It’s a 50/50 chance since there is only 2 sides. (1?2)
1. Derive this identity from the sum and difference formulas for cosine:
sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)]
Calculation:
1.
2.
3.
Reason:
1.
2.
3.
2. Use the trigonometric subtraction formula for sine to verify this identity:
sin((π / 2) – x) = cos x
Calculation:
1.
2.
3.
Reason:
1.
2.
3.
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
Your cell phone bill just arrived. Your plan only allows you to send and receive 130 texts per month, but you sent and received 268 texts. Your plan charges you $0.05 per text sent on your plan, and then $0.25 for each text you send over your plan limit. How much money do you have to pay for the extra texts that you sent and received? What is your total bill?
Answer:
$34.5
Step-by-step explanation:
1. 268 - 130 = 138
2. 138 x .25 = 34.5
Can someone help me on this question
Answer:
9
Step-by-step explanation:
✯Hello✯
↪ There is a quadratic formula that needs to be used. 4ac and b^2 are a part of this formula
↪ First we need to work out the Values for A and B and C
A = 1
B = 5
C= 4
↪ now we can substitute this into what the equation is asking. (5)^2-4(1)(4)=9
↪ The answer is 9
↪ I hope this helps you :)
❤Gianna❤
Solve for x.
mx2 + y
e
= b
A)
x =
be - y
m
B)
x =
be - y
m
C)
x = ±
be - y
m
D)
x = ±
be + y
m
Answer:
its C
Step-by-step explanation:
Answer:
its c
Step-by-step explanation:
many locations require that renters be paid interest on their secuity deposits. If ypu have a security deposit of $1,700, how much interest would you expect to earn per year at 5 percent?
Answer: $85
Step-by-step explanation: The formula for interest is I = PRT, where I equals interest, P equals principal, R equals rate and T equals time.
I = 1,700 x .05 x 1 = $85
You can expect to earn $85 interest for one year on the security deposit.
Suppose the side lengths are multiplied by 2. Describe the change in the perimeter.
Answer:
The perimeter would then be squared
Step-by-step explanation:
Since each length is being multiplied by 2 the you have 2 of the same perimeters. So you just add them together or square it.
Which capacity is most appropriate for a pitcher of lemonade 3 litters or 30 milliliters
Answer:
3 liters.
Step-by-step explanation:
If you go to the store and you buy a 2 liter of soda making a pitcher of lemonade with one more liter won't hurt.
A milliliter is not a lot. It won't even quench your own thirst. So 3 liters is the best option.
D? Marco draws a card and replaces it 10 times from a standard deck of 52 cards. He draws 8 red cards and 2 black cards. What is the experimental probability of drawing a red card?
A) 1/2
B) 1/4
C) 2/3
D) 4/5
Answer:
D) 4/5
Step-by-step explanation:
He drew and replaced cards 10 times.
8 out of the 10 times, he drew a red card.
8/10 = 4/5
Answer: D) 4/5
You are correct.
Final answer:
The experimental probability of drawing a red card, based on the information given, is 4/5, since Marco drew 8 red cards out of 10 total draws.
Explanation:
The student is asking for the experimental probability of drawing a red card based on Marco's actual draws from a standard deck of 52 cards. Experimental probability is calculated by dividing the number of times the event of interest (drawing a red card) occurred by the total number of trials. In this case, Marco drew a red card 8 times out of 10 total draws.
Therefore, the experimental probability is:
Experimental Probability = Number of red cards drawn / Total number of draws = 8/10
When simplified, 8/10 equals 4/5. Therefore, the correct answer is:
Experimental Probability of Drawing a Red Card = 4/5
50 POINTS AND BRAINLIEST!!! NEED HELP NOW!!
The dot plots below show the weights of the players of two teams:
Based on visual inspection of the dot plots, which team appears to have the larger mean weight?
A. Not enough information is available to draw a conclusion.
B. Both groups are similar.
C. Team F
D.Team E
Question 10(Multiple Choice Worth 5 points)
(08.02 MC)
The two dot plots below show the heights of some sixth graders and some seventh graders:
The mean absolute deviation (MAD) for the first set of data is 1.2 and the MAD for the second set of data is 1.7. Approximately how many times the variability in the heights of the sixth graders is the variability in the heights of the seventh graders? (Round all values to the tenths place.)
1.2
1.4
2.4
2.8
1. would have to be team E because add up all the numbers 1058/8 (which is how many numbers that is there) 132.25.
2. (More of an explanation if you still don't understand)
52+52+53+54+55+55=321/6=53.5
52+53+54+55+57+57=328/6=54.66 repeated rounded to 54.7 so your answer is 1.2
what is the inverse of the function below f(x)=3^x
Answer:
[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]
Step-by-step explanation:
Given: [tex]f(x)=3^x[/tex]
To find the inverse, let's first replace the [tex]f(x)[/tex] with [tex]y[/tex].
[tex]y=3^x[/tex]
Switch the [tex]x[/tex] and [tex]y[/tex].
[tex]x=3^y[/tex]
Solve for [tex]y[/tex].
[tex]y=\frac{ln(x)}{ln(3)}[/tex]
Write it in inverse notation.
[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]
Answer: A) f^-1(x) = log₃x
You want to save ₹1,17,000 to buy your first self-driving magic carpet. You deposit ₹90,000 in a bank at an interest rate of 6 % 6%6, percent per annum. How many years do you have to wait before you can buy your magic carpet?
Answer:
4.50 yr
Step-by-step explanation:
I assume that this is compound interest.
The compound interest equation is
[tex]A = P(1+ \frac{r }{ n})^{nt}[/tex]
You don't give the frequency of compounding, so I assume that it is once per year.
Data:
A = ₹117 000
P = ₹90 000
r = 6 % = 0.06
n = 1
Calculations:
[tex]117 000 = 90 000(1+ \frac{0.06 }{ 1})^{1 \times t}[/tex]
[tex]117 000 = 90 000(1+ 0.06)^{t}[/tex]
Divide each side by 90 0000
[tex]1.3 = 1.06^{t}[/tex]
Take the logarithm of each side
log1.3 = tlog1.06
0.1139 = 0.025 31t
Divide each side by 0.025 31
t = 4.50 yr
You can buy your magic carpet in 4.50 yr.
Answer: is 5
all you have to do is \(^o^)/
(1,17,000−90,000)=27,000
1 year =6%of 90,000
1%of 90,000=900
6% of 90,000=(6*900)
1 year =5400
27,000 u divide that by 5400=5 soooooooooo......
ITs Five 5SUUUPPERR URGENT! PLEASE HELP 50 POINTS!!!
When the following quadratic equation is written in general form, what is the value of "c"?
-3/4x^2+2=0
-8
-6
-2
Here is your answer
[tex]\bold{-2}[/tex]
REASON :
Given equation -
[tex] \frac{-3}{4}{x}^{2}+2=0 [/tex]
when, written in general form equation is
[tex] \frac{3}{4}{x}^{2}-2=0 [/tex] (on multiplying both sides by -1)
Now this is quadratic equation in general form, where
[tex] a= \frac{3}{4} [/tex] [coefficient of x^2]
b= 0 [coefficient of x]
c= -2 [constant term]
Hence, c= -2
HOPE IT IS USEFUL
Answer:
-2
Step-by-step explanation:
a = 3/4
[coefficient of x^2]
b= 0 [coefficient of x]
c= -2 [constant term]
Which describes the number and type of roots of the equation x^4 - 64 = 0
a. 2 real roots, 2 imaginary roots
b. 4 real roots
c. 3 real roots, 1 imaginary root
d. 4 imaginary roots
ANSWER
a. 2 real roots, 2 imaginary roots
EXPLANATION
The given equation is
[tex] {x}^{4} - 64 = 0[/tex]
We rewrite as difference of two squares,
[tex]( {x}^{2} )^{2} - {8}^{2} = 0[/tex]
We factor using difference of two squares to get;
[tex]( {x}^{2} - 8)( {x}^{2} + 8) = 0[/tex]
We now use the zero product property to get:
[tex]{x}^{2} = 8 \: or \: {x}^{2} = - 8[/tex]
Take the square root of both sides to get;
[tex]{x} = \pm \sqrt{8} \: or \: {x}^{2} = \pm \sqrt{ - 8} [/tex]
[tex]{x} = \pm 2\sqrt{2} \: or \: {x} = \pm 2\sqrt{ 2} i[/tex]
[tex]{x} = - 2\sqrt{2} \: or \: {x} = 2\sqrt{ 2}[/tex]
are two real roots.
[tex]{x} = - 2\sqrt{2}i \: or \: {x} = 2\sqrt{ 2} i[/tex]
are two imaginary roots.
The correct answer is A.
The correct answer is a. 2 real roots, 2 imaginary roots.
To determine the number and type of roots for the equation [tex]\(x^4 - 64 = 0\)[/tex]
1. Start with the equation:
[tex]\[ x^4 - 64 = 0 \][/tex]
2. Rewrite the equation as a difference of squares:
[tex]\[ x^4 - 64 = (x^2)^2 - 8^2 = (x^2 - 8)(x^2 + 8) = 0 \][/tex]
3. Set each factor equal to zero:
[tex]\[ x^2 - 8 = 0 \]\[ x^2 + 8 = 0 \][/tex]
4. Solve each equation separately:
For [tex]\(x^2 - 8 = 0\)[/tex]:
[tex]\[ x^2 = 8 \]\[ x = \pm \sqrt{8} = \pm 2\sqrt{2} \][/tex]
These are two real roots.
For [tex]\(x^2 + 8 = 0\)[/tex]:
[tex]\[ x^2 = -8 \]\[ x = \pm \sqrt{-8} = \pm \sqrt{8i^2} = \pm 2\sqrt{2}i \][/tex]
These are two imaginary roots.
Therefore, the equation [tex]\(x^4 - 64 = 0\)[/tex] has:
- 2 real roots: [tex]\(2\sqrt{2}\) and \(-2\sqrt{2}\)[/tex]
- 2 imaginary roots: [tex]\(2\sqrt{2}i\) and \(-2\sqrt{2}i\)[/tex]
The correct answer is:
a. 2 real roots, 2 imaginary roots
The complete question is- Which describes the number and type of roots of the equation [tex]x^4 - 64 = 0[/tex]
a. 2 real roots, 2 imaginary roots
b. 4 real roots
c. 3 real roots, 1 imaginary root
d. 4 imaginary roots
Please help! I will mark brainliest if it lets me
The answer you are looking for is the first 1, or a. hope this helps. Please mark me as brainliest.
Answer:
The first line is the correct answer. because of the ≤ sign it means that circle will be closed and the line will be to the left. A trick is if you picture the sign as an arrow then that will be which way the line will go. ;) Hope this helps!
in the equation below, what is the value of Y when X = 100?
5y = 2.3√x
a- 2.46
b- 4.6
c- 18
d- 46
Answer:
b- 4.6
Step-by-step explanation:
5y = 2.3√x
Let x = 100
5y = 2.3 sqrt(100)
5y = 2.3 (10)
5y = 23
Divide by 5
5y/5 = 23/5
y =4.6
Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing intraocular lenses used in the human eye following cataract surgery. 300 lenses were tumble-polished using the first polishing solution, and of this number, 249 had no polishing-induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 196 lenses were satisfactory upon completion. Is there any reason to believe that the two polishing solutions differ? Use α = 0.01. What is the P-value for this test? There significant difference in the proportion of polishing-induced defects produced by the two polishing solutions at the 0.01 level of significance. The P-value is . Round your answer to three decimal places (e.g. 98.765).
Final answer:
To determine if there is a significant difference between two polishing solutions, a two-proportion z-test can be used, comparing the proportions of polishing-induced defects. If the p-value is less than the significance level (0.01), the null hypothesis is rejected.
Explanation:
To determine if there is a significant difference between the two polishing solutions used in tumble-polishing intraocular lenses, we can perform a hypothesis test. The null hypothesis (H0) is that there is no difference between the proportions of polishing-induced defects for the two solutions, while the alternative hypothesis (Ha) is that there is a difference.
We can use a two-proportion z-test to compare the proportions of defects. The z-test statistic is calculated as:
z = (p1 - p2) / [tex]\sqrt{(p1q1/n1)[/tex] + (p2q2/n2))
where p1 and p2 are the proportions of defects, q1 and q2 are 1-p1 and 1-p2 respectively, and n1 and n2 are the number of lenses polished with each solution. The p-value for this test can be calculated using a standard normal distribution table or a statistical software.
If the p-value is less than the significance level α (0.01 in this case), we reject the null hypothesis and conclude that there is a significant difference between the two polishing solutions.
The p-value for this test cannot be determined without the actual values of p1, p2, q1, q2, n1, and n2.
Please help with this problem! :)
Answer:
∠STP = 90°
Step-by-step explanation:
The diagonals of a square are perpendicular bisectors of each other, hence
∠STP = 90°
So Confused!! Somebody Plz Explain How To Do!!!!!!!
For the following system, use the second equation to make a substitution for y in the first equation.
3x + y = 1
y + 4 = 5x
What is the resulting equation?
A.) 3x + 5x - 4 = 1
B.) 3x + 4 - 5x = 1
C.) 3x + 5x + 4 = 1
Answer: A) 3x + 5x - 4 = 1
Step-by-step explanation:
The second equation is y + 4 = 5x. Solve this equation for y by subtracting 4 from both sides. --> y = 5x - 4
Now replace "y" in the first equation with "5x - 4".
3x + y = 1
--> 3x + (5x - 4) = 1
Thirty times the square of a non-zero number is equal to eight times the number. what is the number?
let's say number is x , then
30 × (x)^2 = 8x
subtracting 8x from both side
30x^2 - 8x = 0
taking 2x common
2x( 15x - 4)= 0
one solution is
2x = 0
x= 0
but number is non zero so ignoring it.
next solution is
15x - 4 = 0
adding 4 both side
15x = 4
dividing by 15 both side
x = 4/15
The interest rate r required to increase your investment p to the amount a in t years is found by [tex]r=(\frac{a}{p} )^\frac{1}{t} -1[/tex]. Find the interest rate r for p = 2700, a = 6400, and t = 3. Round to the nearest hundredth.
The interest rate required to increase an investment of $2700 to $6400 in 3 years, using the formula r=(a/p)^(1/t) - 1, is approximately 38.5% per year when compounded annually.
Explanation:The subject at hand deals with the concept of finding the interest rate on an investment. The provided equation, which represents the interest rate formula, is: r=(a/p)^(1/t) - 1. Here, the variables represent the following: r is the interest rate, a is the amount of money accumulated after t years (the future value of the investment), p is the principle/original amount (the initial value of the investment), and t is the time in years. By inserting the given values (p = 2700, a = 6400, t = 3) into the formula, we get: r = (6400 / 2700)^(1 / 3) - 1.
The next step is to calculate the arithmetic for the values inside the parenthesis first, then raise it to the power of 1/3 (which is the cube root), and finally subtract 1 from the result. Doing these calculations you obtain approximately 0.385, or 38.5% when expressed as a percentage. So, the interest rate that is required to increase your investment of $2700 to $6400 in 3 years is approximately 38.5% per year when compounded annually.
Learn more about Interest Rate Calculation here:https://brainly.com/question/32997798
#SPJ3
i am confusion ̿'̿'\̵͇̿̿\з=( ͠° ͟ʖ ͡°)=ε/̵͇̿̿/'̿̿ ̿ ̿ ̿ ̿ ̿
ANSWER:
~~~~~~~~~
Im pretty sure the answer is "Relation"
~~~~~~~~~
Relation definition:
A relation is a set of numbers that have a relationship through the use of a domain and a range.
~~~~~~~~~
HOPE THIS HELPS!!!
≠GoodLuck
It is a relation because even if they are negative they still can have a relation between them. Hope this is helpful for you!
A cheesecheese can be classified as either raw dash milkraw-milk or pasteurizedpasteurized. Suppose that 9797% of cheesescheeses are classified as pasteurizedpasteurized. (a) Two cheesescheeses are chosen at random. What is the probability that both cheesescheeses are pasteurizedpasteurized? (b) NineNine cheesescheeses are chosen at random. What is the probability that all ninenine cheesescheeses are pasteurizedpasteurized? (c) What is the probability that at least one of ninenine randomly selected cheesescheeses is raw dash milkraw-milk? Would it be unusual that at least one of ninenine randomly selected cheesescheeses is raw dash milkraw-milk?
Answer:
chese is th awnser
Step-by-step explanation:
The sophomore class sells tickets to a benefit concert to raise money. Each ticket sells for $15. How much money do they raise?
A. m=15+t
B. m=t/15
C. t=15m
D. m=15t
Answer:
D.m=15t
Step-by-step explanation:
If the number of tickets is t and the total amount of money collected is m then a product of the price per ticket with the cost of the ticket gives the amount of money collected from the sale of the tickets.
therefore m= t×15
m=15t
Answer:
D. m = 15t
Step-by-step explanation:
We have to assume that m is supposed to stand for the money (in dollars) that results from the sale of t tickets. Then the sale of t=1 ticket will result in m=15 dollars. Only one of the offered formulas will give this result:
m = 15t
_____
Comment on the problem
Variables need to be defined. We'd prefer to see some discussion of how concert expenses are covered, so we can be assured that ticket sales directly relate to money raised.
Credit cards can only lead to debt that is difficult to eliminate and should be avoided at all costs. Please select the best answer from the choices provided T F
This statement is false.
Step-by-step explanation:
Credit cards can only lead to debt that is difficult to eliminate and should be avoided at all costs. This is false.
This is not a standard statement that credit cards always lead to debt. A person should use his credit card with responsibility. He should pay the bills timely to avoid accumulation of debt and other fines. Only when a person uses his card irresponsibly and does not pay dues timely, can lead to debts.
So, this is a false statements.
Answer:
False
Step-by-step explanation:
Leah loves chicken wings and is comparing the deals at three different restaurants. Buffalo Bills has 888 wings for \$7$7dollar sign, 7. Buffalo Mild Wings has 121212 wings for \$10$10dollar sign, 10. Wingers has 202020 wings for \$17$17dollar sign, 17. Which restaurant offers the lowest price per wing?
Cost of chicken wings at Buffalo Bills = 8 wings for $7
Cost of 1 wing at Buffalo Bills = [tex]\frac{7}{8} =0.875[/tex]
Cost of chicken wings at Buffalo Mild Wings = 12 wings for $10
Cost of 1 wing at Buffalo Mild Wings = [tex]\frac{10}{12}= 0.833[/tex]
Cost of chicken wings at Wingers = 20 wings at $17
Cost of 1 wing at Wingers = [tex]\frac{17}{20}= 0.850[/tex]
Hence, comparing all the three costs per wing, we can see that Buffalo Mild Wings is serving chicken wings at lowest price of $0.833 per wing.
Answer:
It is B
Step-by-step explanation:
Javier and Kyle work installing windows and can earn extra money by installing doors. Last week, Javier earned $56 more than Kyle because of door installations. The expression below represents Javier's pay for the week: 14w + 56 What does the constant term of the expression represent?
Answer:
The money Javier earned installing doors.
Step-by-step explanation:
The problem statement gives insufficient information to answer the question with certainty.
The $56 extra earnings from door installation seems to match the 56 added as a term in Javier's pay, so we assume they are related. There is nothing else in the problem statement suggesting that to be the case.
_____
Comment on this problem
The problem fails to teach anything about math or critical thinking. Rather, it requires a student to jump to conclusions without any basis in reasoning. If the rest of the curriculum materials are like this, they should be rejected.
Determine if x + 3 is a factor of -3[tex]x^{3}[/tex]+6[tex]x^{2}[/tex]+6x+9. How do you know?
no, because the remainder is 126
yes, because the remainder is 126
no, because the remainder is –108
yes, because the remainder is –108
Answer:
Option C
no, because the remainder is 126
Step-by-step explanation:
Given the polynomial equation in the question
-3x^{3}+6x^{2}+6x+9
factor = x + 3 (divisor)
long division-3x² + 15x - 39 Quotient
--------------------------------
x + 3| -3x³ + 6x² + 6x + 9 Dividend
| -3x³ - 9x²
----------------------
15x² + 6x + 9
15x² + 45x
--------------------
-39x + 9
-39x - 117
-------------
126 Reminder
Since reminder is not zero so (x + 3) is not factor of -3x³ + 6x² + 6x + 9.
(x-3) is the factor of -3x³ + 6x² + 6x + 9.
. Write an equation of the line that passes through (2, -1) and is parallel to the graph of y = 5x – 2.
Write your final equation in slope-intercept form.
PARALLEL slopes always have the same slope no matter what because they are parallel
Which of the equations listed below are linear equations? Equation I: C=2*3.14*r Equation II: A = 3.14*r^2 Equation III: V = 4/3*3.14*r^3
Answer:
Equation I: C=2*3.14*r
Step-by-step explanation:
A linear equation is an equation whose highest exponent on the variable is 1.
C=2*3.14*r.................Exponent of 1
A = 3.14*r^2...............Exponent of 2
A = 3.14*r^2...............Exponent of 3
Given sin theta= 6/11 and sec theta < 0, find cos theta and tan theta.
Answer: option a.
Step-by-step explanation:
By definition, we know that:
[tex]cos^2(\theta)=1-sen^2(\theta)\\\\tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute [tex]sin(\theta)=\frac{6}{11}[/tex] into the first equation, solve for the cosine and simplify. Then, you obtain:
[tex]cos(\theta)=\±\sqrt{1-(\frac{6}{11})^2}\\\\cos(\theta)=\±\sqrt{\frac{85}{121}}\\\\ cos(\theta)=\±\frac{\sqrt{85}}{11}[/tex]
As [tex]sec\theta<0[/tex] then [tex]cos\theta<0[/tex]:
[tex]cos(\theta)=-\frac{\sqrt{85}}{11}[/tex]
Now we can find [tex]tan\theta[/tex]:
[tex]tan\theta=\frac{\frac{6}{11}}{-\frac{\sqrt{85}}{11}}\\\\tan\theta=-\frac{6\sqrt{85}}{85}[/tex]
Answer:
a
Step-by-step explanation: