How many milligrams of zinc ions do the trout need to be exposed to in order for them to survive exactly one minute after exposure?

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.

Answer:

t≅13.33h

Step-by-step explanation:

Adam (A) works at constant rate of 50tiles/h

Briana (B) works at constant rate of 55tiles/h, this means that A=50 tiles per hour and B=55 tiles per hour, then A+B = 105tiles/h together, but the floor consists of 1400tiles, so if 105 tiles are installed in one hour, then 1400 tiles in how long they will be installed?

t = 1400tiles*h/105tiles≅ 13.33 h

[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.

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

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.

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

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.

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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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.

Answer:

Step-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

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

The options are not clear but we can describe exponential function as follows

Exponential  function are of the form

[tex]y = b^x \; where\; b >0 = Exponentially\; Growing\\b<0 \; Exponentially\; Decaying \\\\x = Exponent[/tex]

The exponential functions are curved upwards gradually (figure attached )

Figure  1 (graph attached ) Shows the graph of function

[tex]y = 2^x[/tex]

We can   conclude that exponential function is a monotonous function and

depending upon the value of b the exponential function is either continuously increasing or continuously decreasing

[tex]y = -3^x[/tex]

as shown by Figure 2 (figure attached )

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Answer:

It's D

Hopefully this helps someone :D

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:

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.

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.

Counting these, we have a total of three variations in sign. Hence, the correct answer is C. 3.

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).

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

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.

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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Answer: $4.30

Step-by-step explanation: if you take 6.09 and subtract 1.79 you will get $4.30

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

Answer:

a) [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]

b) [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]

c) [tex]t_{\alpha/2}=-2.11[/tex]

d) [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]

Step-by-step explanation:

Part a

On this case the confidence is 87% or 0.87 so the significance level is [tex]\alpha=1-0.87=0.13[/tex] and [tex]\alpha/2 =0.065[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

We need values a,b on the normal standard distribution such that:

[tex]P(Z<a)=0.065[/tex] or [tex]P(Z>b)=0.065[/tex] and in order to find it we can use the following code in excel:

"NORM.INV(0.065,0,1)" or "NORM.INV(1-0.065,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]

Part b

On this case the confidence is 92% or 0.92 so the significance level is [tex]\alpha=1-0.92=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

First we need to calculate the degrees of freedom given by:

[tex]df=n-1=15-1=14[/tex]

We need values b,c on the t distribution with 14 degrees of freddom such that:

[tex]P(t_{(14)}<b)=0.04[/tex] or [tex]P(t_{(14)}>c)=0.04[/tex] and in order to find it we can use the following code in excel:

"T.INV(0.04,14)" or "T.INV(1-0.04,14)", and we see that the critical values [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]

Part c

The significance level is [tex]\alpha=0.025[/tex] and is a left tailed test. On this case we know that is a left tailed test so then we have just one critical value.

First we need to calculate the degrees of freedom given by:

[tex]df=n-1=18-1=17[/tex]

We need a value c on the t distribution with 17 degrees of freddom such that:

[tex]P(t_{(17)}<c)=0.025[/tex], and in order to find it we can use the following code in excel:

"T.INV(0.025,17)", and we see that the critical values [tex]t_{\alpha/2}=-2.11[/tex]

Part d

The significance level is [tex]\alpha=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we know that w ehave a two tailed proportion test, so we will have two critical values.

We need values a,b on the normal standard distribution such that:

[tex]P(Z<a)=0.04[/tex] or [tex]P(Z>b)=0.04[/tex] and in order to find it we can use the following code in excel:

"NORM.INV(0.04,0,1)" or "NORM.INV(1-0.04,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]

a. The critical value z????/2 for a level of confidence of 87% is approximately 1.475. b. The critical t-value t????/2 for a 92% confidence level and n = 15 is approximately 1.761. c. The critical value for a left-tailed test at α = 0.025 and n = 18 is approximately -2.101. d. The critical value for a two-tailed test of a population proportion with α = 0.08 is approximately 1.755.

a. To find the critical value z????/2 for a level of confidence of 87%, we need to find the z-score that leaves an area of 0.87 in the center. This means the area in each tail is (1 - 0.87) / 2 = 0.065. Using a z-table or calculator, the critical value is approximately 1.475.

b. For a 92% confidence level and a sample size of 15, we need to find the critical t-value t????/2. First, we determine the degrees of freedom, which is n - 1 = 15 - 1 = 14. Using a t-table or calculator, the critical t-value is approximately 1.761.

c. For a left-tailed test at the α = 0.025 level of significance and a sample size of 18, we need to find the critical value. Since the level of significance is α = 0.025, the area in the left tail is 0.025. Using a t-table or calculator, the critical value is approximately -2.101.

d. For a two-tailed test of a population proportion with α = 0.08, we need to find the critical value. Since we have a two-tailed test, we divide α by 2 to get 0.08 / 2 = 0.04. Using a z-table or calculator, the critical value is approximately 1.755.

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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.

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

Question 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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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.

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.

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).

Critical  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:

Read more about the First Derivative Test here:

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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.

The total number of elements in the union of the four sets is 195.

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:

The 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.

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.

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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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

Answer:

5 i)  Space occupied by 1 ball = 137.26 cubic centimeters

5 ii)  Space occupied by 6 tennis balls =  823.56 cubic centimeters

6 i)  19.2 centimeters

6 ii)  12.8 centimeters

6 iii) 6.4 centimeters

6 iv)  1572.86 cubic centimeters

7.  749.3 cubic centimeters

Step-by-step explanation:

5.

i)

A tennis ball is in a shape of a sphere. The space occupied by 1 tennis ball is the volume of a sphere. The formula is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where

V is the volume and r is the radius (half of diameter)

Given diameter is 6.4 , the radius would be:

r = 6.4/2 = 3.2

Now, we substitute and find the volume:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (3.2)^3\\V=137.26[/tex]

Space occupied by 1 ball = 137.26 cubic centimeters

ii)

We found space occupied by 1 ball, so space occupied by 6 balls would be 6 times that. So that would be:

Space occupied by 6 tennis balls = 137.26 * 6 = 823.56 cubic centimeters

6.

i)

The length of the box would be 3 diameters lined up. Since the length comprises of 3 balls side by side, we can say that 6 diameters would make up the length of the box, so:

diameter = 6.4

3 diameters = 6.4 * 3 = 19.2 centimeters

ii)

Now, we want the width of the box. That is 2 tennis balls lined up (as seen in the picture). That would be 2 diameters. so:

diameter = 6.4

2 diameters = 6.4 * 2 = 12.8 centimeters

iii)

The height of the box would be the height of 1 balls (see pic). That would be just 1 diameter of the ball. Given:

Diameter = 6.4 cm

So,

Height = 6.4 cm

iv)

The box is a rectangular prism. Which has a capacity (volume) formula as:

Volume = length * width * height

In the first 3 parts of this problem, we found each. Let's multiply each out to find the capacity of the box.

Volume = 19.2 * 12.8 * 6.4 = 1572.86 cubic centimeters

7.

The amount of empty space in the box is the volume of the rectangular box MINUS the volume of all the 6 balls. We have already found:

Volume of Box = 1572.86

Volume of 6 balls = 823.56

Hence,

Empty Space = 1572.86 - 823.56 = 749.3 cubic centimeters

Answer:

8x-y+4=0

Step-by-step explanation:

because 8x-y+4=-4+4

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%.