Answer:
d) Good, the interval is related to the variable of interest and the population mean analyzed.
Step-by-step explanation:
1) Data given
[tex]\bar x = 23[/tex] represent the mean
[tex]ME=2[/tex] represent the margin of error
[tex]confidence=95\%=0.05[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\bar x \pm ME = 23\pm 3=(21,25)[/tex]
Where the margin of error is given by [tex]ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
Based on the interval obtained we can say that "we have 95% of confidence that the mean winter snowfall would be between 21 and 25"
2) Analyze the possible options
a) Wrong, we are not analyzing the individual winters, the interval is related to the population mean.
b) Wrong, the confidence interval can't be interpreted as a chance that are not related to the population mean of interest.
c) Wrong, the confidence interval is not related to the individual days of winter.
d) Good, the interval is related to the variable of interest and the population mean analyzed.
e) Wrong, the confidence interval is not related to specific events, is related to the population mean.
Viewers should interpret the news by considering the confidence interval and understanding the statements.
The viewers should interpret this news as follows:
a. The statement that during 95 of the past 100 winters, the region got between 21" and 25" of snow is valid.
This is because the average winter snowfall of 23" falls within this range with a margin of error of 2".
b. The statement that there's a 95% chance the region will get between 21" and 25" of snow this winter is not correct.
The confidence interval (21" to 25") represents the range of values in which the true average snowfall is likely to fall, not the probability of the upcoming winter's snowfall falling within that range.
c. The statement that there will be between 21" and 25" of snow on the ground for 95% of the winter days is not supported by the given information.
The confidence interval pertains to the average winter snowfall, not individual daily observations.
d. The statement that residents can be 95% sure that the area's average snowfall is between 21" and 25" is valid.
The confidence interval provides a range of values within which the true average is likely to fall.
e. The statement that residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter is valid.
The confidence interval represents the range of likely values for the true average.
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Organic Food Inc., a multinational company, relies on its media partner Radio Plus to regularly advertise its offers, sales, and new products. Radio Plus is invested in this relationship because it generates most of its revenue from advertising Organic Food's products. In this scenario, Radio Plus is Organic Food Inc.'s
Answer:
External stakeholder.
Step-by-step explanation:
Radio Plus is invested in this relationship because it generates most of its revenue from advertising Organic Food's products.
In this scenario, Radio Plus is Organic Food Inc.'s - external stakeholder.
External stakeholders are those individuals or companies that do not lie within a business itself, but these care about the business and are affected by the business's performance.
There were 128 threatened species of animals and 144 threatened species of plants in the United States in 2001. Write the ratio of threatened species of animals to threatened species of plants as a fraction in simplest form.
If you go by division is is eight to nine.
Final answer:
The ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed in simplest form, is 8:9 or 8/9 after dividing both numbers by their greatest common divisor, which is 16.
Explanation:
The question asks for the ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed as a fraction in simplest form. To find the ratio, we divide the number of threatened animal species by the number of threatened plant species. The given numbers are 128 threatened animal species and 144 threatened plant species.
To simplify the ratio 128:144, we divide both numbers by their greatest common divisor (GCD). The GCD of 128 and 144 is 16. Thus, dividing both sides of the ratio by 16, we obtain:
128 ÷ 16 = 8
144 ÷ 16 = 9
The simplified form of the ratio is 8:9, or written as a fraction 8/9.
Which of the graphs below represents the equation 8x − y = -4?
Answer:
8x-y+4=0
Step-by-step explanation:
because 8x-y+4=-4+4
A college bookstore ordered six boxes of red pens. The store sold 28 red pens last week and 38 red pens this week. 6 pens were left on the shelf. How many pens were in each box?
Answer:
Step-by-step explanation:
28 + 38 = 66
66 divided by 6 = 11
This means that there would be 11 pens in each box.
Answer: there were 12 red pens in each box
Step-by-step explanation:
Let x = the number of red pens that were initially in each box.
The college bookstore ordered six boxes of red pens.
