Which sum or difference identity would you use to verify that cos (180° - q) = -cos q?
a.
sin (a -b) = sin a cos b – cos a sin b
b.
cos (a -b) = cos a cos b – sin a sin b
c.
cos (a -b) = cos a cosb + sin a sin b
d.
sin (a + b) = sin a cos b + cos a sin b
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
In this case, we'd have a = 180 and b = q, so,
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
cos(180 - q) = cos(180)cos(q) + sin(180)sin(q)
cos(180 - q) = -1*cos(q) + 0*sin(q)
cos(180 - q) = -cos(q) + 0
cos(180 - q) = -cos(q)
f(x)=-4x+1 Find the average rate of change from 2 to 5.
Answer:
- 4
Step-by-step explanation:
The slope of the line is the average rate of change of f(x)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
f(x) = - 4x + 1 ← is in slope- intercept form
with m = - 4 ← average rate of change
Find the pattern and use inductive reasoning to predict the next number in the sequence 100,50,80,40,70,35,…
Answer:
65
Step-by-step explanation:
100, 50, 80, 40, 70, 35, 65.
|____|__|___|___|__|__|
÷2. +30. ÷2. +30 ÷2. +30
A pattern is a recurring arrangement of numbers, forms, colors, and so on. The next number in the given pattern will be 65.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colors, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
If the given pattern is observed closely then it can be observed that the second number is decreased by half the previous one, while the next number is formed by adding 30, therefore,
The First Number = 100The second number, half of the previous = 50For the third number, add 30 = 80The fourth number, half of the previous = 40For the fifth number, add 30 = 70The sixth number, half of the previous = 35For the seventh number, add 30 = 65Hence, the next number in the given pattern will be 65.
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This question relates to concepts covered in Lectures 1 & 2. You can use any of the excel files posted to work through the question. Demand at a store can be modeled by a random variable which takes the following values across four different scenarios that occur with following probabilities. Scenario Low: D1 = 10 with probability P1=0. 1 Scenario Medium 1: D2 = 30 with probability P...2=0,4 Scenario Medium 2. D3 = 60 with probability p. 3-0.4 Scenario High: 04 = 90 with probability p_4=0.7 What is the mean of this demand distributional?
Answer:
mean of this demand distribution = 100
Step-by-step explanation:
To find the mean of this demand distribution;
Mean = Expected vale = E[x]
for discrete provability function,
we say E[x] = ∑(x.p(x))
x p(x) x.p(x)
10 0.1 1
30 0.4 12
60 0.4 24
90 0.7 63
∴ ∑(x.p(x)) = ( 1 + 12 + 24 + 63 )
∑(x.p(x)) = 100
A ball player is at bat 55 times as hits the ball 33 times. Want ratio of his times at bat does he not hit the ball?
Answer:55:33
Step-by-step explanation:
55:33
0.4, 0.04, 0.44, 0.444, 0.404, 0.044 in order smallest first
I'm pretty sure it's 0.04, 0.044, 0.4, 0.404, 0.44, 0.444.
Round 630,379,982 to the nearest hundred thousand
Answer:
630,400,000
Step-by-step explanation:
630,379,982
The 3 above that is bold, between the 0 and the 7, is in the hundred thousands place.
To round to a place, change all digits to the right of that place to zero. If the digit immediately to the right is 0 through 4, you're done. If the digit immediately to the right is from 5 to 9, then you raise the digit you are rounding to by 1.
Step 1. Make all digits to the right of the hundred thousands digit 0.
630,300,000
Step 2. Since the digit immediately to the right of the hundred thousands digit was a 7, which is from 5 to 9, the digit we are rounding to goes up by 1. The 3 becomes 4.
630,400,000
Answer: 630,400,000
Which number rounds to 4.3 when rounded to the nearest tenth?
Answer:
it is the same 4.3
Step-by-step explanation:
this numbers didn't add one number when you round(0,1,2.3.4)
this numbers(5,6,7,8,9), you add one number when you add
4.3 (the three is the tenth)and no number after it so its stell the same
The rounding number of 4.3 when rounded to the nearest tenth is 4.3
Here,
The number is 4.3
We have to find the rounding number of 4.3 nearest tenth.
What is Rounding number?
A method of approximating a number to its nearest place value is called Rounding of Numbers.
Now,
The number is 4.3
To round the decimal number to its nearest tenth, look at the hundredth place.
But here is no any number on hundredth number, hence no change occur for rounding 4.3 to the nearest tenth.
So, The rounding number of 4.3 when rounded to the nearest tenth is same as the number 4.3
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Please help me ! So lost rn
Answer:
2.7 meters
Step-by-step explanation:
So, we know that 1 foot is about 0.305 meters.
