Answer:
See below.
Step-by-step explanation:
1. (1 / 2)[cos(a – b) – cos(a + b)]
= 1/2 ( cosa cosb + sina sinb - (cosa cosb - sina sinb)
= 1/2 ( cosa cosb - cosa cos b + sina sinb + sina sinb)
= 1/2 ( 2 sina sinb)
= sina sinb.
(I used the 2 identities cos(a - b) = cosa cosb + sina sinb) and
cos (a + b) = cosa cosb - sina sinb.)
2. sin (π/2 - x) = sin (π/2) cos x - cos(π/2) sin x
= 1 * cos x - 0 * sinx
= cosx - 0
= cos x.
(I used the identity sin(a - b) = sina cosb - cosa sinb
and the fact that sin(π/2) = 1 and cos (π/2) = 0. )
Answer:
1. sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)]
Calculation:
Taking L.H.S. of above equation
(1 / 2)[cos(a – b) – cos(a + b)]
= (1 / 2) [ (cos a cos b + sin a sin b) - (cos a cos b - sin a sin b)]
{∵ cos(a – b) = cos a cos b + sin a sin b & cos(a + b) = cos a cos b - sin a sin b}
= (1 / 2) [ cos a cos b + sin a sin b - cos a cos b + sin a sin b]
= (1 / 2) [2 sin a sin b]
= sin a sin b
2. sin((π / 2) – x) = cos x
Calculation:
sin((π / 2) – x) = sin (π / 2) cos x - cos (π / 2) sin x
{∵sin(a - b) = sin a cos b - cos b sin a
& sin (π / 2) = 1 & cos (π / 2) = 0}
= 1 × cos x - 0 × sin x
= cos x
A survey of eating habits showed that approximately 4% of people in a certain city are vegans. Vegans do not eat meat, poultry, fish, seafood, eggs, or milk. A restaurant in the city expects 350 people on opening night, and the chef is deciding on the menu. Treat the patrons as a simple random sample from the city and the surrounding area, which has a population of about 600,000. If 17 vegan meals are available, what is the approximate probability that there will not be enough vegan mealslong dashthat is, the probability that 18 or more vegans will come to the restaurant? Assume the vegans are independent and there are no families of vegans.
The approximate probability that there will not be enough vegan meals is 94.88%.
Explanation:To calculate the approximate probability that there will not be enough vegan meals, we need to find the probability that 18 or more vegans will come to the restaurant. Since the survey showed that approximately 4% of people in the city are vegans, we can use this information to estimate the probability.
First, we find the number of vegans in the city and surrounding area by multiplying the total population by the percentage of vegans: 600,000 * 0.04 = 24,000.
Next, we calculate the probability of 18 or more vegans showing up out of 24,000 by using a binomial distribution with n = 350 (the number of people expected on opening night) and p = 0.04 (the probability of a person being vegan). We then sum the probabilities for 18, 19, 20, ..., 350 vegans.
Using a calculator or statistical software, we find that the approximate probability is 0.9488, or 94.88%.
Please help !
What are the solutions to the equation?
a) x=-6 and x= -2/3
b) x=-6 and x= 2/3
c) x=6 and x= 2/3
Answer:
a
Step-by-step explanation:
0=3x²+20x+12
0=(3x+2)(x+6)
0=3x+2 0=x+6
-2=3x -6=x
-2/3=x
2. The Geo Air pilot is looking at SCCA from the plane. From the aircraft the angle of depression is 17 degrees. If the plane is at an altitude of 10,000 feet, approximately how far is the plane to SCCA? Round your answer to the nearest tenth. The image is not drawn to scale. (2 points)
Answer:
The distance from the plane to SCCA is 34,203.0 feet approximately, and the horizontal distance is 32,708.5 feet approximately.
Step-by-step explanation:
You can draw a right triangle like the one shown in the figure attached, where:
x: horizontal distance.
y: distance from the plane to SCCA.
You can calculate x as following:
[tex]tan\alpha=\frac{opposit}{adjacent}[/tex]
Where:
[tex]\alpha=17\°\\opposite=10,000\\adjacent=x[/tex]
Substitute and solve for x:
[tex]tan(17\°)=\frac{10,000}{x}\\\\x=\frac{10,000}{tan(17\°)}\\\\x=32,708.5ft[/tex]
You can calculate y as following:
[tex]sin\alpha=\frac{opposit}{hypotenuse}[/tex]
Where:
[tex]\alpha=17\°\\opposite=10,000\\hypotenuse=y[/tex]
Substitute and solve for y:
[tex]sin(17\°)=\frac{10,000}{y}\\\\y=\frac{10,000}{sin(17\°)}\\\\y=34,203.0ft[/tex]
Write 651.12 as a mixed number
Answer:
651 and 3/25 is 651.12 as a mixed number.
