The given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
The identity is
sin(x+ y) - sin (x- y) = 2 cos x sin y
Here we have to use the trigonometric function
Consider the right hand side of the equation
We know
sin (x+ y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y - cos x sin y
Then
sin(x+ y) - sin (x- y) = sin x cos y + cos x sin y - (sin x cos y - cos x sin y)
= sin x cos y + cos x sin y - sin x cos y + cos x sin y
Eliminate the terms
= cos x sin y + cos x sin y
= 2 cos x sin y
Hence, the given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
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Aaron has a smart phone data plan that costs $40 per month that
includes 6 GB of data, but will charge an extra $25 per GB over the
included amount. How much would Aaron have to pay in a month
where he used 3 GB over the limit? How much would Aaron have to
pay in a month where he used went over by x GB?
Total cost when over by 3 GB:
Total cost when over by x GB:
Pls give me correct answer
I need it or else I fail
Aaron has to pay $ 115 when the usage gets over by 3 GBs and
$ (40 + 25x) when the usage gets over by x GBs.
How can one calculate the cost for a multiple of the same entity?
To calculate the cost of a multiple entities when the cost of a single one is given, we linearly multiply a fixed proportion to it to calculate the same.
Given, monthly fixed cost of the smart phone data plan = $ 40
Also, amount charged by the firm for each extra GB used = $ 25
Now, amount charged for three extra GBs = 25*3 = 75
Thus, net total that Aaron has to pay for 9 GBs = 40 + 75 = $ 115
Following similar arguments, amount charged for extra 'x' GBs = 25x
Thus, net total that Aaron has to pay for x GBs = 40 + 25x = $ (40 + 25x)
Therefore, Aaron has to pay $ 115 when the usage gets over by 3 GBs and $ (40 + 25x) when the usage gets over by x GBs.
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Evaluate the function.
f(x) = x² + 6x - 9
-
Find f(7)
Answer:
82
Step-by-step explanation:
Since x=7, you would put that value into the equation. i.e put that value, of 7, instead of x.
x² + 6x - 9
7² + 6(7) - 949 + 42 - 982Find the exact values of the six trigonometric functions of each angle 8.
Given: The trigonometry shown in the image
To Determine: The exact values of the six trogonometric functions of each angle shown
Solution
It can be observed that
Therefore
[tex]\begin{gathered} sin\theta=-1 \\ cos\theta=-\sqrt{2} \end{gathered}[/tex][tex]tan\theta=\frac{sin\theta}{cos\theta}=\frac{-1}{-\sqrt{2}}=\frac{1}{\sqrt{2}}[/tex][tex]\begin{gathered} csc\theta=\frac{1}{sin\theta}=\frac{1}{-1}=-1 \\ sec\theta=\frac{1}{cos\theta}=\frac{1}{-\sqrt{2}}=-\frac{1}{\sqrt{2}} \\ cot\theta=\frac{1}{tan\theta}=\frac{1}{\frac{1}{\sqrt{2}}}=1\times\sqrt{2}=\sqrt{2} \end{gathered}[/tex]Can someone help me on this pleaser
Answer: it should be the third one down
Step-by-step explanation:
Which of the following is not a condition necessary to create a valid probability distribution?
Given
different choices
Find
Which of the following is not a condition necessary to create a valid probability distribution?
