How do you write 308 in expanded form?

a. The probability that no boats arrive in a 2-hour period is approximately 0.0003.

b. The probability that 1 boat arrives in a 2-hour period is approximately 0.0023.

c. The probability that 2 boats arrive in a 2-hour period is approximately 0.0466.

d. The probability that 2 or more boats arrive in a 2-hour period is approximately 0.9511.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

Given that boats arrive at the inlet drawbridge according to a Poisson distribution with a rate of 4 per hour, we can use the Poisson probability formula to calculate the probabilities.

The Poisson probability mass function is given by:

P(x; λ) = \((e^{(-\lambda)} * \lambda^x) / x!\)

where x is the number of events, λ is the average rate of events.

(a) To find the probability that no boats arrive in a 2-hour period, we can calculate P(0; λ), where λ is the average rate of events in a 2-hour period. Since the rate is 4 boats per hour, the average rate in a 2-hour period is λ = 4 * 2 = 8.

P(0; 8) = \((e^{(-8)} * 8^0) / 0! = 8e^{(-8)}\) ≈ 0.0003

The probability that no boats arrive in a 2-hour period is approximately 0.0003.

(b) To find the probability that 1 boat arrives in a 2-hour period, we can calculate P(1; λ), where λ is the average rate of events in a 2-hour period (λ = 8).

P(1; 8) = \((e^{(-8)} * 8^1) / 1! = 8e^{(-8)}\) ≈ 0.0023

The probability that 1 boat arrives in a 2-hour period is approximately 0.0023.

(c) To find the probability that 2 boats arrive in a 2-hour period, we can calculate P(2; λ), where λ is the average rate of events in a 2-hour period (λ = 8).

P(2; 8) = \((e^{(-8)} * 8^2) / 2! = (64/2) * e^{(-8)}\) ≈ 0.0466

The probability that 2 boats arrive in a 2-hour period is approximately 0.0466.

(d) To find the probability that 2 or more boats arrive in a 2-hour period, we need to calculate the complement of the probability that 0 or 1 boat arrives.

P(2 or more; 8) = 1 - (P(0; 8) + P(1; 8))

P(2 or more; 8) \(= 1 - (e^(-8) + 8e^{(-8)})\) ≈ 0.9511

The probability that 2 or more boats arrive in a 2-hour period is approximately 0.9511.

Please note that the above probabilities are calculated based on the assumption of a Poisson distribution with a rate of 4 boats per hour.

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Step-by-step explanation:

the point-slope form is

y - y1 = a(x - x1)

with "a" being the slope, (x1, y1) being a point on the line.

so, we have here

y - 1/2 = 4(x - 3/8)

simplifying this gives us then the slope-intercept form

y = ax + b

with b being the y-intercept.

so, we get

y - 1/2 = 4x - 4×3/8 = 4x - 3/2

y = 4x - 3/2 + 1/2 = 4x - 2/2 = 4x - 1

so,

the first, second and forth statements are true, the third is false.

The squares represent a visual representation of equivalent fractions. Each square is divided into a certain number of equal parts, and the number of parts that are shaded in represents the numerator of the fraction. The total number of parts the square is divided into represents the denominator of the fraction.

In the first square, it is divided into 23 equal parts and 8 of them are shaded in. Therefore, the fraction represented by that square is 8/23.

In the second square, it is divided into 812 equal parts and 23 of them are shaded in. Therefore, the fraction represented by that square is 23/812. Since both squares are divided into the same number of equal parts, the fractions 8/23 and 23/812 represent the same quantity, just in different forms. Therefore, they are equivalent fractions.

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Answer:

2

Step-by-step explanation:

Following the substitution rules:

O becomes P and

E becomes F

because they are vowels(a,e,i,o,u) change to next letter.

C becomes A

L becomes J

G becomes E

because constants change to the letter two before the given letter.

So COLLEGE becomes APJJFEF

so it now has 2 vowels.

Answer:

with what

Step-by-step explanation:

\(\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}\)

\(\Huge \textsf{Step-by-step explanation}\)

\(\LARGE \bold{\textsf{Step 1: Assign Variables}}\)

\(\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}\)

\(\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}\)

\(\large \bold{ \textsf{From the problem, we know that:}}\)

\(\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}\)

\(\large \bold{ \textsf{We can use this information to write two equations:}}\)

\(\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}\)

\(\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}\)

\(\LARGE \bold{\textsf{Step 3: Solve the system of equations}}\)

\(\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}\)

\(\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}\)

\(\large \textsf{Simplifying this expression gives us:}\)

\(\textsf{10\textit{p} + 10 = 260}\)

\(\large \textsf{Subtracting 10 from both sides:}\)

\(\textsf{10\textit{p} = 250}\)

\(\large \textsf{Dividing both sides by 10}\)

\(\textsf{\textit{p} = 25}\)

\(\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}\)

\(\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}\)

\(\large \textsf{So, 25 pizzas and 80 sodas were sold.}\)

----------------------------------------------------------------------------------------------------------

Answer: 70%

Step-by-step explanation:

A basket contains:

5 yellow balls

3 blue balls

2 white balls

What would be the probability of randomly picking a ball and the ball not being blue?

So, we can find the probability of picking up a blue ball. Let's do that first.

To calculate the probability of getting a blue ball, we need to divide the number of blue balls by the number of possible balls.

The number of blue balls = 3

The total number of balls = 2 + 3 + 5 = 10 balls

3 blue balls divided by 10 balls = 0.3.

If you multiply 0.3 by 100%, it will give you a probability of finding a blue ball equal to 30%

Now, we just need to find the probability of NOT finding a blue ball. Because we have 30% of finding a blue ball, we just need to subtract 30% from 100%.

100 - 30$ = 70%

The probability of not getting a blue ball is equal to 70%.

Hope I Helped!

\(|\Omega|=5+3+2=10\\|A|=5+2=7\\\\P(A)=\dfrac{7}{10}=70\%\)

Referring to Table 3.1, if the government imposes a price of $3, a shortage will result.

To determine the outcome when the government imposes a price of $3, we need to compare the quantity demanded and quantity supplied at this price level.
According to Table 3.1, at a price of $3, the quantity demanded is 30 units, while the quantity supplied is 40 units. The quantity demanded (30 units) is less than the quantity supplied (40 units), resulting in a situation known as a shortage.
A shortage occurs when the quantity demanded exceeds the quantity supplied at a given price. In this case, a shortage of 10 units occurs because consumers are willing to buy more than what producers are offering at the price of $3.
To summarize, if the government imposes a price of $3 based on Table 3.1, a shortage will result. This means that the quantity demanded exceeds the quantity supplied at the given price, indicating that consumers are unable to purchase all the units they desire.

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 the complete question is:

Table 3.1
Quantity Demanded.
Price per Unit
Quantity supplied
10
$5
50
20
30
$4
$3
40
30
40
50
$2
$1
20
10
Refer to Table 3.1. If the government imposes a price of $3.
a shortage will result.
Market is in equilibrium.
the price will fall to $1 because producers will be forced to incur losses.
a surplus will result.

The multiple inverse of 16 is 0.0625.

1/N or N-1 is used to denote a number's multiplicative inverse, such as the number N. It also goes by the name reciprocal.

Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.

Inverse of x = 1/x  or  x⁻¹.

It is also called as the reciprocal of a number and 1 is called the multiplicative identity.

Let the multiple inverse of 16 is x, then

16 * x = 1

⇒ x = 1/16

⇒ x = 0.0625

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The simplified form of expression \(\sqrt[4]{\frac{3}{2x} }\) is  \(\frac{\sqrt[4]{24 x^3}}{2x }\)

The correct answer is an option (B)

Consider an expression \(\sqrt[4]{\frac{3}{2x} }\)

Multiply the fraction by an expression to form a perfect square in the denominator.

\(\sqrt[4]{\frac{3}{2x} }\)

\(=\sqrt[4]{\frac{3\times 2^3\times x^3}{2x\times 2^3\times x^3} }\)

We know that the cube of 2 is 8. So, substitute 2³ = 8

\(=\sqrt[4]{\frac{3\times 8\times x^3}{2x\times 8\times x^3} }\)

Now, we multiply the monomials.

\(=\sqrt[4]{\frac{24\times x^3}{16\times x^4} }\)

We know that the exponent rule \((a\times b)^m=a^m\times b^m\)

\(=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{16\times x^4} }\)

We know that 2⁴ = 16

\(=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4\times x^4} }\\\\=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4}\times \sqrt[4]{x^4} }\)        ............(using the exponent rule \((a\times b)^m=a^m\times b^m\))

\(=\frac{\sqrt[4]{24\times x^3}}{2x }\)           .......(Simplify the radical expressions)

Here, \(\frac{\sqrt[4]{24 x^3}}{2x }\) is the simplified form of expression.

Therefore, the correct answer is an option (B)

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Find the complete question below.

Answer:

55 degrees

Step-by-step explanation:

Angles RSP and QPS are Alternate Interior Angles. Given that OQ and RT are parallel, alternate interior angles are always congruent, meaning they have the same measure.

So if angle RSP is 55 degrees and it is congruent to angle QPS, then angle QPS is 55 degrees.

Answer:

B

Step-by-step explanation:

f(x) maxmum value is

\( \frac{ - 4}{ - 4} = 1\)

\( - 2( {1}^{2} ) + 4(1) + 3 =

5\)

G(x) minimum value is 6.

B is the answer.

Answer:

Step-by-step explanation:

The area of a circle is represented by the following equation:

Hence, if the radius is 8 meters.

Now, the circumference is given as:

Given, the weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below, where R() is revenue in dollars. R'(x)= 48 -0.03x +600/( x + 1). R(0)=0. We need to find the revenue function and the revenue from the sale of 1,000 pairs of shoes.

Steps to find the revenue function:

R'(x) = 48 -0.03x + 600/(x+1)∫ dR(x)/dx = ∫ [48 -0.03x + 600/(x+1)]dx R(x) = ∫ [48 -0.03x]dx + ∫ [600/(x+1)]dx R(x) = 48x - 0.015x^2 + 600ln(x+1) + C (where C is a constant of integration).

Now, R(0) = 0C = 0. Therefore, the revenue function is R(x) = 48x - 0.015x^2 + 600ln(x+1).

Revenue from the sale of 1,000 pairs of shoes is R(1000) = 48(1000) - 0.015(1000)^2 + 600ln(1000+1) = $44,097.51 (rounded to the nearest cent).

Therefore, the revenue from the sale of 1,000 pairs of shoes is $44,097.51.

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Answer:

x = 2\(\sqrt{6}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² = (\(\sqrt{12}\) )² + (\(\sqrt{12}\) )² [ the 2 legs are congruent ]

x² = 12 + 12 = 24 ( take square root of both sides )

x = \(\sqrt{24}\) = \(\sqrt{4(6)}\) = \(\sqrt{4}\) × \(\sqrt{6}\) = 2\(\sqrt{6}\)

Answer:

\(m\angle RTS=34^{\circ}\)

Step-by-step explanation:

From the Isosceles Base Theorem, the two base angles of an Isosceles Triangle are equal. Therefore, \(m\angle RTS=m\angle TRS\).

Since the sum of the interior angles of a triangle is 180 degrees, we have:

\(m\angle RTS +m\angle TRS+112=180,\\2\cdot m\angle RTS+112=180,\\2\cdot m\angle RTS=68,\\m\angle RTS=\boxed{34^{\circ}}\)

Answer:

x=25 I believe

Step-by-step explanation:

So, 130° should be for both the angles at the top, so that leaves 100° left for the ones at the bottom because 360 - 260 = 100

So since the 2 angles at the bottom should be equal to each other, we have 4x for the bottom 2 angles.

So, 4x = 100

So, x = 25

Answer:

Step-by-step explanation:

numbers of Ostrich = 8700 ÷ 12

numbers of Ostrich = 725

Answer:

10/(2/5)

Step-by-step explanation:

If you want to find how much of something is in another thing, you divide.

Answer:

The answer is A 10 divided by 2/5=25. I just took the test on Ed

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

So I mostly will focus on the jogging total hours because thats literally what it says lol. Anyways, here I used the percent equation, which is

___ is ___% of ___. Since the question is "what percent", we mark our blank percent part as x, and when I fill the equation in it will seem like this:

"20 is x% of 50 (total hours)". So, now I translate, and this means:

20=x50, or in other words, 20=50x. To get x alone we divide by 50, but we also do it for the 20. 20/50 is .4, but because it has to be a percent, we move the decimal 2 places to the right, which gives 40, and finally it becomes

40%.

Hope it helps

Answer:

40%

Step-by-step explanation:

(20 hours Jogging)/(50 hours Total) = 0.4

0.4 * 100 = 40

The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

We know that the phone numbers of a small town either begin with 373 or 377. We are required to find out the number of phone numbers that are available. To solve this question, we need to count the number of phone numbers that are available for each prefix.

The prefix 373 can have numbers ranging from 3730000 to 3739999. Similarly, the prefix 377 can have numbers ranging from 3770000 to 3779999.

Therefore, the total number of phone numbers that are available is the sum of the phone numbers available for each prefix.

Total number of phone numbers = Number of phone numbers available for prefix 373 + Number of phone numbers available for prefix 377

Total number of phone numbers = 10000 + 10000

Total number of phone numbers = 20000

Therefore, The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

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Answer:

divident

Step-by-step explanation:

The value of the derivatives of f df(x, y, z)/dx + df(x, y, z)/dy is 20, when x = 1, y = 1, and z = 1.

To determine df/dt using the chain rule, we need to compute the partial derivatives of f with respect to x, y, and z, as the derivatives of x(t), y(t), and z(t) with respect to t.

We are given that the function as f (x, y, z)= 3x² + xyz + 4y³ z²

To Find df(x, y, z)/dx + df(x, y, z)/dy when x = 1, y = 1, and z = 1.

f (x, y, z)= 3x² + xyz + 4y³ z²

Therefore,

df(x, y, z)/dx = 6x + yz

df(x, y, z)/dy = xz + 12y² z²

Now we have;

df(x, y, z)/dx + df(x, y, z)/dy

6x + yz + xz + 12y² z²

When x = 1, y = 1, and z = 1 then we get;

6 + 1 + 1 + 12

= 20

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Therefore, the appropriate percent in the pie chart to represent the preference for Klean laundry detergent is 15%.

Percent is a way of expressing a fraction or a ratio as a portion of 100. The word "percent" means "per hundred." It is denoted by the symbol "%". Percentages are commonly used to express rates, proportions, or parts of a whole in various fields, such as mathematics, science, finance, and statistics. For example, an interest rate of 5% per annum means that for every 100 units of money, the lender will receive 5 units of interest each year.

Here,

To find the appropriate percent in the pie chart to represent the preference for Klean laundry detergent, we need to calculate the fraction of people who prefer Klean detergent, and then convert it to a percentage.

The fraction of people who prefer Klean detergent is:

75/500 = 0.15

To convert this fraction to a percentage, we can multiply by 100:

0.15 x 100 = 15%

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Answer:

73.6

Step-by-step explanation:

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

568.2 in

Step-by-step explanation:

To find this we first have to divide 1894/10 then we get 189.4 which we multiply by 3 to find how much more sand we need.

here is your answer.hope it helps you

Answer:

-3/4

Step-by-step explanation:

Use the formula y2-y1/x2-x1. When you plug in your x and y's, you should get -17+2/24-4. Simplify and you get -15/20, Simplify again and you get -3/4