651.12 can be written as the mixed number 651 3/25.
How to write the mixed fractionTo convert hundredths to a fraction, we write the decimal as the numerator and the place value as the denominator. T
Therefore, .12 can be written as 12/100.
651 + 12/100
= 651 12/100
Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
651 12/100 = 651 3/25
Therefore, 651.12 can be written as the mixed number 651 3/25.
Read more on mixed fraction here https://brainly.com/question/12096281
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x + y = 4
x - 2y = -5
If the first equation is multiplied by 2 and then the equations are added, the result is _____.
3x = 13
3x = 3
x = 3
Answer:
Well it would come out to 2x-3y=-9
Step-by-step explanation:
Here's how you solve this problem:
1) Multiply the first equation by 2 (result:2x+2y=8).
2) Add both equations together (result:2x+x+2y-2y=8-5)
3) Simplify (result:3x=3)
The answer is 3x=3.
This could be simplified more, however, to equal x=1, since both sides are divisible by 3.
p.s. Have a good day!
Points A and B split the circle into two arcs. Measure of minor arc is 150°. Point M splits major arc with the ratio 2:5 (point M is closer to point B). Find m?BAM.
Answer:
∠BAM=30°
Step-by-step explanation:
Points A and B split the circle into two arcs. If the measure of minor arc AB is 150°, then the measure of the major arc AB is 360°-150°=210°.
If point M splits major arc with the ratio 2:5, then
∠BOM=2x°;∠AOM=5x°.Angles BOM and AOM together form angle with the measure 210°, thus
2x+5x=210,
7x=210,
x=30°
and ∠BOM=60°, ∠AOM=150°.
Consider isosceles triangle BOM. In this triangle,
∠OBM=1/2(180°-60°)=60°.
Consider isosceles triangle AOB. In this triangle,
∠OAB=1/2(180°-150°)=15°.
Consider isosceles triangle AOM. In this triangle,
∠OAM=1/2(180°-150°)=15°.
Thus, ∠BAM=15°+15°=30°
Answer:
arc BAM = 300°
Step-by-step explanation:
Refer to the figure attached.
arc AB = 150°
then:
arc AMB = 360° - 150° = 210°
arc AMB can be decomposed as:
arc AM + arc MB = arc AMB (eq. 1)
From data:
arc MB/arc AM = 2/5
arc MB*(5/2) = arc AM (eq. 2)
Replacing equation 2 into equation 1:
arc MB*(5/2) + arc MB = 210°
arc MB*(7/2) = 210°
arc MB = (2/7)*210° = 60°
On the other hand:
arc MB + arc BAM = 360°
arc BAM = 360° - 60° = 300°
Please help!! Double points! write the ratios for sin X and cos X (Image attached)
Will give BRAINLIEST to the person correct answer and please please show your work :))
Answer:
The ratio for sin(X) is [tex]\frac{\sqrt{119} }{12}[/tex]
The ratio for cos(X) is [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
- The ratio of the sine of a right triangle is:
[tex]sin(\alpha)=\frac{opposite-side}{hypotenuse}[/tex]
Since we need the ratio for angle X, [tex]\alpha =X[/tex]. From the picture we can infer that the opposite side of X is [tex]\sqrt{119}[/tex]. The hypotenuse (the side opposite to the right angle) is 12, so replacing the values:
[tex]sin(X)=\frac{\sqrt{119} }{12}[/tex]
- The ratio of the cosine is:
[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]
Similarly, [tex]\alpha =X[/tex], adjacent side = 5, and hypotenuse = 12, so
[tex]cos(X)=\frac{5}{12}[/tex]
Answer:
Sin X =√119/12
Cs X = 5/12
Step-by-step explanation:
It is given a right angled triangle.
Points to remember
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
To find the value of Sin X
Here X is an angle
Opposite side = √119
Hypotenuse = 12
Sin X = Opposite side/Hypotenuse = ZY/XY = √119/12
To find the value of Cos X
Adjacent side of X = 5
Cos X = Adjacent side/Hypotenuse = XZ/XY = 5/12
A car factory takes 6 hours to produce 60 cars. How many hours does the factory take to produce 180 cars?