Explanation
Each discrete outcome can have different probability of occuring
Hence the option stating each discrete outcome hsould have equal probability of occuring is not necessary
Final Answer
option (a) is correct option
Identifying Variables and Writing Functions Practice . A function describes how a dependent variable changes with respect to one or more independent variables. When there are only two variables, they are often summarized as an ordered pair with the independent variable first: (independent variable, dependent variable) The dependent variable is a function of the independent variable. If x is the independent variable and y is the dependent variable, write the function as y = f(x) Related Quantities. Write a short statement that expresses a possible relationship between the variables. Example: (age, shoe size) Solution: As a child ages, shoe size increases. Once the child is full-grown, shoe size remains constant. 1. (volume of a gas tank, cost to fill the tank) 2. (time, price of a Ford sedan), where time represents years from 1975 to 2017
Let's begin with what we know:
For an ordered pair, we have (independent variable, dependent variable)
For example, when x is the independent variable & y is the dependent variable, we have (x, y)
y = f(x)
We are to write a short statement that expresses a possible relationship between the variables below:
1. (volume of a gas tank, cost to fill the tank)
Volume of gas is the independent variable & Cost to fill the tank is the independent variable. That means that:
As the volume of the gas tank increases. the cost of filling it increases. Once the volume of the gas tank is filled, the cost to fill the tank is at its maximum
2. (time, price of a Ford sedan), where time represents years from 1975 to 2017
Time is the independent variable & price of a Ford sedan is the independent variable. That means that:
As the time lapses from 1975 to 2017, the price of the Ford sedan depreciates/reduces.
Kaj invests money in an account paying a simple interest of 1.2% per year. If she invests $90 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
Answer:
$91.08
Step-by-step explanation:
Interest = $90 × .012 = $1.08
Total amount = $90 + $1.08 = $91.08
Find the measure of angle b
Answer: B=30
Step-by-step explanation:
because of corresponding angles
Hope this helps! have a great day!
sorry also if you can could you please give a brainliest it would help a lot
Find the max and min values
100 +14.75 %
Step-by-step explanation:
100+14.75%
100+14=114
=114.75%
a company purchases shipments of 600 machine components and uses this acceptance sampling plan: randomly select and test 25 components and accept the whole batch if there are fewer than 3 defective components. it is known that this particular component has a 4% defective rate. what is the probability that shipment will be accepted?
25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. The probability is it that the shipment will be accepted is 0.7323.
Given that,
An organization utilizes the following acceptance sampling strategy for ordering shipments of 600 machine parts: 25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. This specific component is known to have a 4% fault rate.
We have to find how probability is it that the shipment will be accepted.
By binomial we get,
Binomial Problem:
n = 25 ; p = 0.04
P(0<= p <= 2)
= 0.7323
Therefore, The probability is it that the shipment will be accepted is 0.7323.
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 how many years  did Joe serve in prison  if his sentence of 5 year was reduced by three for good behavior 
Answer: 2 years
Step-by-step explanation: If Joe was meant to serve 5 years but then his sentence got shortened by 3 years, that means we need to use subtraction. 5 minus 3 equals 2. Therefore, the answer is 2 years.
oncerns about climate change and co2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). random samples of 47 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) if the true mean is .9340 with a standard deviation of 0.0030, within what interval will 98 percent of the sample means fall? (round your answers to 4 decimal places.)
The interval is from 0.9330 to 0.9350
For given condition;
mean = 0.9340
standard deviation = 0.0030
z-score at 98% = 2.33
n = size of sample = 47
Step 1: calculate the standard error of the mean
standard error of mean = z-score * standard deviation/sqrt(n)
= 2.33 * 0.0030/[tex]\sqrt{47}[/tex]
= 0.0010
step 2: upper limit = mean + standard error
= 0.9340 + 0.0010
= 0.9350
lower limit = mean - standard error
= 0.9340 - 0.0010
= 0.9330
Hence, the interval is from 0.9330 to 0.9350
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Which ordered pair is a solution to the system of linear equations?
2x + 3y= 6
–3x + 5y = 10
(0,2)
(2,0)
(3,2)
(2,3)
The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).
Linear equation:
Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.
Given,
Here we have the following system of linear equations.
2x + 3y = 6
-3x + 5y = 10
Now, we need to find the solution for the equations.
Here we have to use the substitution method to solve this one,
To do the substitution method we have to follow the following steps:
Step 1) Solve anyone of the equations either for the variable x or y
Step 2) Now, substitute the value obtained from step 1 to the other equation
Step 3) Finally, solve the equation to find the value of the remaining variable.
Here we have to take the equation (2), and we have to solve it for the value of y,
For that we have to rewrite the equation as,
5y = 10 + 3x
y = (10 + 3x)/5
Apply the value of y on the equation (1), in order to get the value of x,
So,
2x + 3(10 +3x)/5 = 6
2x + (30 + 9x)/5 = 6
(10x + 9x + 30)/5 = 6
19x + 30 = 30
19x = 0
x = 0
Now, apply the value of x on the equation in order to get the value of y,
y = (10 + 3(0))/5
y = 10/5
y = 2.
Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).
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what is the required flight visibility and distance from clouds if you are operating in class e airspace at 9,500 feet msl with a vfr-on-top clearance during daylight hours? a. 3 sm, 1,000 feet above, 500 feet below, and 2,000 feet horizontal. b. 5 sm, 500 feet above, 1,000 feet below, and 2,000 feet horizontal. c. 3 sm, 500 feet above, 1,000 feet below, and 2,000 feet horizontal.
It should be noted that if you are operating in class e airspace at 9,500 feet MSL with a VFR-on-top clearance during the day, the required flight visibility and distance from clouds are listed as "3 statute miles 1,000 above 500 below and 2,000 horizontal."
What is meant by flight visibility?The average forward horizontal distance of a flying aircraft from the cockpit at which prominent unlit objects can be seen and identified during the day and substantial lighted objects can be seen and identified during the night is known as flight visibility.
Visibility requirements exist the minimal visibility for flying.
According to Aviation Rules,
(a) According to aviation regulations, no person may operate an aircraft under visual flight rules (VFR) in restricted airspace when the ceiling is less than 1,000 feet unless flying vision is at least 2 miles.
b) No person shall work a helicopter under VFR at or below 1,200 feet above the ground or within the lateral boundaries of a specified Class B, C, D, or E airspace surface area of an aerodrome unless there exists clear visibility. exists at least -
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Mamadou spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7325 feet. Mamadou initially measures an angle of elevation of 15 degrees to the plane at point A. At some later time, he measures an angle of elevation of 42 degrees to the plane at point BB. Find the distance the plane traveled from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance between points A and B will be 19201.93 feet.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Mamadou notices an airplane arriving in a straight line and flying directly overhead on the radar. The plane stays at the same height of 7325 feet. Mamadou initially measures a 15-degree angle of inclination to the plane at point A. Later, he detects a 42-degree angle of elevation to the plane at point B.
The distance between points A and B will be given as,
D = 7325 / tan 15° - 7325 / tan 42°
D = 27337.27 - 8135.34
D = 19201.93 feet
The distance between points A and B will be 19201.93 feet.
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Answer:
19202 feet
Step-by-step explanation:
I got the same problem and got it right with that answer.
I’d appreciate the help this is my last few questions and this will save my grade since the first trimester of my school is done this week so I appreciate help
Answer:
260.52cm^
Step-by-step explanation:
What is the equation of the line that passes through the point (−6,−3) and has a slope of 0?
The equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3
The line is passing through the point = (-6,-3)
The slope of the line = 0
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
(y-(-3)) = 0×(x-(-6))
We have to convert this equation the slope intercept form
Slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
(y-(-3)) = 0×(x-(-6))
y+3 = 0×(x+6)
y+3 = 0
y = -3
Hence, the equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3.
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Given:m angle 2+m angle 3 =180, angle 2 and angle 5 are supplementary
Prove:p l l q
The value of x is 29° and it's a supplementary angles.
What are supplementary angles?Supplementary angles simply means the angles that have a sum that is equal to 180°
In this case, we have been given two angles. It's important to equate them together. This will be illustrated as:
2x + 15 + 5x - 38 = 180
Collect like terms
7x - 23 = 180
Collect like terms
7x = 180 + 23
7x = 203
Divide
x = 203/7
x = 29°
The complete question is written below.
