Answer:
[tex]p_v = P(\chi^2_{4,0.05} >3.81)=0.43233[/tex]
Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed. So we can say that the 3 remedies ar approximately equally effective.
Step-by-step explanation:
A chi-square goodness of fit test "determines if a sample data matches a population".
A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".
Assume the following dataset:
NyQuil Robitussin Triaminic Total
No relief 11 13 9 33
Some relief 32 28 27 87
Total relief 7 9 14 30
Total 50 50 50 150
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference in the three remedies
H1: There is a difference in the three remedies
The level os significance assumed for this case is [tex]\alpha=0.05[/tex]
The statistic to check the hypothesis is given by:
[tex]\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The table given represent the observed values, we just need to calculate the expected values with the following formula [tex]E_i = \frac{total col * total row}{grand total}[/tex]
And the calculations are given by:
[tex]E_{1} =\frac{50*33}{150}=11[/tex]
[tex]E_{2} =\frac{50*33}{150}=11[/tex]
[tex]E_{3} =\frac{50*33}{150}=11[/tex]
[tex]E_{4} =\frac{50*87}{150}=29[/tex]
[tex]E_{5} =\frac{50*87}{150}=29[/tex]
[tex]E_{6} =\frac{50*87}{150}=29[/tex]
[tex]E_{7} =\frac{50*30}{150}=10[/tex]
[tex]E_{8} =\frac{50*30}{150}=10[/tex]
[tex]E_{9} =\frac{50*30}{150}=10[/tex]
And the expected values are given by:
NyQuil Robitussin Triaminic Total
No relief 11 11 11 33
Some relief 29 29 29 87
Total relief 10 10 10 30
Total 50 50 50 150
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(11-11)^2}{11}+\frac{(13-11)^2}{11}+\frac{(9-11)^2}{11}+\frac{(32-29)^2}{29}+\frac{(28-29)^2}{29}+\frac{(27-29)^2}{29}+\frac{(7-10)^2}{10}+\frac{(9-10)^2}{10}+\frac{(14-10)^2}{10} =3.81[/tex]
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(rows-1)(cols-1)=(3-1)(3-1)=4[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{4,0.05} >3.81)=0.43233[/tex]
And we can find the p value using the following excel code:
"=1-CHISQ.DIST(3.81,4,TRUE)"
Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed.
To test the hypothesis that three cough remedies are equally effective, conduct an Analysis of Variance (ANOVA) test and use the p-value, compared to the pre-set level of 0.05, to decide if the null hypothesis should be rejected or failed to reject.
Explanation:The subject matter pertains to hypothesis testing, a method used in statistics to test the validity of a claim (hypothesis) about a population. In this case, the null hypothesis in your question is that the three cough remedies are equally effective. The alternative hypothesis (Ha) is that at least one of the remedies is different. The P-value, when set at 0.05, helps to decide on the rejection or non-rejection of the null hypothesis, depending on whether it’s greater or smaller than the P-value.
First, we need to perform an Analysis of Variance (ANOVA) test since we have more than two samples to compare. After conducting the test, we compare the P-value with our pre-set alpha (0.05). If the p-value obtained is less than 0.05, we can reject the null hypothesis, letting us conclude that not all cough remedies are equally effective. If, however, the p-value is more than 0.05, we fail to reject the null hypothesis, and hence, we can't confidently say that one cough remedy is more effective than the others.
Remember that failing to reject the null hypothesis does not prove it true, it only suggests that there's not enough evidence against it given our data and chosen significance level.
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On august 1st, a plant was 79 centimeters tall. in june of that year it grew 12 centimeters, then 9 more centimeters in july. how many centimeters tall was it on june 1st?
a.67
b.70
c.100
d.5
Answer: d. 58
The height of the plant in June 1st is 58 centimeters.
Step-by-step explanation:
Given : On August 1st, a plant was 79 centimeters tall.
In June of that year it grew 12 centimeters, then 9 more centimeters in July.
Order of Month = June → July → August
Then , the height of the plant on June 1st would be
Height in August 1st - Height grew in June - height grew in July
= 79-12-9 centimeters
= 67-9 centimeters
= 58 centimeters
Therefore , the height of the plant in June 1st = 58 centimeters
Hence, the correct answer is d. 58
Simplify the expression.
