Verify the identity.
sin (x + y) - sin (x - y) = 2 cos x sin y
Answers
Answer:
Step-by-step explanation:
Related Questions
a rectangular feild 70m long and 50m wide has a path of uniform width around it if the area of the path is 104m² find the width of the path
Answers
The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.
What is the quadratic formula?The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.
The length of the rectangular field = 70 meters
The width of the rectangular field = 50 meters
The width of the path around the field = Uniform width
Area of the path around the field = 104 m²
Let x represent the width of the path, we get;
(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104
4·x² + 240·x = 104
4·x² + 240·x - 104 = 0
The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;
\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)
Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;
a = 4, b = 240, c = -104
Therefore;
\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)
x ≈ 0.430 or x ≈ -60.4
The possible value of the width of the path is x ≈ 0.43 metersLearn more about the quadratic formula here:
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A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?
Answers
Answer:
Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet
Step-by-step explanation:
The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)
In an experiment, the probability that event A occurs is 0.2 and the probability that event B
occurs is 0.5. If A and B are independent events, which statement is true?
A.
B.
P(A and B) = 0.1
P(A or B) = 0.1
P(A and B) = 0.7
P(A or B) = 0.7
C.
D.
Answers
Answer:
Step-by-step explanation:
P(A and B) = 0.1
Which statement correctly compares the centers of the distributions?Penguin Heights at Park Zoo(in cm)Penguin Heights at Countyside Zoo(in cm)35 36 37 38 39 40 41 42 43 44 45O35 36 37 38 39 40 41 42 43 44 45
Answers
The Solution:
The correct answer is [option B ]
Given:
Required:
Compare the centers of the distributions.
Explanation:
\(\begin{gathered} The\text{ Median of pengium Height at park zoo}=41 \\ \\ The\text{ median of pengium Height at countryside zoo}=40 \end{gathered}\)Thus, the median height of penguin at the park zoo is greater than that at the countryside zoo.
Answer:
[option B]
Question 3 of 5
A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.
Let x represent the canoe's speed with no water current (in still water) and y represent the speed of the water current, in miles per hour. Then the situation can be represented by this system of equations:
x+y=7
x-y=1
Choose the two correct options.
A. The speed of the canoe in still water is 3 miles per hour.
B. The speed of the water current is 4 miles per hour.
C. The speed of the canoe in still water is 4 miles per hour.
D. The speed of the water current is 3 miles per hour.
Answers
Two correct options are option (C) The speed of the canoe in still water is 4 miles per hour and option (D) The speed of the water current is 3 miles per hour.
A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.
x is the Canoe's speed with no water current in miles per hour
y is the speed of the water current, in miles per hour
The equations are
x + y = 7
x - y = 1
Here we have to use the elimination method
Add both the equation
2x = 7 + 1
2x = 8
x = 8/2
x = 4
Then substitute the value of x in the first equation
4 + y = 7
y = 7 -4
y = 3
Therefore, the correct options are option (C) and option (D)
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Find the SURFACE AREA of this composite solid.
Answers
FINDING THE SURFACE AREA OF A COMPOSITE SOLID
About "Finding the surface area of a composite solid"
Finding the surface area of a composite solid :
A composite solid is made up of two or more solid figures.
To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Finding the surface area of a composite solid - Examples
Example 1 :
Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?
Solution :
Step 1 :
Identify the important information.
• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.
• One face of each prism is not on the surface of the figure.
Step 2 :
Find the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
Step 3 :
Find the area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Step 4 :
Find the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Step 5 :
Add. Then subtract twice the areas of the parts not on the surface.
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
The surface area before the hole was drilled was 3,720 sq.cm.
The surface area before the hole was drilled was; 3,720 sq.cm.
What is composite solid?A composite solid is made up of two or more solid figures.
To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
The bottom is a rectangular prism with h = 18 cm.
The base is a 30 cm x 24 cm rectangle.
One face of each prism is not on the surface of the figure.
Then the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
The area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Now the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Now,
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
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How many miles does he run in one year
Answers
Answer Key:
1. Since the question says Mr. Smith runs 2.7 miles every day of the week, you will need to multiply it with 365, the days of the year. The total answer you would get D. 985.5 miles.
| I just want to help you with #2 anyway
−3/5×8/6= helpplease
Answers
Answer:
-4/5 OR -0.8
Step-by-step explanation:
This problem is very simple but it can be broken down
First we do -3 times 8 and get -24
Then we do 5 times 6 and get 30
We put the first answer over the second which equals
-24/30
This can then be simplified further if we divide both sides by 6
-4/5 as a fraction
-0.8 as a decimal
-80% as a percent
Can someone answer and provide an explanation for these problems? Find the midpoint of the line segment with the given endpoints.
Answers
52) The midpoint of the line segment is (-0.5, 9).
53) The midpoint of the line segment is (3, -8.5).
52) To find the midpoint of the line segment with endpoints (8,9) and (-9,9), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) are the average of the corresponding coordinates of the endpoints.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-9)) / 2 = (-1) / 2 = -0.5
For the y-coordinate:
(y₁ + y₂) / 2 = (9 + 9) / 2 = 18 / 2 = 9
Therefore, the midpoint of the line segment is (-0.5, 9).
53) To find the midpoint of the line segment with endpoints (8,-10) and (-2,-7), we apply the same process using the midpoint formula.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-2)) / 2 = 6 / 2 = 3
For the y-coordinate:
(y₁ + y₂) / 2 = (-10 + (-7)) / 2 = -17 / 2 = -8.5
Hence, the midpoint of the line segment is (3, -8.5).
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In ΔEFG, e = 34 inches, f = 73 inches and g=89 inches. Find the area of ΔEFG to the nearest square inch.
Answers
Step-by-step explanation:
Heron's formula when all 3 sides (a, b, c) are given :
s = (a + b + c)/2
A = sqrt(s(s-a)(s-b)(s-c))
in our case
s = (34+73+89)/2 = 98
A = sqrt(98(98-34)(98-73)(98-89)) =
= sqrt(98×64×25×9) = sqrt(98)×8×5×3 =
= sqrt(2×49)×120 = sqrt(2)×7×120 =
= sqrt(2)×840 = 1,187.939392... ≈ 1,188 in²
Using the graph below, determine the employee's hourly wage.
Answers
By using the graph, the employee's hourly wages is calculated as $10.6
Graph:
Basically, a graph is a collection of points, called vertices, and lines between those points, called edges.
Given,
Here we have the graph with straight line.
And we need to determine the employee's hourly wage.
While we looking into the graph we have identified that the x axis refers the number of hours the employ is working and the y axis refers the money earned by them.
In order to find the wages for one hour, we need to select one point from the graph.
Here we have take the point (5,53)
The first point refers the number of hours that is 5.
And the second one refers the wages for 5 hours that is 53.
So, the one hour wages is calculated as,
=> 53/5
=> 10.6
Therefore, the employee's hourly wage is $10.6.
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4) Look at this set of 5 numbers: 5 3 5 3 4
By how much would the mean increase if the number 8 replaced one of the 3's in the
set?
Answers
==========================================================
Explanation:
To compute the mean, we first add up the numbers
5+3+5+3+4 = 20
Then divide by 5 since there are 5 numbers in the set
20/5 = 4
The mean is 4.
---------------
Now replace one of the '3's with 8 and recompute the mean
5+8+5+3+4 = 25
25/5 = 5
The mean is now 5.
The old mean in the previous section was 4.
The mean has increased by 1 since 5-4 = 1.
Side note: The increase from 3 to 8 is +5, which when dividing by 5, we're basically incrementing the mean by +1.
Answer:
1
Step-by-step explanation:
Mean=Sum of terms/ No.of terms
→5+3+5+3+4/5
20/5=4
If we replace 3 as 8 in one of the place values, Then:5+3+5+8+4/5=25/5
→5
Increment= 5-4=1
THUS, 1 is increased.
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A 9th grade teacher at a local high school wants to know which subject the 9th grade students in the high school like best which group of people should make up a sample that will best answer her question a, other 9th grade teachers in her school
B, parents of 9th graders in her school
C, 9th graders in her school
D,9th graders in her homeroom
Answers
The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.
What are subjects?Subjects are the different sets of information which is studied.
9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.
The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.
Thus, the correct option is C, 9th graders in her school.
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In one season, a basketball player missed 50% of her free throws. How many free throws did she attempt if she made 183 free throws?
Answers
Answer:
Step-by-step explanation:
50% of 366 is 183, therefore your answer is 366.
Ana works 25 hours a week at the library. If she is paid $10 an hour, and her net salary each week is $212.50, what percent of her salary is withheld for taxes?
Answers
Approximately 17.65% of Ana's salary is withheld for taxes.
To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.
Number of hours worked per week (H) = 25 hours
Hourly wage (W) = $10
Net salary (S) = $212.50
Calculate the total earnings before taxes:
Total earnings = Hours worked * Hourly wage
Total earnings = 25 hours * $10/hour
Total earnings = $250
Determine the amount of tax withheld:
Tax withheld = Total earnings - Net salary
Tax withheld = $250 - $212.50
Tax withheld = $37.50
Calculate the percentage of salary withheld for taxes:
Percentage withheld = (Tax withheld / Net salary) * 100
Percentage withheld = ($37.50 / $212.50) * 100
Percentage withheld ≈ 17.65%
Therefore, approximately 17.65% of Ana's salary is withheld for taxes.
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Find the volume of a cube that has a taotal surface area of 96 squares feet.
A.) 84.0ft³
B.) 84.06ft
C.) 84.06ft³
D.) 84.06ft^2
Answers
Surface area = 6 * side length^2
In this case, the surface area of the cube is 96ft², so you can set up the equation:
96ft² = 6 * side length^2
Solving for side length gives:
side length = sqrt(96ft² / 6) = 4ft
The volume of the cube is side length^3, so the volume of the cube is 4ft^3 = 64ft^3.
Therefore, the correct answer is C) 84.06ft³.
A punter kicked a 41 yard punt. The pth of the football can be modeled by y=-0.035x2 + 1.4x + 1 where x is the distance in yards the football id kicked and y id the height in yards the football kicked
Answers
This means that the football’s height when it was kicked 41 yards away was -1.762 yards.
What is yard?A yard is a unit of length measurement in the imperial and US customary systems of measurement. It is equal to 3 feet or 36 inches.
The equation given is a parabolic equation which models the path of the football. It is a quadratic equation in the form of y = ax² + bx + c, where a, b, and c are coefficients that determine the shape of the path. The coefficient a represents the rate of change in the football’s height as it moves away from the punter. In this equation, a is -0.035, which indicates that the football’s height decreases as it moves away from the punter. The coefficient b indicates the rate of change in the football’s height as it moves back toward the punter, and in this equation, b is 1.4, which means that the football’s height increases as it moves back towards the punter. Finally, the coefficient c is 1, which indicates the height of the football when it is kicked.
In this case, the football was kicked 41 yards, so plugging x = 41 into the equation gives us y = -0.035(41²) + 1.4(41) + 1 = -1.762.
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Mark Ogara rented a truck from Avis Rent-A-Car for the weekend (2 days). The base rental price was $32.35 per day plus 20 1/2 cents per mile. Mark drove 434.85 miles.
How much does Mark owe? Round to the nearest cent.
Answers
Answer:
Mark owes $163.84
Step-by-step explanation:
The base price (per day) is $32.35, we know he has the truck for 2 days so it will cost him $74.70
The cost per mile is 20.5 cents, and he drives 434.85 miles
20.5 cents is 0.205 dollars
0.205 times 434.85 = $89.14
$89.14 + $74.70 = $163.84
Apples are on sale for $5.75 for 5 pounds. What is the cost per pound?
Answers
Answer: 1.15
Explanation:
You model your investment account using the formula y = 20000(1.035)x where x represents the
number of years and y represents the account balance after x years. What is the growth rate of your
investment?
Answers
Answer:
Step-by-step explanation:
The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.
To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.
So, the growth rate of the investment is:
1.035 - 1 = 0.035
0.035 * 100 = 3.5%
Therefore, the growth rate of the investment is 3.5%.
The growth rate of the investment can be found by subtracting 1 from the base of the exponential function and converting the result to a percentage:
growth rate = (base - 1) x 100%
growth rate = (1.035 - 1) x 100%
growth rate = 0.035 x 100%
growth rate = 3.5%
Therefore, the growth rate of the investment is 3.5%.
A medical researcher wishes to investigate the relationship between hours exercised and weight lost. The researcher randomly samples 50 people on an exercise program and asks them to report how many hours they have exercised on average over the last 6 weeks and how many pounds they have lost. The researcher runs a correlation and finds a test statistic of .34. Knowing that the critical value is .279, what should the researcher conclude
Answers
Answer:
The researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program
Step-by-step explanation:
Here, we want to state what the conclusion of the researcher should be:
From the last part of the question, we can see that the test statistic is greater than the critical value
So what do we do in a case like this?
We can see that the researcher is trying to see if there is a correlation between hours worked out and the number of pounds lost over a specific period of time.
