Answer:
See explanation
Step-by-step explanation:
Solution:-
The random variable, Y be the temperature of chemical reaction in degree fahrenheit be a linear expression of a random variable X : The temperature in at which a certain chemical reaction takes place.
Y = 1.8*X + 32
- The median of the random variate "X" is given to be equal to "η". We can mathematically express it as:
P ( X ≤ η ) = 0.5
- Then the median of "Y" distribution can be expressed with the help of the relation given:
P ( Y ≤ 1.8*η + 32 )
- The left hand side of the inequality can be replaced by the linear relation:
P ( 1.8*X + 32 ≤ 1.8*η + 32 )
P ( 1.8*X ≤ 1.8*η ) ..... Cancel "1.8" on both sides.
P ( X ≤ η ) = 0.5 ...... Proven
Hence,
- Through conjecture we proved that: (1.8*η + 32) has to be the median of distribution "Y".
b)
- Recall that the definition of proportion (p) of distribution that lie within the 90th percentile. It can be mathematically expressed as the probability of random variate "X" at 90th percentile :
P ( X ≤ p_.9 ) = 0.9 ..... 90th percentile
- Now use the conjecture given as a linear expression random variate "Y",
P ( Y ≤ 1.8*p_0.9 + 32 ) = P ( 1.8*X + 32 ≤ 1.8*p_0.9 + 32 )
= P ( 1.8*X ≤ 1.8*p_0.9 )
= P ( X ≤ p_0.9 )
= 0.9
- So from conjecture we saw that the 90th percentile of "X" distribution is also the 90th percentile of "Y" distribution.
c)
- The more general relation between two random variate "Y" and "X" is given:
Y = aX + b
Where, a : is either a positive or negative constant.
- Denote, (np) as the 100th percentile of the X distribution, so the corresponding 100th percentile of the Y distribution would be : (a*np + b).
- When a is positive,
P ( Y ≤ a*p_% + b ) = P ( a*X + b ≤ a*p_% + b )
= P ( a*X ≤ a*p_% )
= P ( X ≤ p_% )
= np_%
- When a is negative,
P ( Y ≤ a*p_% + b ) = P ( a*X + b ≤ a*p_% + b )
= P ( a*X ≤ a*p_% )
= P ( X ≥ p_% )
= 1 - np_%
In a temperature conversion equation Y = 1.8X + 32, medians and percentiles of Y are related to the corresponding values of X through the equation itself. For an arbitrary linear transformation Y = aX + b, percentiles of Y and X are related as aX + b, with ordering depending on the sign of a.
Explanation:Lets start by talking about the relationship between X and Y. In the context of the temperature conversion between Celsius (X) and Fahrenheit (Y), Y equals to 1.8 times X plus 32.
1. If the median of X is M, substituting M into the equation Y = 1.8X + 32 gives the median of Y as 1.8M + 32, since the transformation is linear.
2. The 90th percentile of the Y distribution will relate to the 90th percentile of X distribution in a similar fashion. If we denote the 90th percentile of X as P, then the 90th percentile of Y will be 1.8P + 32.
3. For a general linear transformation Y = aX + b, where a is non-zero, any percentile of Y is related to the corresponding percentile of X as aX + b. If a is positive, the transformation will preserve the ordering of percentiles (e.g., higher values of X correspond to higher values of Y). If a is negative, it will reverse the ordering of percentiles (e.g., higher values of X will correspond to lower values of Y).
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A conductor that’s described as a 750 MCM wire has an area of
A store sells two different kinds of nuts. Cashews come in 6-ounce cans and walnuts come in 10-ounce cans. On Friday, the store sold 30 of each can of nuts. Which of the statements below are true? (1 pound = 16 ounces). Choose all the correct answers.
Answer:
The store sold 120 ounces fewer ounces of cashew than walnut.
The store sold 11.25 pounds of cashews and 18.75 pounds of walnuts.
Explanation:To find out how many pounds of each type of nut were sold, we first need to multiply the number of cans sold by the weight of each can. This gives us the total weight in ounces. Then, we convert from ounces to pounds.
For the cashews: 30 cans * 6 ounces/can = 180 ounces. 180 ounces / 16 ounces/pound = 11.25 pounds of cashews.
For the walnuts: 30 cans * 10 ounces/can = 300 ounces. 300 ounces / 16 ounces/pound = 18.75 pounds of walnuts.
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Anna is three times as old as Diane.If the sum of their ages is 44,how old is Anne? ( Use d as the variable )
Answer:
Anna33 diane11
Step-by-step explanation:
11×3=33
33+11=44
A psychology professor assigns letter grades on a test according to the following scheme. A: Top 7% of scores B: Scores below the top 7% and above the bottom 64% C: Scores below the top 36% and above the bottom 25% D: Scores below the top 75% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 78.4 and a standard deviation of 7.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for an A grade is 89.8.
Step-by-step explanation:
We are given that a psychology professor assigns letter grades on a test according to the following scheme. A : Top 7% of scores. B : Scores below the top 7% and above the bottom 64%. C : Scores below the top 36% and above the bottom 25%. D : Scores below the top 75% and above the bottom 6%. F : Bottom 6% of scores.
Scores on the test are normally distributed with a mean of 78.4 and a standard deviation of 7.6.
Let X = Scores on the test
SO, X ~ Normal([tex]\mu=78.4,\sigma^{2} =7.6^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 78.4
[tex]\sigma[/tex] = standard deviation = 7.6
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, the minimum score required for an A grade so that it represents Top 7% of scores is given by;
P(X [tex]\geq[/tex] x) = 0.07 {where x is the required minimum score
P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{x-78.4}{7.6}[/tex] ) = 0.07
P(Z [tex]\geq[/tex] [tex]\frac{x-78.4}{7.6}[/tex] ) = 0.07
So, the critical value of x in the z table which represents the top 7% of the area is given as 1.4996, that is;
[tex]\frac{x-78.4}{7.6} =1.4996[/tex]
[tex]{x-78.4}{} =1.4996\times 7.6[/tex]
[tex]x[/tex] = 78.4 + 11.39696 = 89.8 or 90
Hence, the minimum score required for an A grade is 89.8.
The box plots show the average speeds, in miles per hour, for the race cars in two different races.
Average Speeds of Cars in Race A
120
125 130
135
140 145
150
155
160
165
170
Average Speeds of Cars in Race B
One-half of cars travel at which speeds?
between 120 and 143 mph in race A between 125 and 140 mph in race B
between 120 and 170 mph in race A; between 125 and 165 mph in race B
O between 120 and 153 mph in race A between 125 and 145 mph in race B
O between 165 and 170 mph in race A between 150 and 165 mph in race B
Answer:
between 120 and 153 mph in race A between 125 and 145 mph in race B
Step-by-step explanation:
i got it right on my test
Answer:
its
C.between 120 and 153 mph in race A; between 125 and 145 mph in race B
Step-by-step explanation:
The diameter of a circle is 9 centimeters. Find the area to the nearest tenth.
Answer:
63.6 square cm
Step-by-step explanation:
[tex]d = 9 \: cm \implies \: r = 4.5 \: cm \\ area \: of \: circle \\ = \pi {r}^{2} \\ = 3.14 \times ( {4.5})^{2} \\ = 3.14 \times 20.25 \\ = 63.585 \\ = 63.6 \: {cm}^{2} \\ [/tex]
Determine whether −9x−3y2=6 represents a function of x.
The equation -9x - 3y^2 = 6 does not represent a function of x because each x-value has two possible y-values.
Explanation:The equation -9x - 3y^2 = 6 represents a function of x.In order to determine if an equation represents a function of x, we need to check if each value of x produces a unique y-value. This means that for any x-value, there cannot be more than one y-value.
When we rearrange the given equation, we can solve for y in terms of x: y = sqrt((-9x - 6)/3). Since the square root of a positive number always has two possible values (positive and negative), we have two possible y-values for each x-value. Therefore, the given equation does not represent a function of x.
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Which is the exponential form shown 2/5 2/5 2/5 2/5
Answer:
[tex] \bigg(\frac{2}{5} \bigg)^{4} [/tex]
Step-by-step explanation:
[tex] \frac{2}{5} \times \frac{2}{5} \times \frac{2}{5} \times \frac{2}{5} = \bigg(\frac{2}{5} \bigg)^{4} \\ [/tex]
Please help me I need help
two high school students took equivalent language tests, one in German and one in French. The student taking the German test, for which the mean was 66 and the standard deviation was 8, scired ab 82, while the student taking the French test, for which the mean was 27 and the standard deviation was 5, scored a 35. Compare the scores.
Answer:
The student who did the German test scored 2 standard deviations above the mean and the student who did the French test scored 1.6 standard deviations above the mean. Relative to their classmates, the student who did the German test scored better due to the higher z-score.
Step-by-step explanation:
Z-score
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
German test
Mean was 66 and the standard deviation was 8, scored an 82.
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 66}{8}[/tex]
[tex]Z = 2[/tex]
French test:
Mean was 27 and the standard deviation was 5, scored a 35.
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 27}{5}[/tex]
[tex]Z = 1.6[/tex]
The student who did the German test scored 2 standard deviations above the mean and the student who did the French test scored 1.6 standard deviations above the mean. Relative to their classmates, the student who did the German test scored better due to the higher z-score.
Final answer:
The German test taker scored 2 standard deviations above the mean, while the French test taker scored 1.6 standard deviations above the mean. Thus, the German test taker scored comparatively higher relative to their peers.
Explanation:
To compare the scores of the two high school students who took equivalent language tests in German and French, we need to calculate the z-scores for each. The z-score is a measure that describes how far an individual test score is from the mean of the respective test, in terms of standard deviations. Let's calculate:
For the German test:
ZGerman = (Score - Mean) / Standard Deviation
ZGerman = (82 - 66) / 8
ZGerman = 16 / 8
ZGerman = 2.0
For the French test:
ZFrench = (Score - Mean) / Standard Deviation
ZFrench = (35 - 27) / 5
ZFrench = 8 / 5
ZFrench = 1.6
Comparing these z-scores, the student who took the German test scored higher relative to their peers (2 standard deviations above the mean) compared to the student who took the French test (1.6 standard deviations above the mean).
six-sided die is rolled. Find the probability of rolling an odd number or a number less than 6.
Answer:
Both three and six are divisible by three. Therefore, this fraction could be simplified to one-half.
Step-by-step explanation:
Three divided by three is equal to one.
Answer: odd number:1/2
number less than six:5/6
Step-by-step explanation:
x+7=-8 what does x equal
Answer:x=-15
Step-by-step explanation:You want to isolate x so u would subtract 7 from one side and subtract 7 from the other side
X+7=-8
X=-15
Miguel is selling tickets to a barbecue. Adult tickets cost $7.00 and children's tickets cost $5.00. He sells six more children's tickets than adult tickets. The total amount of money he collects is $234.00. How many adult tickets and how many children's tickets did he sell?
Answer:
17 adult tickets
23 children's tickets
Step-by-step explanation:
Adult tickets 17x7=119
Child tickets 23x5=115 23 is 6 more than 17.
119+115=234
What can be best described as a relationship between two quantities in which one quantity is dependent upon the other?
Conjunction
Input
Function
Output
Disjunction
Answer:
a function
Step-by-step explanation:
a function is where u plug something in and get another thing out. the entire function is dependent on another independent variable
find an explicit formula for the arithmetic sequence 10, -10, -30, -50, ...
Step-by-step explanation:
The formula is subtracting by 20 you can count it so the next - 70
Answer:
10-20(n-1)
Step-by-step explanation:
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 502 judges, it was found that 283 were introverts. (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)
Answer:
The point estimate for p is 0.5637.
Step-by-step explanation:
Point estimate for the proportion of all judges who are introverts.
We have a big sample.
So the proportion of the sample proportion of introverted judges can be used as the estimation of the population proportion.
