Answer:
4x² + 30x - 2 = 0
Step-by-step explanation:
Given:
Area = 58 square feet
Width = 7 feet
Length = 8 feet
Since the area is 58, writing the equation, we have:
(8 + 2x)(7 + 2x) = 58
Now expand the equation:
56 + 16x + 14x + 4x² = 58
56 + 30x + 4x² = 58
Collect like terms:
30x + 4x² + 56 - 58 = 0
30x + 4x² - 2 = 0
Rearrange the equation to a proper quadratic equation:
4x² + 30x - 2 = 0
The quadratic equation that can be used to determine the thickness of the frame, x is 4x² + 30x - 2 = 0
Penyelesaian
0.02 m: 3 cm: 4.6 cm = 2 cm : 3 cm: 4.6 cm
= 2 : 3 : 4.6
20 : 30 : 46
10 : 15
23
Latih Diri 4.1a
1. Wakilkan hubungan antara tiga kuantiti berikut dalam bentuk a : b:c.
(a) 2 minggu kepada 16 hari kepada 1 minggu
(b) 0.1 kg kepada 50 g kepada 0.25 kg
(c) 4 minit kepada 120 saat kepada 1.6 jam
(d 3 m kepada 480 cm kepada 6 400 mm
2. Tahir membayar RM5.60 untuk sepinggan nasi beriani, RM1.20 untuk segelas teh
dan 30 sen untuk sekeping kuih. Wakilkan hubungan harga bagi nasi beriani, teh dan
kuih dalam bentuk a:b:c.
76
BAB 4
Answer:
a:b:c
1a) 14:16:7
b) 2:1:5
c) 2:1:48
d) 15:24:32
2) 56:12:3
Step-by-step explanation:
Untuk membentuk nisbah tiga kuantiti, pertama-tama kita menukar masing-masing menjadi unit yang sama.
a) 2 minggu hingga 16 hari hingga 1 minggu
Menukar semuanya menjadi bilangan hari, kerana ia sangat setanding.
2 minggu = 14 hari
16 hari = 16 hari
1 minggu = 7 hari
2 minggu hingga 16 hari hingga 1 minggu = 14 hari hingga 16 hari hingga 7 hari
14: 16: 7
b) 0.1 kg hingga 50 g hingga 0.25 kg
Menukar semua menjadi gram
= 100 g hingga 50 g hingga 250 g
= 100: 50: 250
Bahagikan dengan 50
= 2 : 1 : 5
c) 4 minit hingga 120 saat hingga 1.6 jam
Menukar semua menjadi beberapa saat
= 240 saat hingga 120 saat hingga (1.6 × 60 × 60) saat
= 240 saat hingga 120 saat hingga 5,760 saat
= 2: 1: 48
d) 3 m hingga 480 cm hingga 6 400 mm
Menukar semua ini menjadi mm
= 3000 mm hingga 4800 mm hingga 6400 mm
Membahagi hingga 200 mm
= 15:24:32
2) RM5.60 hingga RM1.20 hingga 30 sen
Menukar semuanya kepada sen
= 560 sen hingga 120 sen hingga 30 sen
Membahagi hingga 10
= 56: 12: 3
Semoga ini Membantu !!!
English Translation
Solution
0.02 m: 3 cm: 4.6 cm = 2 cm: 3 cm: 4.6 cm = 2: 3: 4.6
20:30:46
10:15:23
Self Training 4.1a
1. Represent the relationship between the following three quantities in the form a: b: c.
(a) 2 weeks to 16 days to 1 week
(b) 0.1 kg to 50 g to 0.25 kg
(c) 4 minutes to 120 seconds to 1.6 hours
(d) 3 m to 480 cm to 6 400 mm
2. Tahir pays RM5.60 for a plate of beriani rice, RM1.20 for a glass of tea and 30 cents for a piece of cake.
Represent the price relationship for beriani rice, tea and cake in the form of a: b: c.
Solution
To form a ratio of three quantities, we first convert each of them to the same units.
a) 2 weeks to 16 days to 1 week
Converting all of it to number of days, as itnis very comparable.
2 weeks = 14 days
16 days = 16 days
1 week = 7 days
2 weeks to 16 days to 1 week
= 14 days to 16 days to 7 days
14 : 16 : 7
b) 0.1 kg to 50 g to 0.25 kg
Converting all into grams
= 100 g to 50 g to 250 g
= 100 : 50 : 250
Divide through by 50
= 2 : 1 : 5
(c) 4 minutes to 120 seconds to 1.6 hours
Converting all into seconds
= 240 seconds to 120 seconds to (1.6×60×60) seconds
= 240 seconds to 120 seconds to 5,760 seconds
= 2:1:48
(d) 3 m to 480 cm to 6 400 mm
Converting all of this to mm
= 3000 mm to 4800 mm to 6400 mm
Dividing through by 200 mm
= 15:24:32
2) RM5.60 to RM1.20 to 30 cents
Converting it all to cents
= 560 cents to 120 cents to 30 cents
Dividing through by 10
= 56:12:3
Hope this Helps!!!
Find the slope of the line passing through the given points. State whether the line is increasing, decreasing, horizontal, or vertical. (7,3) and (8,7)
Answer:
slope = 4
The line is increasing
Step-by-step explanation:
slope can be found through the equation [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. So, if we plug these points in, we get [tex]\frac{7-3}{8-7}[/tex], which simplifies to 4. So, the slope is 4.
Since the slope is positive, the line is increasing.
please help me out with these questions. Its trigonometry.
Find the value of the lettered angles
In case the pic's not clear;
[tex] \cos \alpha = \sin(50 + \alpha ) [/tex]
Answer: i) θ = 30°, 60°, 210°, & 240°
ii) θ = 20° & 200°
Step-by-step explanation:
i) sin (2θ) = cos 30°
[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]
To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above. θ = 30°, 60°, 210°, 240°
If you need ALL of the solutions (more than one rotation), add 180n to the solutions. θ = 30° + 180n & 60° + 180n
*********************************************************************************************
ii) cos α = sin (50 + α)
Use the Identity: cos α = sin (90 - α)
Use Transitive Property to get: sin (50° + α) = sin (90° - α)
50° + α = 90° - α
50° + 2α = 90°
2α = 40°
α = 20°
To find all solutions for one rotation, add 360/2 = 180 to the solution above.
α = 20°, 200°
If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n
easy math please help!
Answer:
[tex]\boxed{ \sf 41.81}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(?)=\frac{2}{3}[/tex]
[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]
[tex]\sf ?= 41.81031489...[/tex]
Answer:
[tex]\boxed{41.81}[/tex]
Step-by-step explanation:
∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.
The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).
However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.
Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.
You can use both the t statistic and the z statistic to test hypotheses about the mean of population. The test that uses the t statistic is typically referred to as a t test, while the test that uses z statistic is commonly called a z test.
Which of the following statements are true of the t statistic? Check all that apply.
a. If you know the population standard deviation, you should use the t statistic.
b. The t statistic could be considered as an estimated z statistic.
c. The t statistic provides a relatively poor estimate of z with small sample sizes.
d. The formula for the t statistic is t = (M - s) / SM.
Answer:
An apple a day keeps the doctor away
Step-by-step explanation:
Type in the answer
Its gonna be right
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced?
Answer:
The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.
Justin's hot water tank quits working and the landlord purchases a new one. He is concerned about its size and whether or not it can hold about 700 gallons. To do
so, it must have a volume of around 94 cubic feet.
What is the volume of a cylindrical water tank with a diameter of 4 and a height of 7 feet?
Answer:
87.92 ft³
Step-by-step explanation:
The formula for the volume of a cylinder is πr² · h
1. Set up the equation
π2² · 7
2. Solve
(3.14)(4)(7) = 87.92
The volume of a cylindrical water tank with a diameter of 4 feet and a height of 7 feet is 87.92 cubic feet.
Given that, a cylindrical water tank with a diameter of 4 feet and a height of 7 feet.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
We know that, the volume of a cylinder πr²h
Here, radius =4/2 = 2 feet
The volume of a cylinder = 3.14×2²×7
= 3.14×4×7
= 87.92 cubic feet
Therefore, the volume of a cylindrical water tank with a diameter of 4 feet and a height of 7 feet is 87.92 cubic feet.
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A 12 inch ruler is closest in length to which of the following metric units of measure 30cm 30000 mm 0.030 km or 30 m
Answer:
30 cm
Step-by-step explanation:
1 inch is 2.54 centimeters, and 2.54 times 12 is 30.48, which would be the closest.
The following metric units of measure is 30 cm
The correct option is (A)
What is measurement?Measurement” is the act of determining a target's size, length, weight, capacity, or other aspect.
How do you calculate unit conversion?Step 1: Write the conversion as a fraction.
Step 2: Multiply or divide, as required.
Step 3: Cancel the units (same units from top and bottom)
Step 4: Write the simplified answer with its correct unit.
Now, as we know that
1 inch = 2.54 cm
So, we can write
12 inch = 2.54 * 12
12 inch= 30.48 cm
Hence, the closest unit is 30 cm in the given metric system.
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Charli believes that if he flips a coin 650 times, it will land heads up exactly 325 times. What would you tell charli about her prediction?
Answer:
What I would tell Charli is that his prediction is somewhat right because there is a 50/50 chance of landing the coin on each side because 325 is half of 650.
Step-by-step explanation:
Cerra Co. expects to receive 5 million euros tomorrow as a result of selling goods to the Netherlands. Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days. Assume that these percentage changes are normally distributed. Use the value-at-risk (VaR) method based on a 95 percent confidence level. What is the maximum one-day percentage loss if the expected percentage change of the euro tomorrow is 0.5 percent
Answer:
The maximum one-day percentage loss = -1.15%
Step-by-step explanation:
Let assume that with the normal distribution, 95% of observations are smaller than 1.65 standard deviations above the mean.
Given that:
Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days.
if the expected percentage change of the euro tomorrow is 0.5 percent
and that Z value at 95% C.I level = 1.65
∵ The maximum one-day percentage loss = (expected percentage change - Z-Value) × standard deviation
The maximum one-day percentage loss = (0.5 - 1.65) × 1
The maximum one-day percentage loss = -1.15 × 1
The maximum one-day percentage loss = -1.15%
A pile of 55 coins consisting of nickels and dimes is worth $3.90 . Find the number of each.
Answer:
23 dimes, 32 nickels
Step-by-step explanation:
Let n equal the number of nickels and d be the number of dimes. We can use the information given to create a system of equations, as follows:
The total number of coins (the number of nickels plus the number of dimes) is 55, giving us the equation n + d = 55.
The total amount is $3.90. Since each nickel is worth $0.05 and each dime is worth $0.10, we get the equation 0.05n + 0.10d = 3.90.
Multiplying the second equation by 20, we get n + 2d = 78. We can subtract the first equation to get d = 23. Substituting this into the first equation, we get that n = 32.
Therefore, there are 23 dimes and 32 nickels.
Answer: 100 penny 2 qtrs 50 noclke
Step-by-step explanation:
Determine the value of x using a trigonometric ratio.
A) 10.11 units
B) 4.98 units
C) 4.18 units
D) 8.49 units
We have a known hypotenuse, but unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.
sin(angle) = opposite/hypotenuse
sin(50) = x/6.5
6.5*sin(50) = x
x = 6.5*sin(50)
x = 4.97928888027336 make sure your calculator is in degree mode
x = 4.98
Answer is choice B
Answer:
b
Step-by-step explanation:
How can I factor these complex conjuages? a^2 + b^2 and a^2 - b
Answer:
1) [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2+i^2b[/tex]
Step-by-step explanation:
1) [tex]a^2+b^2[/tex]
=> [tex]a^2 - (-1)b^2[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2-i^2b^2[/tex]
=> [tex](a)^2-(ib)^2[/tex]
Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]
=> [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2-b[/tex]
=> [tex]a^2+(-1)b[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2+i^2b[/tex] (It cannot be simplified further)
Answer:
[tex]\boxed{(a+ib)(a-ib)}[/tex]
[tex]\boxed{a^2+i^2b}[/tex]
Step-by-step explanation:
[tex]a^2 + b^2[/tex]
Rewrite expression.