This means that the total number of red pens ordered is 6×x = 6x
The store sold 28 red pens last week and 38 red pens this week. This means that the total number of red pens sold = 28 + 38 = 66
The number of red pens left will be the total number of red pens minus the number of red pens that were sold. It becomes 6x - 66
6 pens were left on the shelf. This means that
6x - 66 = 6
6x = 6 + 66 = 72
x = 72/6 = 12
A method for determining whether a critical point is a minimum, maximum, or neither using the slope of the curveA) First Derivative TestB) Absolute MaximumC) AccelerationD) Concavity
Answer:
a. First derivative
Step-by-step explanation:
To determine the nature of the stationary points:
Either Find dy/dx or d2y/dx2
If the result is: positive—the point is a minimum one; negative—the point is a maximum one; zero—the point is a point of inflexion
or
Determine the sign of the gradient of the curve just before and just after the stationary points.
If the sign change for the gradient of the curve is: positive to negative—the point is a maximum one; negative to positive—the point is a minimum one; positive to positive or negative to negative— the point is a point of inflexion
A method for determining whether a critical point is a minimum, maximum, or neither using the slope of the curve is the First Derivative Test (Letter A).
First Derivative TestCritical points represent the values of x for that f '(x) is zero or the derivative doesn't exist. Therefore, they represent the only places where a function can have a local minimum, maximum or neither using the slope of the curve. See the rules for this method:
If f′(x) changes from positive to negative at c, then f(c) is a local maximum.If f′(x) changes from negative to positive at c, then f(c) is a local minimum.If f′(x) does not change sign at c, then f(c) is neither a local maximum or minimum.Read more about the First Derivative Test here:
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Assume 2 kg of apples is 1 dozen and that each apple has 8 seeds. How many apple seeds are in 14 kg of apples?
Answer:
There are 672 seeds in 14 kg of apples
Step-by-step explanation:
2 kg of apples = 1 dozen
1 dozen = 12 apples
So, 2 kg of apples =12 apples
1 kg of apples = [tex]\frac{12}{2} apples[/tex]
1 kg of apples = [tex]6 apples[/tex]
14 kg of apples =[tex]6 \times 14=84 apples [/tex]
Each apples has 8 seeds
So, 84 apples has seeds = [tex]8 \times 84= 672 seeds[/tex]
Hence there are 672 seeds in 14 kg of apples
Apple seeds are in 14 kg of apples is mathematically given as
672 seeds
Apple seeds are in 14 kg of applesQuestion Parameters:
2 kg of apples is 1 dozen and that each apple has 8 seeds. How many apple seeds are in 14 kg of apples
Generally the equation for the is mathematically given as
2 kg of apples = 1 dozen
1 dozen = 12 apples
Hence
1 kg of apples = 12/2
1 kg of apples = 6
14 kg of apples = 6*14
84 apples has seeds = 8*84
84 apples has seeds = 672
There are 672 seeds in 14 kg of apples
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Aurora is selling tickets to a carnival. The function f(x) = 0.5x represents the amount of money Aurora earns per ticket, where x is the number of tickets she sells. The function g(x) = 8x represents the number of tickets Aurora sells per hour, where x is the number of hours she works. Find f(g(x)), and explain what it represents.
a. f(g(x)) = 4x, which represents the money Aurora made in dollars per hour
b. f(g(x)) = 4x, which represents the number of tickets Aurora sold per hour
c. f(g(x)) = 16x, which represents the money Aurora made in dollars per hour
d. f(g(x)) = 16x, which represents the number of tickets Aurora sold per hour
f(x) = 0.5x - money per ticket
g(x) = 8x - tickets per hour
We replace g(x) with its value (8x).
f(g(x)) = f(8x)
We replace the x in f(x) with 8x.
f(8x) = 0,5 × 8x
f(8x) = 4x
⇒ f(g(x)) = 4x
Correct answer:
a. f(g(x)) = 4x, which represents the money Aurora made in dollars per hour
Composing functions means to use the output of the inner function as the input for the outer function.
In this case, the inner function is g(x)=8x, which means that Aurora sells 8 tickets per hour.
So, if we give 8x (number of tickets sold) as input to the function f(x)=0.5x, we'll get
[tex]f(x)=0.5x \implies f(8x)=0.5(8x)=4x[/tex]
Since the function f tells us how much Aurora gains per ticket, f(g(x)) basically means:
Aurora gains 0.5 dollars per ticket, and she sells 8 ticket per hour, so she gains 4 dollars per hour.
Prove that y=x² at x=0 has both a local and global minimum using first derivative test. I can prove it with a graph looking at it visually but how would you prove it with written words.
[tex] \frac{d}{dx} {x}^{2} = 2x \\ x = 0 \\ 2 \times 0 = 0[/tex]
When the derivative equals zero, that point is either the maximum or minimum.
[tex] {x}^{2} \geqslant 0[/tex]
The smallest real value of x² is 0, which is at x = 0.
Hence, x² at x = 0 has both a local and global minimum.
Step-by-step explanation:
y = x²
Find the first derivative:
dy/dx = 2x
Find the critical values by setting dy/dx to 0:
0 = 2x
x = 0
Evaluating the first derivative before and after x=0, we see that dy/dx changes signs from negative to positive.
x < 0, dy/dx < 0
x > 0, dy/dx > 0
That means x=0 is a local minimum.
To find the global minimum, we need evaluate the function at x=0 and at the end points.
x = -∞, y = ∞
x = 0, y = 0
x = ∞, y = ∞
So x=0 is also the global minimum.
Erica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notices that the population is two-thirds of the previous year. Write an equation for the situation? How long will it take for her to have around 5 sheep?
The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]
It will take around 9 years for her to have around 5 sheep
Step-by-step explanation:
The exponential decay growth/decay equation is [tex]y=a(b)^{x}[/tex] , where
a is the initial valueb is the growth/decay factorIf b > 1, then it is a growth factorIf 0 < b < 1, then it is a decay factorErica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notices that the population is two-thirds of the previous year
∵ The population is decreased
∴ The equation is decay
∵ The population is two-thirds of the previous year
∴ The decay factor is [tex]\frac{2}{3}[/tex]
∵ She starts with an initial 200 sheep
∴ the initial value is 200
∵ The decay equation is [tex]y=a(b)^{x}[/tex] , where y represent the
population in x years
∵ a = 200
∵ b = [tex]\frac{2}{3}[/tex]
∴ [tex]y=200(\frac{2}{3})^{x}[/tex]
The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]
∵ The population after x years is around 5 sheep
- Substitute y by 5 to find x
∵ [tex]5=200(\frac{2}{3})^{x}[/tex]
- Divide both sides by 200
∴ [tex]0.025=(\frac{2}{3})^{x}[/tex]
- Insert ㏒ for both sides
∴ [tex]log(0.025)=log(\frac{2}{3})^{x}[/tex]
∴ [tex]log(0.025)=xlog(\frac{2}{3})[/tex]
- Divide both sides by [tex]log(\frac{2}{3})[/tex]
∴ 9.098 = x
∴ x is around 9 years
It will take around 9 years for her to have around 5 sheep
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The major difference between a calculator and a computer, when performing calculations, is that a
A. calculator is slower and needs more human assistance.
B. calculator is faster but needs more human assistance.
C. computer is slower but needs less human assistance.
D. computer is faster but needs more human assistance.
Final answer:
The major difference between a calculator and a computer in performing calculations is that a calculator requires more human interaction for input and verification, whereas a computer can process complex tasks with less human assistance and is generally faster. Therefore, option A is the correct answer.
Explanation:
The primary difference between a calculator and a computer when performing calculations is that calculators typically require more human interaction to input and verify data, while computers can process complex tasks with less human assistance. A calculator is designed for straightforward numerical computations and requires accurate input from the user. Meanwhile, a computer can carry out a wide range of tasks, including calculations, with greater speed and autonomy, thanks to its ability to run complex software programs. However, even though computers are powerful, solving certain mathematical problems, such as differential equations, can be challenging since they cannot make infinitely fine time steps and must approximate using small ones. Moreover, calculators, being simpler devices, require very little energy to operate and often rely on solar cells or small batteries, unlike computers, which have a greater energy demand. Therefore, option A is the correct answer.
A chi-square test for independence is used to evaluate the relationship between two variables. If both variables are classified into two categories, then what is the df value for the chi-square statistic?
The degrees of freedom (df) value for a chi-square test for independence is calculated using the formula: df = (number of columns - 1) x (number of rows - 1).
Explanation:The degrees of freedom (df) value for a chi-square test for independence when both variables are classified into two categories can be calculated using the formula:
df = (number of columns - 1) x (number of rows - 1)
For example, if we have a contingency table with 2 columns and 2 rows, the df value would be:
df = (2 - 1) x (2 - 1) = 1 x 1 = 1
The size of each interior angle of a regular polygon with n n sides is 140° Work out the size of each interior angle of a regular polygon with 2n sides.
Answer:
160°
Step-by-step explanation:
The corresponding exterior angle is 180°-140° = 40°. When the polygon has 2n sides, that angle will be cut in half to 20°. The interior angle of that polygon will be 180°-20° = 160°.
_____
The exterior angles always sum to 360°. Since their sum is a constant, doubling the number of them will cut their measure in half.
To find the size of each interior angle in a regular polygon with 2n sides, when n sides gives 140° each, we use the interior angle formula (n-2) * 180 / n. First, we find n using 140 = (n-2) * 180 / n and substitute n into ((2*n) - 2) * 180 / (2*n) for the result.
Explanation:The size of each interior angle in a regular polygon is calculated using the formula (n-2) * 180 / n, where n is the number of sides. Given that a polygon with n sides has an interior angle of 140°, we can use this formula to calculate the size of each interior angle in a regular polygon with 2*n sides. The calculation would be: ((2*n) - 2) * 180 / (2*n).
Therefore, to calculate the size of each interior angle in a regular polygon with 2*n sides - if n sides gives 140° each, we must first calculate n using 140 = (n-2) * 180 / n and then substitute n in ((2*n) - 2) * 180 / (2*n) to get the result.
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Vector V is in standard position and makes an angle of 50° with the positive x-axis. Its magnitude is 18. Write V in component form a, b and in vector component form ai + bj. (Round each answer to one decimal place.)
Answer:
11.57 units east, 13.79 units upwards
11.57i + 13.79j
Step-by-step explanation:
V = 18 units at an angle of 50° to the positive x-axis
In component Form, this is how each component is calculated
a = 18cos50° = 11.57 units east
b = 18sin50° = 13.79 units upwards
check if your answer is correct
[tex]\sqrt{11.57^{2} +13.79^{2} } = 18.0[/tex]
In vector component form ai + bj = 11.57i + 13.79j
Assume that a hat contains four bills: a $1 bill, a $5 bill, a $10 bill and a $20 bill. Two bills are to be selected at a random with replacement. find the probability that
a) both bills are $1 bill if the first selected is a $1 bill
b) both bills have a value greater than a $5 bill if the second bill is a $10 bill
Answer:
a)1/4
b)1/2
Step-by-step explanation:
a) The selection is with replacement, then we already have 1 $ bill and in the hat again the four bills. What is the probability of select 1$ bill ? well it is 1/4.
The point here is, replacement condition make the second trial totally independent of the first one
b)Following the same reasoning now we have selected a 10 $ bill, and we have two possibles positive outcome a 10 $ and a 20 $ bill and a total of 4 outcomes th th probability is 1/2
The probabilities are:
a) 1/16
b) 1/8.
How to find the probabilities?
We assume that all the bills have the same probability of being randomly selected.
a) Then the probability of randomly selecting a $1 bill is equal to the number of $1 bills on the hat divided by the total number of bills.
There is one $1 bill on the hat, and 4 bills in total, so the probability is:
p = 1/4.
Then you return the $1 bill to the hat and want to draw it again, with the same probability as before.
q = 1/4.
The joint probability is the product of the individual probabilities, so we have:
P = p*q = (1/4)*(1/4) = 1/16.
b) There are 2 bills that have a larger value than $5, then the probability for the first draw is:
p = 2/4
For the second draw, we must get the $10 bill, and the probability of getting it is:
q = 1/4.
The joint probability is:
P = p*q = (2/4)*(1/4) = 1/8.
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Consider the sequence: 1536, 768, 384, 192, 96, ... Determine the 11th term of the sequence. Group of answer choices
1.5
3
6
12
Answer:
The answer is 1.5
Step-by-step explanation:
You have to find the pattern and work your way down to the 11th term.
Answer:
1.5
Step-by-step explanation:
The sequence given is a geometric progression (G.P). For a G.P where the first term is a, the common ratio (which is the ratio between successive terms), the nth term of the GP is given as
Tn = ar^n-1
From the sequence given
a = 1536
r = 768/1536
= 1/2
= 0.5
Hence the 11th term of the sequence
T11 = 1536 (1/2)^11-1
= 1536 (1/2)^10
= 1536/1024
= 1.5
A producer of personal computer mouse pads determines that the number, N, of pads sold is related to the price, X, of a pad by N=35x-x^2. at what roice is th ecost so high, that no one wants to buy the any mouse pads?
Answer:
If the cost X is higher or equal than 35, then no one wants to buy the any mouse pads.
Step-by-step explanation:
When N is 0 or lower then it means that no one buys it.
N=35x-[tex]x^{2}[/tex], if N=0 then
0=35x-[tex]x^{2}[/tex] or
35x=[tex]x^{2}[/tex] dividing each side by x we get:
35=x
This is the cost which nobody will buy the mouse pad anymore.
Answer:
oooooooooo yea
Step-by-step explanation:
Hello Kitty has created a new system of conversion for the residents of Kitty Nation. The standard for measurement of length in Kitty Nation is that 3 lenthii = 35 inches and 3 gianthii = 380.5 lenthii. If a design to be sent to Kitty Nation is 287.4 feet long, how many gianthii long will it be? (Include units)
Answer:
A local café serves tea, coffee, cookies, scones, and muffins. They recently gathered data about their customers who purchase both a drink and a snack. The given frequency table shows the results of the survey.
If approximately 24% of the customers surveyed have a scone with their tea and approximately 36% of the customers surveyed buy a muffin, complete the column and row headings for the given table.
Step-by-step explanation:
you have a list of conversion factors.Just use them to cancel the unwanted units:246.6ft * 12in/1ft * 6lenthi/39in * 7ganthi/345.6lenthii= (246.6*12*6*7)/(1*39*345.6) ganthii
Carson bought two loaves of bread and one dozen eggs at the grocery store yesterday he paid a total of $6.09.If one dozen of eggs cost $1.79,how much is a loaf of bread?
Answer: $4.30
Step-by-step explanation: if you take 6.09 and subtract 1.79 you will get $4.30
With both the cold water and hot water faucets open it takes five minutes to fill a bathtub. The cold water facet alone takes 15 minutes to fill the tub. How long will it take to fill the tub with just the hot water faucet?
Answer:
7 1/2 minutes
Step-by-step explanation:
When the time with both faucets is a submultiple of the time with one faucet, you can use this sort of reasoning to figure the missing time.
Filling the tub in 5 minutes is equivalent to having 3 faucets open, each of which can fill the tub in 15 minutes. Since we know the cold water faucet can fill the tub in 15 minutes, the hot water faucet is equivalent to two open 15-minute faucets. That is, it can fill the tub in 15/2 = 7 1/2 minutes.
_____
Perhaps a more conventional way to approach the problem is to consider "tubs per minute." The cold faucet runs at 1/15 tubs per minute, and the two faucets together run at 1/5 tub per minute. Then the hot runs at ...
(1/5) - (1/15) = (3 -1)/15 = 2/15 . . . tubs per minute
So it will fill 2 tubs in 15 minutes, or 1 tub in 7 1/2 minutes.
Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 95.8% confidence interval of width of at most .14 for the probability of flipping a head? (note that the z-score was rounded to three decimal places in the calculation)
a) 217
b) 153
c) 212
d) 209
e) 150
f) None of the above
Answer:
153 times
Step-by-step explanation:
We have to flip the coin in order to obtain a 95.8% confidence interval of width of at most .14
Width = 0.14
ME = [tex]\frac{width}{2}[/tex]
ME = [tex]\frac{0.14}{2}[/tex]
ME = [tex]0.07[/tex]
[tex]ME\geq z \times \sqrt{\frac{\widecap{p}(1-\widecap{p})}{n}}[/tex]
use p = 0.5
z at 95.8% is 1.727(using calculator)
[tex]0.07 \geq 1.727 \times \sqrt{\frac{0.5(1-0.5)}{n}}[/tex]
[tex]\frac{0.07}{1.727}\geq sqrt{\frac{0.5(1-0.5)}{n}}[/tex]
[tex](\frac{0.07}{1.727})^2 \geq \frac{0.5(1-0.5)}{n}[/tex]
[tex]n \geq \frac{0.5(1-0.5)}{(\frac{0.07}{1.727})^2}[/tex]
[tex]n \geq 152.169[/tex]
So, Option B is true
Hence we have to flip 153 times the coin in order to obtain a 95.8% confidence interval of width of at most .14 for the probability of flipping a head
To get a 95.8% confidence interval of width 0.14 for the probability of flipping a head with a fair coin, we need to flip the coin approximately 213 times. This is achieved by setting the standard error of the confidence interval to half the desired width, and solving for n, the number of flips.
Explanation:To answer the question, we need to use the formula for the confidence interval for a proportion, which uses the Z-score, the standard deviation of the distribution of sample proportions, and the desired width of the confidence interval.
In this case, we want a 95.8% confidence interval. The Z-score for a 95.8% confidence interval is approximately 2.054 (since the z-score was mentioned to be rounded to 3 decimal places in the question).
The standard deviation of the distribution of sample proportions (standard error, SE) is sqrt([P*(1-P)]/n), where P is the assumed probability of heads (0.5 for a fair coin), and n is the number of flips.
The desired width of the confidence interval is 0.14, so the maximum standard error we want is 0.14/2, or 0.07. Setting the standard error formula equal to 0.07 and solving for n, we get n = 0.5*(1-0.5)/(0.07/2.054)^2, which comes out to approximately 212.6.
However, since we can't have a partial flip of a coin, we round this up to the next whole number, 213, which is close to the choice (c) 212. Hence, the answer should be (f), None of the above.
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How many elements are in the union of four sets if
each of the sets has 100 elements,
each pair of the sets shares 50 elements,
each three of the sets share 25 elements,
and there are 5 elements in all four sets?
The total number of elements in the union of the four sets is 195.
Explanation:To find the total number of elements in the union of four sets, we need to subtract the number of elements shared by each pair of sets and the number of elements shared by each three of the sets. Here's the step-by-step calculation:
First, we add the number of elements in each set: 4 * 100 = 400 elementsNext, we subtract the number of elements shared by each pair: 6 * (50) = 300 elementsThen, we add the number of elements shared by each three: 4 * (25) = 100 elementsFinally, we subtract the number of elements shared by all four sets: 1 * (5) = 5 elementsThe total number of elements in the union of the four sets is 400 - 300 + 100 - 5 = 195 elements.
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The number of elements in the union of the four sets is 195.
To determine how many elements are in the union of four sets, we will use the principle of inclusion-exclusion. Let's denote the four sets as A, B, C, and D. According to the problem:
Each set has 100 elements:
|A| = |B| = |C| = |D| = 100
Each pair of sets shares 50 elements:
|A ∩ B| = |A ∩ C| = |A ∩ D| = |B ∩ C| = |B ∩ D| = |C ∩ D| = 50
Each three of the sets share 25 elements:
|A ∩ B ∩ C| = |A ∩ B ∩ D| = |A ∩ C ∩ D| = |B ∩ C ∩ D| = 25
All four sets share 5 elements: |A ∩ B ∩ C ∩ D| = 5
Using the principle of inclusion-exclusion for four sets, we have:
|A ∪ B ∪ C ∪ D| = |A| + |B| + |C| + |D| - (|A ∩ B| + |A ∩ C| + |A ∩ D| + |B ∩ C| + |B ∩ D| + |C ∩ D|) + (|A ∩ B ∩ C| + |A ∩ B ∩ D| + |A ∩ C ∩ D| + |B ∩ C ∩ D|) - |A ∩ B ∩ C ∩ D|
Substituting the given values:
|A ∪ B ∪ C ∪ D| = 100 + 100 + 100 + 100 - (50 + 50 + 50 + 50 + 50 + 50) + (25 + 25 + 25 + 25) -5
Combining these, we get:
|A ∪ B ∪ C ∪ D| = 400 - 300 + 100 - 5 = 195
So, the number of elements in the union of the four sets is 195.
A child throws a ball with a speed of 5 feet per second at an angle of 73 degrees with the horizontal. Express the vector described in terms of i and j.
Answer:
v = 5cos(73°)i +5sin(73°)j
Step-by-step explanation:
The components of the velocity vector are ...
horizontal (i direction): 5·cos(73°)
vertical (j direction): 5·sin(73°)
Then the velocity vector is the sum of these component vectors:
v = 5cos(73°)i +5sin(73°)j
In 2016 the Bureau of Labor Statistics reported that there were 71.9 million people over age 25 who had at least a bachelor’s degree. Of these 52.1 million were employed and 1.3 million were unemployed. What were the labor-force participation rate and the unemployment rate for this group?
Answer: a) Labor force participation rate = 72.46%, b) Unemployment rate = 1.8%.
Step-by-step explanation:
Since we have given that
Number of people who have at least a bachelor's degree = 71.9 millions
Number of people who were employed = 52.1 millions
Number of people who were unemployed = 1.3 millions
So, Labor- force participation rate would be
[tex]\dfrac{Employed}{Total}\times 100\\\\=\dfrac{52.1}{71.9}\times 100\\\\=72.46\%[/tex]
Unemployment rate for this group would be
[tex]\dfrac{Unemployed}{total}\times 100\\\\=\dfrac{1.3}{71.9}\times 100\\\\=1.8\%[/tex]
Hence, a) 72.46%, b) 1.8%.
Write the equation of the ellipse 36x^2 + 25y^2 + 360x + 100y + 100 = 0 in standard form
Answer:
Step-by-step explanation:
An ellipse is of the form:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex] if it is horizontally stretched, or
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex] if it is vertically stretched.
To begin writing the equation of the ellipse, we will group together all the x-terms and then all the y-terms, moving the constant to the other side of the equals sign in order to make completing the square on these 2 terms a bit easier.
[tex](36x^2+360x)+(25y^2+100y)=-100[/tex]
The first rule for completing the square is that the leading coefficients on the squared terms HAVE to be a 1. Neither of ours is, so we factor those out, getting:
[tex]36(x^2+10x)+25(y^2+4y)=-100[/tex]
Now we can complete the squares. We will start with the x-term. The rule is to take half the linear term, square it, then add it to both sides. Our linear x-term is a 10. Half of 10 is 5, and 5 squared is 25. So we add 25 inside the parenthesis with the x stuff, BUT we cannot forget about that 36 hanging around out front refusing to be ignored. It is a multiplier. That means that we didn't just add in 25, we added in 25 * 36 which is 900. So what we have right now is
[tex]36(x^2+10x+25)+25(y^2+4y)=-100+900[/tex]
Now we will do the same with the y-term. Take half the linear term, square it, and add it (along with its multiplier) to both sides. Our linear y-term is 4. Half of 4 is 2, and 2 squared is 4, so now we have:
[tex]36(x^2+10x+25)+25(y^2+4y+4)=-100+900+100[/tex]
Now we will do 2 things simultaneously. We will simplify the right side which is easy, and then create the perfect square binomials on the left that was the whole point of doing all that. It now looks like this:
[tex]36(x+5)^2+25(y+2)^2=900[/tex]
Almost there. Last thing we do is divide everything by 900 so we get a 1 on the right:
[tex]\frac{36(x+5)^2}{900}+\frac{25(y+2)^2}{900}=1[/tex]
Simplifying by division in both the rational terms:
[tex]\frac{(x+5)^2}{25}+\frac{(y+2)^2}{36}=1[/tex]
That means that this is a vertically stretched ellipse with a = 6 and b = 5. In an ellipse, the a value is always the bigger one. So if the bigger value in the denominator is under the x fraction, then it is a horizontal ellipse. If the bigger value in the denominator is under the y fraction, like ours, then it is a vertical ellipse.
determine the domain of the function f(x) = x^2 + 6x +5/x^2 - 25
a. (-1, 5)
b. (5, 5)
c. (-infinity, -1) U (-1,5) U (5, infinity)
d. (-infinity, -5) U (-5, 5) U (5, infinity)
Answer:
The answer to your question is the last option
Step-by-step explanation:
Here there is a rational function so, we need to find the values where the denominator equals zero.
[tex]f(x) = \frac{x^{2} + 6x + 5}{x^{2}- 25 }[/tex]
[tex]x^{2} - 25 = 0[/tex]
Factor (x - 5)(x + 5) = 0
x₁ - 5 = 0 x₂ + 5 = 0
The function does not exist in -5 and 5
x₁ = 5 x₂ = -5
Domain
( -∞ , -5) U (-5, 5) U (5, ∞)
Answer:
the answer is d in edge
Step-by-step explanation:
(–∞, –5) U (–5, 5) U (5, ∞)
A school has two computer labs Each lap has 30 computers a total of six computers in the school or not working which expression can be used to find the number of working computers in the school
Answer:
Step-by-step explanation:
A school has two computer labs and each lan has 30 computers. This means that the total number of computers is the sum of the number of computers in each lab
Total number of computers = 30+30 = 60
A total of six computers in the school or not working.
The expression that can be used to find the number of working computers in the school will be
Let the number of computers that are working be x
the number of computers that are working is total number of computers minus the number of computers that are not working be
The expression that can be used to find the number of working computers in the school will be
x = 60 - 6
x = 54
At 4 P.M., the total snowfall is 4 centimeters. At 7 P.M., the total snow fall is 11 centimeters. What is the mean hourly snowfall? Write you answer in simplest form as a fraction or decimal
Answer:
Mean hourly snowfall = [tex]\frac{7}{3}[/tex] cm/hrStep-by-step explanation:
At 4 P.M., the total snowfall is 4 centimeters
Snowfall at 4 P.M = 4 cm
At 7 P.M., the total snow fall is 11 centimeters.
Snowfall at 7 P.M = 11 cm
Duration = 7 - 4 = 3 hours
Snowfall = 11 - 4 = 7 cm
[tex]\texttt{Mean hourly snowfall = }\frac{\texttt{Snowfall}}{\texttt{Duration}}=\frac{7}{3}cm/hr[/tex]
Mean hourly snowfall = [tex]\frac{7}{3}[/tex] cm/hr
A bank Certificate of Deposit is a: a Cash deposit in a savings account that earns interest b Certificate for deposits that are issued for half the face value c Savings instrument that requires a deposit for a period of time during which there is a penalty for withdrawals d Savings instrument that requires a deposit for a period of time during which the saver can withdraw money from the plan at any time without a penalty
Answer:
C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.
Step-by-step explanation:
A Certificate of Deposit is a financial savings product offered by banks. A Certificate of Deposit, also known as a CD, can be obtained from a bank or a credit union.
CDs have a greater interest rate return than savings accounts due the conditions that savings from a CD cannot be withrawn for a fixed period of time. The higher the return the longer the period the savings cannot be withdrawn or the higher the intital investment.
CDs are insured by the Federal Deposit Insurance Corporation (FDIC) and if savings are not needed for a known period of time offer a better return than a savings account.
Answer:
C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.
For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, –3, 2, 5, –4, –6 ?
A. 1
B. 2
C. 3
D. 4
E. 5
Answer:
Option C.
Step-by-step explanation:
The given given sequence is
1, –3, 2, 5, –4, –6
We need to find the pairs of consecutive terms of the sequence and their product.
Pairs of consecutive terms | Product
1, -3 -3
-3, 2 -6
2, 5 10
5, -4 -20
-4, -6 24
Here the product of three pairs of consecutive terms is negative.
The number of variations in sign for the sequence is 3. Therefore, the correct option is C.
To find the number of sign variations in the sequence 1, -3, 2, 5, -4, -6, you count the changes from positive to negative or negative to positive between consecutive terms. The sequence has three such changes, so the answer is C. 3.
Explanation:The question asks for the number of variations in sign within a given finite sequence of nonzero numbers. To find this, we need to count how many times the sign changes between consecutive numbers in the sequence 1, -3, 2, 5, -4, -6.
Between 1 and -3 the sign changes from positive to negative.Between -3 and 2 the sign changes from negative to positive.Between 2 and 5, both numbers are positive so there's no sign change.Between 5 and -4 the sign changes from positive to negative.Finally, between -4 and -6, both numbers are negative, and thus, no sign change here either.Counting these, we have a total of three variations in sign. Hence, the correct answer is C. 3.
Why do internal users need financial data? A. to make business decisions and compare business performance with previous years B. to invest in the business’s stocks C. to invest in stocks and make business decisions D. to analyze the risk involved in lending money to the business E. to understand the risk involved in lending resources to the business
Answer:
Internal users refer to management members of a company and other people who use financial information to run and manage the business
Explanation:
They work within the business and make business decisions. Accounting information is important for all management levels. In order to make decisions about the company's future, the top managers need information about the past performance of the company.
To determine the results of their past decisions, they need data. The financial statements will determine the company's performance and its financial position and guide them in making future decisions.
Answer: A. To make business decisions and compare business performance with previous years
Explanation:
Management uses accounting information for evaluating and analyzing an organization's financial performance and position, to take important decisions and appropriate actions to improve the business performance in terms of profitability, financial position, and cash flows.
Internal users refer to the members of a company's management and other individuals who use financial information in running and managing the business. They work within the company and make decisions for the business.