The critical values for a Chi-square distribution with 80% confidence level and sample size of 15 (thus 14 degrees of freedom) are: χ2L = 18.475 and χ2R = 8.897.
Explanation:The question is asking for the critical values for a Chi-square distribution which can be found using Chi-square tables usually found in statistics textbooks or online. The critical values refer to the boundary values for the acceptance region of a hypothesis test.
When trying to find the critical values for an 80% confidence level with 14 degrees of freedom (since degrees of freedom = n - 1 for sample, thus 15 - 1 = 14), you need the 90th percentile for the χ2L and the 10th percentile for the χ2R (since α = 20%, then α/2 = 10%).
Using a Chi-square table for these percentiles, we get:
χ2L = 18.475
χ2R = 8.897
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A person saves €1 in the first month and decides to double the amount he saves the next month. He continues this pattern of saving twice the amount he saved the previous month for 12 months how much will he save on the 12th month and how much will he have saved in total for the year ignoring any interest he received?
Answer:
(a)€2048
(b)€4095
Step-by-step explanation:
So the amount of money we would save at nth month is
[tex]2^{n-1}[/tex] where n = 1, 2, 3, 4, ...
At the 12th month, meaning n = 12, we would save
[tex]2^{12-1}[/tex] = €2048 for that month
The total amount we would save in a year is
1 + 2 + 4 + 8 + 16 + ... + 2048
[tex]2^{n} - 1 = 2^{12} - 1 [/tex] = €4095
Please help me!! Due today
Answer:
Step-by-step explanation:
y = (-1/4)x - 4 has a y-intercept of (0, -4). Place a dark dot at (0, -4).
Now we use the info from the slope, -1/4:
Starting with your pencil point on the dot (0, -4), move the pencil point 4 units to the right and then 1 unit down. You will now be at (4, -5). Place a dark dot there.
Then draw a straight, solid line through (0, -4) and (4, -5).
Write a quadratic function in vertex form whose graph has the vertex (-2,-4 ) and passes through the point (-1,-6)
Answer:
[tex]y = (-2)(x + 2)^2 - 4[/tex].
Step-by-step explanation:
The vertex form of a quadratic function is in the form
[tex]y = a (x - h)^2 + k[/tex],
where
[tex]a[/tex] is a coefficient that needs to be found, and [tex](h, k)[/tex] is the vertex of this function.In this question, the vertex of this quadratic function is at the point [tex](-2, -4)[/tex]. In other words, [tex]h = (-2)[/tex] and [tex]k = (-4)[/tex]. Substitute these value into the general equation:
[tex]y = a (x - (-2))^2 +(- 4)[/tex].
Simplify to obtain:
[tex]y = a (x + 2)^2 - 4[/tex].
The only missing piece here is the coefficient [tex]a[/tex]. That's likely why the problem gave [tex](-1, -6)[/tex], yet another point on this quadratic function. If this function indeed contains the point [tex](-1, -6)[/tex], [tex]y[/tex] should be equal to [tex](-6)[/tex] when [tex]x = (-1)[/tex]. That is:
[tex]-6 = a(-1 + 2)^2 -4[/tex].
Solve this equation for [tex]a[/tex]:
[tex]a = -6 - (-4) = -2[/tex].
Hence the equation of the quadratic function in its vertex form:
[tex]y = (-2)(x + 2)^2 - 4[/tex].
The quadratic function in vertex form that the student is looking for is f(x) = -2(x+2)² - 4. We obtained this by substituting the given vertex (-2, -4) and the point (-1, -6) into the general form of a vertex form quadratic function.
Explanation:The question is asking us to find the equation of a quadratic function, also known as a second-order polynomial, in vertex form. The vertex form of a quadratic function can be written as f(x) = a(x-h)² + k, where (h, k) is the vertex and 'a' is a non-zero number.
The vertex is given as (-2, -4). Therefore, h = -2 and k = -4. The equation becomes f(x) = a(x+2)² - 4. We also know that the graph passes through the point (-1, -6), which we can substitute into the equation to get: -6 = a(-1 + 2)² - 4. We solve this equation for 'a', and find that a = -2. Therefore, the quadratic function in vertex form is f(x) = -2(x+2)² - 4.
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A hovercraft takes off from a platform. Its height (in meters), xxx seconds after takeoff, is modeled by h(x)=-(x-11)(x+3)h(x)=−(x−11)(x+3)h, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 11, right parenthesis, left parenthesis, x, plus, 3, right parenthesis How many seconds after takeoff will the hovercraft land on the ground?
Answer:
After 11 seconds the hovercraft will land on ground
Step-by-step explanation:
Given function that shows the height of a hovercraft,
[tex]h(x) = -(x-11)(x+3)[/tex]
Where,
x = number of second.
When the hovercraft land the ground,
[tex]h(x) = 0[/tex]
[tex]-(x-11)(x+3)=0[/tex]
[tex]\implies (x-11)(x+3)=0[/tex]
By zero product property,
x - 11 = 0 or x + 3 = 0
⇒ x = 11 or x = -3 ( not possible ),
Hence, after 11 seconds the hovercraft will land on ground.
at the time I am writing this the other answer only has a 3.2 rating, but I can vouch that the answer is still correct: 11 seconds !
A formula for finding SA, the surface area of a rectangular prism, is SA = 2(ab + ac + bc), where a, b, and c represent the lengths of the edges of the prism. What is the surface area of this prism if a = 12 inches, b = 6 inches, and c = 4 inches?
Answer:
144
Step-by-step explanation:
We simply need to input these values into the equation.
S = (ab + ac + bc)
Where: a = 12 b = 6 and c = 4
S = ( 12 × 6 + 12 × 4 + 6 × 4)
S = 72 + 48 + 24 = 144 inch^2
Answer:
the correct answer is c (288 in. squared)
Step-by-step explanation:
i got i correct on the quiz;)
hope this helps you out
(also please let me know if i am wrong)
find the quotient following this pattern
image attached
Answer:
x⁵ +x⁴ +x³ +x² +x +1
Step-by-step explanation:
Your expression matches the pattern with n=6, so fill in that value of n in the quotient the pattern shows:
[tex]\dfrac{x^6-1}{x-1}=x^5+x^4+x^3+x^2+x+1[/tex]
When to use chain rule and product rule?
How do I differentiate between these two. Thanks very much!!
Chain rule when it's one function inside another.
d/dx f(g(x)) = f’(g(x))*g’(x)
Product rule when two functions are multiplied side by side.
d/dx f(x)g(x) = f’(x)g(x) + f(x)g’(x)
Final answer:
The chain rule is used when you have a composite function, while the product rule is used when you have a product of two functions.
Explanation:
The chain rule and product rule are both rules used in calculus to differentiate functions.
Chain Rule:The chain rule is used when you have a composite function, where one function is inside another function. To differentiate a composite function, you multiply the derivative of the outer function by the derivative of the inner function.
For example, if you have y = f(g(x)), where f(x) and g(x) are functions, the chain rule states that dy/dx = f'(g(x)) * g'(x).
Product Rule:The product rule is used when you have a product of two functions. To differentiate a product, you take the derivative of the first function times the second function, plus the first function times the derivative of the second function.
For example, if you have y = f(x) * g(x), the product rule states that dy/dx = f'(x) * g(x) + f(x) * g'(x).
You are given a choice of taking the simple interest on $10,000 invested for 2 years at a rate of 3% or the interest on $100,000 invested for 2 years at an interest rate of 3% compounded daily (use the Banker's rule ).
Which investment earns the greater amount of interest?
Give the difference between the amounts of interest earned by the two investments.
Answer:
Compount interest earns more. Difference between 2 interest is $92 445.39
Step-by-step explanation:
Simple Interest:
[tex]I = \frac{prt}{100} [/tex]
p = $10000
r = 3%
t = 2years
I = (10000×3×2)/100
= $600
Total amount = $10 600
Compound Interest:
[tex]A = p( {1 + \frac{r}{100}) }^{n} [/tex]
p = $100000
r = 3/730 (daily)
t = 730 (2yrs)
A = 100000[1+(3/73000)]^730
= $103 045.39 (2d.p)
Difference = $103045.39 -
$10600
= $92 445.39
(Correct me if i am wrong)
In a one-way ANOVA, the __________ is calculated by taking the squared difference between each person and their specific groups mean, while the ______________ is calculated by taking the squared difference between each group and the grand mean.
Answer:
In a one-way ANOVA, the [tex]SS_{within}[/tex] is calculated by taking the squared difference between each person and their specific groups mean, while the [tex]SS_{between}[/tex] is calculated by taking the squared difference between each group and the grand mean.
Step-by-step explanation:
The one-way analysis of variance (ANOVA) is used "to determine whether there are any statistically significant differences between the means of two or more independent groups".
The sum of squares is the sum of the square of variation, where variation is defined as the spread between each individual value and the mean.
If we assume that we have p groups and each gtoup have a size [tex]n_j[/tex] then we have different sources of variation, the formulas related to the sum of squares are:
[tex]SS_{total}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]
A measure of total variation.
[tex]SS_{between}=\sum_{j=1}^{p} n_j (\bar x_{j}-\bar x)^2 [/tex]
A measure of variation between each group and the grand mean.
[tex]SS_{within}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]
A measure of variation between each person and their specific groups mean.
A warehouse employs 21 workers on first shift, 15 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly two second shift workers and two third shift workers.
Answer: Our required probability is 0.11.
Step-by-step explanation:
Since we have given that
Number of workers in first shift = 21
Number of workers in second shift = 15
Number of workers in third shift = 13
We need to find the probability of choosing exactly two second shift workers and two third shift workers.
So, it becomes,
[tex]\dfrac{^{15}C_2\times ^{13}C_2\times ^{21}C_4}{^{49}C_8}\\\\=0.11[/tex]
Hence, our required probability is 0.11.
The probability question asks to determine the chance of choosing two second shift and two third shift workers from a warehouse workforce. Combinations are used to calculate the number of ways to select the workers, and the probability is found by dividing the desired combination by the total number of ways to choose eight workers.
Explanation:The question involves calculating the probability of choosing a specific combination of warehouse workers from different shifts for interviews. There are a total of 49 workers (21 first shift, 15 second shift, and 13 third shift). To find the probability of choosing exactly two second shift workers and two third shift workers, we need to consider the total number of ways to choose eight workers and the number of ways to choose two workers from each of the specified shifts.
The probability of selecting exactly two second shift workers is calculated as the combination of 2 from 15, and the probability of selecting exactly two third shift workers is the combination of 2 from 13. Since we're choosing 8 workers in total, we also have to choose the remaining 4 workers from the first shift, which can be done in combinations of 4 from 21. The probability is then calculated by dividing these combinations by the total number of ways 8 workers can be chosen from all 49 workers.
To calculate the combinations, we use the combination formula C(n, k) = n! / (k!(n-k)!). Then the overall probability is a fraction where the numerator is the product of the combinations for each selection and the denominator is the combination of 8 from 49.
Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Write an equation relates the total amount of gasoline in the tank
Answer: y = x + 4
Step-by-step explanation:
Let "y" be the total number of gallons in the tank, and let "x" be the total number of unfilled gasoline.
Since we already have an initial "4 gallons" in the tank, the total capacity of the tank will be "x + 4".
Answer:
A y=4+x
Step-by-step explanation:
All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? . The margin of error is multiplied by . The margin of error is multiplied by . The margin of error is multiplied by 0.5. The margin of error is multiplied by 2.
Answer:
The margin of error is multiplied by [tex]\sqrt{2}[/tex]
Step-by-step explanation:
margin of error (ME) from the mean can be calculated using the formula
ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where
z is the corresponding statistic of the given confidence levels is the standard deviation of the sample (or of the population if it is known) N is the sample sizeSince margin of error is proportional with inverse of [tex]\sqrt{N}[/tex],
if we cut the sample size in half, the margin of error is multiplied by [tex]\sqrt{2}[/tex].
Cutting the sample size in half increases the margin of error. The new margin of error will be approximately 1.414 times larger than the original margin of error. Essentially, this effect multiplies the margin of error by 2.
If you cut the sample size in half, the margin of error will increase. The margin of error is inversely proportional to the square root of the sample size. Specifically, the margin of error is multiplied by the square root of the ratio of the original sample size to the new sample size.
Mathematically, if the original sample size is N and the new sample size is N/2, the margin of error (MOE) changes as follows:
Original MOE formula: MOE = critical value × (standard deviation / √N)New MOE formula: MOE = critical value × (standard deviation / √(N/2))Since √(N/2) = √(N) / √(2), the new margin of error will be:
New MOE = Original MOE × √(2) approximately equal to Original MOE × 1.414.
Therefore, cutting the sample size in half multiplies the margin of error by 1.414, roughly 2 times.
Complete Question:
All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? ME= 2·5/√(n) . The margin of error is multiplied by √(0.5)· The margin of error is multiplied by √(2)· The margin of error is multiplied by 0.5. The margin of error is multiplied by 2.
A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 35°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 39°. At that time, what is the distance between him and his friend
Answer:
322.21 feet
Step-by-step explanation:
Flying rate = 6 ft/s
Angle of depression from his balloon to a friend's car= 35 °
One and half minutes later, he observed the angle of depression to be 39°
Time = 1 mins 1/2 seconds
= 3/2 mins
= 3/2 * 60
= 3*30
= 90 secs
Speed = distance /time
Distance = speed * time
= 6*90
= 540 ft
The angle on the ground = 180° - 35° - 39°
= 180° - 74°
= 106°
Let the distance between him and his friend be x
Using sine rule
x/sin 35 = 540/sin 106
x = (540sin 35) / sin 106
x = 322.21ft
A survey found that women's heights are normally distributed with mean 63.6 in and standard deviation 2.3 in. A branch of the military requires women's heights to be between 58 in and 80 in.
a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
a. The percentage of women who meet the height requirement is
(Round to two decimal places as needed.)
Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
A. No, because the percentage of women who meet the height requirement is fairly small.
B. Yes, because the percentage of women who meet the height requirement is fairly large.
C. Yes, because a large percentage of women are not allowed to join this branch of the military because of their height.
D. No, because only a small percentage of women are not allowed to join this branch of the military because of their height.
b. For the new height requirements, this branch of the military requires women's heights to be at least ___ in and at most ___ in.
(Round to one decimal place as needed.)
Answer:
Your answer id D.
Step-by-step explanation:
PLEASE MARK BRAINLIEST!!!
What property is shown in step 8?
D??
I think, because its in brackets, you multiply? not too sure though!
An exam consists of 47 multiple-choice questions. Each question has a choice of five answers, only one of which is correct. For each correct answer, a candidate gets 1 mark, and no penalty is applied for getting an incorrect answer. A particular candidate answers each question purely by guess-work. Using Normal approximation to Binomial distribution with continuity correction, what is the estimated probability this student obtains a score greater than or equal to 10?
Calculate the mean and standard deviation for the binomial distribution, adjust for continuity correction, find the z-score, and use the standard normal distribution to estimate the probability of scoring at least 10 correct out of 47 purely guessed multiple-choice questions.
Explanation:To estimate the probability of a student guessing and scoring at least 10 correct answers out of 47 multiple-choice questions using normal approximation to binomial distribution, we start by finding the mean ( extmu) and standard deviation ( extsigma) of the binomial distribution. Since each question has five options, the probability of guessing a question correctly (p) is 1/5, and the probability of guessing incorrectly (q) is 4/5.
The expected number of correct answers (mean) is extmu = np = 47(1/5) = 9.4, and the variance ( extsigma^2) is npq = 47(1/5)(4/5) = 7.52. So, the standard deviation is extsigma = extsqrt{7.52}.
To apply the continuity correction, we adjust the score of 10 down by 0.5, giving us a z-score. The z-score is calculated by (X - extmu)/ extsigma, where X is the adjusted score. Finally, we use the standard normal distribution to find the probability associated with this z-score, which will yield the likelihood of the student scoring at least 10 correct answers.
I need help with this problem
Answer:
65.56°
Step-by-step explanation:
We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them
That is let p and q be any two vectors and A be the angle between them
So, p·q=|p|*|q|*cosA
⇒[tex]cosA=\frac{u.v}{|u||v|}[/tex]
Given u=-8i-3j and v=-8i+8j
[tex]|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544[/tex]
[tex]|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137[/tex]
let A be angle before u and v
therefore, [tex]cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}[/tex]
⇒[tex]A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56[/tex]
Therefore angle between u and v is 65.56°
The value of a car is 18,500. It loses 10.3% of its value every year. Find the approximate monthly decrease in value. Round your answer to the nearest tenth
Final answer:
The value of a car worth $18,500 that loses 10.3% annually decreases by approximately $158.8 per month.
Explanation:
To find the approximate monthly decrease in value of a car worth $18,500 that loses 10.3% of its value every year, we first calculate the annual decrease and then divide by 12 to get the monthly decrease.
The annual decrease is calculated as 10.3% of $18,500, which is:
0.103 imes $18,500 = $1,905.50 per year.
To find the monthly decrease, we divide the annual decrease by 12:
$1,905.50 \/ 12 \\approx $158.79 per month.
Therefore, the car's value decreases approximately $158.8 per month.
Determine the value of x so that the line containing the given points is parallel to another line whose slope is also given.
12. A(x, 5) and B(-4,3)
slope = -1
13. R(3, -5) and S(1, x)
slope = -2
Answer:
Step-by-step explanation:
12) A(x, 5) and B(-4,3)
slope = -1
We want to determine the value of x so that the line AB is parallel to another line whose slope is given as -1
Slope, m is expressed as change in y divided by change in x. This means
Slope = (y2 - y1)/(x2 - x1)
From the information given
y2= 3
y1 = 5
x2 = -4
x1 = x
Slope = (3-5) / (-4-x) = -2/-4-x
Recall, if two lines are parallel, it means that their slopes are equal. Since the slope of the parallel line is -1, therefore
-2/-4-x = -1
-2 = -1(-4-x)
-2 = 4 + x
x = -2 - 4 = - 6
x = -6
13) R(3, -5) and S(1, x)
slope = -2
We want to determine the value of x so that the line RS is parallel to another line whose slope is given as -2
Slope = (y2 - y1)/(x2 - x1)
From the information given
y2= x
y1 = -5
x2 = 1
x1 = 3
Slope = (x - -5) / (1 - 3) = (x+5)/-2
Since the slope of the parallel line is -2, therefore
(x+5)/-2 = -2
x + 5 = -2×-2
x + 5 = 4
x = 4 - 5 = - 1
A random sample selected from an infinite population is a sample selected such that each element selected comes from the same _____________ and each element is selected __________________ . Group of answer choices
Answer: population; independently
Step-by-step explanation:
A random sample selected from an infinite population is a sample selected such that each element selected comes from the same *population* and each element is selected *independently*.
Each element in a random sample is selected independently and comes from the same population, with the principle goal of achieving representation and independence in sample selection.
Explanation:A random sample selected from an infinite population is a sample selected such that each element selected comes from the same population and each element is selected independently. The crux of random sampling theory is ensuring each member of the population has an equal chance of being selected, maintaining the independence of each selection. For example, if a student wanted to make a study group out of a class of 31 students, she could write each student's name on a separate piece of paper, put all the names in a hat, and pick out three without looking. This is a classic case of simple random sampling, each selection being representative and independent.
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Please Help
What is the solution for x in the equation?
9 − 10x = 2x + 1 − 8x
Answer:
x=2
Step-by-step explanation:
9-10x=2x+1-8x
9-10x=1-6x
8=4x
x=2
Combine like terms in the equation 9 − 10x = 2x + 1 − 8x to simplify it to 9 − 10x = −6x + 1. Rearranging the equation to -4x = -8 and dividing by -4, we find that x = 2.
Explanation:The solution for x in the equation 9 − 10x = 2x + 1 − 8x can be found by first combining like terms on both sides of the equation.
On both the left and right side, the terms involving x are −10x and 2x − 8x respectively. After combining, the equation simplifies to 9 − 10x = −6x + 1.
Then, we can solve for x by shifting terms around. Getting all x-terms on one side and constant terms on the other side, we get -10x + 6x = 1 - 9. This simplifies to -4x = -8.
Finally, dividing the equation by -4 which is the coefficient of x, we obtain the solution x = 2.
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A stockbroker trades shares she does not own with an obligation of later repayment, and in the hope that the price of traded shares will fall. She then repays share debt with shares purchased at a lower price and pockets the spread between initial share price and repayment price. This attempt to profit from a falling stock price is known as ___________.
Answer:
short selling
Step-by-step explanation:
Short-selling is a process when a shareholder buys shares and sold them instantly and expecting that he or she will be able to have them at cheaper price later on .After then seller transfer them to lender from where he/she borrow the stock and after keep the difference as a income.
Short selling is a simple idea in which a shareholder borrow a stock, sells the stock to other person, then again buys that stock to give it back to a lender. Short sellers believe that the stock they have sell is going to fall in value
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion, so we assume p=.5. You would like to be 99% confident that you estimate is within 0.2% of the true population proportion. How large of a sample size is required?
Answer:
416025
Step-by-step explanation:
For confidence interval of 99%, the range is (0.005, 0.995). Using a z-table, the z-score for 0.995 is 2.58.
Margin of error = 0.2% = 0.002.
Proportion is unknown. So, worse case proportion is 50%. p = 50% = 0.5.
\\ [tex]n = \left(\frac{\texttt{z-score}}{\texttt{margin of error}} \right )^2\cdot p\cdot (1-p) \\ = \left(\frac{2.58}{0.002} \right )^2\cdot 0.5\cdot (1-0.5)=416025[/tex]
So, sample size required is 416025.
Franks electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used. Approximately how many kilowatt-hours of electricity did frank use in March?
Answer:
I got 469.8 kilowatt-hours. I got this by taking the total of Frank's bill, which was $85.78, and subtracting the flat monthly fee of $20.00. I did this because I need to find out the number of kilowatt-hours Frank used. Then, I divided $65.78 by $0.14 since that is the price per kilowatt-hour and got about 469.8 kilowatt-hours used by Frank.
The power utilised by frank in the month of march is 470 kilowatts - per hour.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Franks's electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used.
The equation will be written as,
B = 20 + 0.14K
85.78 = 20 + 0.14k
k = ( 80.78 - 20 ) / 0.14
K = 65.78 / 0.14
K = 470 Kilowatt-hour
Therefore, the power utilised by frank in the month of march is 470 kilowatts - per hour.
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A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:
Brown 22
Red 22
Yellow 22
Orange 12
Green 15
Blue 15
Find the 95% confidence interval for the proportion of yellow M&Ms in that bag
Answer: 95% confidence interval for the proportion of yellow is (0.125,0.275).
Step-by-step explanation:
Since we have given that
n = 22+22+22+12+15+15=108
x = yellow = 22
So, [tex]\hat{p}=\dfrac{22}{108}=0.20[/tex]
We need to find the 95% confidence interval.
So, z = 1.96
So, Interval would be
[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.20\pm 1.96\times \sqrt{\dfrac{0.2\times 0.8}{108}}\\\\=0.20\pm 0.075\\\\=(0.20-0.075, 0.20+0.075)\\\\=(0.125, 0.275)[/tex]
Hence, 95% confidence interval for the proportion of yellow is (0.125,0.275).
At a restaurant you order a lunch that costs $6.50 and a beverage that costs $1.50.You leave a 20% tip and the sales tax is 7%.What is the cost of the meal
Answer:8.45
Step-by-step explanation:
Which equation shows how (-10, 8) can be used to write the
equation of this line in point-slope form?
oy-8 = -0.15(x - 10)
y + 8 = -0.15(x - 10)
oy-8= -0.2(x + 10)
y + 8 = -0.2(x - 10)
For this case we have that by definition, the equation of a line in the point-slope form is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
m: It is the slope of the line
[tex](x_ {0}, y_ {0})[/tex]: It is a point that belongs to the line
According to the statement we have the following point:
[tex](x_ {0}, y_ {0}): (- 10,8)[/tex]
Substituting we have:
[tex]y-8 = m (x - (- 10))\\y-8 = m (x + 10)[/tex]
Thus, the most appropriate option is option C. Where the slope is[tex]m = -0.2[/tex]
Answer:
Option C
v11.1% complete This is a Single Choice Question; skip ahead to question content A B C D E Confirm The label on a ceiling lighting fixture warns you to use a lightbulb of 60 watts or less. The voltage to the lightbulb is 120 volts. An intern calculated how much amperage a bulb of the maximum allowed wattage will draw. You are checking her work, shown below. If there is an error, what is the first step that has an error, and why is it an error? Step 1 volts × amps = watts write down formula Step 2 120 × ? = 60 fill in what is known Step 3 It looks like 0.5 will work 120 × 0.5 = 60 check Step 4 amps = 0.5 Step 1, because the formula should be amps = watts ÷ volts. Step 2, because the question mark should be by itself on the right side of the equation. Step 3, because you can’t just guess at a solution. Step 4, because the answer in the previous step was 60. There is no error. Report Content Errors © 2019 by ACT, Inc. All rights reserved. Terms of UsePrivacy PolicyContact Support
Answer:
There is no error
Step-by-step explanation:
While it is not necessary to guess an answer, because the answer can be calculated using the properties of equality, guessing is a legitimate solution method actually taught in (some) schools these days.*
The equation is properly written, data properly filled in, and the solution properly verified. There is no error.
_____
* What doesn't seem to be taught in US schools are methods of refining an incorrect guess. These are actually well-developed, and are legitimate ways to get to a good answer.
Final answer:
The correct formula to find the current is I = P ÷ V, which gives 0.5 amps for a 60W lightbulb at 120V. The error in the calculation is in Step 1 where the formula was not rearranged to solve for current.
Explanation:
The calculation for determining the current drawn by a 60-watt (W) lightbulb with a voltage supply of 120 volts (V) requires use of the power formula, which relates power (P), voltage (V), and current (I): P = V × I, where P stands for power in watts, V for voltage in volts, and I for current in amperes (amps).
In this scenario, the correct step to find the amperage of the bulb would be to rearrange the power formula to solve for current (I): I = P ÷ V. By inserting the known values, we get I = 60 W ÷ 120 V, which simplifies to I = 0.5 amps.
The error in the intern's calculation is in Step 1, as the formula written should be amps = watts ÷ volts, not volts × amps = watts as it needs to be rearranged to solve for the unknown current.
Which statement can be used to prove that a given parallelogram is a rectangle? A) The opposite sides of the parallelogram are congruent. B) The diagonals of the parallelogram are congruent. C) The diagonals of the parallelogram bisect the angles. D) The opposite angles of the parallelogram are congruent.
Answer:
B) The diagonals of the parallelogram are congruent.
Step-by-step explanation:
Since, If the diagonals of a parallelogram are equal in length, then is the parallelogram a rectangle.
For proving this statement.
Suppose PQRS is a parallelogram such that AC = BD,
In triangles ABC and BCD,
AB = CD, ( opposite sides of parallelogram )
AD = CB, ( opposite sides of parallelogram )
AC = BD ( given ),
By SSS congruence postulate,
[tex]\triangle ABC\cong \triangle BCD[/tex]
By CPCTC,
[tex]m\angle ABC = m\angle BCD[/tex]
Now, Adjacent angles of a parallelogram are supplementary,
[tex]\implies m\angle ABC + m\angle BCD = 180^{\circ}[/tex]
[tex]\implies m\angle ABC + m\angle ABC = 180^{\circ}[/tex]
[tex]\implies 2 m\angle ABC = 180^{\circ}[/tex]
[tex]\implies m\angle ABC = 90^{\circ}[/tex]
Since, opposite angles of a parallelogram are congruent,
[tex]\implies m\angle ADC = 90^{\circ}[/tex]
Similarly,
We can prove,
[tex]m\angle DAB = m\angle BCD = 90^{\circ}[/tex]
Hence, ABCD is a rectangle.
That is, OPTION B is correct.
Answer:
B
Step-by-step explanation:
I just took it
Trixie has 3/4 packages on marigold seeds he plants 1/6 of those seeds in this garden and divides the rest equally into 10 fraction packages of seed is planted in each flower pot
Answer:
[tex]\frac{7}{120}[/tex] of seed planted in each flower pot.
Step-by-step explanation:
Given:
Total number of marigold seeds packages Trixie have= ¾
Number of seeds Trixie planted in the garden= 1/6
Number of fraction into which Trixie dived the remaining seed =10
To Find:
Fraction of seed planted in each flower pot=?
Solution:
Seed left after planting 1/6 of seeds in the garden = [tex]\frac{3}{4}-\frac{1}{6}[/tex]
=>[tex]\frac{18-4}{24}[/tex]
=>[tex]\frac{14}{24}[/tex]
=>[tex]\frac{7}{12}[/tex]
Now Trixie divides these remaining seeds into 10 parts
=>[tex]\frac{\frac{7}{12} }{10}[/tex]
=>[tex]\frac{7}{12}\times\frac{1}{10}[/tex]
=>[tex]\frac{7}{120}[/tex]