Final answer:
The factory takes 18 hours to produce 180 cars.
Explanation:
To find out how many hours the factory takes to produce 180 cars, we need to set up a proportion. Since the factory takes 6 hours to produce 60 cars, we can set up the proportion:
6 hours / 60 cars = x hours / 180 cars
Cross-multiplying, we get:
6(180) = 60(x)
Simplifying, we have:
1080 = 60x
Dividing both sides by 60, we find:
x = 18
So, the factory takes 18 hours to produce 180 cars.
HELP!!!
An equal inch is equal to about 2.54 centimeters . Write an expression which estimate the numbers of centimeters in x inches. Then estimate the number of centimeters in 12 inches
Answer: The answers are 2.54x and 30.48 cm.
Step-by-step explanation: The formula to determine the number of centimeters in x inches is 2.54x. To solve for the number of centimeters in 12 inches the formula is 2.54 x 12 = 30.48 cm.
Can somebody please help me with my hw
Answer:
Each base is 40
Step-by-step explanation:
An isosceles triangle has a total of 180. An isosceles has two sides that are the same and one different. Think of “sos” in the word isosceles to help. If one is 100, then you have 80 left. 80 divided by 2 is 40.
Gloria traveler a total of 8 miles to get from school to her apartment. Gloria took the bus from school to the closest bus stop to her apartment and then walked the remaining 880 yards home.
Well you didn't include a direct question but she traveled 7.5 miles on the bus and she walked .5 miles home.
5. Evaluate the series 50 + 10 + 2 + . . . 62 The series diverges; it does not have a sum. 62.5
Answer:
62.5
Step-by-step explanation:
By dividing 50 by 10 and 10 by 2 we can find that r, or the common ratio is 1/5, meaning that this series converges, so it is solvable. The formula for a convergent series is [tex]\frac{a_{1}}{1-r}[/tex]. By plugging in 1/5 for r and 50 for [tex]a_{1}[/tex] we can find that the sum of this infinite series is 62.5
Write three fractions that are not greater than 1/2 . Explain how you determine your fractions.
1/2 is .5
and knowing this, just make a fraction out of the numbers before .5 .
2/5 is .4
3/10 is .3
1/5 is .2
1/10 is .1
and there are your fractions less than 1/2
The three fractions that are not greater than 1/2 will be 1/3, 1/4, and 1/5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The three fractions that are not greater than 1/2. If the denominator increases then the value gets decreases. Then the three fractions are given as,
1/3, 1/4, 1/5
The three fractions that are not greater than 1/2 will be 1/3, 1/4, and 1/5.
More about the Algebra link is given below.
https://brainly.com/question/953809
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If you know the radius, r, of a circle, what do you multiply r by to get the circle's CIRCUMFERENCE?
Answer:
multiply the radius by 2π
Step-by-step explanation:
The formulas for circumference of a circle is
C = πD where D is the diameter,
or
C = 2πr where r is the radius.
Either formula is correct, but we will work with the second one since the question is asking about radius.
We see that 2π(r) = the circumference, so multiply r by 2π to get the circumference
Hello there! How are you doing? I am doing fine! I'll answer the question now.
So basically when wanting to find the circumference of a circle you simply use the formula, C = 2 times PI times R. PI is the infamous number known for 3.1415912654... and the R represents the radius. You would multiply 2 times PI and then after getting that you would basically multiply it by the radius. And then that would be the circumference and be the answer to any problem you face like this. Know that diameter is 2 times the radius and that all.
Hope this helped! Your welcome! I can help with other history stuff too! And byee! :)
Victoria can make 8 necklaces in 4 days. How long does it take her to make ond necklace?
Answer:
[tex]0.5\ days[/tex]
Step-by-step explanation:
we know that
Using proportion
[tex]\frac{4}{8}\frac{days}{necklaces} =\frac{x}{1}\frac{days}{necklace} \\ \\x=4/8\\ \\x=0.5\ days[/tex]
Sadie made a rectangular cake. If she wants to cut it into 1/8 portions,how many portions can she cut?
Answer:
8
Step-by-step explanation:
If each portion is 1/8 of the cake, there are 8 equal-size portions. That is what the denominator of the fraction means.
Sadie can cut the rectangular cake into 8 portions if each portion is 1/8 of the whole cake.
To determine how many portions Sadie can cut the rectangular cake into if each portion is 1/8, we need to understand that she is essentially dividing the cake into 8 equal parts.
Here's a step-by-step explanation:
Whole Cake: The entire rectangular cake represents one whole (1).
→ Portion Size: Each portion is 1/8 of the whole cake.
→ Calculation: We divide 1 by 1/8. Mathematically, this is the same as multiplying by the reciprocal,
so 1 ÷ (1/8) = 1 × 8
= 8.
Therefore, Sadie can cut the rectangular cake into 8 portions of size 1/8 each.
Can someone help please?!? ):
Answer:
5, 6, 11, 17, 28Step-by-step explanation:
[tex]a_1=5,\ a_2=6,\ a_n=a_{n-1}+a_{n-2}\\\\a_3=a_2+a_1\\a_4=a_3+a_2\\a_5=a_4+a_3\\\\\text{first term:}\ 5\\\text{second term:}\ 6\\\text{third term:}\ 6+5=11\\\text{fourth term:}\ 11+6=17\\\text{fifth term:}\ 17+11=28[/tex]
A rectangular prism has side lengths of 4 inches, 6 inches, and 7 inches. If all side lengths are multiplied by 5, what happens to the surface area. A) It remains the same. B) It is multiplied by 5. C) It is multiplied by 25. D) It is multiplied by 125.
Answer:
C
Step-by-step explanation:
The surface are of the prism will be the area of a each side added together. The work would look like this:
SA = 2[(l×h)+(l×b)+(b×h)]
SA = 2(lh+lb+bh)
But if you multiply each dimension by 5, the area becomes
SA = 2[(5l×5h)+(5l×5b)+(5b×5h)]
SA = 2(5²lh+5²lb+5²bh)
SA = 5²×2(lh+lb+bh)
SA = 5²area
Since 5² = 25, then the the surface area is multiplied in size by 25.
WILL MARK THE BRAINILEST!!!!!
Richard is 25 years old and starting an IRA (individual retirement account). He is going to invest $200 at the beginning of each month. The account is expected to earn 2.85% interest, compounded monthly. How much money will Ricky have in his IRA when he retires, at age 65?
$87,564.17
$452,588.21
$14,993.11
$179,165.14
What are the coordinates for the function of the vertex for the quadratic function below
We will need to picture for this.
Johnny wants to buy a 60" LED Smart TV, so he opened a savings account and added money to it every month. The chart below shows the relationship between the number of months Johnny has been saving and the total amount of money in his account.
Nakesha’s Sporting Goods is running a sale on golf shoes this week. The sale price is $95.98. The shoes cost Nakesha’s $63.45. What is the markup rate based on cost?
Answer:
Markup rate = 0.512 or 51.2%
Step-by-step explanation:
Mark up rate is the increase amount added to the original price.
Sales Price = $95.98
Original Price= $63.45
Gross profit margin = Sales Price - Original cost
= $95.98 - $63.45
= $ 32.53
Mark up Rate = Gross profit margin/ original price
= 32.53 / 63. 45
= 0.51
converting into percentage by multiplying with 100
Mark up Percentage = 0.512 * 100
= 51.2 %
A package of strawberries costs 1.50 while they are in season and 2.25 when they aren't in season. What is the percent increse.
The answer is 50%.
Divide 2.25 by 1.50. That equals 1.5. That’s the equivalent to 50% because if you subtract 1 from 1.5 and multiply by 100. You get the same answer. Only do that for numbers greater than one, otherwise it won’t work
What kind of symmetry is displayed by the graph of catenary y=e^x+e^-x/2
Answer:
Option b
Step-by-step explanation:
To solve this problem we must test if the function is even.
If f(-x) = f(x) then the function is even and is symmetric with respect to the y-axis.
If f(-x) = -f(x) then the function is odd and has symmetry with respect to the origin.
We have the function:
[tex]f(x) = \frac{e^x + e^{-x}}{2}[/tex]
We make:
[tex]f(-x) = \frac{e^{-x} + e^{-(-x)}}{2}[/tex]
Rewriting the function we have
[tex]f(-x) = \frac{e^{-x} + e^{x}}{2} = \frac{e^{x} + e^{-x}}{2}\\\\f(-x) = f(x)[/tex]
Finally, the function has symmetry with respect to the y axis.