[tex]a^2- (-1)b^2[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2- i^2 b^2[/tex]
Factor out square.
[tex]a^2-(ib)^2[/tex]
Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]
[tex](a+ib)(a-ib)[/tex]
[tex]a^2-b[/tex]
Rewrite expression.
[tex]a^2+(-1)b[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2+i^2b[/tex]
Twice a number plus three times a second number is twenty two. Three times the first number plus four times the second is thirty one. Find the numbers
Answer:
The numbers are 5 and 4Step-by-step explanation:
Let the first number be x
Let the second number be y
For the first equation
2x + 3y = 22
For the second equation
3x + 4y = 31
Multiply the first one by 3 and the second one by 2
That's
First equation
6x + 9y = 66
Second equation
6x + 8y = 62
Subtract the second equation from the first one
That's
6x - 6x + 9y - 8y = 66 - 62
y = 4Substitute y = 4 into 2x + 3y = 22
That's
2x + 3(4) = 22
2x = 22 - 12
2x = 10
Divide both sides by 2
x = 5Hope this helps you
What is the range of possible sizes for side x? x, 8.0, and 8.8
Answer:
0.8 < x < 16.8
Step-by-step explanation:
8.0 + 8.8 = 16.8
The range of possible sizes for the side x are 0.8 < x < 16.8.
What is Triangle?A triangle is a geometrical shape in two dimensional geometry which has three sides, three vertices and three angles.
The sum of all the three angles inside the triangle is supplementary.
This implies that if a, b and c are the three interior angles of a triangle, then, a + b + c = 180°.
If two sides of a triangle are given, then the third side of the triangle will always be in between the difference of the length of the other two sides and the sum of the length of the other two sides.
Here two lengths are given as 8.0 and 8.8.
Difference of the lengths = 8.8 - 8.0 = 0.8
Sum of the lengths = 8.8 + 8.0 = 16.8
So the x lies between 0.8 and 16.8.
Hence the range of the possible length of the given triangle is 0.8 < x < 16.8.
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An article in the Journal of Aircraft (Vol. 23, 1986, pp. 859-864) described a new equivalent plate analysis method formulation that is capable of modeling aircraft structures such as cranked wing boxes and that produces results similar to the more computationally intensive finite element analysis method. Natural vibration frequencies for the cranked wing box structure are calculated using both methods, and results for the first seven natural frequencies follow:
Frequency Finite Element Equivalent Plate
1 14.48 14.79
2 48.45 49.08
3 97.13 99.98
4 113.97 117.43
5 174.75 181.18
6 212.54 220.06
7 277.40 294.79
(a) Do the data suggest that the two methods provide the same mean value for natural vibration frequency? Use
α = 0.05.
(b) Find a 95% confidence interval on the mean difference between the two methods. Round your answers to three decimal places (e.g. 98.765).
Answer: (a) No, the data suggests it is possible to reject the hypothesis which states that the 2 methods provide same mean value.
(b) (-10.957,-0.063)
Step-by-step explanation:
(a) Hypotheses for this data are:
[tex]H_{0}[/tex]: [tex]\mu_{1} = \mu_{2}[/tex]
[tex]H_{a}: \mu_{1} \neq \mu_{2}[/tex]
First find the differences in values:
1 => -0.31
2 => -0.63
3 => -2.85
4 => -3.46
5 => -6.43
6 => -7.52
7 => -17.39
Now, find the mean and standard deviation of the differences:
mean = [tex]\frac{-0.31+(-0.63)+...+(-17.39)}{7}[/tex] = - 5.51
sd = [tex]\sqrt{\frac{(-0.31-(-5.51))^{2}+...+(-17.39-(-5.51))^{2}}{7-1} }[/tex] = 5.89
The value of test statistics is:
t = [tex]\frac{mean}{\frac{s}{\sqrt{n} } }[/tex] = [tex]\frac{-5.51}{\frac{5.89}{\sqrt{7} } }[/tex] = - 2.4750
Analysing Student's T distribution, at a df = 7-1 = 6:
p-value = 0.025*2 = 0.05
To reject the null hypothesis, p-value must be less or equal than α. Since they are equal, reject the null hypothesis, i.e., reject the claim suggesting the 2 methods provide the same mean value for natural vibration frequency.
(b) For a CI = 95%:
t-score for α = 0.025 and df = 6 is 2.447.
mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]
-5.51 ± 2.447.[tex]\frac{5.89}{\sqrt{7} }[/tex]
-5.51 ± 5.4471
lower limit: -5.51 - 5.4471 = - 10.957
upper limit: -5.51 + 5.4471 = - 0.063
The interval on the mean difference is (-10.957,-0.063)
Find the distance between a point (–7, –19) and a horizontal line at y = 3. Question 18 options: A) 13 B) 22 C) –16 D) 16
Answer: B) 22
Step-by-step explanation:
y coordinate of line = 3
y coordinate of point = -19
On a number line, distance between 3 & -19 = 22
Y= 2/3x – 18 What is the rate of change from -5 to 10? What is the average rate of change from 0 to 3?
Answer:
this is all i got for the second question.
Step-by-step explanation:
That is, the average rate of change of from 3 to 0 is 1. That is, over the interval [0,3], for every 1 unit change in x, there is a 1 unit change in the value of the function. Here is a graph of the function, the two points used, and the line connecting those two points.
hope this kinda helps
-lvr
4 (5 points)
What is the range of y =|3x + 1)?
a) {y\y >0}
b) {y\y > 1}
8
c) {all real numbers)
d) {y|y23]
Answer:
[0, infinity)
Step-by-step explanation:
clarence, I believe you meant y = |3x + 1|. The absolute value of 3x + 1 is never less than 0, so the range of the given function (above) is [0, infinity).
Because of a manufacturing error, 3 cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack. Determine the probability that at least one contain regular soda.
Answer:
161/184 or 0.875
Step-by-step explanation:
Total number of cans = 24 cans
Total number of diet soda = 3 cans
Total number of regular soda = 21 cans
We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly
We have two ways for this happening
a) two of the cans are regular soda
b) one of the cans is regular , while one is diet
Hence,
Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)
Probability(that two of the cans are regular soda) = 21/24 × 20/23
= 35/46
Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23
= 21/184
Probability (that at least one contain regular soda) = 35/46 + 21/184
We find the Lowest common multiple of the denominators = 184
= 35/46 + 21/184
= (35 × 4) + (21 × 1)/184
= 140 + 21/184
= 161/184
= 0.875
Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875
According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017 . Data for the sale of randomly selected 40 homes sold in Greene County, Ohio, in showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in . Round your answer to four decimal places.
P-value =
Answer:
t= 1.89736659
Step-by-step explanation:
Write in expanded form
3
(-a)
Answer:
-3a
Step-by-step explanation:
3(-a)
Expand brackets.
3 × -1a
-3a
Which of the following statement is incorrect?
4
A.3/4<4/5
B.5/6>0.83
C.2/3>0.66
D.1/3>0.3
درا
Answer:
None,
they are all correct.
Step-by-step explanation:
A)
3/4 - 75%
4/5 - 80%
3/4 < 4/5
B)
5 ÷ 6 = .83333333333
5/6 > .83
C)
2 ÷ 3 = .666666666
2/3 > .66
D)
1 ÷ 3 = .33333333333
1/3 > .3
Thus,
all of the given statements are correct.
Hope this helps :)
If F(x) = f(g(x)), where f(−4) = 8, f '(−4) = 3, f '(−3) = 5, g(−3) = −4, and g'(−3) = 6, find F '(−3). F '(−3)
Answer:
F'(-3) = 18
Step-by-step explanation:
Let g(x) = u and apply the chain rule
[tex]F(x)=f(g(x))=f(u)\\F'(x)=\frac{df(u)}{du}[/tex]
[tex]\frac{du}{dx}=g'(x)[/tex]
[tex]\frac{df(u)}{du}*\frac{du}{dx} = \frac{df(u)}{dx}\\F'(x)= \frac{df(u)}{du}*g'(x)\\F'(x)= f'(u)*g'(x)\\F'(x)= f'(g(x))*g'(x)[/tex]
We now have all of the necessary definite values to solve the expression for x= -3:
[tex]F'(-3)= f'(g(-3))*g'(-3)\\F'(-3)= f'(-4)*6\\F'(-3)= 3*6\\F'(-3)= 18[/tex]
Finally, we have that F'(-3)= 18.
What is the cube of the square of the second smallest prime number?
Answer:8
Step-by-step explanation:
The smallest prime is 2
cube of 2 is equal to 8
2*2*2=8
Answer:
729
Step-by-step explanation:
The second smallest prime number is 3 (preceded by 2). We have (3^2)^3=3^6=729.
Hope this helped! :)
Which expressions are equivalent to: 3(−2a - 4)+3a? A: -6a - 12 +3a B: 3a+12 C: none of the above smh
Answer:
AStep-by-step explanation:
3(−2a - 4)+3a
=-6a - 12 +3a
A: -6a - 12 +3a
[tex]hope \: this \: helps[/tex]
Answer:
the answer is A
Step-by-step explanation:
you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a
A bowl of Halloween candy contains 7 chocolate candies and 3 lemon candies. Tanya will choose one piece of candy at random.
Use double-angle identities to verify that sin(4x) = 4 sinx cosx(1 − 2sin2x.
Answer:
Step-by-step explanation:
In double angle, sin2x = sin(x+x) = sinxcosx+cosxsinx
sin2x = 2sinxcosx ... 1
Applying this formula to prove that sin(4x) = 4 sinx cosx(1 − 2sin2x is shown below;
sin(4x) = sin(2x+2x)
= sin2xcos2x+cox2xsin2x
sin4x = 2sin2xcos2x ..2
also cos2x = cos(x+x) = cosxcox-sinxsinx
cos 2x = cos²x - sin²x ...3
Substituting equation 1 and 3 into 2, we will have;
sin4x = 2(2sinxcosx(cos²x - sin²x ))
sin4x = 4sinxcosx(cos²x - sin²x )
From sin²x+cos²x =1; cos²x = 1-sin²x
Substituting the expression into the resulting equation will give;
sin4x = 4sinxcosx(1-sin²x - sin²x )
sin4x = 4sinxcosx(1-2sin²x) Verified!
Every year the United States Department of Transportation publishes reports on the number of alcohol related and non-alcohol related highway vehicle fatalities. Below is a summary of the number of alcohol related highway vehicle fatalities from 2001 to 2010.
Line graph about Alcohol related fatalities
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
Complete question:
The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.
Answer:
17,209
Step-by-step explanation:
The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :
From the graph:
Year - - - - - - - - - - Number of fatalities
2001 - - - - - - - - - - 17401
2002 - - - - - - - - - 17525
2003 - - - - - - - - - 17013
2004 - - - - - - - - - 16694
2005 - - - - - - - - - 16885
2006 - - - - - - - - - 17738
To get the average :
Sum of fatalities / number of years
(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6
= 103256 / 6
= 17209.333
Average number of alcohol related fatalities is 17,209 (to the nearest whole number)
1. Draw the multiplication table on the set P= {3,5,7,9) in modulo twelve.
(b) From your table, evaluate;
(0 (305) (509)
() (589)®(789)
3*5 ≡ 15 ≡ 3 (mod 12)
3*7 ≡ 21 ≡ 9 (mod 12)
3*9 ≡ 27 ≡ 3 (mod 12)
5*7 ≡ 35 ≡ 11 (mod 12)
5*9 ≡ 45 ≡ 9 (mod 12)
7*9 ≡ 63 ≡ 3 (mod 12)
Your table should look like the attached.
It's unclear what you're supposed to evaluate for part (b)...