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Complete question
Given angle P is 2x + 15. and angle Q is 5x - 38. Prove that they are supplementary
please see attached question
correct answer will get brainliest
Answer:
Step-by-step explanation:
[tex]\frac{y}{\sqrt{x} }[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} }{\sqrt{x} \sqrt{x} }[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} }{x}[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} -\sqrt{x} }{x}[/tex]
PLEASE HELP ASAP (100 POINTS) If the line of best fit is y = 1.416x − 0.76, what is the residual value for the coordinate (7, 8)?
A. −1.152
B. 1.152
C. −3.568
D. 3.568
Answer:
A: -1.152Step-by-step explanation:
y = 1.416x − 0.76
For (7, 8):
residual value = Measured value - Predicted value
residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)
When x = 7:
value of y from the equation, y1 = 1.416*7 - 0.76
y1 = 9.912 - 0.76
y1 = 9.152actual y-coordinate of the point, y2 = 8
From:
residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)
residual value = y2 - y1
residual value = 8 - 9.152
residual value = -1.152Answer:
A: -1.152
Step-by-step explanation:
I did it and it was right!
10. The data set below shows the mileage and selling prices of eight used cars of the same model. Mileage Price 21,000 $16,000 34,000 $11,000 41,000 $13,000 43,000 $14,000 65,000 $10,000 72,000 $12,000 76,000 $7,000 84,000 $7,000 (a) Calculate r , the correlation coefficient between these two variables. r = (b) Interpret the value of r : the association is positive or negative and (strong or moderate or weak or negligible) (c) Compute the regression line for predicting price from mileage. ˆ y = x + (d) Predict the price of a car with 30,000 miles. $ (e) Does the student with 43,000 miles on it have a higher or lower price than the one predicted by the regression line? Higher Lower
Step 1
Plot a graph with the given table.
Step 2
Calculate r, the correlation coefficient between the two variables.
[tex]\begin{gathered} \text{From the graph,} \\ r\text{ = }-0.839 \end{gathered}[/tex]Step 3
Interprete the value of r
[tex]\text{The association is a strong and negative relationship}[/tex]Step 3
Compute the regression line for predicting price from mileage
[tex]\hat{y}=-0.118136x+17688.4[/tex]Step 4
Predict the price of a car with 30,000 miles
[tex]\begin{gathered} \hat{y}=-0.118136(30000)+17688.4 \\ \hat{y}=-3,544.08+17688.4 \\ \hat{y}=\text{\$}14,144.32 \end{gathered}[/tex]Step 5
[tex]\begin{gathered} \hat{y}=-0.118136(43000)\text{ + 17688.4} \\ \hat{y}=-5079.848+17688.4 \\ \hat{y}=\text{\$}12608.552\text{ } \\ \hat{y}\approx\text{\$12608.55} \\ \text{The given price for the mileage of 43000 is \$}14000 \\ \text{Therefore, the student with 43000 mileage on it will have a higher price than the one predicted by the regression line.} \end{gathered}[/tex]HELP PSLSPSLAPSLSPSLSPSLSPSLSPSL
Answer: D) 40
Step-by-step explanation:
mph (miles per hour)
60 minutes is an hour, so the number of miles above 60 minutes (which is 40) is the answer.
Hope this helps!
4. En un vecindario, un camión de helados pasa cada 8 días y un food truck pasa cada 2
semanas. Se sabe que 15 días atrás ambos vehículos pasaron en el mismo día. Raúl M
cree que dentro de un mes los vehículos volverán a encontrarse y Oscar cree esto
ocurrirá dentro de dos semanas. ¿Quién está en lo cierto?
Answer:
???
Step-by-step explanation:
Is there a English version for this question?
Alvin paddled for 2 hours with a 5-km/h current to reach a campsite. The returntrip against the same current took 7 hours. Find the speed of the boat in stillwater.
Given:
Alvin paddled for 2 hours with a 5-km/h current to reach a campsite.
Let n be the speed of boat.
Distance is calculated as,
[tex]\begin{gathered} d=rt \\ d=2\mleft(n+5\mright) \end{gathered}[/tex]The return trip against the same current took 7 hours.
