Answer:
See below
Step-by-step explanation:
[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]
Thus proved
What is the slops of this line? Enter your answer as a fraction in simplest term in the box.
Answer:
It is 1/4
Step-by-step explanation:
If you go from dot to dot on the line, starting with the first dot:
you go to the right 4 times and then up 1 to get to the next dot.
If you put that into a fraction it is [tex]\frac{rise}{run}[/tex] so going up (1) is ontop of going to the right (4), which is 1/4.
Number of Certified Organic Farms in the United States, 2001–2008
Year Farms
2001 6,231
2002 6,574
2003 7,237
2004 7,211
2005 7,701
2006 8,581
2007 10,302
2008 11,796
Click here for the Excel Data File
(a) Fit three trends (linear, quadratic, exponential) to the time series. (A negative value should be indicated by a minus sign. Do not round the intermediate calculations. Round your final answers to 2 decimal places.)
(b) Use each of the three fitted trend equations to make numerical forecasts for the next 3 years. (Round the intermediate calculations to 2 decimal places and round your final answers to 1 decimal place.)
Answer:
ŷ = 739.49X + 4876.43
y = 6755.98 - 388.24x + 125.30x²
y = 5428.98(1.09)^x
B.)
Linear:
ŷ = 739.49(9) + 4876.43
y = 11531.8
Year 2010 ; x = 10
y = 739.49(10) + 4876.43
y = 12271.3
Year 2011 ; x = 11
y = 739.49(11) + 4876.43
y = 13010.8
Quadratic :
Year 2009 ; x = 9
y = 6755.98 - 388.24(9) + 125.30(9^2)
y = 13411.1
Year 2010 ; x = 10
y = 6755.98 - 388.24(10) + 125.30(10^2)
y = 15403.6
Year 2011 ; x = 11
y = 6755.98 - 388.24(11) + 125.30(11^2)
y = 17646.6
Exponential:
Year 2009 ; x = 9
y = 5428.98(1.09)^9
y = 11791.2
Year 2010 ; x = 10
y = 5428.98(1.09)^10
y = 12852.4
Year 2011 ; x = 11
y = 5428.98(1.09)^11
y = 14009.1
Step-by-step explanation:
X :
1
2
3
4
5
6
7
8
Y:
6231
6574
7237
7211
7701
8581
10302
11796
Using the online linear regression calculator :
The linear trend :
ŷ = 739.49X + 4876.43
Where x = year
With 2006 representing 1 ; and so on
Slope = m = 739.49
Intercept (c) = 4876.43
y = predicted variable
The quadratic model:
General form:
y = A + Bx + Cx²
y = 6755.98 - 388.24x + 125.30x²
The exponential model:
y = AB^x
y = 5428.98(1.09)^x
B.) Next three years :
Year 2009 ; x = 9
Year 2010 ; x = 10
Year 2011 ; x = 11
Linear:
ŷ = 739.49(9) + 4876.43
y = 11531.8
Year 2010 ; x = 10
y = 739.49(10) + 4876.43
y = 12271.3
Year 2011 ; x = 11
y = 739.49(11) + 4876.43
y = 13010.8
Quadratic :
Year 2009 ; x = 9
y = 6755.98 - 388.24(9) + 125.30(9^2)
y = 13411.1
Year 2010 ; x = 10
y = 6755.98 - 388.24(10) + 125.30(10^2)
y = 15403.6
Year 2011 ; x = 11
y = 6755.98 - 388.24(11) + 125.30(11^2)
y = 17646.6
Exponential:
Year 2009 ; x = 9
y = 5428.98(1.09)^9
y = 11791.2
Year 2010 ; x = 10
y = 5428.98(1.09)^10
y = 12852.4
Year 2011 ; x = 11
y = 5428.98(1.09)^11
y = 14009.1
Wow, using grammar makes me feel like an adult!
Answer:
I asked my teacher if we could use that she said it's considered cheating, I still use it
Step-by-step explanation:
What is 2s + 5 > 49 ?
Answer:
s>22
Step-by-step explanation:
2s>49−5
2s>44
s>44/2
s>22
(GIVING EXTRA POINTS ON THIS ONE!! IM ALSO GIVING AWAY BRAINLIEST TO WHO EVER HELPS ME OUT :D)
If you roll a ball down a ramp, which factor will have the greatest effect on the amount of friction created?