To find how many meters are in 9 feet, multiply 0.305 by 9.
Therefore:
[tex]9(1\text{ foot})=9(0.305\text{ meters})[/tex]
Multiply:
[tex]9\text{ feet}=2.745\text{ meters}[/tex]
To the nearest, tenth this would be 2.7 meters.
And we're done!
21 2/3 Divided by 3 1/4
Answer:
the answer is 20/3 or 6 2/3
Step-by-step explanation:
Can you please help me with this I’ll give you a Brainly list please it’s hard
Answer:
Your answer will be 6+6-17 hope this helps :)
Step-by-step explanation:
Find A∩B, given A={−6,−2,0,2,6} and B={−4,0,1,2,5,6}.
Answer:
Step-by-step explanation:
A ∩ B = {0, 2, 6}
give an example of a set of five different numbers whose mean is 290
Answer:
200,300,290,320,340
Step-by-step explanation:
If the mean of five numbers = 290
Then the total sum of the five numbers should be= 290*5
= 1450
an example of a set of five different numbers whose mean is 290
= 200,300,290,320,340
Summation of the above
=( 200+300+290+320+340)
= 1450
So the above set of numbers is a good example of a set of five different numbers whose mean is 290
Dan is 5 years older than David. Bridget is 8 years younger than David. If the total of their ages is 57, how old is the eldest of them
Answer:
The oldest person is 25 years old
Step-by-step explanation:
Represent David's age by d.
Then Dan's age is d + 5, and Bridget's is d - 8.
The sum of these three ages is 57:
d + (d + 5) + (d - 8) = 57
This simplifies to
3d - 3 = 57, or 3d = 60. Then d must be 20.
David is 20, Dan is 25 (5 years older than David), and Bridget is 12 (8 years younger than David).
Check: Do these three ages add up to 57?
20 + 25 + 12 = 57 YES\
The oldest person is 25 years old. That's Dan's age.
Find the equation for the set of points whose distance from the y-axis equals the distance from the xz-plane.
Answer:
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
Step-by-step explanation:
Let [tex]$ p(x_1, y_1, z_1)$[/tex] be the point.
Any point on y-axis is (0, y, 0)
So, distance is
= [tex]$ \sqrt{x_1^2+0 + z_1^2} $[/tex]
= [tex]$ \sqrt{x_1^2 + z_1^2} $[/tex] ......(1)
Now any point on x-z plane is [tex]$ ( x_1, 0, z_1 ) $[/tex]
Distance from p to this point is
= [tex]$ \sqrt{0+y_1^2 + 0} $[/tex]
= [tex]$\sqrt{y_1^2}$[/tex] .........(2)
Equating (1) and (2), we get
[tex]$ \sqrt{x_1^2 + z_1^2} = \sqrt{y_1^2}$[/tex]
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
This is the required equation.
G(x)= -x^2 + 9 find: g(-4)
Answer:
G(-4) = -7
Step-by-step explanation:
G(x)= -x^2 + 9
x= -4
G(-4)= - (-4)^2 + 9
= -16 +9
= -7
I NEED HELP...finding the slope-intercept form equation
of the line passing through this points
(-12, 6) and (-36, 32)
Answer: y=-13/12x-7
Step-by-step explanation:
To find the slope-intercept form, we first need to find the slope. To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We use the two given points to find the slope.
[tex]m=\frac{32-6}{-36-(-12)} =\frac{26}{-24} =-\frac{13}{12}[/tex]
Now that we have our slope, we can start filling out the slope-intercept form equation.
y=mx+b
y=-13/12x+b
Since we don't know the y-intercept, we can use one of the given points and solve for b.
6=(-13/12)(-12)+b [multiply (-13/12) and -12]
6=13+b [subtract both sides by 13]
b=-7
With the y-intercept, we can complete our equation.
y=-13/12x-7
195.21 is 24.10% of what number?
Turn the percentage into a decimal.
24.10 / 100 = 0.241
Divide.
195.21 / 0.241 = 810
Therefore, 195.21 is 24.10% of 810
Best of Luck!
Hector works in a gas station and earns $15.50 per hour. Last week he worked 29 hours. What was his gross pay?
Answer:
449.50
Step-by-step explanation:
because gross pay is before taxes and everything else and he worked 29 hours so 15.50 × 29 = $449.50
The amount of money that Hector works in a gas station will be $449.50.
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.
Hector works in a service station and procures $15.50 each hour. Last week he worked 29 hours.
The total cost that Hector can earn will be given as,
⇒ $15.50 x 29
⇒ $449.5
The gross pay that Hector works in a corner store will be $449.50.
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Three-fifths of the students on a school trip are boys. There are 33 boys on the trip. How many students are on the trip?