Now, let us form the null hypothesis;
The null hypothesis here H0 is that we do not have a correlation between number of hours spent working out and the amount of pounds lost
The alternative hypothesis here H1 is that there is a correlation between the number of hours spent working out and the amount of pounds lost
Since we have the value of the test statistic greater than the critical value, we reject the null hypothesis and accept the alternative hypothesis
So therefore, the researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program
Evan swims 321 laps in a month. He swims for 22 days in the month, How
many laps does he swim each day? Write your answer as a mixed number,
14 laps
14 13/22 laps
15 5/22 laps
14 7/22 laps
Answers
Answer:
Step-by-step explanation:
321
The sum of five and two times a number is 23. What is the number?
Answers
Answer:
5+2x=23 | x=9
Step-by-step explanation:
We would begin by using the Subtraction Property of Equality to isolate the variable (Subtract 5 from both sides.). Our product would now be 18. Then, we would use the Division Property Of Equality to isolate the 2 from the x (Divide 2 on both sides.). We would be left with x=9.
how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
multiple and convert to simplest form
Answers
Answer:
1)4
2)28
3)18.3
4)38.5
5)22.5
6)19.25
7)25.5
8)69.666
9)6.5
10)22.666
Step-by-step explanation:
To do this first you should convert the mix numbers into inproper fractions and then solve.1)8/5*5/2=4
2)21/5*20/3=7*4
=28
3)33/4*20/9=11*5/3
=55/3
=18.33...
=18.3
4)35/6*33/5=7*11/2
=77/2
=38.5
5)22/8*90/11=45/2
=22.5
6)11/3*21/4=11*7/4
=77/4
=19.25
7)34/5*15/4=34*3/4
=25.5
8)22/3*57/6=11*19/3
=209/3
=69.666
9)39/8*4/3=13/2
=6.5
10)17/2*8/3=17*4/3
=68/3
=22.666
Hope you got this
If you have any doubt please ask me
If you need this in fraction form just check the attachment
The staff at an advertising company took a survey of 350 people, each of
whom had visited one of two branches, East and West, of a store. Each
person surveyed was asked whether he or she had purchased a certain
product within the past month. The results of the survey, by location, are
shown in the table.
Answers
7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.
Out of the 168 people who visited the West branch of the store,
98 indicated that they had not purchased the product.
Therefore, the fraction of people who visited the West branch and had not purchased the product is:
98/168
Simplifying this fraction by dividing the numerator and denominator by 14, we get:
7/12
Hence, 7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.
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Question 2 The current report quantitatively analyzes three variables - load factors, revenue passenger mile, and available seat miles for American Airlines. The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics, focusing on domestic flights from January 2006 to December 2012. The quantitative analysis focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. Table 2: Summary Statistics of American Airlines (Domestic) Revenue Passenger Miles Mean 6,624,897 Median 6,522,230 Mode NONE Minimum 5,208,159 Maximum 8,277,155 Standard Dev 720,158.571 Variance 518,628,367,282.42 Load Factors Mean 82.934 Median 83.355 Mode 84.56 Minimum 74.91 Maximum 89.94 Standard Dev 3.972 Variance 15.762 Revenue Passenger Miles 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 0 10 American Airlines (Domestic) Performance 20 30 ● Revenue Passenger Miles 40 50 Load Factors Available Seat Miles 60 Mean 7,984,735 Median 7,753,372 Mode NONE Minimum 6,734,620 Maximum 9,424,489 Standard Dev 744,469.8849 Variance 554,235,409,510.06 70 80 Linear (Revenue Passenger Miles) 90 100 Figure 1: American Airlines (Domestic) Performance Write a report based on the given data. Please include additional tests such as hypothesis testing, skewness, z statistic, level of significance, and other necessary tests, as well as a discussion of the results obtained.
Answers
The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.
The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.
Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).
The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.
The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.
The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).
Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
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At an amusement park, 15 riders ride the race cars every 20 minutes and 35 riders ride the ferris wheel every 60 minutes. Which ride has the greater ratio of riders?
Answers
Answer: the Ferris Wheel
Step-by-step explanation:
I need help on this geometry thing someone plz hell
Answers
Answer:
Step-by-step explanation:
Gayla’s mom bought 9.5 gallons of gas for $21.85 . What is the cost of a gallon of gas?
Answers
Answer:
$2.30
Step-by-step explanation: