since we need to round up to the next largest minute, the minimum class width is 7 minutes.
To determine the minimum class width in minutes, we first need to calculate the total range of the data, which is the difference between the maximum and minimum values. In this case, the total range is 130 - 14 = 116 minutes.
Next, we divide the total range by the number of classes we have chosen, which is 17. This gives us the approximate class width, which is 6.82 minutes. However, since we need to round up to the next largest minute, the minimum class width is 7 minutes.
Choosing an appropriate class width is important in constructing a frequency distribution. If the class width is too large, we may lose important information about the distribution of the data. On the other hand, if the class width is too small, we may end up with too many classes, making it difficult to interpret the results.
In this case, we have chosen 17 classes, which is a reasonable number for the range of data we have. However, it is also important to consider the nature of the data and the purpose of the analysis when choosing the number of classes and the class width. For example, if we were interested in identifying outliers or extreme values, we may choose a smaller class width to better capture these values.
Overall, the choice of class width is an important consideration in constructing a frequency distribution, and it should be chosen based on the characteristics of the data and the goals of the analysis
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Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of
�
x that support your conclusion.
�
−
3
=
x−3=
−
10
−10
Answer:
There is only one solution.
The solution is -7
Step-by-step explanation:
x - 3 = -10 Add 3 to both sides
x - 3 + 3 = -10 + 3
x = -7
Helping in the name of Jesus.
Consider the vector function given below.
Do the following.
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
(b) Find the curvature.
(a) The unit tangent and unit normal vectors T(t) and N(t) is ⟨-sin t, 0, -cos t⟩.
(b) The curvature is 3/(9 cos² t + 4 + 9 sin² t)
To find T(t), we first take the derivative of r(t) with respect to t, which gives us the velocity vector v(t) = ⟨3 cos t, 2, -3 sin t⟩. Then, we divide this vector by its magnitude to get the unit tangent vector T(t) = v(t)/||v(t)||, where ||v(t)|| is the magnitude of v(t). This gives us:
T(t) = ⟨(3/√(9 cos² t + 4 + 9 sin² t)), 2/√(9 cos² t + 4 + 9 sin² t), (-3/√(9 cos² t + 4 + 9 sin² t)))⟩
To find N(t), we take the derivative of T(t) with respect to t, and divide by the magnitude of this derivative:
N(t) = T'(t)/||T'(t)||, where T'(t) is the derivative of T(t) with respect to t.
After some algebraic simplification, we find that T'(t) = ⟨-3 sin t, 0, -3 cos t⟩, so
||T'(t)|| = 3, and
N(t) = ⟨-sin t, 0, -cos t⟩.
Now that we have the unit tangent and unit normal vectors, we can move on to finding the curvature, denoted k(t). Specifically, the curvature is given by the formula:
k(t) = ||T'(t)||/||v(t)||²
where ||T'(t)|| is the magnitude of the derivative of the unit tangent vector, and ||v(t)||² is the square of the magnitude of the velocity vector.
We already found ||T'(t)|| and ||v(t)|| in the previous steps, so we can plug these values into the formula to get:
k(t) = 3/(9 cos² t + 4 + 9 sin² t)
This gives us the curvature for every value of t.
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Complete Question:
Consider the vector function given below. r ( t ) = ⟨ 3 sin t , 2 t , 3 cos t ⟩ Do the following:
(a) Find the unit tangent and unit normal vectors, T(t) and N(t).
(b) Find the curvature, k(t).
The equation of a line passing through points (-2,-4) and (4,4) is
The equation of the line passing through the points (-2,-4) and (4,4) is y = (4/3)x - 4/3.
To find the equation of the line passing through the points (-2,-4) and (4,4), we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where:
m is the slope of the line
(x1, y1) are the coordinates of one of the points on the line
First, we need to find the slope of the line using the two points:
m = (y2 - y1)/(x2 - x1)
m = (4 - (-4))/(4 - (-2))
m = 8/6
m = 4/3
Now, we can choose either point to plug into the equation. Let's choose (-2,-4):
y - (-4) = (4/3)(x - (-2))
Simplifying the equation:
y + 4 = (4/3)(x + 2)
Distributing the 4/3:
y + 4 = (4/3)x + (8/3)
Subtracting 4 from both sides:
y = (4/3)x + (8/3) - 4
Simplifying:
y = (4/3)x - 4/3
Therefore, the equation of the line passing through the points (-2,-4) and (4,4) is y = (4/3)x - 4/3.
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A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 4%. What will the area be after 10 years Use the calculator provided and round your answer to the nearest square kilometer
After 10 years, the area of the forest will be approximately 1384 km² (rounded to the nearest square kilometer) assuming the decrease in area is consistent at 4% each year.
The problem provides us with the initial area of the forest which is 2100 km². It also tells us that each year the area of the forest decreases by 4%. We need to find out what will be the area of the forest after 10 years.
The initial area of the forest is 2100 km². After the first year, the area will decrease by 4%, which means it will be 0.96 times the original area:
2100 km² x 0.96 = 2016 km²
After the second year, the area will decrease again by 4%, which means it will be 0.96 times the area from the first year:
2016 km² x 0.96 = 1935.36 km²
Continuing this pattern for 10 years, the area of the forest will be:
2100 km² x [tex](0.96)^10[/tex] = 1364.59 km²
Rounding this to the nearest square kilometer, the area of the forest after 10 years will be approximately 1365 km².
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John's employer withheld $13,956. 95 in federal income tax. After completing his return, John determined that his tax is $11,874. 82. Will John get a refund or does he owe the government money?
John will receive a tax refund from the government because his employer withheld more taxes than he actually owes, resulting in an overpayment. The amount of John's refund is $2,082.13.
In this problem, John's employer withheld $13,956.95 in federal income tax over the course of the year. When John completed his tax return, he determined that his actual tax liability for the year was only $11,874.82. This means that John's employer withheld more than the amount of tax that John actually owes, resulting in an overpayment of taxes.
To determine whether John will receive a refund or owe the government money, we need to compare the total tax withheld to the amount of tax owed. If the total tax withheld is greater than the tax owed, then John will receive a refund. If the tax owed is greater than the total tax withheld, then John will owe the government money.
In this case, John's refund can be calculated as the difference between the total tax withheld and the tax owed:
Refund = Total Tax Withheld - Tax Owed
Refund = $13,956.95 - $11,874.82
Refund = $2,082.13
Since the refund amount is positive, it means that John overpaid his taxes and is entitled to receive a refund from the government.
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a study is to be conducted to investigate the proportion of college professors who wear eyeglasses. (a) in a random sample of 250 professors, 139 of them wore eyeglasses. from this information, generate an 88% confidence interval (using tables) for the proportion of professors who wear eyeglasses.
the 88% confidence interval for the proportion of college professors who wear eyeglasses is (0.487, 0.625).
To generate an 88% confidence interval for the proportion of college professors who wear eyeglasses, we can use the normal approximation to the binomial distribution. The formula for the confidence interval is:
p ± z*√(p(1-p)/n)
where p is the sample proportion, z is the z-score corresponding to the desired level of confidence (88% in this case), and n is the sample size.
First, we need to calculate the sample proportion:
p = 139/250 = 0.556
Next, we need to find the z-score corresponding to the 88% confidence level. We can use a standard normal distribution table or calculator to find this value. For an 88% confidence level, the z-score is approximately 1.553.
Now, we can substitute these values into the formula to calculate the confidence interval:
0.556 ± 1.553*√(0.556(1-0.556)/250)
Simplifying the expression gives us:
0.556 ± 0.069
the 88% confidence interval for the proportion of college professors who wear eyeglasses is (0.487, 0.625).
This means that we are 88% confident that the true proportion of college professors who wear eyeglasses is between 0.487 and 0.625. In other words, if we were to repeat this study multiple times, we would expect the true proportion to fall within this interval in 88% of the cases.
It is important to note that confidence intervals are a range of plausible values for the population parameter (in this case, the proportion of college professors who wear eyeglasses), and do not provide definitive answers. Therefore, it is necessary to interpret the interval in the context of the study and the research question.
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suppose that the mean daily viewing time of television is hours per household. use a normal probability distribution with a standard deviation of hours to answer the following questions about daily television viewing per household.
(a) What is the probability that a household views television between 5 and 11 hours a day? (Round your answer to four decimal places.) (b) How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households? (Round your answer to two decimal places.) (c) What is the probability that a household views television more than 3 hours a day? (Round your answer to four decimal places.)
The probability that a household watches more than 3 hours of television a day is 0.0478.
The mean daily viewing time of television is 8 hours per household. Use a normal probability distribution with a standard deviation of 3 hours to answer the following questions about daily television viewing per household.
(a) Probability that a household views television between 5 and 11 hours a day:P(5 < x < 11) = P(z < (11-8)/3) - P(z < (5-8)/3) = P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826(b) Hours of television viewing must a household have in order to be in the top 3% of all television viewing households:
The top 3% of all households correspond to z = 1.88. Therefore, the number of hours that a household must watch television to be in the top 3% is:1.88 = (x - 8) / 3x - 8 = 5.64x = 13.64
(c) Probability that a household views television more than 3 hours a day:P(x > 3) = P(z < (3-8)/3) = P(z < -5/3) = 0.0478.the probability that a household watches more than 3 hours of television a day is 0.0478.
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A vendor purchases 50 dozen bananas for $600. Five if them got rotten and could not be sold. At what price should the vendor sell the remaining of them to get a profit of 20%?
Please help
The vendοr shοuld sell the remaining 595 bananas fοr a tοtal price οf 595 x $1.20 = $714.
What is Prοfit and Lοss?In mathematics, prοfit is the amοunt by which revenue exceeds the cοst οf gοοds sοld, while lοss is the amοunt by which cοst exceeds revenue.
There are 50 dοzen bananas, which means there are 50 x 12 = 600 bananas in tοtal.
Five bananas gοt rοtten and cοuld nοt be sοld, sο the vendοr has 600 - 5 = 595 bananas tο sell.
The cοst price οf 50 dοzen bananas is $600, which means the cοst price οf οne dοzen bananas is $600/50 = $12.
The cοst price οf οne banana is $12/12 = $1.
Tο get a prοfit οf 20%, the vendοr needs tο sell the bananas at a price that is 20% higher than the cοst price.
The selling price οf οne banana is $1 + ($1 x 20%) = $1.20.
Therefοre, the vendοr shοuld sell the remaining 595 bananas fοr a tοtal price οf 595 x $1.20 = $714.
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Given the vectors w=<-5,3> and z=<1,4>, find the results of the vector subtractions
-w-z=
z-w=
w-z=
Answer:
To subtract vectors, we subtract corresponding components.
Step-by-step explanation:
-w = <-(-5), -3> = <5, -3>
-w-z = <5, -3> - <1, 4> = <5-1, -3-4> = <4, -7>
z-w = <1, 4> - <(-5), -3> = <1+5, 4+3> = <6, 7>
w-z = <-5, 3> - <1, 4> = <-5-1, 3-4> = <-6, -1>
raise b to the 2nd power, then find the quotient of the result and 8
Do not simplify any part of the expression.
pls help
The expression "raise b to the 2nd power" means to multiply b by itself, which can be written as [tex]b^2[/tex]. The expression [tex](b^2)/8[/tex] represents this quotient.
When we say "raise b to the 2nd power", it means we are squaring b, which is equivalent to multiplying b by itself. So, [tex]b^2[/tex] represents the result of multiplying b by itself.
Next, the phrase "find the quotient of the result and 8" means we need to divide [tex]b^2[/tex] by 8. Dividing [tex]b^2[/tex] by 8 gives us the expression [tex](b^2)/8[/tex], which represents the quotient we are looking for. We do not simplify the expression any further, because the instructions say to "not simplify any part of the expression."
So, [tex](b^2)/8[/tex] is the final answer. This expression is still in fraction form, and it can be useful to keep it in this form if we are using it to solve a larger problem or if we want to keep the answer as precise as possible. If we want to convert it to decimal form, we can use a calculator to divide [tex]b^2[/tex] by 8.
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Which is greater 3.515 or 3 107/125
The number 3 107/125 is greater than 3.151.
What distinguishes an incοrrect fractiοn frοm a mixed number?A number that is stated as bοth a whοle number and a fractiοn, such 3 1/2, is referred tο as a mixed number. A fractiοn, such as 7/2, that has the numeratοr higher than οr equal tο the denοminatοr is referred tο as an imprοper fractiοn. Yοu must multiply the whοle number by the denοminatοr, add the numeratοr, and then place it οver the οriginal denοminatοr in οrder tο cοnvert a mixed number tο an imprοper fractiοn.
Divide the numeratοr by the denοminatοr and then write the residue as a fractiοn with the same denοminatοr tο turn an imprοper fractiοn intο a mixed number.
The given numbers are: 3.515 οr 3 107/125.
Cοnvert 3 107/125 tο a decimal.
3 107/125 = (3 * 125 + 107)/125 = 482/125 = 3.856
Cοmparing the twο 3.515 and 3.856 we οbserve that 3.856 is greater than 3.515.
Hence, the number 3 107/125 is greater than 3.151.
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The table below shows the number of homes in a certain city which have computers, C(x), as a function of x, the number of years since 1990.
Which function best models this set of data?
A.
C(x) = 29,800x + 745,000
B.
C(x) = 745,000(1.04)x
C.
C(x) = 1.04(745,000)x
D.
C(x) = 30,992x + 743,808
The best function that models this set of data is option B. C(x) = 745000 * [tex](1.04)^2[/tex]
What is exponential?Exponential refers to a mathematical operation or function involving a constant called the base, raised to a power that is a variable, which is usually represented by the letter x.
According to question:The best function that models this set of data is option B.
C(x) = 745000 [tex]* (1.04) ^ x[/tex]
This is an exponential function that models the growth of the number of homes with computers over time. The base of the exponential function is 1.04, which indicates that the number of homes with computers is growing at a rate of 4% per year.
We can verify this by checking the values in the table.
When x = 1,
C(1) = 745000 * [tex](1.04) ^ 1[/tex]
C(1) = 774800
When x = 2,
C(2) = 745000 * [tex](1.04) ^ 2[/tex]
C(2) = 805792
We can see that the function closely matches the given data points. Therefore, option B is the best function that models this set of data.
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In excerise 3-8 find sin D ,sin E , Cos D write each answer as a fraction and as a decimal rounded to four places image is below giving brainliest to whoever gets it right
sin D is 4/5 or 0.8, sin E is 3/5 or 0.6, and cos D is 3/5 or 0.6.
How may a fraction be changed into a decimal?Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal. Nothing else needs to be said!
Divide the opposite side by the hypotenuse to find sin D and sin E; similarly, divide the adjacent side by the hypotenuse to find cos D.
opposite/hypotenuse = 4/5 = 0.8 sin D (rounded to 4 decimal places)
opposite/hypotenuse = 3/5 = 0.6 sin E (rounded to 4 decimal places)
adjacent/hypotenuse = 3/5 = 0.6 cos D (rounded to 4 decimal places)
The resulting values for sin D, sin E, and cos D are 4/5, 0.8, 3/5, and 0.6 respectively.
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5. The following data set represents the number
of broken cookies in a test of eight boxes of Girl
Scout Cookies.
0,1,1,2,4,4,6,7
Mean:?
Median:?
Answer:
Mean 3.125
Median 3
Step-by-step explanation:
Ella finished a bike race in 22.6 minutes. Miranda finished the race 9 and 1/10 minutes faster than Ella finished it. How many minutes did it take Miranda to finish the race?
Miranda took 28.5 minutes to finish the race according to the give time about the race.
Given,
Ella finished a bike race = 37.6 minutes
Let 'x' be the time taken for finishing the bike race.
Miranda finished the race sooner than Ella = [tex]9 \frac{1}{10}[/tex] = 91/10
Miranda finished the race sooner than Ella = 9.1 min
Now, we need to find the minutes did it take Miranda to finish the race.
From the statement, 9.1 minutes sooner than Ella finished it while Ella finished the same bike race in 37.6 minutes.
So, from the expression
time taken by Miranda to finish the race:
[tex]Miranda[/tex] [tex]finished[/tex] [tex]the race[/tex] = (Ella finished a bike race - 9.1)
x = 37.6 - 9.1
x= 28.5 minutes
Therefore, Miranda finished the bike race in 28.5 minutes.
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I roll a fair die twice and obtain two numbers. X_1 = result of the first roll, X_2 = result of the second roll. a. Find the probability that X_2 = 4. b. Find the probability that X_1 + X_2 = 7. c. Find the probability that X_1 notequato 2 and X_2 greaterthanorequalto 4.
The (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)Out of these possible outcomes, there are only 11 such outcomes where X1 ≠ 2 and X2 ≥ 4: (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5)P(X1 ≠ 2 and X2 ≥ 4) = 11/36
Probability that X2 = 4:Since we rolled a fair dice, so the probability of getting a number 4 on the dice would be 1/6.P(X2 = 4) = 1/6b) Probability that X1 + X2 = 7:Now we know that the sum of the outcomes of two fair dices rolled is 7, this can be obtained by the following possibilities:(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)Since each outcome is equally likely, so each of these outcomes has a probability of 1/36.P(X1 + X2 = 7) = 6/36 = 1/6c) Probability that X1 ≠ 2 and X2 ≥ 4:
If we look at the possible outcomes of X1 and X2 then we have the following possibilities:(1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)Out of these possible outcomes, there are only 11 such outcomes where X1 ≠ 2 and X2 ≥ 4: (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5)P(X1 ≠ 2 and X2 ≥ 4) = 11/36
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What is the five number summary of the following data set? 68, 162, 163, 167, 167, 168, 168, 169, 170, 178, 180, 180, 182, 182, 185. Identify any outliers.
The data set contains no outliers since all of the values are within the bounds of 148.5 and 198.5.
The following is the five-number summary of the given data set 68, 162, 163, 167, 167, 168, 168, 169, 170, 178, 180, 180, 182, 182, 185. Identify any outliers.
The five-number summary of the data set are as follows:Minimum value = 68 First quartile = 167Median = 169Third quartile = 180Maximum value = 185 We use the following formula to find outliers in the data set:IQR = Q3 - Q1 Here, Q1 and Q3 are the first and third quartiles, respectively.So,IQR = 180 - 167IQR = 13 To find the lower and upper bounds, we use the following formulas:Lower bound = Q1 - (1.5 × IQR)Upper bound = Q3 + (1.5 × IQR)Here, the lower bound and upper bound values are calculated as follows:Lower bound = 167 - (1.5 × 13)Lower bound = 148.5Upper bound = 180 + (1.5 × 13)Upper bound = 198.5
Now, any values that are less than the lower bound or greater than the upper bound are considered outliers.The data set contains no outliers since all of the values are within the bounds of 148.5 and 198.5.
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Suppose sin t =5/7
and cos t < 0. Find each of the following (exact values):
cos t =
tan t =
csc t =
sec t =
cot t =
Suppose sin t = 5/7 and cos t < 0. The exact value :
cos t = -√(1 - (5/7²)
tan t = -(5√6)/12
csc t =7/5
sec t = -(7√6)/12
cot t = -12/(5√6)
Since sin t = 5/7 and cos t < 0, we can use the Pythagorean identity cos² t + sin² t = 1 to find cos t:
cos² t + (5/7)²= 1
cos² t = 1 - (5/7)²
cos t = -√(1 - (5/7)²) (since cos t < 0)
Next, we can use the definitions of the trigonometric functions to find the remaining values:
tan t = sin t / cos t = (5/7) / (-√(1 - (5/7)^2)) = -5/√24 = -(5√6)/12
csc t = 1/sin t = 7/5
sec t = 1/cos t = -1/√(1 - (5/7)²) = -7/√24 = -(7√6)/12
cot t = 1/tan t = -12/(5√6)
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Zayden painted 3/4 of a picture in 2 1/2 hours. How many can he paint in 5 hours?
Answer:
trust me on this it's 1 1/2
Step-by-step explanation:
Please help I’ll give brainliest
Answer:
x1 = √3/3 - 1 or -0.42
x2 = -√3/3 - 1 or -1.58
Step-by-step explanation:
(3x + 3)^2 - 42 = -39
9x^2 + 18x + 9 - 42 + 39 = 0
9x^2 + 18x + 6 = 0
divide both sides by 3:
3x^2 + 6x + 2 = 0
Using quadratic equation
x = [-b ± √(b^2 - 4ac)] / 2a
x = [-6 ± √(6^2 - 4(3)(2))] / 2(3)
x = [-6 ± √(36 - 24)] / 6
x = [-6 ±√12] / 6
x = [-6 ±2√3] / 6
x = [-3 ±√3] / 3
x = -3/3 ± √3/3
x = ± √3/3 - 3/3
x1 = √3/3 - 1 = -0.42
x2 = -√3/3 - 1 = -1.58
Hope this help
Identify the inside function, u = g(x), and the outside function, y = f(u). y = (x^2 – 7x + 9)^4 u = g(x) = y = f(u) =
x = 2, y = 81.
u = g(x) = x^2 – 7x + 9
y = f(u) = u^4.
The inside function and outside function in a composite function can be identified by examining the structure of the function. The inside function is the function that is being acted upon by the outside function. In this case, the inside function is u = g(x) = x^2 – 7x + 9, and the outside function is y = f(u) = u^4.
To find the value of y for a given value of x, we first need to find the value of u by substituting the value of x into the inside function. Then, we can substitute the value of u into the outside function to find the value of y.
For example, if x = 2, then:
u = g(x) = x^2 – 7x + 9 = 2^2 – 7(2) + 9 = -3
y = f(u) = u^4 = (-3)^4 = 81
So, when x = 2, y = 81.
In conclusion, the inside function is u = g(x) = x^2 – 7x + 9, and the outside function is y = f(u) = u^4. To find the value of y for a given value of x, we first need to find the value of u by substituting the value of x into the inside function, and then substitute the value of u into the outside function to find the value of y.
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The average price of 1 acre of land in Berrien County is currently $6236 and is increasing at an annual rate of 3.2%. Which function represents the estimated average price of 1 acre of land in Berrien County after x years?
The function that represents the estimated average price of 1 acre of land in Berrien County after x years can be written as:
[tex]$$P(x) = 6236(1 + 0.032)^x$$[/tex]
What is average?
In mathematics, the average, also known as the mean, is a measure of central tendency that represents the sum of a set of values divided by the number of values in the set.
The current price of 1 acre of land in Berrien County is $6236. After one year, the price of land will increase by 3.2%, which is equivalent to multiplying the current price by 1.032. After two years, the price will increase by another 3.2%, which is equivalent to multiplying the price after one year by 1.032, and so on.
Therefore, the function that represents the estimated average price of 1 acre of land in Berrien County after x years can be written as:
[tex]$$P(x) = 6236(1 + 0.032)^x$$[/tex]
where [tex]$P(x)$[/tex] is the estimated average price of 1 acre of land in Berrien County after [tex]$x$[/tex] years.
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∠
ABC = 74° and
x
= 4 cm. Find the length of AC. Give your answer rounded to 1 DP
If ∠ABC = 74° and x = 4 cm, then the length of AC is 4.8 cm.
We know that : AB = BC and ∠ABC = 74°,
So, ∠BCA = ∠BAC = (180° - ∠ABC)/2 = 53°.
Now, By using law of sines to find the length of AC.
The "Law-Of-Sines" states that in any triangle-ABC having sides a, b, and c and the opposite angles A, B, and C:
⇒ a/sin(A) = b/sin(B) = c/sin(C)
In this case, the side AC, is opposite angle C.
and we know that AB = x = 4 cm and ∠BAC = 53°,
So, We can write,
⇒ x/sin(53°) = AC/sin(74°)
⇒ AC = (x/sin(53°)) × sin(74°)
⇒ AC = (4/sin(53°)) × sin(74°)
⇒ AC ≈ 4.8 cm
Therefore, the length of AC is approximately 4.8 cm.
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The given question is incomplete, the complete question is
In the triangle ABC, ∠ABC = 74° and AB = x = 4 cm, and side AB = BC. Find the length of AC. Give your answer rounded to 1 DP.
demand for bottled water dispensed by the vending machines located in anderson student center is normally distributed with a mean of 100 bottles/day and standard deviation of 10 bottles/day. it costs $50.00 per order to replenish the vending machines and $0.91 to carry a bottle of water in inventory for one year. a) determine the target inventory (u) for maintaining a service level of 95% if the ust food services manages the inventory with a delivery lead- time of 4 days.
As per the given standard deviation, the target inventory level for maintaining a service level of 95% is 416.6 bottles of water.
To calculate the target inventory level, we need to take into account the delivery lead-time of 4 days. This means that we need to order enough inventory to cover the demand for the next 4 days, plus a safety stock to cover any unexpected variations in demand during that time. The safety stock is the extra inventory that we keep on hand to avoid stockouts.
To determine the target inventory level, we can use the following formula
u = d x L + z x σ x √(L)
where:
u = target inventory level
d = average daily demand (mean)
L = delivery lead-time (in days)
z = z-score corresponding to the desired service level (in this case, z = 1.65 for a service level of 95%)
σ = standard deviation of daily demand
Substituting the given values, we get:
u = 100 x 4 + 1.65 x 10 x √(4)
u = 400 + 16.6
u = 416.6
This means that we need to order enough inventory to cover the demand for the next 4 days, plus an extra 416.6 bottles to ensure that we don't run out of stock. The cost of carrying this inventory will be $0.91 per bottle per year.
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HELPPPP NUMBER 6!!!!!!!!!
Answer: x ∈ (10; +∞)
Step-by-step explanation:
Since x isn't the longest side of the triangle, it is one of the shorter ones, so the sum of two shorter sides must be greater than the longest side of the triangle (that's the property):
x + 16 ﹥ 26
x ﹥ 26 - 16
x ﹥ 10 (x ∈ N)
x ∈ (10; +∞)
Let's say, I chose x = 20
Since x can be on either shorter side of the triangle, she can make 2 triangles (I think)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."
What is variable?In mathematics, a variable is a symbol or letter that represents a quantity that can vary or change. Variables are used to express mathematical relationships and to represent unknown values.
For example, in the equation "y = 2x + 3", "x" and "y" are variables. "x" represents an unknown value that can vary, while "y" represents the output value that is dependent on the input value of "x".
Variables can take on different values depending on the context of the problem being solved. In algebra, variables are commonly used to solve equations and to represent unknowns in formulas.
It's important to note that variables are not the same as constants, which are values that remain fixed throughout a mathematical expression or equation.
by the question.
The appropriate measure of variability for the data represented by the box plot is the interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data, and it is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). In this case, the box extends from 17 to 21, with a line at 19, which means that Q1 is 17 and Q3 is 21. Therefore, the IQR is:
IQR = Q3 - Q1 = 21 - 17 = 4
So, the appropriate measure of variability for the data is the IQR, and its value is 4.
Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."
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The number less than zero are called
Answer:
Step-by-step explanation: Negatives because a number lower than 0 go like this -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 see? so the answer is Negatives.
statue of liberty is 305 feet tall. a model of the statue is 60 inches tall. what is the ratio of the height of the model
Thus, the ratio of height of the model of the statue of liberty is: 5.08 ft .
Explain about the ratio of the number?In maths, a ratio is the comparison of two like or corresponding values. Both a part-to-part and a part-to-whole comparison are possible.
Consider various types of information when computing a ratio. Analyze the ratio to see if it calls for a part-to-part or part-to-whole ratio.
Ratio does not imply multiplication. Fractions can be used to represent ratios, and the fraction's simplest form is division. Divided means a ratio. The ratio 1 to 3, for example, is 1 divided by 3.
Given data:
Height statue of liberty = 305 feet
Height of model of the statue = 60 inches.
Thus, Ratios of their heights.
Height statue of liberty/ Height of model of the statue = 305 feet / 60 inches.
= 5.08 ft / 1 in
Thus, the ratio of the height of the given model of the statue of liberty is: 5.08 ft .
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The function fis defined by the following rule.
f(x)=-3x-3
Complete the function table.
X
-5
-1
0
2
X
√(x)
0
0
0
0
0
15
Answer:
X
-5
-1
0
2
4
/(×)
12
0
-3
-9
-15
A fair coin is tossed until either a tail occurs or a total of 4 tosses have been made, whichever comes first. Let X denote the number of tosses. a) Build the probability distribution of X. b) Find the mean value of X c) Find the standard deviation of X.
Answer: i don’t know
Step-by-step explanation:
