the mean number of patients admitted per day to the emergency room of a small hospital is 2.5 . if, on any given day, there are only 1 beds available for new patients, what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients?

Answer:

Step-by-step explanation:

We know that the bag has dark chocolates and milk chocolates, and the probability of randomly choosing a dark chocolate is g. And, we know that there are 18 dark chocolates in the bag and each is equally likely to be chosen.

Now, let's use this information to find the number of milk chocolates. If there are n total chocolates in the bag, then the probability of choosing a dark chocolate is g, and the probability of choosing a milk chocolate is 1-g. We can write these probabilities as:

g = 18/n

1-g = (n-18)/n

So, if we equate the two expressions, we get:

18/n = (n-18)/n

That means:

18 = n - 18

And finally:

n = 36

So, there must be 36 chocolates in the bag, and 18 of them are dark chocolates, which means there must be 18 milk chocolates!

The number of possible outcomes will be 524160.

When an order or sequence of arrangement is required, permutations are used. Combinations are used when there are only a limited number of possible groups to find and there is no requirement for the order or sequence of arrangements. For different kinds of things, permutations are used. Combinations are employed for similar items.

Given that a lottery exists where balls numbered 1 to 16 are placed in an urn. To​ win, you must match the balls chosen in the correct order.

The arrangement can be calculated as:-

¹⁶C₅ = 16 x 15 x 14 x 13 x 12

¹⁶C₅ = 524160

Therefore, the number of possible outcomes will be 524160.

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The percent error would be : {c - 78}/{c} x 100

Given is that the team ends up selling 78 cookies at next year's opening game.

Let the estimated value be {c} cookies. Now, we know -

%error = {a - x}/{x} x 100

%error = {c - 78}/{c} x 100

Therefore, the percent error would be : {c - 78}/{c} x 100.

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Let x be the price per pound of apples and y be the price per pound of potatoes.

For Ethan, the total cost for apples was $25.50 - 5y and the total cost for potatoes was $25.50 - 8x.

So, we have the following two equations:

8x + 5y = 25.5

3x + 10y = 18.5

Solving this system of linear equations, we get:

x = 1.71 and y = 2.36.

So, the ordered pair (x,y) = (1.71, 2.36) represents the price per pound of apples and potatoes.

By applying the transformation formula (x,y) -> (x-6,y+8) to the location (-4, 1), the pre-image would be (-4+6, 1-8) = (2,-7).

So the appropriate response is: (-2, -7).

Shifts and scaling are two common transformations used in geometry to create new shapes from figures in a plane. Images are the new (modified) shapes, and preimages are the original, unmodified shapes.

The preimage is the body of the object as it was originally, and the transformed shape of the object is termed the image.

The word "preimage" is plural (mathematics) The collection of all domain elements mapped onto a specific subset of the function's arguments.

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If the probability of Dan winning is 'p', then the probability that he does not win is ' 1-p' .

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. The probability of a event happening and the same event not happening is 1 or 100%.

Let Dan winning in a raffle is Event A.

Let Dan not winning in a raffle is Event B.

Probability of Dan winning + Probability of not winning = 1

   p + P(B) = 1

P(B) = 1 - p

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The 3 couples can be seated in 20 ways.

The answer I provided uses the concept of permutations. In permutation, we calculate the number of arrangements or ways in which a set of elements can be arranged.

In this case, the question is asking for the number of ways in which 6 individuals (3 married couples) can be seated in a row. To find the number of arrangements, we can use the formula for permutations of multiples:

P(n, k) = n! / (n-k)!

Where n is the number of items to arrange and k is the number of identical items. In this case, n = 6 (number of individuals) and k = 3 (number of married couples).

However, we need to also account for the fact that within each married couple, the two individuals can be seated in either order. Hence, we need to divide the result by 2! for each couple, giving us the formula:

P(6, 3) / (2! * 2! * 2!) = 6! / (3! * 3!) = 20

So there are 20 different ways in which the 3 married couples can be seated in a row.

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Answer:The function rule for Thalia's height (h) in years (t) is h(t) = 104 + 2.2t.

The linear function's parameters are: h0 = 104 (initial height), and k = 2.2 (the rate of growth in cm per year).

The function rule for the population of manatees (P) in years (t) is P(t) = 5,067 * (1.011)^(-t), where t is the number of years passed since 2011.

The exponential function's parameters are: P0 = 5,067 (the initial population), t (the number of years passed since 2011), and k = 0.011 (the decay rate).

Problem 3 describes decay. The population of manatees is decreasing by a certain percentage each year, indicating a decrease in the number of animals over time.

The decay rate in problem 3 is 1.1% (or 0.011 in decimal form).

Step-by-step explanation:

1.) The function rule (equation) for Thalia's height over time can be modeled as h(t) = 104 + 2.2t, where h(t) is her height in cm at time t in years.

2.) In the equation for Thalia's height, 104 is the y-intercept and 2.2 is the slope.

3.) The function rule for the manatee population in Florida can be modeled as P(t) = P0 * 0.989^t, where P(t) is the population at time t in years and P0 is the initial population (5,067).

4.) In the equation for the manatee population, P0 is the initial population and 0.989 is the decay rate. The independent variable is t (time in years) and the dependent variable is P (population).

5.) Problem 3 describes decay. This is because the population of manatees in Florida is decreasing at a constant rate of 1.1% per year.

6.) The growth or decay rate in problem 3 is -1.1%.

Step-by-step explanation:

hope you appreciate it.

Answer: 78

Step-by-step explanation:

(3) + 3 = 6

6(3) - 5 = 13

13 x 6 = 78

:)

Jorge has a ticket has a probability of 0.3 of winning a prize. after seven days, probability that jorge has won at least one prize is 0.9176

Let the probability of Jorge winning be 0.3 so ,

Probability of not winning be (1-0.3)⁷

(0.7)⁷

= 0.0823

Therefore, Jorge not winning is 0.0823.

If he wins at least one prize is,

1 - P(win nothing)

1 - 0.0823

= 0.9176

Therefore, the probability that the Jorge wins at least one prize is 0.9176.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

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Answer: -12

Step-by-step explanation: -6*-2 = 12 and then 12*-1 = -12.

Answer: -12

Step-by-step explanation:

-6 x -2 x-1

12 x -1

-12

This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

1. x + 191 ≥ 214

2. x - 214 ≤ -23

1. To solve this inequality, we add 23 to both sides of the equation: x - 23 = 191.

x + 191 ≥ 214

2. To solve this inequality, we subtract 191 from both sides of the equation: x - 23 = 191.

x - 214 ≤ -23

1. x + 191 ≥ 214

This inequality can be expanded to x + 191 ≥ 214, which means that any value of x that is greater than or equal to 214 satisfies the inequality.

2. x - 214 ≤ -23

This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

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Answer:

Step-by-step explanation:

0.96!

0.5568 divided by 0.58 is approximately 0.9593.

Here, we have,

To divide 0.5568 by 0.58, you can follow these steps:

Step 1: Write down the dividend (the number being divided), which is 0.5568.

Step 2: Write down the divisor (the number you're dividing by), which is 0.58.

Step 3: To simplify the division, you can multiply both the dividend and divisor by a power of 10 to remove the decimal places. In this case, we can multiply both numbers by 100 to move the decimal point two places to the right.

0.5568 * 100 = 55.68 (new dividend)

0.58 * 100 = 58 (new divisor)

Step 4: Divide the new dividend by the new divisor:

55.68 / 58 ≈ 0.95931034

Step 5: Round the result to the desired number of decimal places. In this case, since the original dividend had four decimal places, we can round the result to four decimal places:

0.9593

Therefore, 0.5568 divided by 0.58 is approximately 0.9593.

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According to the data, the highway is 84 miles, the length of Valley Road is 60 miles, and the shortest mile is 24 miles less than the longest.

To calculate the length of the Highway route we must perform the following mathematical procedure:

To calculate the length of the Valley Road Route we must perform the following mathematical procedure:

To calculate the length that is saved by taking the shortest route we must carry out the following mathematical procedure:

Note: This question is incomplete due to missing information. Here is the missing information.

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The image here given an example of perpendicular line.

Correct option is: yes, the lines are intersect at right angle.

Two lines are perpendicular if they cross at a point where they provide a pair of linear angles that are congruent. If a transversal in a plane is parallel to one of two parallel lines, it is also parallel to the other line. Lines that cross at a straight angle (90°) are said to be perpendicular. Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

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The sum in degrees of Angle A and Angle B is 28 degrees

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

3x + 2 = x + 10

This means that

2x = 8

Divide by 2

x = 4

S, we have

Sum = 3x + 2 + x+ 10

Evaluate

Sum = 3 * 4 + 2 + 4 + 10

Sum = 28

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Answer:

54.9

Step-by-step explanation:

Substitute the provided values of x and y into the provided expression:

           8.3(3) + 7.5(4)

           = 24.9 + 30.0

           = 54.9

Answer:

The length of the hypotenuse is 6.4 yards.

Step-by-step explanation:

We can use the Pythagorean Theorem to evaluate the hypotenuse.

The formula for the Pythagorean Theorem is

[tex]a^2+b^2=c^2[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the legs of the triangle; and [tex]c[/tex] is the hypotenuse.