Answer:
b
Step-by-step explanation:
Find the annual interest rate I equals $562.50 P equals to $1500 T equals five years
Answer: The rate is 7.5%.
Step-by-step explanation: The formula to calculate simple interest is:
Interest = Principal x Rate x Time
So, we need to plug our information into the formula:
$562.50 = $1,500 x R x 5
Now, perform the multiplication that you can:
$562.50 - $7,500R
Next, divide both sides by $7,500:
.075 = R
Therefore, the rate is 7.5%.
Find the polar equation of the conic with the focus at the pole, directrix x = 4, and eccentricity 1.
Answer:
Choice D is correct
Step-by-step explanation:
The eccentricity of the conic section is 1, implying we are looking at a parabola. Parabolas are the only conic sections with an eccentricity of 1.
Next, the directrix of this parabola is located at x = 4. This implies that the parabola opens towards the left and thus the denominator of its polar equation contains a positive cosine function.
Finally, the value of k in the numerator is simply the product of the eccentricity and the absolute value of the directrix;
k = 1*4 = 4
This polar equation is given by alternative D.
Answer:
D
Step-by-step explanation:
it's right on edge, i just took the test :)
A parallelogram has a base of 14 centimeters and a height of 20 centimeters.What is the area of the parralegram
Answer:
44444444444444444444444444444444444444444444467
Step-by-step explanation:
HELP ME PLEASE!!!
Teague is participating in a 50K run to raise money for a charity. He has already raised $102 and will receive $1.40 for each kilometer he travels. If he wants to raise a minimum of $165, how many kilometers does he need to run?
Equation: _________
Define Variable: _________
Solve Equation: _________
Final Answer: _________
Answer: 45 kilometers
Step-by-step explanation:
The equation to solve this problem is:
$165 = 1.4x + 102
The variable x represents the number of kilometers he travels.
To solve the equation:
Subtract 102 from each side-
63 = 1.4x
Next divide each side by 1.4-
45 = x
Teague needs to run 45 kilometers in order to raise $165.
165=1.40x+102 (equation) x = amount run and final answer is x=45
A number is divided by 3 and then 5 is subtracted from the quotient the result is 1. Whats the number?
ANSWER
The number is 18.
EXPLANATION
Let the number be x.
When this number is divided by 3, we obtain the quotient,
[tex] \frac{x}{3} [/tex]
When 5 is subtracted from this quotient, we get,
[tex] \frac{x}{3} - 5[/tex]
If the result is 1, then we have;
[tex] \frac{x}{3} - 5 = 1[/tex]
We group similar terms to get,
[tex] \frac{x}{3} = 1 + 5[/tex]
This gives us,
[tex] \frac{x}{3} = 6[/tex]
Multiply both sides by 3.
[tex]x = 6 \times 3[/tex]
[tex]x = 18[/tex]
Therefore the number is 18.
What is the value of the remainder if 10x4 – 6x3 + 5x2 – x + 1 is divided by x – 3?
Answer:
Remainder is 691.
Step-by-step explanation:
Given function is [tex]10x^4-6x^3+5x^2-x+1[/tex].
Now we need to find remainder if we divide given function [tex]10x^4-6x^3+5x^2-x+1[/tex] by (x-3)
(x-3) means plug x=3 into [tex]10x^4-6x^3+5x^2-x+1[/tex] to find remainder.
[tex]10x^4-6x^3+5x^2-x+1[/tex]
[tex]=10(3)^4-6(3)^3+5(3)^2-(3)+1[/tex]
[tex]=10(81)-6(27)+5(9)-(3)+1[/tex]
[tex]=810-162+45-3+1[/tex]
[tex]=856-162-3[/tex]
[tex]=856-165[/tex]
[tex]=691[/tex]
Hence remainder is 691.
Answer:
The remainder = 691
Step-by-step explanation:
Let p(x) = 10x⁴ - 6x³ + 5x² - x + 1
We have to divide p(x) by (x - 3)
To find the remainder we have to find p(3)
To find the remainder
p(x) = 10x⁴ - 6x³ + 5x² - x + 1
p(3) = 10 * (3)⁴ - 6*(3)³ + 5* (3)² - 3 + 1
= (10 * 81 ) - ( 6 * 27 ) + (5 * 9) - 3 + 1
= 810 - 162 + 45 - 3 + 1 = 691
Therefore the remainder is 691