Answer:
[tex]cos \beta = -\sqrt\dfrac{2}{3}[/tex]
Step-by-step explanation:
It is given that [tex]\angle \beta[/tex] lies in the third quadrant.
In 3rd quadrant, sine and cosine both are negative.
Also given that:
[tex]sin \beta =-\dfrac{\sqrt3}{3}[/tex]
We know that identity between sine and cosine as:
[tex]sin^2\theta + cos^2\theta = 1[/tex]
Here, [tex]\angle \theta\ is\ \angle \beta[/tex]
Therefore, the identity can be written as:
[tex]sin^2\beta + cos^2\beta= 1[/tex]
Putting the value of [tex]sin\beta[/tex]:
[tex](-\dfrac{\sqrt3}{3})^2+ cos^2\beta= 1\\\Rightarrow cos^2\beta = 1 -\dfrac{3}{9}\\\Rightarrow cos^2\beta = \dfrac{9-3}{9}\\\Rightarrow cos^2\beta = \dfrac{6}{9}\\\Rightarrow cos\beta = \pm \sqrt{\dfrac{6}{9}}\\\Rightarrow cos\beta = \pm \sqrt{\dfrac{2}{3}}[/tex]
But, it is given that [tex]\beta[/tex] is in 3rd quadrant. That means, value of cos[tex]\beta[/tex] will be negative.
Therefore, the correct answer is:
[tex]cos \beta = -\sqrt\dfrac{2}{3}[/tex]
All the angles in the diagram are measured to the nearest degree. Work out the upper bound and lower bound of angle x 59 degree 108 degree 81 degree X degree ??????
Answer: lower bound, x = 110.5°
upper bound, x = 113.5°
Step-by-step explanation:
There is no diagram but I am going to assume it is a quadrilateral since it has 4 angles. The sum of the angles of a quadrilateral is 360°.
Upper Lower
59° 58.5° ≤ a < 59.5
108° 107.5° ≤ b < 108.5°
81° 80.5° ≤ c < 81.5°
Total: 246.6° ≤ x < 249.5°
Subtract the lower and upper bound totals from 360° :
360.0 360.0
- 246.5 - 249.5
x = 1 1 3.5 1 1 0.5
↓ ↓
upper lower
bound bound
Micah is running a 6-mile race. There are water stops
every mile, including at the 6-mile finish line.
How many water stops are there?
Finish
Solve the problem and explain how the model can be used to find the answer.
Which fraction is equivalent to 2/-6? -2/6 2/6 -2/-6 6/2
A piece of wire of length 7070 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square?
Answer:
a.x=39.2
b.Use whole wire as a circle
Step-by-step explanation:
We are given that
Length of piece of wire=70 units
Let length of wire used to make a square =x units
Length of wire used in circle=70- x
Side of square=[tex]\frac{perimeter\;of\;square}{4}=\frac{x}{4}[/tex]
Circumference of circle=[tex]2\pi r[/tex]
[tex]70-x=2\pi r[/tex]
[tex]r=\frac{70-x}{2\pi}[/tex]
Combined area of circle and square,A=[tex](\frac{x}{4})^2+\pi(\frac{70-x}{2\pi})^2[/tex]
Using the formula
Area of circle=[tex]\pi r^2[/tex]
Area of square=[tex](side)^2[/tex]
a.[tex]A=\frac{x^2}{16}+\frac{4900+x^2-140x}{4\pi}[/tex]
Differentiate w.r.t x
[tex]\frac{dA}{dx}=\frac{x}{8}+\frac{2x-140}{4\pi}[/tex]
[tex]\frac{dA}{dx}=0[/tex]
[tex]\frac{x}{8}+\frac{2x-140}{4\pi}=0[/tex]
[tex]\frac{\pi x+4x-280}{4\pi}=0[/tex]
[tex]\pi x+4x-280=0[/tex]
[tex]x(\pi+4)=280[/tex]
[tex]x=\frac{280}{\pi+4}[/tex]
x=39.2
Again differentiate w.r.t x
[tex]\frac{d^2A}{dx^2}=\frac{1}{8}+\frac{1}{2\pi}[/tex]>0
Hence, the combined area of circle and the square is minimum at x=39.2
b.When the wire is not cut and whole wire used as a circle . Then, combined area is maximum.
Rearrange the following steps in the correct order to locate the last occurrence of the smallest element in a finite list of integers, where the integers in the list are not necessarily distinct.
a. return location
b. min ≔a1 and location ≔1
c. min ≔ai and location≔i
d. procedure last smallest(a1,a2,...,an: integers)
e. If min >= ai then
Answer:
The rearranged steps is as follows:
d. procedure last smallest(a1,a2,...,an: integers)
b. min ≔a1 and location ≔1
e. If min >= ai then
c. min ≔ai and location≔i
a. return location
Step-by-step explanation:
The proper steps to perform the task in the question above is dbeca
Here, the procedure (or function) was defined along with necessary parameters
d. procedure last smallest(a1,a2,...,an: integers)
The smallest number is initialized to the first number on the list and its location is initialized to 1
b. min ≔a1 and location ≔1
The next line is an if conditional statement that checks if the current smallest number is greater than a particular number
e. If min >= ai then
If the above condition is true, the smallest value is assigned to variable min; it's location is also assigned to variable location
c. min ≔ai and location≔i
The last step returns the location of the smallest number
a. return location
A bag contains 6 red balls and 9 black balls. Two balls are drawn, one after the other with replacement. Find the probability that
a. Both are of the same colours
b. Both are of different colours
Answer:
a) 13/25
b) 12/15
Step-by-step explanation:
a) Since it is with replacement, the chance of them being both the same colour will be
P(both red) + P(both black) = (6/15*6/15) + (9/15*9/15)
= 13/25
b) If they are both different colours, then we will be working out
P(both colours) = (6/15*9/15)*2 = 12/25 (Its *2 because the other way of pulling both colours is 9/15*6/15 which is the same but flipped)
Another way of working this question out is
P(1-All red or all blue) which from above we know that All red or all blue is 13/25 so
P(1-All red or all blue) = 1 - 13/25 = 12/25
To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times How large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001?
Answer:
[tex]n=(\frac{1.960(1)}{0.0001})^2 =384160000[/tex]
So the answer for this case would be n=384160000 rounded up to the nearest integer
Step-by-step explanation:
We know the following info:
[tex] ME = 0.0001[/tex] represent the margin of error desired
[tex] \sigma= 1[/tex] we assume that the population deviation is this value
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.0001 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. If we use the normal standard distribution or excel we got: [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(1)}{0.0001})^2 =384160000[/tex]
So the answer for this case would be n=384160000 rounded up to the nearest integer
All math teachers are smart. Ms. Smith is your math teacher, so she is smart. What type of reasoning is this? inductive or deductive
Answer:
I believe it is Inductive Reasoning.
Step-by-step explanation:
Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.
Deductive Reasoning is a basic form of valid reasoning.
which equation is point slope form represents a line with m equals -1/2 that goes through the origin
Answer:
see below
Step-by-step explanation:
The origin is (0,0) m = -1/2
Point slope form is
y-y1 = m(x-x1) where m is the slope
y -0 = -1/2 ( x -0)
y = -1/2x
A poll showed that 69.39% of Americans say they believe that Marilyn Monroe had an affair with JFK. What is the probability of randomly selecting someone who does not believe that Marilyn Monroe had an affair with JFK. Report the answer as a decimal rounded to four places.
Answer:
The probability of randomly selecting someone who does not believe that Marilyn Monroe had an affair with JFK is P=0.3061.
Step-by-step explanation:
The probability of randomly selecting someone who does not believe that Marilyn Monroe had an affair with JFK is calculated as the complement of the probability of randomly selecting someone who does believe that Marilyn Monroe had an affair with JFK. This last value is the one estimated from the poll: 0.6939.
Then, the probability of randomly selecting someone who does not believe that Marilyn Monroe had an affair with JFK is:
[tex]P=1-0.6939=0.3061[/tex]
Find the common ratio for this geometric sequence. 243, 27, 3, 1/3, 1/27.
Answer:
1/9
Step-by-step explanation:
Since each next term is 1/9 of the last, the common ratio is 1/9. This can be confirmed by the fact that 243*1/9=27, 27*1/9=3, 3*1/9=1/3, and so on. Hope this helps!
Please answer this correctly
Answer:
yes
Step-by-step explanation:
not every person is going to have the same opinion, so it is yes.
// have a great day //
Answer:
Yes, because if Pedro asked them the question "what do you think of public transportation?" the majority would probably say that they like it or something along those lines. This is biased because there may be other city inhabitants who don't think very highly of public transportation. Basically, what I'm trying to say is that not everyone will have the same opinion.
assume that when adults with smartphones are randomly selected, 45% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 3 of them use their smartphones in meetins or classes.
Answer:
0.3032
Step-by-step explanation:
Use binomial probability.
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
P = ₆C₃ (0.45)³ (0.55)³
P = 0.3032
can 10/12 be simplified
Answer:
5/6
Step-by-step explanation:
10/12
Divide the top and bottom by 2
10/2 = 5
12/2 =6
the fraction becomes 5/6
Answer :
10/12
Reduce the fraction
= 5/6
There are 5 gallons of distilled water in science supplies. If 8 students each use an equal amount of distilled water and there is 1 gallon left in supplies, how much will each student get?
Answer:
0.5 gallon
Step-by-step explanation:
let x refer to students
5 = 8x + 1
8x = 4
x= 0.5 gallon
Find the value of x and the value of y.
A r= 15, y = 10/3
B. r=20, p=10/3
C. x=20/3, y = 513
D. r=15, y =53
Answer:
Step by step solution:
Rebecca is a real estate agent who would like to find evidence supporting the claim that the population mean market value of houses in the neighborhood where she works is greater than $250,000. To test the claim, she randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922. The test statistic t for a hypothesis test of H0 : μ = 250.000 versus Ha : μ > 250.000 is t 2.34 , which has 34 degrees of freedom. If 0.01
A) Fail to reject the null hypothesis that the true population mean market value of houses in the neighborhood where Rebecca works is equal to $250,000.
B) Reject the null hypothesis that the true population mean market value of houses in the neighborhood where Rebecca works is equal to $250,000.
C) There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.
D) There is not enough evidence at the α-_ 0.05 level of significance to suggest that the true population mean market value of houses in the neighborhood where Rebecca works is not equal to $250,000.
Answer:
There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.
Step-by-step explanation:
We are given that Rebecca randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922.
Let [tex]\mu[/tex] = population mean market value of houses in the neighborhood.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $250,000 {means that the population mean market value of houses in the neighborhood where she works is equal to $250,000}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $250,000 {means that the population mean market value of houses in the neighborhood where she works is greater than $250,000}
The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean market value = $259,860
s = sample standard deviation = $24,922
n = sample of houses = 35
So, the test statistics = [tex]\frac{259,860-250,000}{\frac{24,922}{\sqrt{35} } }[/tex] ~ [tex]t_3_4[/tex]
= 2.34
The value of t-test statistic is 2.34.
Also, P-value of the test statistics is given by;
P-value = P([tex]t_3_4[/tex] > 2.34) = 0.0137
Since our P-value is less than the level of significance as 0.0137 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the population mean market value of houses in the neighborhood where she works is greater than $250,000.
You are standing 5 miles away from the peak. You look up at a 47-degree angle to the peak. How tall is the mountain? Hint: 5280 feet = 1 mile. Round your answer to the nearest foot.
Answer:
19272 feet
Step-by-step explanation:
We are given that the distance between the person and peak is 5 miles.
and angle is [tex]47^\circ[/tex] when we look up at the mountain peak.
The given situation is best represented as a right angled triangle as shown in the attached figure.
[tex]\triangle[/tex]IKJ where [tex]\angle K = 90^\circ[/tex]
IK is the mountain.
J is the point where we are standing.
Distance JI = 5 miles
[tex]\angle J = 47^\circ[/tex]
To find: Distance IK = ?
We can use trigonometric identities to find IK.
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]sinJ = \dfrac{IK}{JI}\\\Rightarrow sin47 = \dfrac{IK}{5}\\\Rightarrow IK = sin47^\circ \times 5\\\Rightarrow IK = 0.73 \times 5\\\Rightarrow IK = 3.65\ miles \\\Rightarrow IK = 3.65 \times 5280\ ft\\\Rightarrow IK = 19272\ ft[/tex]
Hence, height of mountain = 19272 ft
Brand name producers of aspirin claim that one advantage of their aspirin over generic aspirin is that brand name aspirin is much more consistent in the amount of active ingredient used. This in turn means that users can expect the same results each time they use the brand name aspirin, while the effects of the generic aspirin can be a lot more variable. A random sample of 200 brand name aspirin tablets had a mean and standard deviation of active ingredient of 325.01 and 10.12 mg. A second independent sample of 180 generic aspirin tablets was measured for the amount of active ingredient, and the mean standard deviation were 323.47 and 11.43 mg. Given that the amount of active ingredient is normally distributed for both the brand name and the generic aspirin, do these data support the brand name producers claim? Let alpha = 0.025.
Answer:
Step-by-step explanation:
The claim here is that the brand name aspirin is more consistent in the amount of active ingredient used than the generic aspirin.
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean amount of active ingredients in brand name aspirin and μ2 be the mean amount of active ingredients in generic name aspirin
The random variable is μ1 - μ2 = difference in the mean amount of active ingredients between the brand name and generic aspirin
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 ≥ μ2 H0 : μ1 - μ2 ≥ 0
The alternative hypothesis is
H1 : μ1 < μ2 H1 : μ1 - μ2 < 0
This is a left tailed test
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
x1 = 325.01
x2 = 323.47
s1 = 10.12
s2 = 11.43
n1 = 200
n2 = 180
t = (325.01 - 323.47)/√(10.12²/200 + 11.43²/180)
t = 1.24
1.237877
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [10.12²/200 + 11.43²/180]²/[(1/200 - 1)(10.12²/200)² + (1/180 - 1)(11.43²/180)²] = 1.53233946713/0.00537245359
df = 285
We would determine the probability value from the t test calculator. It becomes
p value = 0.108
Since alpha, 0.025 < than the p value, 0.108, then we would fail to reject the null hypothesis. Therefore, at 2.5% level of significance, these data support the brand name producers claim
12x - y = -4
4x - 3y = -6 (1 point)
Answer:
Step-by-step explanation:
12x - y = -4 ----------------------(I)
4x - 3y = -6 ---------------------(II)
Multiply equation (I) by (-3)
(I)*(-3) -36x + 3y = 12
(II) 4x - 3y = - 6 {Add and y will be eliminated}
- 32x = 6
x = 6/-32
x = -3/16
Plugin the value of x in equation (I)
[tex]12*\frac{-3}{16} -y=-4\\\\3*\frac{-3}{4}-y=-4\\\\\frac{-9}{4}-y = -4\\\\-y=-4+\frac{9}{4}\\\\-y=\frac{-4*4}{1*4}+\frac{9}{4}\\\\-y=\frac{-16}{4}+\frac{9}{4}\\\\-y=\frac{-7}{4}\\\\y=\frac{7}{4}\\\\y=1\frac{3}{4}[/tex]
this is a grade 4 maths question. i need help with doing a model from this question as well. thank you! —————————————————- a rope was cut into 2 pieces. The first piece was twice the length of the second piece. If the first piece was 5m 50cm long what was the length of the rope before it was cut
Answer:825cm
Step-by-step explanation:550cm/2=275cm
275*3=825cm
3.249 thousandths rounded to the nearest tenth
Answer:
3.2
Step-by-step explanation:
Rounded to the nearest 10
please help and please show your work
Answer:
The volume of all 9 spheres is 301.6 [tex]in^3[/tex]
Step-by-step explanation:
Notice that three of the identical spheres fit perfectly along the 12 in side box, therefore we know that the diameter of each is 12 in/3 = 4 in.
Then the radius of each sphere must be 2 inches (half of the diameter). Now that we know the radius of each sphere, we use the formula for the volume of a sphere to find it:
[tex]V=\frac{4}{3} \pi R^3\\V=\frac{4}{3} \pi (2\,in)^3\\V=\frac{4}{3} \pi\, 8\,\,in^3\\V=\frac{32}{3} \pi\,\,in^3[/tex]
Now, the total volume of all nine spheres is the product of 9 times the volume we just found:
[tex]V_{all \,9}=9\,*\frac{32}{3} \pi\,\,in^3\\V_{all \,9}=96 \pi\,\,in^3\\V_{all \,9}\approx \,301.6\,\,in^3[/tex]
Need help with what I did they all add up to 4 which is what the question asks for but it says that it not right
Answer: Try putting the positive number and then the negative number after the and like the example.
Step-by-step explanation:
Your answers are right, it could be a glitch.
how many nickels equal $18.45? (show your work)
Answer:
369
Step-by-step explanation:
One nickel = 0.05
0.05x=18.45
x=369
A random sample of 4000 U.S. citizens yielded 2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.
Answer:
[tex] n= 4000[/tex] represent the sample size of citizens selected
[tex] X= 2280[/tex] represent the people who are in favor of gun control legislation
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p= \frac{2280}{4000}= 0.57[/tex]
Step-by-step explanation:
For this problem we have the following info given:
[tex] n= 4000[/tex] represent the sample size of citizens selected
[tex] X= 2280[/tex] represent the people who are in favor of gun control legislation
And for this case we want to estimate the roportion of all Americans who are in favor of gun control legislation and for this case we can use the following formula:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p= \frac{2280}{4000}= 0.57[/tex]
Describe the steps to solve a rational equation. Create your own example and solve it following your steps. Then, provide an additional example for other people to try to solve as they reply to your post.
Answer:
Here is an exampls
Step-by-step explanation:
The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 3 years, how long will it take to triple
What is the answer to this question?
32
\y-step explanation:
Answer: 9.20 am
Step-by-step explanation:
Every hour the difference between the two watches increases by 3 minutes 3x3=9
That gives us 3 hours and then divide 60 into 3 to make 20 minutes
3hours + 20mins = 3 20mins
6:00 a.m. + 3hrs 20 mins = 9:20 a.m.
Kyle has 3 cards 6, 1, 2, what is all the numbers he can make using these cards, including one, two and three digit numbers
Answer: he can make 21 different numbers.
Step-by-step explanation:
If he uses only one card, the numbers are:
1, 2 and 6, so here we have 3 combinations.
If he uses two cards, for the first digit he has 3 options (because he has 3 cards) and for the second digit he has two options (because he already selected one of the cards) then he has:
3*2 = 6 different options
If uses the 3 cards, then he has 3 options for the first card, 2 options for the second card and one option for the third card, then the number of combinations is:
c = 3*2*1 = 6 combinations.
Adding all together we have C = 3 + 6 + 6 = 21 combinations.