Answer:
55 students
Step-by-step explanation:
Write an equation.
3/5 = 33
Divide by 3 to get a unit fraction.
3/5 / 3 = 1/5
33 / 3 = 11
1/5 = 11
Multiply by 5
1/5 x 5 = 1
11 x 5 = 55
1 = 55
So, there are 55 students on the school trip.
PLEASE HELP!! ALGEBRA! For a movie theater 4,000 tickets were sold, and the proceeds were $37,000. Tickets for children 16 and younger, were $10, adults were $12, and seniors 60 and older were $8. There were 4 times more seniors than adults at the movie theater. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the movie theater?
Answer: Fourth answer choice
c+a+s = 4000
10c+12a+8s = 37000
4a = s
==========================================
Explanation:
The first equation
c+a+s = 4000
is fairly straightforward. We add the individual counts of children (c), adults (a) and seniors (s) to get the total number of people (4000) who attended
-------------
If 1 child ticket costs $10, then 2 of them cost 20, and so on. If we don't know how many children there are, then we say 10c is the total cost for just the children alone. The c is a placeholder for some number.
Similarly, 12a represents the total cost for just the adults since 1 adult pays $12
8s is the total cost for all the seniors only
10c+12a+8s is the total cost of everyone and this total cost is 37000 dollars
The second equation is therefore
10c+12a+8s = 37000
----------------
We're told that "There were 4 times more seniors than adults at the movie theater" meaning
number of seniors = 4*(number of adults)
s = 4a
which is the same as 4a = s since we can flip both sides. So this is the third equation of our system.
------------------
We found these three equations
c+a+s = 4000
10c+12a+8s = 37000
4a = s
Solve the following inequality. Write the answer in interval notation. 3×+13≤8×+2
Answer:
[ 11/ 5 , ∞ )
Step-by-step explanation:
6. Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges? F. H. G. J. CARDS, c 2 9 11 15 DOLLARS, d 9 40.5 50.5 67.5 CARDS, c 9 18 27 36 DOLLARS, d 2 4 6 8 CARDS, c 2 4 7 10 DOLLARS, d 9 18 31.5 45 CARDS, c 2 3 4 5 DOLLARS, d 9 10 11 12
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
What is the value of the underline digit?
14.097
Answer:14.097
Step-by-step explanation:
Find the indicated side of the
triangle.
Answer:
8
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Which one of the following correctly states the VaR for a 3-year period with a 2.5 percent probability?
a) Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]
b) Prob[Rp, I S E(Rp) x 13 - 1.645 x Op 3]
c) Prob[Rp, T = E(Rp) x V3 - 1.960 x Op 3]
Answer: Option A
Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]
Step-by-step explanation:
It should be noted that, the VaR for a 3-year period with a 2.5 percent probability is Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]. Therefore, option A only is correct while other options are wrong
Answer:
A: Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]
Step-by-step explanation:
7. If a school has 70 computers in the ratio of 3 desktops for every 4 laptops, how many
are desktops? Explain your answer.
Step-by-step explanation:
As ratio of desktops to laptops=3:4
Take no. of desktops= 3x
Take no. of Laptops=4x
Total no. of desktops+ Total no. of laptops = Total no. of computers
3x+4x=70
7x=70
x=10
Hence, the total no, of desktops= 3x
Hence, Total no. of desktops= 3×10
=30 desktops
Which step in the problem-solving process includes the following statement? Identify the information the problem gives you. A. Understand B. Look back C. Solve D. Plan
Answer:plan
Step-by-step explanation:
the domain for f(x) is all real numbers. (Blank) than or equal to 3
Answer:
greater
Step-by-step explanation:
The domain is the number that x can be
sqrt(x-3) must be greater than or equal to zero
x-3 must be greater than or equal to zero
x must be greater than or equal to three
The other restriction is x+2 cannot equal zero
x cannot equal -2
The first restriction is more restrictive so that is the one we go with
You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?
Answer:
y = 7.8x + 26
Step-by-step explanation:
Given the following :
Pearson's r = 0.78
Average consumption of ice cream = 5 grams per week (m) with Standard deviation (sd) = 1.5 grams
Average weight = 65 kg with standard deviation of 15kg
Formular for the regression line :
General regression formula :
y = mx + c
y = predicted variable ; m = slope or gradient ; x = predictor variable ; c = intercept
Gradient (m) = change in y / change in x
m = (sd y / sd x) * r
m = (sd weight / sd ice cream) × r
m = (15 / 1.5) × r
m = 10 × 0.78 = 7.8
Intercept:
mean of weight(y) - [Slope×mean of icecream(x)]
65 - [7.8 × 5]
65 - 39 = 26
Hence,
y = 7.8x + 26