In the sample:
502 judges
283 introverts.
So
p = 283/502 = 0.5637
The point estimate for p is 0.5637.
The point estimate for the proportion of judges who are introverts, denoted by p, is found by dividing the number of introverts (283) by the total number of judges in the sample (502), which gives a point estimate of 0.5637 when rounded to four decimal places.
Explanation:To estimate the proportion of judges who are introverts, we use the given data from the random sample. The point estimate for p, representing the proportion of all judges who are introverts, can be calculated by dividing the number of introverts in the sample by the total number of judges in the sample. The formula for the point estimate p' is:
p' = X / n
where:
X is the number of introverts in the sample (283).n is the total number of judges in the sample (502).Using the given data:
p' = 283 / 502
Calculating this gives us a point estimate for p' of 0.5637 after rounding to four decimal places.
This result represents the estimated proportion of the population of judges who are introverts based on the sample.
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31.24 to 1 decimal place
Answer:
31.2
Step-by-step explanation:
Because you only round up if the number next to the 1st decimal place is greater than 5, you just drop the 4 and keep 31.2.
you just drop the 4 and keep 31.2.
Write and simplify an expression for the surface area of a rectangular prism with a height of h yards, a length of 2.6 yards, and a width of 3.5 yards. What is the surface area if the height is 4 yards?
SA =
+
h
The surface area is
yd2.
You will get BRAINLIEST
Given:
Given that the rectangular prism with length l = 2..6 yards.
The width of the rectangular prism is 3.5 yards.
The height of the prism is h yards.
We need to determine the simplified expression for the surface area of the rectangular prism.
We also need to determine the surface area of the prism if the height is 4 yards.
Expression for the surface area of the prism:
The surface area of the rectangular prism can be determined using the formula,
[tex]SA=2(lw+wh+lh)[/tex]
Substituting l = 2.6, w = 3.5, h = h, we get;
[tex]SA=2[(2.6)(3.5)+(3.5)h+(2.6)h][/tex]
[tex]SA=2(9.1+3.5h+2.6h)[/tex]
[tex]SA=2(9.1+6.1 h)[/tex]
[tex]SA=18.2+12.2h[/tex]
Thus, the simplified expression for the surface area of the prism is [tex]SA=18.2+12.2h[/tex]
Surface area of the prism:
Now, we shall determine the surface area of the prism if the height is 4 yards.
Substituting the value h = 4 in the expression [tex]SA=18.2+12.2h[/tex], we have;
[tex]SA=18.2+12.2(4)[/tex]
[tex]SA=18.2+48.8[/tex]
[tex]SA=67 \ yd^2[/tex]
Thus, the surface area of the rectangular prism is 67 square yards.
A bus arrives at a bus stop at a randomly selected time within a 1-hour period. A passenger arrives at the bus stop at a randomly selected time with the same hour. The passenger is willing to wait for the bus for up to 1/4 of an hour. What is the probability that the passenger will catch the bus?
Answer:
75%
Step-by-step explanation:
Which of the following is not a form of bias? Multiple Choice Portions of the population are excluded or underrepresented from the sample. Information from the sample overemphasizes a particular stratum of the population. Those responding to a survey or poll differ systematically from the nonrespondents. Certain groups in the population are systematically underrepresented in the sample.
Answer:
B. Information from the sample is typical of information in the population.
Step-by-step explanation:
In Statistical Research, a Bias refers to the tendency of a sample statistic to systematically overestimate or underestimate a population parameter.
(A)When portions of the population are excluded or underrepresented from the sample, it is a Sampling Bias.
(C)When those responding to a survey or poll differ systematically from the nonrespondents, it is referred to as Non-Response Bias.
(D)When certain groups in the population are systematically underrepresented in the sample, it is referred to as Selection Bias.
Therefore option B is not an example of a Bias.
Final answer:
The correct answer is "Information from the sample overemphasizes a particular stratum of the population."
Explanation:
Bias in research refers to systematic errors or deviations from the true population value. It can occur at various stages, including during sampling, data collection, analysis, and interpretation. The options provided describe different forms of bias commonly encountered in research:
1. Exclusion or underrepresentation of portions of the population from the sample is known as sampling bias. This can lead to results that do not accurately reflect the characteristics of the entire population.
2. Overemphasizing a particular stratum of the population is an example of selection bias. This occurs when certain groups within the population are disproportionately represented in the sample, leading to skewed or inaccurate results.
3. Differences between respondents and nonrespondents in a survey or poll can lead to nonresponse bias. This occurs when those who choose to respond to a survey differ systematically from those who do not respond, leading to results that may not be generalizable to the entire population.
4. Systematic underrepresentation of certain groups in the sample can also lead to bias. This is similar to sampling bias but specifically refers to the consistent exclusion or underrepresentation of certain demographic groups.
It is important to recognize and address bias in research to ensure the validity and reliability of the findings. Researchers can use various techniques such as random sampling, stratified sampling, and sensitivity analysis to mitigate bias and improve the quality of their research.
It has long been stated that the mean temperature of humans is 98.6degreesF. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6degreesF. They measured the temperatures of 44 healthy adults 1 to 4 times daily for 3 days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.3degreesF and a sample standard deviation of 1 degrees F.
a. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6 degrees F at the α= 0.01 level of significance.
b. State the hypotheses.
Answer:
We conclude that the mean temperature of humans is more than or equal to 98.6°F.
Step-by-step explanation:
We are given that it has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F.
They measured the temperatures of 44 healthy adults 1 to 4 times daily for 3 days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.3°F and a sample standard deviation of 1°F.
Let [tex]\mu[/tex] = true mean temperature of humans.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 98.6°F {means that the mean temperature of humans is more than or equal to 98.6°F}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 98.6°F {means that the mean temperature of humans is less than 98.6°F}
The test statistics that will be used here is One-sample t test statistics as we don't know about the 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 temperature of 44 adults = 98.3°F
s = sample standard deviation = 1°F
n = sample of healthy adults = 44
So, test statistics = [tex]\frac{98.3-98.6}{\frac{1}{\sqrt{43} } }[/tex] ~ [tex]t_4_3[/tex]
= -1.967
Hence, the value of test statistics is -1.967.
Now, P-value of the test statistics is given by;
P-value = P( [tex]t_4_3[/tex] < -1.967) = 0.029 or 2.9%
If the P-value of test statistics is more than the level of significance, then we will not reject our null hypothesis as it will not fall in the rejection region.If the P-value of test statistics is less than the level of significance, then we will reject our null hypothesis as it will fall in the rejection region.
Now, here the P-value is 0.029 which is clearly higher than the level of significance of 0.01, so we will not reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean temperature of humans is more than or equal to 98.6°F.
Subtract. [5 0 − 2]− [− 1 3 8 ] Enter your answer in the boxes. [ ]
To subtract the matrices [5 0 - 2] and [-1 3 8], subtract each corresponding element, resulting in the matrix [6 -3 -10].
Explanation:The question asks for the result of the subtraction of two matrices: [5 0 - 2] minus [-1 3 8]. When we subtract matrices, we subtract the corresponding elements from each matrix. Therefore, this subtraction will result in a new matrix where each element is the subtraction of the corresponding elements from the given matrices.
To perform the subtraction, we subtract each element in the second matrix from the corresponding element in the first matrix:
So, the result of the matrix subtraction is [6 -3 -10].
What is the volume of a rectangular prism whose length, width and height are 1/3m 1/5m and 1/7m, respectively?
Answer:
1/105 m³
Step-by-step explanation:
the volume of a rectangular prism = base area x height
1/3 x 1/5 x 1/7 = 1/105 m³
Answer:
1/105m^3
Step-by-step explanation:
I did the question and it was correct
Worked for 5 hours and 30 minutes. How should she write that on her time card
It would actually depend on the way that you want your result. It can be in h, min, s
For example, in hours it would be 5.5h
in minutes, 330min
in seconds, 19800s
She should write 5.5 hours on her time card.