1-cot x / tan x-1
A) cot x
B) tan x
C) -cot x
D) csc x
Answer:
The answer to your question is letter A) cot x
Step-by-step explanation:
[tex]\frac{1 - cot x}{tan x - 1}[/tex]
Remember that cot x = [tex]\frac{1}{tan x}[/tex]
Then
[tex]\frac{1 - \frac{1}{tan x} }{tanx -1}[/tex]
Simplify
[tex]\frac{\frac{tan x - 1}{tan x} }{tan x - 1}[/tex]
[tex]\frac{tan x - 1}{tan x (tan x - 1)}[/tex]
[tex]\frac{1}{tan x}[/tex]
Result
[tex]\frac{1}{tan x} = cot x[/tex]
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone? (1) Jack is painting twice as fast as Tom. (2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours.
What are the conditions a sample needs to meet before you can assume it's binomial and that it approximates a normal distribution?
Answer:
1) [tex]np\geq 5[/tex]
2) [tex]nq = n(1-p)\geq 5[/tex]
Other conditions that are important are:
3) n is large
4) p is close to 1/2 or 0.5
Step-by-step explanation:
1) Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
2) Solution to the problem
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n, p)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
In order to apply the normal apprximation we need to satisfy these two conditions:
1) [tex]np\geq 5[/tex]
2) [tex]nq = n(1-p)\geq 5[/tex]
Other conditions that are important are:
3) n is large
4) p is close to 1/2 or 0.5
Each signal that a certain ship can make is comprised of 3 different flags hanging vertically in a particular order. How many unique signals can be made by using 4 different flags?A. 10B. 12C. 20D. 24E. 36
Answer:
24
Step-by-step explanation:
This problem solution involves permutation to calculate number of arrangements of flags. The reason of using permutation in this scenario is that it is mention in the statement that flags are hanging in a particular order and when order is concern we use permutation. According to permutation definition nPr=n!/(n-r)! and so, the unique signals that are made by using 4 flags are 4P3=4!/(4-3)!=24. Here n=total number=4 and r=number chosen=3.
Final Answer:
The correct answer is D. 24.
Explanation:
To solve this problem, we will calculate the number of permutations of 4 distinct flags taken 3 at a time because the order of the flags matters and no flag can be used more than once in a single signal.
The formula for permutations of n items taken k at a time is given by:
P(n, k) = n! / (n - k)!
Where n! represents the factorial of n, which is the product of all positive integers up to n.
In our case, we have n = 4 flags, and we want to take k = 3 flags to form a signal.
First, we evaluate 4 factorial (4!):
4! = 4 × 3 × 2 × 1 = 24
Now, we need to evaluate the factorial of (4 - 3), which is (1!):
1! = 1
Using the permutation formula, we find the number of unique signals:
P(4, 3) = 4! / (4 - 3)!
P(4, 3) = 24 / 1! (since (4 - 3)! is 1!)
P(4, 3) = 24 / 1
P(4, 3) = 24
Therefore, there are 24 unique signals that can be made using 4 different flags.
The correct answer is D. 24.
Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) = 100
Answer: The required solution is [tex]y=50e^{0.1386t}.[/tex]
Step-by-step explanation:
We are given to solve the following differential equation :
[tex]\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.
From equation (i), we have
[tex]\dfrac{dy}{y}=kdt.[/tex]
Integrating both sides, we get
[tex]\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}][/tex]
Also, the conditions are
[tex]y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50[/tex]
and
[tex]y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.[/tex]
Thus, the required solution is [tex]y=50e^{0.1386t}.[/tex]
Answer:
[tex]\frac{1}{5}\ln(2)=k[/tex]
Solution without isolating [tex]y[/tex]:
[tex]\ln|y|=\frac{1}{5}\ln(2)x+\ln(50)[/tex]
Solution with isolating [tex]y[/tex]:
[tex]y=50 \cdot 2^{\frac{1}{5}x}[/tex]
Step-by-step explanation:
[tex]\frac{dy}{dx}=ky[/tex]
We will separate the variables so we can integrate both sides.
Multiply [tex]dx[/tex] on both sides:
[tex]dy=ky dx[/tex]
Divide both sides by [tex]y[/tex]:
[tex]\frac{dy}{y}=k dx[/tex]
Now we may integrate both sides:
[tex]\ln|y|=kx+C[/tex]
The first condition says [tex]y(0)=50[/tex].
Using this into our equation gives us:
[tex]\ln|50|=k(0)+C[/tex]
[tex]\ln|50|=C[/tex]
So now our equation is:
[tex]\ln|y|=kx+\ln(50)[/tex]
The second condition says [tex]y(5)=100[/tex].
Using this into our equation gives us:
[tex]\ln|100|=k(5)+\ln(50)[/tex]
[tex]\ln(100)=k(5)+\ln(50)[/tex]
Let's find [tex]k[/tex].
Subtract [tex]\ln(50)[/tex] on both sides:
[tex]\ln(100)-\ln(50)=k(5)[/tex]
I'm going to rewrite the left hand side using quotient rule for logarithms:
[tex]\ln(\frac{100}{50})=k(5)[/tex]
Reducing fraction:
[tex]\ln(2)=k(5)[/tex]
Divide both sides by 5:
[tex]\frac{\ln(2)}{5}=k[/tex]
[tex]\frac{1}{5}\ln(2)=k[/tex]
So the solution to the differential equation satisfying the give conditions is:
[tex]\ln|y|=\frac{1}{5}\ln(2)x+\ln(50)[/tex]
Most likely they will prefer the equation where [tex]y[/tex] is isolated.
Let's write our equation in equivalent logarithm form:
[tex]y=e^{\frac{1}{5}\ln(2)x+\ln(50)}[/tex]
We could rewrite this a bit more.
By power rule for logarithms:
[tex]y=e^{\ln(2^{\frac{1}{5}x})+\ln(50)}[/tex]
By product rule for logarithms:
[tex]y=e^{\ln(2^{\frac{1}{5}x} \cdot 50)}[/tex]
Since the natual logarithm and given exponential function are inverses:
[tex]y=2^{\frac{1}{5}x} \cdot 50[/tex]
By commutative property of multiplication:
[tex]y=50 \cdot 2^{\frac{1}{5}x}[/tex]
How many positive integer values of x are possible to solve the equation 5x²+3y+2.
Answer:
Step-by-step explanation:
I would divide the answer in two parts
part A
If the given equation is correct, then the equation has no answer
Process
let y = 0 then 5x^2 + 2 = 0. We subtract 2 from both sides 5x^2= -2.
Now we divide each side by 5 and apply square root property
x^2=-2/5 --> x=square root(-2/5). Therefore, the equation has no solution. Complex solution.
Part B
If the given equation is not correct (the exercise is badly copied), then the correct exercise would be 5x^2+3x-2=0
We can solve the polynomial using quadratic formula, and we will obtain
x=-1 and x=2/5.
So the answer X cannot be integer.
Mohammad borrowed $809 for 9 months with monthly payments of $96.00. What is the amount of total payments?a. $864b. $896c. $809d. $960
Answer:$864
Step-by-step explanation:
Since Mohammad makes a payment of $96 monthly, the amount paid by Mohammad for 9months will be 9×$96 that's $96 in 9places
9 × $96 = $864
Exhibit 5-3 The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of Goals Probability 0 .05 1 .15 2 .35 3 .30 4 .15 Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score less than 3 goals?
Answer:
0.55 is the probability that Lions will score less than 3 goals.
Step-by-step explanation:
We are given the following in the question:
Number of goals(x): 0 1 2 3 4
Probability: 0.05 0.15 0.35 0.30 0.25
We have to find the probability that Lions will score less than 3 goals.
[tex]P(X<x) = \displaystyle\sum_{X=0}^{X=x-1}P(x_i)\\\\P(x<3)=P(x=0)+P(x=1)+P(x=2)\\P(x<3)=0.05 + 0.15 + 0.35=0.55[/tex]
0.55 is the probability that Lions will score less than 3 goals.
Final answer:
The probability that the Lions soccer team will score less than 3 goals in a game is 0.55 or 55%.
Explanation:
To find the probability that the Lions soccer team scores less than 3 goals in a game, we need to add up the probabilities of scoring 0, 1, and 2 goals. From Exhibit 5-3, the probability of scoring 0 goals is 0.05, 1 goal is 0.15, and 2 goals is 0.35.
The total probability of scoring less than 3 goals is the sum of these probabilities:
P(0 goals) = 0.05
P(1 goal) = 0.15
P(2 goals) = 0.35
Thus, P(score < 3 goals) = P(0 goals) + P(1 goal) + P(2 goals) = 0.05 + 0.15 + 0.35 = 0.55.
Therefore, the probability that the Lions will score less than 3 goals in a given game is 0.55 or 55%.
Sajia has 30 books in her library she sold 9 books at a thrift store on Saturday write and solve an inquality to determine how many more books she can sell if she comes back on Sunday
Answer:
see the explanation
Step-by-step explanation:
Let
x ---->the number of books she can sell if she comes back on Sunday
y ----> the number of books sold on Saturday
we know that
The number of books sold on Saturday plus the number of books she can sell if she comes back on Sunday must be less than or equal to the initial number of books in the library (30 books)
so
The inequality that represent this situation is
[tex]x+y\leq 30[/tex]
we have
[tex]y=9\ books[/tex]
substitute
[tex]x+9\leq 30[/tex]
solve for x
subtract 9 both sides
[tex]x\leq 30-9[/tex]
[tex]x\leq 21\ books[/tex]
therefore
The maximum number of books she can sell on Sunday is 21
If you assume that there are exactly 365 days in a year, how many seconds are there in one year? Give your answer to the nearest 1000 seconds.
Answer:
31,536,000
Step-by-step explanation:
There are 3600 seconds in an hour and 24 hours in a day, so ...
(3600 s/h)(24 h/da) = 86400 s/da
Then in 365 days, there are ...
(365 da)(86400 s/da) = 31,536,000 s
_____
No rounding is needed.
There are 31,536,000 seconds in a year. This is calculated by multiplying 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year.
Explanation:To calculate the number of seconds in a year, start with the known values of time:
There are 60 seconds in 1 minute,60 minutes in 1 hour,24 hours in one day,and 365 days in one year (for this question, we're ignoring leap years).
We multiply all these values together to get the number of seconds in a year.
60 seconds/minute * 60 minutes/hour * 24 hours/day * 365 days/year = 31,536,000 seconds/year
To give the answer to the nearest 1000 seconds, we would round it to 31,536,000.
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From the point on the ground 500 ft from the base of a building, it is observed that the angle of elevation to the top of the building is 24 degrees and the angle of tlevation to top top of a flagpole atop the building is 27 degress. Find the height of the building and the length of the flagpole.
Answer:
building: 222.61 ftflagpole: 32.15 ftStep-by-step explanation:
The tangent function of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the adjacent side is 500 ft, so we have ...
tan(24°) = (building height)/(500 ft)
building height = (500 ft)tan(24°) ≈ 222.61 ft
__
Similarly, the height to the top of the flagpole is ...
total height = (500 ft)tan(27°) ≈ 254.76 ft
The length of the flagpole is the difference of these heights:
flagpole length = 254.76 ft -222.61 ft = 32.15 ft
The height of the building is 222.61 ft; the length of the flagpole is 32.15 ft.
The height of the building is approximately 250.4 feet, and the length of the flagpole is approximately 24.4 feet, according to the principle of trigonometry using tangent function.
Explanation:The question deals with a mathematical concept called trigonometry. Specifically, we will use the tangent function. Tangent of an angle in a right triangle is the ratio of the side opposite to the angle over the side adjacent to the angle.
Let's denote H as the height of the building and F as the length of the flagpole. We know that Tan(24°) = H / 500 and Tan(27°) = (H+F) / 500. Now we can solve these two equations to find H and F.
First, calculate H. Using the first equation, H = Tan(24°) * 500 ≈ 250.37 feet.
Next, calculate H+F. Using the second equation, H+F = Tan(27°) * 500 ≈ 274.73 feet.
Then, calculate F by subtracting H from the second result. So F = 274.73 - 250.37 = 24.36 feet.
Therefore, the height of the building is approximately 250.4 feet, and the length of the flagpole is approximately 24.4 feet.
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You are riding your bicycle. It takes you 9 minutes to go 2.5 miles. If you continue traveling at the same rate, how long will it take you to go 9 miles.
Rewrite with only sin x and cos x.
cos 3x
A. cos x - 4 cos x sin2x
B. -sin3x + 2 sin x cos x
C. -sin2x + 2 sin x cos x
D. 2 sin2x cos x - 2 sin x cos x
Option A
[tex]\cos 3 x=\cos x-4 \cos x \sin ^{2} x[/tex]
Solution:
Given that we have to rewrite with only sin x and cos x
Given is cos 3x
[tex]cos 3x = cos(x + 2x)[/tex]
We know that,
[tex]\cos (a+b)=\cos a \cos b-\sin a \sin b[/tex]
Therefore,
[tex]\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x[/tex] ---- eqn 1
We know that,
[tex]\sin 2 x=2 \sin x \cos x[/tex]
[tex]\cos 2 x=\cos ^{2} x-\sin ^{2} x[/tex]
Substituting these values in eqn 1
[tex]\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)[/tex] -------- eqn 2
We know that,
[tex]\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x[/tex]
Applying this in above eqn 2, we get
[tex]\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)[/tex]
[tex]\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}[/tex]
[tex]\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x[/tex]
Therefore,
[tex]\cos 3 x=\cos x-4 \cos x \sin ^{2} x[/tex]
Option A is correct
Alex has a truck. 42% of the miles he drove last month were for work. If Alex drove 588 miles for work, how many miles did he drive last month all together?
Answer:
Alex has driven Total of 1400 miles.
Step-by-step explanation:
Given:
Miles Driven by Alex = 588 miles
Percentage mile driven by Alex = 42%
Solution:
Let the total miles driven by Alex be 'x'.
And given that 42% of the total miles he drive for work, which is 588 miles.
That means x multiplied with 42% is equal to 588.
So framing the above sentence in equation form, we get;
[tex]x\times 42\% =588[/tex]
Now we have to remove the percentile.
For this we have to divide 42 by 100, then we get;
[tex]x\times\frac{42}{100} = 588[/tex]
Multiplying by 100 on both side, using Multiplication Property we get;
[tex]x\times\frac{42}{100}\times 100 = 588\times 100\\\\42x=58800[/tex]
Dividing both side by 42 using Division Property we get;
[tex]\frac{42x}{42}=\frac{58800}{42}\\\\x= 1400 \ miles[/tex]
Hence Alex has driven Total of 1400 miles.
Answer: 1,400
Step-by-step explanation:%
100
=
part
whole
42
100
=
588
x
42x = 58,800
x = 1,400
Sam watched television the past five nights for 42 minutes, 23 minutes, 56 minutes, 19 minutes, and 67 minutes. What was the median amount of time Sam watched TV the past five nights?
Answer:
42 minutes is the median amount of time
Step-by-step explanation:
The Median is the middle value of data set.
If there is "odd" number of numbers, and there are n numbers, the median is:
(n/2) + 1 th number
If there is "even" number of numbers, and there are n numbers, the median is:
Average of n/2th and (n/2) + 1 th number
Here, we have 5 numbers, so the median would be:
(5/2) + 1 th number
That is
3rd number
But, we need to arrange the numbers from least to greatest. Lets write it:
19, 23, 42, 56, 67
The third number is 42, this is the median
Type the correct answer in the box. Use a comma to separate the x- and y-coordinates of each point. The coordinates of the point on the unit circle that corresponds to an angle of 0º are ( ). The coordinates of the point on the unit circle that corresponds to an angle of 90º are ( ).
Answer:
On a unit circle, the point that corresponds to an angle of [tex]0^{\circ}[/tex] is at position [tex](1, \, 0)[/tex].
The point that corresponds to an angle of [tex]90^{\circ}[/tex] is at position [tex](0, \, 1)[/tex].
Step-by-step explanation:
On a cartesian plane, a unit circle is
a circle of radius [tex]1[/tex],centered at the origin [tex](0, \, 0)[/tex].The circle crosses the x- and y-axis at four points:
[tex](1, \, 0)[/tex],[tex](0, \, 1)[/tex], [tex](-1,\, 0)[/tex], and[tex](0,\, -1)[/tex].Join a point on the circle with the origin using a segment. The "angle" here likely refers to the counter-clockwise angle between the positive x-axis and that segment.
When the angle is equal to [tex]0^\circ[/tex], the segment overlaps with the positive x-axis. The point is on both the circle and the positive x-axis. Its coordinates would be [tex](1, \, 0)[/tex].
To locate the point with a [tex]90^{\circ}[/tex] angle, rotate the [tex]0^\circ[/tex] segment counter-clockwise by [tex]90^{\circ}[/tex]. The segment would land on the positive y-axis. In other words, the [tex]90^{\circ}[/tex]-point would be at the intersection of the positive y-axis and the circle. Its coordinates would be [tex](0, \, 1)[/tex].
Answer:
Angle of 0º: (1,0)
Angle of 90º: (0,1)
Step-by-step explanation:
A unit circle has a radius of 1.
Therefore, the points on the x- and y-axis are as follows:
Angle of 0º: (1,0)
Angle of 90º: (0,1)
Angle of 180º: (-1,0)
Angle of 270º: (0,-1)
Angle of 360º [have now circled back to an angle of 0º]: (1,0)
The base of a 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall (round to the nearest foot)?
Answer:
39 feet.
Step-by-step explanation:
E use the Pythagoras theorem:
40^2 = 8^2 + h^2 as h is the height we require.
h^2 = 1600 - 64
h^2 = 1536
h = 39.19 feet
If quadrilateral WXYZ is inscribed in a circle with center O, the measure of angle W = 45 and the measure of angle X = 110, then the measure of angle Z = _____.
Check the picture below.
Jackson sells two types of toolboxes. He plans on selling them during a farming fair this weekend. He estimates he will sell 20 of the smaller boxes and 12 of the larger boxes. If he'd like the profit to be $1300, which of the following best displays the equation that represents this information?
A. y = −5/3x + 325/3 ~~
B. 20x + 12y = 1300
C. y + 12 = 20(x–1300)
D. 12y = 20x – 1300
Answer:
B
Step-by-step explanation:
In this case, we use variables to represent the the cost of the big and the smaller boxes. Let x be the selling price of the big boxes while y be the selling price of the bigger boxes.
The total selling price of the smaller boxes is 20x. The total selling price of the bigger ones is 12y.
Now we know he is making a profit of $1,300
Hence in equation form, all the information above can be represented as:
20x + 12y = 1,300
The cost of a burger is Rs 20 more than a cup of ice cream. The total cost of a burger and two ice cream cups is Rs 80. Find the price of a burger and a cup of ice cream?
The price of one burger is Rs 40 and a cup of ice cream is Rs 20.
Step-by-step explanation:
Let,
Price of one burger = x
Price of cup of ice cream = y
According to given statement;
x = y+20 Eqn 1
x+2y=80 Eqn 2
Putting value of x from Eqn 1 in Eqn 2
[tex](y+20)+2y=80\\y+20+2y=80\\3y=80-20\\3y=60[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{60}{3}\\y=20[/tex]
Putting y=20 in Eqn 1
[tex]x=20+20\\x=40[/tex]
The price of one burger is Rs 40 and a cup of ice cream is Rs 20.
Keywords: linear equation, substitution method
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The price of a cup of ice cream is Rs 20, and the price of a burger is Rs 40, determined by setting up equations based on the given cost relationship and total cost.
To find the price of a burger and a cup of ice cream, let's use the information given in the problem. Let B represent the cost of a burger, and I represent the cost of a cup of ice cream. We are told that a burger costs Rs 20 more than a cup of ice cream, so we can write this as B = I + 20. Additionally, we know that the total cost of a burger and two ice creams is Rs 80, which can be represented as B + 2I = 80. Now we can substitute the first equation into the second one to find the cost of each item.
Step 1: Substitute B = I + 20 into B + 2I = 80.
Returns: (I + 20) + 2I = 80
Step 2: Combine like terms.
Returns: 3I + 20 = 80
Step 3: Subtract 20 from both sides.
Returns: 3I = 60
Step 4: Divide both sides by 3.
Returns: I = 20
Now we know that a cup of ice cream costs Rs 20, and from the first equation, a burger costs Rs 20 more than the ice cream, so:
Returns: B = I + 20 = 20 + 20 = Rs 40
The price of a burger is Rs 40, and the price of a cup of ice cream is Rs 20.
can anybody help me with this?
This question is confusing and I don't get it.
Answer:
JH = 8, GH = 12, and GJ = 10.6
Step-by-step explanation:
According to Midsegment Theorem, a segment that connects the midpoints of two sides of a triangle is half the length of the third side.
GH = ½ DE
JH = ½ DF
GJ = ½ EF
DE is 24, so GH = 12.
JH is half of DF. Since G is the midpoint of DF, DG is also half of DF. So JH = DG = 8.
GJ is half of EF. Since H is the midpoint of EF, HE is also half of EF. So GJ = HE = 10.6.
Mrs. Allan's car uses 8 gallons of gas for a 224-mile trip. Mrs. Owen's car uses 6 gallons of gas for a 210-mile trip. How many gallons of gas would each car use if both cars traveled 560 miles?
Answer:
Mrs. Allan's Car will use 20 gallons of gas for 560 miles trip.
Mrs. Owen's Car will use 16 gallons of gas for 560 miles trip.
Step-by-step explanation:
Given:
Number of Miles for Mrs Allan car = 224 miles
Number of gallons of gas required = 8
We need to find the number of gallons of gas required for 560 miles for Mrs. Allan's car.
First we will find, in 1 gallons how many miles does Mrs Allan's Car drives.
For 8 gallons = 224 miles
So for 1 gallons = Number of miles in 1 gallon of gas
By using Unitary method we get;
Number of miles in 1 gallon of gas = [tex]\frac{224}{8}= 28\ miles[/tex]
Now we know that;
for 28 miles = 1 gallon of gas is required.
So for 560 miles = Number of gallon of gas required in 560 miles.
Again by using Unitary method we get;
Number of gallon of gas required in 560 miles = [tex]\frac{560}{28}= 20\ gallons[/tex]
Hence Mrs. Allan's Car will use 20 gallons of gas for 560 miles trip.
Also Given:
Number of Miles for Mrs Owen's car = 210 miles
Number of gallons of gas required = 6
We need to find the number of gallons of gas required for 560 miles for Mrs. Owen's car.
First we will find, in 1 gallons how many miles does Mrs Owen's Car drives.
For 6 gallons = 210 miles
So for 1 gallons = Number of miles in 1 gallon of gas
By using Unitary method we get;
Number of miles in 1 gallon of gas = [tex]\frac{210}{6}= 35\ miles[/tex]
Now we know that;
for 35 miles = 1 gallon of gas is required.
So for 560 miles = Number of gallon of gas required in 560 miles.
Again by using Unitary method we get;
Number of gallon of gas required in 560 miles = [tex]\frac{560}{35}= 16\ gallons[/tex]
Hence Mrs. Owen's Car will use 16 gallons of gas for 560 miles trip.
Jim places $10,000 in a bank account that pays 9.8% compounded continuously. After 2 years, will he have enough money to buy a car that costs $12 comma 160? If another bank will pay Jim 10% compounded semiannually, is this a better deal?
Final answer:
Jim will not have enough money to buy the car after 2 years with a bank account that pays 9.8% interest compounded continuously. The other bank offering 10% interest compounded semiannually is a better deal as Jim will have enough money to buy the car.
Explanation:
To determine if Jim will have enough money to buy a car that costs $12,160 after 2 years with a bank account that pays 9.8% interest compounded continuously, we can use the formula for compound interest:
A = P * e^(rt)
where A is the ending amount, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the number of years. Plugging in the values, we have:
A = $10,000 * e^(0.098*2) = $10,000 * e^0.196 ≈ $11,961.34
Therefore, Jim will not have enough money to buy the car.
To determine if the other bank offering 10% interest compounded semiannually is a better deal, we can use the same formula:
A = P * (1 + r/n)^(nt)
where n is the number of times interest is compounded per year. Plugging in the values, we have:
A = $10,000 * (1 + 0.10/2)^(2*2) = $10,000 * (1 + 0.05)^4 = $10,000 * 1.05^4 ≈ $12,265.63
Therefore, the other bank is a better deal as Jim will have enough money to buy the car.
In one country, residents were asked to name their primary language. The ratio of residents who said French to those who said Punjabi was 110 to 7. If there 7,260,000 residents who said French, about how many thousands of residents said Punjabi?
Answer:
462000
Step-by-step explanation:
here,let the punjabi be x
110/7=7260000/x
110x=7260000*7
x=462000
Answer: 462
Step-by-step explanation: I had the question and it said it was 462
Asking for help in the following question #1 and #2 are based of algebra 2.
≅
⇒⇒⇒⇒⇒⇒
Answer:
Step-by-step explanation:
For the first one, revenue - cost = profit. We have equations for revenue and profit, so filling in:
[tex]-.3x^2+150x-cost=-.5x^2+250x-300[/tex]
Let's add cost to both sides to make it positive and bring everything on the right over to the left and combine like terms:
[tex].2x^2-100x+300=cost[/tex]
For the second one:
P(x)*T(x) = [tex](x^2-3x-7)(3x)[/tex]
Distribute the 3x into everything inside the parenthesis to get
[tex]3x^3-9x^2-21x[/tex]
For the second part of that problem, C(x)*P(x) = [tex](x-4)(x^2-3x-7)[/tex]
Distribute the x into everything first to get:
[tex]x^3-3x^2-7x[/tex]
The distribute the -4 into everything to get:
[tex]-4x^2+12x+28[/tex]
Combine the like terms and put everything together to get
[tex]x^3-7x^2+5x+28[/tex]
Neural networks, fuzzy systems, and evolutionary computation are all forms of __________, where systems develop intelligence through an iterative learning process.a. relational intelligenceb. conventional intelligencec. fuzzy logicd. computational intelligence
Answer:
d. computational intelligence
Step-by-step explanation:
Neural networks, fuzzy systems, and evolutionary computation are all forms of computational intelligence, where systems develop intelligence through an iterative learning process.
Computational intelligence (CI) is a machine intelligence which usually refers to the ability of a computer to learn or perform a specific task from data or experimental observation. This implies the systems have the ability to learn and generalize from examples and develop intelligence through an iterative process. Computer intelligence is also known as soft computing. The major Computational intelligence are Fuzzy logic, Neural networks and Evolutionary Computing. Presently, Computational Intelligence is an evolving field. New additions are evolving in addition to the three major CI. These new CI include soft computing like artificial endocrine networks, artificial life, ambient intelligence, cultural learning and social reasoning.
Neural networks, fuzzy systems, and evolutionary computation contribute to the field of computational intelligence, demonstrating adaptive learning capabilities and continuous improvement. Option d) is the correct answer.
Neural networks, fuzzy systems, and evolutionary computation are all forms of computational intelligence, where systems develop intelligence through an iterative learning process. Concepts such as evolution and adaptation, which originate in evolutionary biology, stretch to the domain of complex systems involving the development of adaptive, non-biological processes that have dynamic learning and creative abilities.
These systems are part of artificial intelligence, where computer systems learn from data to improve over time. These forms of artificial intelligence have been rapidly developing since the 1980s and are often associated with machine learning, suggesting a broad category where systems can adapt, process information, and optimize problems.
Kylo bought a pizza for $12.75 and four medium drinks at Pauli's Pizza. Define a variable and write an expression to represent the total amount of money he spent. Then find the total cost if one drink cost $3.
Answer:
Step-by-step explanation:
Let d be the cost of a drink. The expression for the cost of the pizza and 4 drinks is
12.75 + 4d
If each drink costs $3, then
12.75 + 4(3) simpifies to
12.75 + 12 which equals 24.75
The final agreed-to sample size is a trade-off between acceptable error and research cost.
Answer:
True
Step-by-step explanation:
Sample size selection is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is important in any empirical statistical study in which the goal is to make inferences about a population from a sample. The actual sample size used in a study is determined based on the time money and technical cost of data collection, and the need to have sufficient statistical accuracy.
Finding a balance between acceptable error and research cost gives rise to concepts like Confidence Interval and Margin of Error.
Identify an attribute of the "a" element that indicates the media type of z linked document
Answer:
Step-by-step explanation:
The id attribute requires a unique string to identify the element.
Among the options provided, the attribute of the "an" element that indicates the media type of a linked document is:
C) type="mime-type"
In HTML, when creating links to external resources or documents, the "an" element is typically represented by the "a" anchor tag. This tag often uses the 'type' attribute to specify the media type of the linked document.
For instance, if you have an anchor tag (<a>) linking to a document like a stylesheet, image, or script, you can specify the media type using the 'type' attribute. The 'type' attribute helps the browser interpret the linked document's format or MIME (Multipurpose Internet Mail Extensions) type. An example might look like:
<a href="url_to_linked_document" type="text/css">Link Text</a>
In this example, 'type="text/css"' indicates that the linked document is a CSS file (text/css MIME type), which helps browsers understand how to handle the resource being linked. Therefore, option C) type="mime-type" is the attribute used to indicate the media type of the linked document.
Complete Question:
Identify an attribute of the "an" element that indicates the media type of z linked document.
A) rel-"type"
B) hrefland="lang"
C) type="mime-type"
D) href="url"