A) Force applied to the ball
B) Speed of the ball
C) Texture of the surface
D) Weight of the ramp
(Here is an image if needed) :
Answer:
C. The Texture of the Surface
Step-by-step explanation:
I know it's confusing because of A.. But if you think about what would happen if you were to bounce a ball with a lot of force onto the surface, it wouldn't cause a difference in the friction because it would still just bounce right back up. D. is also not applicable because the weight of the ramp wouldn't matter if the ball is rolling on top of it.
The odds that it will snow tomorrow are 9 to 6. What is the probability that it will not snow tomorrow?a) 0.1818
b) 0.2222
c) 0.1111
d) 0.1667
e) 0.8182
Answer:
a) 0.1818
Step-by-step explanation:
Given that:
The odd that it'll snow tomorrow is 9 to 6
The probability that it will snow tomorrow [tex]=\dfrac{9}{9+6}[/tex]
[tex]=\dfrac{9}{15}[/tex]
= 0.6
The probability that it'll not snow tomorrow [tex]= 1 - \dfrac{9}{15}[/tex]
[tex]= \dfrac{15-9}{15}[/tex]
[tex]=\dfrac{6}{15}[/tex]
= 0.4
Let assume that the odd that it'll snow tomorrow is 9 to 2
The probability that it will snow tomorrow [tex]=\dfrac{9}{9+2}[/tex]
[tex]=\dfrac{9}{11}[/tex]
= 0.8181
The probability that it'll not snow tomorrow [tex]= 1 - \dfrac{9}{11}[/tex]
[tex]= \dfrac{11-9}{11}[/tex]
[tex]=\dfrac{2}{11}[/tex]
= 0.1818
None of the options is correct.
Probability that it will not snow tomorrow = 0.4
The odds of an event E is defined as formulated in equation (1)
[tex]\rm Odd\; of\; event\; E = P(E)/P(\bar E) = P(E)/(1-P(E)).......(1)[/tex]
Let P(E) represents the probability that it will snow tomorrow.
Let event E represents the event that " it will snow tomorrow "
So the odds of the event that it will snow tomorrow
[tex]\rm \dfrac{P(E)}{P(\bar E)} =\dfrac{9}{6} = \dfrac{P(E)}{1-P(E)}.......(2)[/tex]
On solving equation (2) we get
[tex]\rm P(E) = \dfrac{9}{15}[/tex]
So the probability that it will snow tomorrow is 9/15
Hence the probability that it will not snow tomorrow
[tex]\rm P(\bar E) = 1- \dfrac{9}{15} = \dfrac{6}{15} =\bold{0.4}[/tex]
Probability that it will not snow tomorrow = 0.4
For more information please refer to the link below
https://brainly.com/question/7538150
Find the measure of the arc or angle indicated. Assume GE is the diameter of
the circle
O 70°
0 47
O 54
O 60°
Answer: 70 degrees (i had that question got it right)
Step-by-step explanation:
Solve four and six eighths minus two and three fifths.
(GIVING EXTRA POINTS AND GIVING BRAINLIEST!!)
A) one and six thirteenths
B) one and three fortieths
C) two and six fortieths
D) two and three thirteens
(Here is an image if needed) :
Answer:
I am not really sure but I asume it is C honestly I am sorry if I am wrong. But if I am right I really hope this helps
A recent study investigated whether renowned violinists were able to classify the age of a violin. In the study, violins constructed before 1900 and violins constructed after 2010 were used. The violinists played each violin and were asked to classify the violin as old (constructed before 1900) or new (constructed after 2010). The responses are shown in the following table.
Which of the following statements is supported by the results in the table?
1.)The proportion of all new violins that are correctly classified is equal to the proportion of all old violins that are correctly classified.
2.)The proportion of all new violins that are incorrectly classified is equal to the proportion of all old violins that are correctly classified.
3.)The proportion of all incorrectly classified violins that are old is equal to the proportion of all correctly classified violins that are new.
4.)The proportion of all incorrectly classified violins that are new is equal to the proportion of all correctly classified violins that are new.