[tex]\begin{gathered} d=rt \\ d=7(n-5) \end{gathered}[/tex]Equate both the equations,
[tex]\begin{gathered} 2(n+5)=7(n-5) \\ 2n+10=7n-35 \\ 7n-2n=10+35 \\ 5n=45 \\ n=\frac{45}{5} \\ n=9 \end{gathered}[/tex]Answer: the speed of the boat is 9 mph.
Question
Evaluate the expression when k = 3 and j = 10.
(5k−j)2+2k
Responses
80
80
45
45
31
31
20
Answer:
31Step-by-step explanation:
Given Expression (5k − j)² + 2kEvaluateWhen k = 3, j = 10SolutionSubstitute and calculate:
(5k − j)² + 2k = (5*3 - 10)² + 2*3 = (15 - 10)² + 6 = 5² + 6 = 25 + 6 = 31suppose we want to choose 2 letters without replacement from four letters ABCD. (A)how many ways can the speed on if the order of choices is taken into consideration?(B) how many ways can this be done if the order of choices is not taken into consideration ?
A)
If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:
[tex]4\cdot3=12[/tex]B)
If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):
[tex]\frac{12}{2}=6[/tex]jessica jogs on a path that is 25 meters long to get a park that is south of her location.it takes her 2.5hrs. what is her velocity
Answer:
10 meters per hour
Step-by-step explanation:
Velocity = Distance / Time
If cosA is equal to sin65 find the value of A
Answer:
A = 25Step-by-step explanation:
We know that:
cos A = sin (90 - A)Apply it to the given to get:
90 - A = 65A = 90 - 65A = 25the weights of items produced by a certain company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. the manager of the production line wants to discard any item whose weight is in the lower 2.5%. what is the maximum possible weight for the items discarded?
Using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
What is meant by standard deviation?The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. A low standard deviation means that the values tend to be close to the established mean, whereas a large standard deviation suggests that the values exist distributed throughout a greater range.A measure of a data set's variance from the mean is referred to as "standard deviation." While a high standard deviation indicates that the data are more spread, a low standard deviation suggests that the data are clustered around the mean.So,
Mean = 4.5Standard deviation = 0.3(A) P(x > 4.14)
z = (4.14 - 4.5) / 0.3= -1.20P(z > -1.20) = P(z < 1.20)= 0.8849(B) P(4.8 < x < 5.04)
= P (4.8 - 4.5/0.3 < x - μ/σ < 5.04 - 4.5/0.3)= P(1 < z < 1.80)= P(z < 1.80) - P(z < 1)= 0.9641 - 0.8413= 0.1228 or 12.28 %(C) P(x > x) = 0.05
z value will be, 1.6451.645 = (x - 4.5) / 0.3x = 4.9935(D) P(x < 5.01)
= (z = x - μ/σ)= (5.01 - 4.5) / 0.3 = 1.7P(z < 1.70) = 0.9554n = 27875/0.9954= 28004Therefore, using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
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Correct question:
The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weighs between 4.8 and 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 items of the entire production weigh at least 5.01 ounces, how many items have been produced?
alues there is action youThe ton presents a function because
Answer:
The equivalent expression is;
[tex]\frac{1}{x^{19}}[/tex]Explanation:
Given the expression;
[tex]\frac{(x^{-5})^4}{x^{-1}}[/tex]we want to simplify;
[tex]\begin{gathered} \frac{(x^{-5})^4}{x^{-1}} \\ =\frac{x^{-5}^{(4)}}{x^{-1}} \\ =\frac{x^{-20}}{x^{-1}} \end{gathered}[/tex]Applying the rules of exponent;
[tex]\begin{gathered} =\frac{x^{-20}}{x^{-1}} \\ =\frac{1}{x^{20}}\times\frac{1}{x^{-1}} \\ =\frac{1}{x^{20-1}} \\ =\frac{1}{x^{19}} \end{gathered}[/tex]Therefore, the equivalent expression is;
[tex]\frac{1}{x^{19}}[/tex]