Answer:
[tex](a)\ \cos(180 - x)[/tex] --- Never true
[tex](b)\ \cos(90 -x)[/tex] --- Always true
[tex](c)\ \cos(x)[/tex] ---- Sometimes true
[tex](d)\ \cos(2x)[/tex] ---- Sometimes true
Step-by-step explanation:
Given
[tex]\sin(x )[/tex]
Required
Determine if the following expression is always, sometimes of never true
[tex](a)\ \cos(180 - x)[/tex]
Expand using cosine rule
[tex]\cos(180 - x) = \cos(180)\cos(x) + \sin(180)\sin(x)[/tex]
[tex]\cos(180) = -1\ \ \sin(180) =0[/tex]
So, we have:
[tex]\cos(180 - x) = -1*\cos(x) + 0*\sin(x)[/tex]
[tex]\cos(180 - x) = -\cos(x) + 0[/tex]
[tex]\cos(180 - x) = -\cos(x)[/tex]
[tex]-\cos(x) \ne \sin(x)[/tex]
Hence: (a) is never true
[tex](b)\ \cos(90 -x)[/tex]
Expand using cosine rule
[tex]\cos(90 -x) = \cos(90)\cos(x) + \sin(90)\sin(x)[/tex]
[tex]\cos(90) = 0\ \ \sin(90) =1[/tex]
So, we have:
[tex]\cos(90 -x) = 0*\cos(x) + 1*\sin(x)[/tex]
[tex]\cos(90 -x) = 0+ \sin(x)[/tex]
[tex]\cos(90 -x) = \sin(x)[/tex]
Hence: (b) is always true
[tex](c)\ \cos(x)[/tex]
If
[tex]\sin(x) = \cos(x)[/tex]
Then:
[tex]x + x = 90[/tex]
[tex]2x = 90[/tex]
Divide both sides by 2
[tex]x = 45[/tex]
(c) is only true for [tex]x = 45[/tex]
Hence: (c) is sometimes true
[tex](d)\ \cos(2x)[/tex]
If
[tex]\sin(x) = \cos(2x)[/tex]
Then:
[tex]x + 2x = 90[/tex]
[tex]3x = 90[/tex]
Divide both sides by 2
[tex]x = 30[/tex]
(d) is only true for [tex]x = 30[/tex]
Hence: (d) is sometimes true
Hey! Can someone please help me with this question? Really appreciate it
Answer:
[tex]d = 0.112* 10^3[/tex]
Step-by-step explanation:
Given
[tex]h = 8.4 * 10^3[/tex]
[tex]d = \sqrt{\frac{3h}{2}}[/tex]
Required
Find d
We have:
[tex]d = \sqrt{\frac{3h}{2}}[/tex]
Substitute: [tex]h = 8.4 * 10^3[/tex]
[tex]d = \sqrt{\frac{3*8.4 * 10^3}{2}}[/tex]
[tex]d = \sqrt{\frac{25.2 * 10^3}{2}}[/tex]
[tex]d = \sqrt{12.6 * 10^3}[/tex]
Express as:
[tex]d = \sqrt{1.26 *10* 10^3}[/tex]
[tex]d = \sqrt{1.26 *10^4}[/tex]
Split
[tex]d = \sqrt{1.26} *\sqrt{10^4}[/tex]
[tex]d = 1.122* 10^2[/tex]
To write in form of: [tex]a * 10^b[/tex]
The value of a must be: [tex]0 \le a \le 1[/tex]
So, we have:
[tex]d = 0.1122* 10 * 10^2[/tex]
[tex]d = 0.1122* 10^3[/tex]
Approximate
[tex]d = 0.112* 10^3[/tex]
Tina wrote 2 equivalent expressions that could be used to calculate the number of books on her shelves. Which pair of expressions is equivalent?
4+(9+8) and 4−(9−8)
3(9+8) and 9(3+8)
(4×9)×8 and 9×(4×8)
(5+4)+1 and 5(4+1)
Answer:b
Step-by-step explanation:
Not D
Answer:
(4×9)×8 and 9×(4×8)
Step-by-step explanation:
According to the following graph, which service took the longest to download the podcast? How much longer did it take than Groove Box in minutes and seconds?
51000711
The service will take the longest to download the podcast.
It will take minutes and seconds longer than Groove Box.
Answer:
- Top Hat
- 14
- 37
Step-by-step explanation:
Abag contain 3 red ,5 black and 4 white marbles. one marble is drawn at random. what is the probablity not black marble
=================================================
Explanation:
There are B = 3+5+4 = 12 marbles total, of which A = 12-5 = 7 are not black. Or you could note that we have A = 3 red + 4 white = 7 marbles that are not black.
The probability of selecting a non-black marble is A/B = 7/12
7/12 = 0.5833 = 58.33% approximately
Annabelle works in a deli and has been tracking the daily sales of different items over several months. Anabelle found that when there was an increase in the number of cups of hot chocolate sold, the number of cups of coffee sold also increased similarly, when there was a decrease in the number of cups of hot chocolate sold, the number of cups of coffee also decreased
Answer:
When hot chocolate sales increase, so do coffee sales, but the sale of one does not increase the other. There were just more customers that day.
Step-by-step explanation:
Help please just write the ratio like #1 300: ?
uppose you are performing a hypothesis test with H subscript 0 superscript blank space colon space mu equals 10 and H subscript A colon mu greater than 10, using a sample size of 50 observations. You sample data has a mean of 10.7, with a standard deviation of 3.1. Compute the test statistic for this hypothesis test
Answer: The test statistic for this hypothesis test =1.597
Step-by-step explanation:
When population standard deviation is unknown, we use t-test statistic:
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]\overline{x}[/tex] = sample mean, [tex]\mu[/tex] = population mean , s= sample standard deviation, n = sample size.
As per given,
[tex]t=\dfrac{10.7-10}{\dfrac{3.1}{\sqrt{50}}}\\\\=1.59669273171\approx1.597[/tex]
Hence, the test statistic for this hypothesis test =1.597
what is the time in Nigeria WHOEVER GETS IT ROGHT I WILL GIVE YOU BRAINLIEST
Answer:
7:55 PM
hope this helps
have a good day :)
Step-by-step explanation:
Mrs. Smith decides to buy three sweaters and a pair of Jeans. She has $129 in her wallet.
If the price of the Jeans Is $40.05, what is the highest possible price of a sweater, each sweater is the
same price?
Variable:
Equation:
Solution:
Answer:
Step-by-step explanation:Herely/3fcEdSx's li[tex]^{}[/tex]nk to the answer:
bit.[tex]^{}[/tex]
When testing joint hypothesis, you can use: Group of answer choices the F- statistic. the chi-squared statistic. either the F-statistic or the chi-square statistic. none of the above. g
Answer:
F Statistics
Step-by-step explanation:
In a joint hypothesis, the researcher is interested to determine the significance of each independent variable individually as well joint impact of all independent variable on the dependent variable. Hence, F statistics would be used as researcher would be interested to know about the the significance of all the independent variable jointly
PLS HELP 40 POINTS
If the dimensions of the following cylinder are quadrupled, what will be the volume of the new similar cylinder?
340,426.24 in. 3
20,724 in. 3
63,829.92 in. 3
110,528 in. 3
Volume of the new similar cylinder is equals to 340,426.24 in.³.
What is volume?
" Volume is defined as the total space occupied by any three dimensional objects enclosed in it."
Formula used
Volume of the cylinder = πr²h
r = radius of the cylinder
h = height of the cylinder
value of π = 3.14
According to the question,
radius of the cylinder = 11 in.
height of the cylinder = 14 in.
Dimensions of new cylinder are quadrupled means 4times.
New radius = 44 in.
New height = 56 in.
Substitute the value in the formula we get,
Volume of the new cylinder = (3.14) ×(44)² × (56)
= 340,426.24 in.³
Hence, volume of the new similar cylinder is equals to 340,426.24 in.³.
Learn more about volume here
https://brainly.com/question/1578538
#SPJ2
If you rolled two dice, what is the probability
that you would roll a sum of 4?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
3
second
first
1 2
4 5 6
11,1 1,2 1,3 1,4 1,5 1,6
22,1 2,2 2,3 2,4 2,5 2,6
33,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
55,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Enter
Answer:
1/12
Step-by-step explanation:
3/36=1/12
Let f (x) = 10/x-4
What is the average rate of change of f (x) from 2 to 8 ?
Enter your response as a decimal.
Answer:
1.875
Step-by-step explanation:
The rate of change is the derivative of the function.
[tex]f(x) = \frac{10}{x-4}\\\\f'(x)=10\times \frac {d}{dx}\frac{1}{x-4}\\\\f'(x)=\frac{-10}{(x-4)^{2}}\\\\f'(2) = \frac{-10}{(2-4)^{2}} =-2.5\\\\f'(8)= \frac{-10}{(8-4)^{2}} =-0.625\\[/tex]
So, the rate of change is
f'(8) - f'(2) = - 0.625 + 2.5 = 1.875
please answer this, I need help
Answer:
-$7
Step-by-step explanation:
20 - 15 = 5
5 + 5 = 10
10 - 10 = 0
0 - 7 = -7
If 25 counters are a whole set how many are there in four fifths of the set
Answer:
20
Step-by-step explanation:
25*4/5=5*4=20
Answer:
20
Step-by-step explanation:
25 x 4/5=100/5=20
Victoria took a test and got 80% of the questions right. She answered 20 questions correctly. How many questions were on the test?
Answer:
25 questions :D
Step-by-step explanation:
According to a study, 50 % of adult smokers started smoking before 21 years old. 5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded. a) The probability that at least 2 of them started smoking before 21 years of age is b) The probability that at most 4 of them started smoking before 21 years of age is c) The probability that exactly 3 of them started smoking before 21 years of age is
Answer:
a) The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.
b) The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.
c) The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.
Step-by-step explanation:
For each smoker, there are only two possible outcomes. Either they started smoking before 21 years old, or they did not. Smokers are independent, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
50% of adult smokers started smoking before 21 years old.
This means that [tex]p = 0.5[/tex]
5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.
This means that [tex]n = 5[/tex].
a) The probability that at least 2 of them started smoking before 21 years of age is
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]
[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.03125 + 0.15625 = 0.1875[/tex]
The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.
b) The probability that at most 4 of them started smoking before 21 years of age is
This is:
[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.03125 = 0.96875[/tex]
The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.
c) The probability that exactly 3 of them started smoking before 21 years of age is
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]
The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.
The cost of off-campus living for U of O students is normally distributed. The Office of the Registrar estimates that on average it costs students $1,225 per month to live off-campus. A student group suspects that the average cost of living is lower than what is listed by the registrars office. They decide to conduct a hypothesis test. The student group randomly surveys 21 students and finds that they pay an average of $1,150 per month with a standard deviation of $400. What is the alternative hypothesis
Answer:
H1 : μ < 1225
Step-by-step explanation:
The alternative hypothesis in carrying out a statistical test could be explained as a notion which aims to displace or rival an initial position, the null hypothesis.
When declaring an hypothesis, the statement compares the initial or population mean in the hypothesis statement and not the result or outcome of the sample statistic.
In the scenario above :
The null is of the notion that :
H0 : μ = 1225 ;
Hence, the stance of the alternative which is that the mean is lower or less will be written as :
H1 : μ < 1225
The hypothesis test is carried out by the students where the alternate hypothesis is [tex]\rm H_1 : \mu < 1225[/tex] and this can be determined by using the given data.
Given :
The cost of off-campus living for U of O students is normally distributed. The Office of the Registrar estimates that on average it costs students $1,225 per month to live off-campus.The student group randomly surveys 21 students and finds that they pay an average of $1,150 per month with a standard deviation of $400.Given that the office of the Registrar estimates that on average it costs students $1,225 per month to live off-campus that means the mean is 1225.
The hypothesis test is carried out by the students where the null hypothesis and alternate hypothesis is given by:
Null hypothesis is given by -- [tex]\rm H_0 : \mu = 1225[/tex]
Alternate Hypothesis is given by -- [tex]\rm H_1 : \mu < 1225[/tex]
The hypothesis test is carried out by the students where the alternate hypothesis is [tex]\rm H_1 : \mu < 1225[/tex].
For more information, refer to the link given below:
https://brainly.com/question/23017717
Katherine is 17 years younger than Joe. If Joe is 44 years old, how old is Katherine?
_____years old
Answer:
Katherine is 27 years old.
Step-by-step explanation:
44-17=27.
Answer:
27
Step-by-step explanation:
44 age of Joe
-17 years younger
______________
27 years of age
In a random sample of 60 shoppers 12 said that they only buy products that are on sale. If there are 3000 shoppers at the mall today about how many would you predict only buy items on sale?
Answer:
Number of shopper buy from sale [3,000shopper] = 600 (Approx.)
Step-by-step explanation:
Given:
Number of shopper in mall = 60
Number of shopper buy from sale = 12
Find:
Number of shopper buy from sale if total number number of shopper are 3,000
Computation:
Number of shopper buy from sale [3,000shopper] = 3000[Number of shopper buy from sale/Number of shopper in mall]
Number of shopper buy from sale [3,000shopper] = 3000[12 / 60]
Number of shopper buy from sale [3,000shopper] = 3000[1/5]
Number of shopper buy from sale [3,000shopper] = 600 (Approx.)
HELP MEEEEEEEEEE
solve and show your work
3x^2-14x-5
Answer:
Step-by-step explanation:
x − 5 = 0 ⇒ x1 = 5
3x + 1 = 0 ⇒ x2 = −1
3
≈ −0.333333
Factorization:
(x − 5)(3x + 1) = 0
Standard form:
3x2 − 14x − 5 = 0
Extrema:
Min = (2.333333, −21.333333)
Answer:
( 3 x + 1 ) ( x − 5 )
please help asap!!!!
Answer:
12inches
Step-by-step explanation:
You are given a number. Do you know the number that is 1/5 as big?
Need answer ASAP ❤️❤️❤️
Answer:
Step-by-step explanation:
yes, (given number) / 5
Maria has a bag with 6 red marbles, 6 blue marbles, and 4 green marbles. Without looking, Maria picks one marble. She does not replace it, she picks another one. On the first pick, Maria gets a green marble.
What is the probability that she gets a red marble on her second pick?
Answer: 2/5
Step-by-step explanation:
Answer: 6/15
1. Drawing a red marble from a bag that contains 3 red marbles and 5 purple marbles. ... 4. A bag contains 6 red chips, 9 white chips, and 5 blue chips. A chip is selected and then replaced. ... from the box without replacement of the first draw. ... d. green first, purple second. E. -DO. 6. Find the probability of each event for more than one
Please help me out with this .
Answer:
36.07
Step-by-step explanation:
Method 1:
[tex]A_1 = b * h = 3.1 * 3.4 = 10.54[/tex]
[tex]A_2 = b * h = 3.8 * 3.7 = 14.06[/tex]
[tex]A_3 = b * h = 3.1 * 3.7 = 11.47[/tex]
[tex]A = A_1 + A_2 + A_3 = 10.54 + 14.06 + 11.47 = 36.07[/tex]
Method 2:
[tex]A_1 = b * h = (3.1 + 3.8)(3.4 + 3.7) = 6.9 * 7.1 = 48.99[/tex]
[tex]A_2 = b * h = 3.4 * 3.8 = 12.92[/tex]
[tex]A = A_1 - A_2 = 48.99 - 12.92 = 36.07[/tex]
Both solutions point to the same answer, so we can confirm it's correct
An owner wants to discount his pizza from $15 to $14.25, how much percent does he need to discount?
Answer:
5%
Step-by-step explanation:
Amount of money that is discounted
= $15 - $14.25
$0.75
Percentage that needed to be discount
=(0.75/15) * 100%
= 5%
Thus, owner needs to discount 5% to discount his pizza from $15 to $14.25.
320% of 69 is what number?
Answer:
220.8
Step-by-step explanation:
I believe 220.8
sorry if I am wrong.
Answer:
320×69÷100
answer * number is 220
Consider the following 8 numbers, where one labelled
x
is unknown.
18, 36, 16, x, 39, 27, 8, 34
Given that the range of the numbers is 56,
work out 2 values of
x
.
====================================================
Explanation
Consider three scenarios:
A) The value of x is the smallest of the set (aka the min)B) The value of x is the largest of the set (aka the max)C) The value of x is neither the min, nor the max. So 8 < x < 39.These scenarios cover all the possible cases of what x could be. It's either the min, the max, or somewhere in between the min and max.
--------------------
We'll start with scenario A.
If x is the min, then that must mean 39 is the max as it's the largest of the set {18, 36, 16, 39, 27, 8, 34}
The range is 56, so,
range = max - min
56 = 39 - x
56+x= 39
x = 39-56
x = -17 which is one possible answer
--------------------
If instead we go with scenario B, then x is the max and 8 is the min
range = max - min
56 = x - 8
56+8 = x
64 = x
x = 64 is the other possible answer
--------------------
Lastly, let's consider scenario C. If x is not the min or the max, then it's somewhere between the min 8 and max 39. in short, 8 < x < 39.
Note that range = max - min = 39-8 = 31 which is not the range of 56 that we want. So there's no way scenario C can be possible here.
HELP PLISS
Which Trig ratio should be used to find the missing side?
A.Sin
B.Cos
C.Tan
Answer:
It's Cos.
Hope this helps
if y+1/y=5 then show that (y^3+1/y^3)=110