5.)The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.
Answer:
The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.
Step-by-step explanation:
According to the table, we have that the correct option is:
5.)The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.
Statement 1:
15 of 33 new are correctly classified, thus, the proportion is:
[tex]p_N = \frac{15}{33} = 0.4545[/tex]
18 out of 31 old, thus:
[tex]p_O = \frac{18}{31} = 0.58[/tex]
Proportions are different, thus, statement 1 is false.
Statement 2:
13 out of 31 old are incorrectly classified, thus:
[tex]p = \frac{13}{31} = 0.4194[/tex]
Different than 0.4545, thus, statement 2 is false.
Statement 3:
Out of 31 incorrectly classified, 13 are old.
Out of 33 correctly classified, 15 are new.
Different proportions, thus, statement 3 is false.
Statement 4:
Out of the 33 new, 15 are correctly classified and 18 incorrectly, different proportions, thus, statement 4 is false.
Statement 5:
18 out of 33 correctly classified are old.
18 out of 33 new violins are incorrectly classified.
Same proportion, thus, statement 5 is true.
A similar problem is given at https://brainly.com/question/12612621
The graph shows the number of centimeters a particular plant grows over time. Given the points (0,0) and (6,9), how many centimeters does the plant grow per week?
Answer: 4/5 or 0.8
Step-by-step explanation: To find how much it grows over time, we have to find the slope. to do that, we need to have two points with exact points on the graph, so (0,0) and (4,5). the equation for slope is rise/run. it rises 4, and runs 5. so 4/5.
Fill in the blanks to complete the sentence.
Last month, the online price of a powered ride-on car was $250. This month, the online price is $330. What is the percent of increase in the price of the car? Round the percent to the nearest tenth if necessary. :)
Answer:32%
Step-by-step explanation:
330-250=80
80/250=0.32 or 32%
What is the equation of the line that passes through the point (-1,7) and has a slope of -2?
what is the absolute minimum and maximum of this graph
Answer:
The minimum is 0 because the lowest point the line reaches is 0. The maximum is infinity because the arrow keeps going up.
Answer:
There is no max since the arrow is continuous and the minimum is zero
Step-by-step explanation:
write a possible equation for each graph. Help me please
Answer:
a. y = -x² + 2x - 8
b. y = [tex]\frac{1}{x-2}[/tex]
c. y = x³+ 3
Step-by-step explanation:
Write an explicit formula for an, the nth term of the sequence 19,24,29
Answer:
explicit formula for an, the nth term of the sequence 19,24,29
[tex]a_1=19 ; \ a_n=a_{n-1}+5[/tex]
Step-by-step explanation:
We need to Write an explicit formula for an, the nth term of the sequence 19,24,29
In the sequence the First term a₁= 19
Common Difference d= 5
The Formula used for explicit formula is: [tex]a_1=First \ term ; \ a_n=a_{n-1}+d[/tex]
Where d is common difference and n is nth term of sequence.
So, explicit formula for an, the nth term of the sequence 19,24,29
[tex]a_1=19 ; \ a_n=a_{n-1}+5[/tex]
There were 5 ice cream cones for every 3 brownies sold at the ice cream shop. If there were 24 brownies sold, how many ice cream cones were sold?
Answer:
THe answere is 40
Step-by-step explanation:
If 24 brownies are sold, the number of ice cream cones sold is 40.
A linear equation is in the form:
y = mx + b;
where y, x is variable, m is the rate of change and b is the y intercept.
Let y represent the number of ice cream cones and x represent the number of brownies sold.
Since there were 5 ice cream cones for every 3 brownies sold at the ice cream shop. Hence:
y = (5/3)x
If 24 brownies are sold:
y = (5/3)x
y = (5/3) * 24 = 40
If 24 brownies are sold, the number of ice cream cones sold is 40.
Find out more at: https://brainly.com/question/13911928
Please answer the bottom one
Answer:
The first one is 109, the 2nd one is the 2nd and 4th choices
Step-by-step explanation:
DONT HAVE MUCH TIME LEFT, THIS WILL BE DUE SOON!!!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
the slope is 2 I am pretty sure
What is the variable in Samuel is six inches taller than his brother Elijah.if Samuel is 48 inches tall,how tall is Elijah
Answer: Elijah would be 42 inches tall
Step-by-step explanation:
We all know that Samuel is 48 inches while Elijah is 6 inches shorter.
You subtract 6 from 48 to get 42.
Hopefully, this helped. :D
What is the midpoint of the segment below?
(2,3)
(-3,-2)
O A. (2.5, 2.5)
O B. (5,5)
O C. (-0.5, 0.5)
O D. (0,0)
Answer:
C
Step-by-step explanation:
use midpoint formula
midpt = ((2 + (- 3))/2 , (3 + (- 2))/2) = (-0.5, 0.5)
24 = 3(n–5)
What is the answer
Step-by-step explanation:
24=3n-15 or,25+15=3n or,39=3n or,39/3=n or,n=13 therefore the value of n is 13. I think this answer is helpful for you
Answer: n = 13
Step-by-step explanation:
24=3(n-5) - First distribute the 3 to the n and the 5. Which you would than get 3n and -15
24=3n-15 - Now add the 15 to both sides which would cause it to cancel out on the left side of the equal side.
39=3n - Now divide the 3 from 3n on both sides of the equal side.
n=13 - Once you do that you will get n = 13. That is your answer!
1. Jared borrowed $300 from his mother to buy an x-box 360. Jared will pay her back in 4 years with 3.5% simple interest. How much total money will he payback to his mother at the end of the 4 years? (Hint: which formula should you use simple or compound, what is the principal, what is the rate, what is the time.)
2. Jackie deposits $225 in an account that pays 4.1% interest compound annually. How much money would Jackie have in her account after 1.5 years? (Hint: which formula should you use simple or compound, what is the principal, what is the rate, what is the time.)
3. Stephanie placed $1,700 in an account that earns 6% interest compounded annually. How much money will she have in the account at the end of 48 months? (Hint: which formula should you use simple or compound, what is the principal, what is the rate, what is the time.)
Answer:
1) future value = present value x [1 + (i x n)] = $300 x [1 + (3.5% x 4)] = $342
2) using the compound interest formula:
future value = $225 x (1 + 4.1%)¹°⁵ = $238.98
Using the simple interest formula doesn't yield the same answer = $225 x [1 + (4.1% x 1.5)] = $238.84. In this case it is close due to a very short period of time and low interest rate.
3) future value = present value x (1 + i)ⁿ = $1,700 x (1 + 6%)⁴ = $2,146.21
since the interest is annual, we must convert 48 months to 4 years
can someone please help me thank you
Answer:
Neither of the students are correct.
Step-by-step explanation:
Sarah:
P = 3x + x +7 + 3x + x +7 ..... this first step is correct
= 6x + 14 .... this step is incorrect, Sarah forgot to add the other 2 xs
John:
P = 2(x + 7) + 2(3x)
= 2x + 7 + 6x .... this step is incorrect, John forgot to distribute the 2 to the 7
= 8x + 7 .... incorrect because of the previous step
The answer should've been 8x + 14.
X
I ㅗ
]
Factor: -2/3
out of -3X
- 12
Answer:what is this
Step-by-step explanation:
bruh
PLEASE HELP MATH 100%: How does Newton’s Second Law apply to the field of robotics? why is this a litreal math question like i know-
Can someone help? I really don’t understand this at all!
is this pathogroem therom?
Evaluate 3/11 × 11/13 Give your answer as a fraction in its simplest form.
Answer: 3/13
Step-by-step explanation:
help with this question please
Question 6
Ryan spent half of his weekly allowance on candy. To earn more money, his parents let him clean the windows in his house for $9. He
ended with $15. Which equation would represent this situation?
Answer:
x=6
Step-by-step explanation:
Let X = Rob's weekly allowance
If he spent 1/2 of it on candy, then he had 1/2 of it left (1/2)X
After he earned $6 for cleaning the oven, he had $9.
So,
(1/2)X + 6 = 9
(1/2)X = 3
X = 6
helppppp pleaseee!!
Evaluate the function
Answer:
10
Step-by-step explanation:
go to mathaway.com and type in the equation and when x=-6. Press show graph and it says 10. The graph is my proof.