We are given the values of both legs.

[tex]a=4\\b=5[/tex]

Inserting these values into the equation gives us

[tex]4^2+5^2=c^2[/tex]

Lets solve for [tex]c[/tex].

Evaluate [tex]4^2[/tex].

[tex]16+5^2=c^2[/tex]

Evaluate [tex]5^2[/tex].

[tex]16+25=c^2[/tex]

Add [tex]16[/tex] and [tex]25[/tex].

[tex]41=c^2[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]\sqrt{41} =c[/tex]

[tex]\sqrt{41}=6.40312[/tex]

Rounding to the nearest tenth leaves us with

[tex]c=6.4[/tex]

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When YQ and XP are altitudes to the congruent sides of isosceles triangle, the true statement are:

WXY = WXY

PXY = QYX

Isosceles triangle has three sides out of which two are equal. It has two congruent sides. The angle opposite to base is vertex. It should be noted that the two sides of the triangle are congruent and the angles opposite to these sides are also congruent

From the information WXY is an isosceles triangle.

WXY = WXY

XY = XY

QXY == PYX (property of congruent triangle}

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Answer:

9p, because 9x4=36

Step-by-step explanation:

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 200\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 200[1+(0.03)(1)] \implies A = 206[/tex]

Answer:

Step-by-step explanation:

It would be 4+g

Since we are trying to find how many lbs in total we would add the total we already know which is 4 and then add the g pounds of green apples

To calculate the total amount of apples Alan has bought, we simply apply the concept of Algebraic Expressions and add the pounds of red apples (which is 4) to the pounds of green apples (which is represented by g). This can be represented in a mathematical expression as 4 + g.

Alan bought 4 pounds of red apples and g pounds of green apples. To find out how many pounds of apples he bought in total, we need to add the quantities together. So, the expression that shows that is 4 + g. This means that Alan bought 4 pounds of red apples and g pounds of green apples, adding those two quantities together gives the total pounds of apples he bought.

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Answer:

10.4

Step-by-step explanation:

m² =10²+3² = 109

so m =√109 = 10.4

The expression for x² in standard form is x² = (yˣ×10)²= y²×10².

Expression  is a mathematics combination of symbol such as number and operators which produce the mathematical result and expression can involve a single trauma multiple term and usually consist of a combination of constant variables operators function.

This means that if x is given in the form of x = y×10, then x² can be expressed as y² × 10². This form is advantageous because it allows for easier manipulation of the numbers. For example, if x = 5 ×10², then x²can be expressed as (5×10²)²= 5²× 10²×²= 25 × 10⁴. This expression is much easier to understand than the expanded form of x² = 5²× 10² × 10² = 25 ×10².

In addition, this expression for x²allows for efficient calculation of larger powers of x. For example, if x = 5 ×10², then x²can be expressed as (5×10² = 5³ × 10²×³= 125 × 10⁶. This is much faster to calculate than the expanded form of x³= 5³ ×10² ×10²× 10² = 125 ×10⁶.

Therefore, the expression for x² in standard form is an effective way to manipulate and calculate larger powers of x.

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Answer:

x = 2

Step-by-step explanation:

Product = muliplication

Let x represent the number

14x = 28

x = 2

Median of the probability distribution is 1.

Correct option is B.

The median of a set of data is the middlemost number or center value in the set. The median is also the number that is halfway into the set.

The median for a random variable X is m such that P(X≤m)≥1/2 and P(X≥m)≥1/2.

Given,

The probability distribution for the number of events in which a student competes is provided.

X is number of events,

P(X) is probability

Here,

For median value, P(x) ≥ 1/2

P(x) = 4/8 = 1/2

Value of X for P(x) = 1/2 is 1.

Median = 1

Hence, 1 is the median of probability distribution.

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Answer:

2a^2b^3−a^2b^4

The translated function is g(x) = ∛(x + 4) + 3, so the correct option is C.

We can see that function g(x) is a translation of f(x), which is the parent cubic root function:

f(x) = ∛x

We can see that g(x) is a translation of 3 units up, and 4 units to the left.

Then the function will be written as:

g(x) = f(x + 4) + 3

Replacing f(x) we will get:

g(x) = ∛(x + 4) + 3

Then the correct option is C.

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Answer:

y = - 8x + 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 8x - 5 ← is in slope- intercept form

with slope m = - 8

• Parallel lines have equal slopes , then

y = - 8x + c ← is the partial equation of the parallel line

to find c substitute (3, - 4 ) into the partial equation

- 4 = - 8(3) + c = - 24 + c ( add 24 to both sides )

20 = c

y = - 8x + 20 ← equation of parallel line