], what are x.length and x[2].length? a. 4 and 4
b. 4 and 5 c. 5 and 4 d. 5 and 5
The x.length is the number of rows, which is 4. x[2].length is the number of columns in the 3rd row, which is 5. The expression "new double[4][5]" creates a 2D array of doubles with 4 rows and 5 columns. The correct answer is (b) 4 and 5.
The expression double[][] x = new double[4][5] creates a 2D array x with 4 rows and 5 columns. Therefore, x.length gives the number of rows, which is 4. And x[2].length gives the number of columns in the 3rd row (since array indices start at 0), which is 5. Therefore, the correct option is (b) 4 and 5.
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a university student is selecting courses for his next semester. he can choose from humanities courses and science courses. in how many ways can he choose courses if or more must be humanities courses?
a university student is selecting courses for his next semester. he can choose from humanities courses and science courses. the number of ways in which he can choose courses if or more must be humanities courses can be found using combinations
C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)
To determine the number of ways a university student can choose courses for the next semester with a requirement of at least "r" humanities courses, we can use combinatorial techniques.
Let's assume there are "n" total courses available, "h" of which are humanities courses, and "s" of which are science courses.
The student needs to select "r" or more humanities courses. We can calculate the number of ways to choose "r" or more humanities courses by summing the combinations for "r" to "h" humanities courses.
The formula to calculate the number of ways to choose "k" items from a set of "n" items is given by the combination formula: C(n, k) = n! / (k! * (n - k)!)
Using this formula, the calculation for the number of ways to choose "r" or more humanities courses can be expressed as:
Number of ways = C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)
Now, let's substitute the values and calculate the number of ways:
Number of ways = C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)
In conclusion, the number of ways the university student can choose courses, with a requirement of at least "r" humanities courses, is obtained by summing the combinations for "r" to "h" humanities courses using the combination formula.
the number of ways in which he can choose courses if or more must be humanities courses can be found using combinations
C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)
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plz answer this!I need to know the answer!
A local nonprofit organization is selling popcorn to raise money for hurricane relief. The organization paid $4 per bag for the popcorn and sold it for $5 per bag. What was the percent markup on each bag of popcorn?
What is the set builder equation for
x y
1/125 -3
1/25 -2
1/5 -1
1 0
5 1
25 2
125 3
The set builder nοtatiοn wοuld be {(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}
What is a set builder equatiοn?A set builder nοtatiοn is a cοncise way οf representing a set οf elements based οn a rule οr cοnditiοn. In set builder nοtatiοn, we use braces { } tο enclοse the set οf elements, and a vertical bar | οr a cοlοn : tο separate the cοnditiοn frοm the elements. The general fοrmat οf a set builder nοtatiοn is:
{elements | cοnditiοn}
Using this nοtatiοn, we can represent the set οf οrdered pairs (x, y) given in the questiοn as:
{(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}
This nοtatiοn reads as "the set οf all οrdered pairs (x, y) such that x takes οn the values 1/125, 1/25, 1/5, 1, 5, 25, and 125, and y takes οn the values -3, -2, -1, 0, 1, 2, and 3."
Hence, the set builder nοtatiοn wοuld be {(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}
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15 POINTS GIVEN⁉️⁉️
Using the scatter graph, decide whether each of the following statements is true or false: a) The same athlete had the longest javelin throw and the longest discus throw. b) The shortest javelin throw was longer than the shortest discus throw. c) The longest discus throw was shorter than the longest javelin throw. Athletes' javelin and discus throws 60 Length of discus throw (m) 5 55 90 0 X 40 X X X x X X X X X 45 50 55 60 Length of javelin throw (m) X X 65 70
Scatter graphs are used to represent data by using dots or symbols to represent data on two variables. There are two axes, a horizontal (x-axis) and a vertical (y-axis), where the horizontal axis is used for one variable and the vertical axis is used for the other variable. the statement is true.
Scatter graphs can be used to answer different questions about data by analyzing the pattern of the data. The questions that we want to answer using the scatter graph given in the question are:
a) The same athlete had the longest javelin throw and the longest discus throw.
b) The shortest javelin throw was longer than the shortest discus throw.
c) The longest discus throw was shorter than the longest javelin throw.
Answer: a) The same athlete had the longest javelin throw and the longest discus throw. This statement can be observed from the scatter graph by identifying the dots that are the highest and on the right of the graph.
The athlete who had the longest javelin throw also had the longest discus throw. Therefore, the statement is true.
b) The shortest javelin throw was longer than the shortest discus throw.
This statement can be observed from the scatter graph by identifying the dots that are the lowest and on the left of the graph.
The shortest javelin throw is longer than the shortest discus throw. Therefore, the statement is true. c) The longest discus throw was shorter than the longest javelin throw.
This statement can be observed from the scatter graph by identifying the dots that are the highest and on the right of the graph. The longest discus throw is shorter than the longest javelin throw. Therefore, the statement is false.
To conclude, scatter graphs are used to represent data by using dots or symbols to represent data on two variables. They can be used to answer different questions about data by analyzing the pattern of the data.
The scatter graph in the question can be used to determine whether a statement is true or false by identifying the dots that represent the data.
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Pls helpppp: Find the value of x.
Answer:
101
Step-by-step explanation:
Opposite of 79 must add to 180 which is 101 and x is equivalent
Answer:
101°
Step-by-step explanation:
x + 79° = 180° ( being co-interior angles )
x = 180° - 79°
x = 101°
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A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996
Answer:
The answer is "1:2"
Step-by-step explanation:
Let 96 car sales are X and 96 truck sales are Y And income from 97 cars is 0.89X, income from 97 trucks is 1.07Y
\(\to \frac{(0.89X+1.07Y)}{(X+Y)}=1.01\\\\\frac{X}{Y}=?\\\\\to \frac{(0.89X+1.07Y)}{(X+Y)}\ \ \text{Divide by Y and get}\ \ \frac{( \frac{0.89X}{Y}+1.07)}{(\frac{X}{Y}+1)} =1.01\\\\\)
Then
\(\to \frac{X}{Y}=1:2\)
Is median a measure of center or a measure of variation
a measure of center
b. measure of variation
Answer:
a
Step-by-step explanation:
Answer + method / explanation please
The expressions for the lengths of the segments obtained using vectors notation are;
a. i. \(\overrightarrow{LA}\) = q - (1/2)·p ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)
b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;
\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)
What are vectors?A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)
a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) = \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)
\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p
\(\overrightarrow{LA}\) = q - (1/2)·p
ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)
\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)
\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)
\(\overrightarrow{AN}\) = (2/7) × (p - q)
b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)
\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)
\(\overrightarrow{LA}\) = q - (1/2)·p
\(\overrightarrow{AN}\) = (2/7) × (p - q)
Therefore;
\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)
\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)
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The coordinates of the vertices of a triangle
are P(2,3), R(4, 5), and S(6,3). The
triangle PRS is reflected across the x-axis
to create triangle P'R'S. Which rule
describes this transformation?
A. (x, y)--(-x, -y)
B. (x, y)--(-x, y)
C. (x, y) --(x, -y)
D. (x,y) --(x,y)
Answer:
B?
Step-by-step explanation:
a solid cube of side 8cm is dropped into a cylindrical tank of radius 7cm . calculate the rise in the water level if the original depth of water was 9cm
What is the slope and does it pass?
Answer: no.
Step-by-step explanation:
it's 1 tenth