Explanation:To write 5 hours and 30 minutes on her time card, she can simply write 5.5 hours. This is because 30 minutes is half of an hour, so it can be represented as 0.5 hours.
Lupe sold 39 bags of cheese popcorn. She sold 3 times as many bags as Frances. How many bags did Frances sell?
Answer:
13
Step-by-step explanation:
Since Lupe is 3 times as many as Frances
39 ÷ 3= 13
Answer:
13
Step-by-step explanation:
Make an equation. Let x represent the bags that Frances sold. Since Lupe sold 3 times the popcorn Frances did, use multiplication.
[tex]39=3x[/tex]
Solve for x to find the amount Frances sold:
Divide both sides by 3:
[tex]\frac{39}{3}=\frac{3x}{3} \\\\13=x[/tex]
[tex]x=13[/tex]
Frances sold 13 bags.
How do u convert 3 and 4/7 to an improper fraction?
Answer:
3 4/7 = 25/7
Step-by-step explanation:
multiply the whole number(3) by the denominator(7).
Then you have 21.
Add the product of the last 2 numbers to the numerator(4)
21 + 4 = 25
Note: (denominator x whole number) + numerator
We are required to convert 3 and 4/7 to an improper fraction.
The fraction 3 and 4/7 to an improper fraction is 25 / 7
An improper fraction is a fraction in which the numerator is greater than the denominator.Numerator refers to the upper number in a fractionDenominator refers to the bottom number in a fraction.Given:
3 4/7
= {7(3) + 4} / 7
= (21 + 4) / 7
= 25 / 7
Therefore, the fraction 3 and 4/7 to an improper fraction is 25 / 7
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1 thenth + 5 hundredths
Answer:
0.15
Step-by-step explanation:
According to the American Red Cross, 9.2% of all Connecticut residents have Type B blood. A random sample of 18 Connecticut residents is taken. What is the standard deviation of the random variable X?
According to the American Red Cross, 9.2% of all Connecticut residents have Type B blood. If 18 Connecticut residents are taken at random, the standard deviation of the binomial distribution is about 1.214.
Explanation:The question is asking for the standard deviation of a binomial distribution. To calculate the standard deviation for a binomial distribution, the formula used is √npq, where n is the number of trials, p is the probability of success, and q is the probability of failure (1 - p).
In this case, we have n equals to 18 (number of Connecticut residents randomly sampled), p equals to 0.092 (since 9.2% have Type B blood), and then, by subtraction, q equals to 0.908.
Therefore, the standard deviation would be √18*0.092*0.908, which is about 1.214 when evaluated.
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The standard deviation of the random variable X is approximately 0.067.
Explanation:The standard deviation of the random variable X can be calculated using the formula:
Standard Deviation (SD) = sqrt(p(1-p)/n)
Given that p is the probability of success (9.2% or 0.092) and n is the sample size (18), we can substitute these values into the formula to find:
SD = sqrt(0.092(1-0.092)/18) = 0.067
Therefore, the standard deviation of the random variable X is approximately 0.067.
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A fan is marked up 40% on the original price. The original price was $20. What is the new price of the fan before sales tax?
Answer:
$28
Step-by-step explanation:
The markup was 0.40×$20 = $8, so the new price is ...
$20 +8 = $28
An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 sin(2θ) = 1 (a) Find all solutions of the equation. θ = (b) Find the solutions in the interval [0, 2π). θ =
To solve the equation 2 sin(2θ) = 1, find the angles θ where sin(2θ) equals 1/2. The solutions for θ are π/12 + kπ, where k is any integer.
To solve the equation 2 sin(2θ) = 1, we can divide both sides of the equation by 2 to get sin(2θ) = 1/2. Since the range of sin function is -1 to 1, we need to find the angles θ where sin(2θ) equals 1/2.
Using the inverse sine function, we can find the principal value of 2θ which is π/6 radians. This gives us one solution for θ: π/12.
Since sin function is periodic with period of 2π, we can find additional solutions by adding integer multiples of π to the principal value. Therefore, the solutions for θ are π/12 + kπ, where k is any integer.
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