A ski gondola carries skiers to the top of a mountain. Assume that the total weights of adult skiers (including their equipment) are normally distributed with a mean of 200 lb and a standard deviation of 40 lb. Further assume that the gondola can carry a maximum of 25 skiers and has a maximum load limit of 5,000 lb. If the gondola is full, it will be overloaded if the mean total weight of the skiers exceeds 5,000 lb / 25 skiers = 200 lb/skier. If the gondola is filled with 25 randomly selected skiers, what is the probability that it will be overloaded? (Round your answer to three decimal places; add trailing zeros as needed.)

Yes, these -1098.15 and -2,784.75 are rational numbers.

Rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively

A rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer (e.g., 5 = 5/1) and, for instance, the number 3/7 are rational numbers. Boldface Q, also known as blackboard bold, is typically used to signify the set of all rational numbers, also known as "the rationals," the field of rationals, or the field of rational numbers.

Real numbers are those that are sensible. The rational real numbers are those whose decimal expansion either ends after a finite number of digits (for instance, 3/4=0.75) or eventually starts to repeatedly repeat the same finite sequence of digits (9/44=0.204545454). This assertion is accurate not just in base 10, but also in every other integer base, such as the binary and hexadecimal ones

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In an inscribed quadrilateral, the sum of the opposite angles are always equal to 180 degrees

so that

10z +

(14z-7) + 8z = 180 degrees-------------(2)

From equation (2)

14z+8z= 180+7

22z = 187

22z/22 = 187/22

z= 8.5

From equation (1) and substituting for z

10(8.5) + 85 +

Rectangular garden has sides:

width, length, width, length

The perimeter is sum of all the 4 sides.

So, we can say:

84 = 2w + 2l

Where

w is width

l is length

Width is 19.5, so we find length:

84 = 2(19.5) + 2l

84 = 39 + 2l

2l = 45

l = 22.5 feet

Now, area is given by:

Area = length * width

Area = 22.5 * 19.5 = 438.75 sq. ft.

Answer:

The answer would be C or 9.

Step-by-step explanation:

Figure out how many times 8 can fit into 24.(That would be 3 times) Then multiply 3 by the number of times 8 fit into 24 and get to your answer! (Please let me know if I am wrong)

Answer:

[C] 9

Step-by-step explanation:

Given:

Roland has a basket of 24 fruits. If 3 out of 8 of these fruits are oranges, how many oranges are in Roland's basket?

Solve:

" 3 out of 8 " is the same things as "⅜"

Therefore,

24 × ⅜

Now solving 24 × ⅜:

24 is the same as 24/1 since 24 divided by 1 is 24.

Hence, the problem will be like this:

[tex]\frac{24}{1}\times\frac{3}{8}[/tex]

Multiply the numerators together (24 x 3 = 72) and multiply the denominators together (1 x 8 = 8) and make it into one fraction like so:

[tex]\frac{72}{8}[/tex]

Now we have to find the GCF: GCF = Greatest Common Factor;

The greatest common factor of 72 and 8 is 8.

Dividing the numerator and the denominator by its greatest common factor to get:

[tex]\frac{9}{1}[/tex]

Convert the improper fraction above to a whole number to get the answer:

[tex]\frac{9}{1}=9[/tex]

Hence, there are 9 oranges in Roland's basket.

As a result, [C] 9 is the correct answer.

Kavinsky~

x = 1.37 after solving the given equation.

So, the equation here is: 5x⁵ + 16 = 41

Now, solve the equation normally as follows:

Now, take the roots on both sides and solve as follows:

In decimal form:

Therefore, x = 1.37 after solving the given equation.

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This is a case of indices

The third option is the right answer.

The size of the shift from function f to function g is 12 units down

The table of values is given as

x 0 1 2 3 4

g(x) -11 -10 -8 -4 4

From the question, we understand that the function g(x) is an exponential function

The parent function of an exponential function in this case, is represented as

f(x) = 2^x

When represented on a table of values, we have

x 0 1 2 3 4

f(x) 1 2 4 8 16

So, we have

x 0 1 2 3 4

f(x) 1 2 4 8 16

g(x) -11 -10 -8 -4 4

Notice that the difference between the values of f(x) and g(x) is 12

This means that

g(x) = f(x) - 12

So, we have

g(x) = 2^x - 12

Hence, the size of the shift is 12 units down

See attachment for the graphs of f(x) and g(x)

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Clare can go 3 times for her workout cycle

Clare follows the same workout cycle each time she goes to the gym

She spends 1 1/2 hour at the gym

First, she runs 1/3 of an hour

After that, she lifts 1/3 of an hour

The first step is to convert to minutes

60 mins = 1 hour

1/2 × 60

= 30

30 + 60

= 90 mins

convert 1/3 to mins

1/3 × 60

= 20 mins

convert 1/6 to mins

1/6 × 60

= 10 mins

Total mins= 20 + 10

= 30 mins

The number of workout cycles can be calculated as follows

= 90/30

= 3

Hence Clare can go 3 times for her workout cycle

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Answer:

hajajJzjzjzjzjzjzkzkzkzkzksk

eatmyass

The length of pipe required to produce a pitch of 220 Hz is 2.26 feet.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

The length of a pipe in a panpipe L, in ft, is inversely proportional to its pitch p, in hertz.

The inverse variation is modeled by the equation p = 497/L.

The length of pipe required to produce a pitch of 220 Hz,

= 497/220

= 2.26 feet

Therefore, the length is 2.26 feet.

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filled in the blanks : -

  348

* 784

_____________

        1392  

      2784      

    2436

______________

   272832

a mathematical operation that, at its most basic, is the quick addition of an integer to zero a certain number of times, expanded to other numbers using principles that apply to integers.

  348

* 784

_____________

        1392  

      2784      

    2436

______________

   272832

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Missing numbers are 30, 4, 30 and 300.

Equivalent fractions are those that, despite their visual differences, reflect the same value. You will have consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces. Two or more fractions that are equal despite having dissimilar numerators and denominators are said to be equivalent. Every time, the fraction is written as "one half" in its simplest form.

Given Data

20/?=?/6=10/?=?/900=8/12​

Fraction which is given

[tex]\frac{8}{12}[/tex]

= [tex]\frac{2}{3}[/tex]

As they are equivalent fraction, so their simplest form will be equal

Let the missing numbers be x

1) [tex]\frac{20}{x}[/tex]

= [tex]\frac{20}{30}[/tex]

2) [tex]\frac{x}{6}[/tex]

= [tex]\frac{4}{6}[/tex]

3) [tex]\frac{10}{x}[/tex]

= [tex]\frac{10}{30}[/tex]

4) [tex]\frac{x}{900}[/tex]

= [tex]\frac{600}{900}[/tex]

Missing numbers are 30, 4, 30 and 300.

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Answer:

Step-by-step explanation:

34 units.

Step-by-step explanation:

1/8, 2/8, 3/8, 4/8, etc...

Answer: 13

Step-by-step explanation:

3.To find:

The right angle congruence theorem is used to prove that two triangles are congruent.

Solution:

In the given triangles, the corresponding hypotenuse and the corresponding angle are equal. So, the congruence used here is the Hypotenuse-Angle congruence that implies ABC is congruent to DEF.

Thus, the answer is Hypotenuse-Angle congruence.

Answer: y + 3 = 1 ⋅ (x + 2)

Step-by-step explanation:

The CSC of the expression [tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)[/tex] is mathematically given as

[tex]\csc (\theta)=-\frac{8 \sqrt{55}}{55}[/tex]

This is further explained below.

Generally, the equation for the Problem is mathematically given as

[tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)[/tex]

Therefore

To find the [tex]$\csc (\theta)$[/tex] between the x-axis and the line between the points (0,0) and [tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right),[/tex] draw the triangle between the three points [tex](0,0),\left(\frac{3}{8}, 0\right)$, and $\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)$[/tex]

Opposite [tex]$:-\frac{\sqrt{55}}{8}$[/tex]

Adjacent :[tex]$\frac{3}{8}$[/tex]

Find the hypotenuse using the Pythagorean theorem [tex]$c=\sqrt{a^2+b^2}.[/tex]

[tex]$\csc (\theta)=\frac{\text { Hypotenuse }}{\text { Opposite }}$[/tex]

therefore

[tex]\csc (\theta)=\frac{1}{-\frac{\sqrt{65}}{8}}$.[/tex]

[tex]\frac{1}{-\frac{\sqrt{55}}{8}}[/tex]

Simplify[tex]\csc (\theta)[/tex]

[tex]\csc (\theta)=-\frac{8 \sqrt{55}}{55}[/tex]

Approximate the result.

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Answer:

(x / 8) + 4 = 9

Step-by-step explanation:

follow the instructions of the question and then write the values

at X= 0 the function f(x) = 2/6x^3 is not differentiable

Since 1/0 cannot be differentiated and the denominator will become zero when x=O, the function is not defined. Sharp points, cusps, and discontinuities in the graph indicate that a function is "not differentiable." Additionally, it implies that at that same location, we can draw an endless number of tangents. There is therefore no special tangent at that place. Even at x=0, the provided function is not defined. (If you plug in x=0, you get (1/0), which is undefined and leaves you with nothing to do.)) Only after a function is clearly defined at a certain moment do we discuss its continuation. And only if the function is continuous at the place do we talk about differentiability.

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Answer: 52900 Naira

Step-by-step explanation:

1) Use the equation A = P(1+r/n)^nt

A = Ammount

(Starting Cash) P = 40,000

(Intrest rate) R = 15%

(Number of periods) n = N/A

(Time) t = 2

2) Make an equation

A = 40,000(1+15%)^2

3) Solve the equation.

A = 40,000(1+0.15)^2

A = 40,000(1.15)^2

A = 40,000(1.3225)

A = 52900

Answer: -4/3

Step-by-step explanation:

[tex]\csc \theta=\frac{1}{\sin \theta}=\frac{1}{-3/4}=-4/3[/tex]

The value of (fg)(6) is -6x³ + 72x² + 72x - 864 after doing the mathematical operations.

So, f(x) = x² - 12 and g(x) = 12 - x.

Then, (fg)(6) will be:

Therefore, the value of (fg)(6) is -6x³ + 72x² + 72x - 864 after doing the mathematical operations.

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The defition of a function is a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set.

So, Your ques

Answers:

================================================

Explanation:

Focus on (4,5) and (4,-4)

The input x = 4 leads to simultaneous outputs y = 5 and y = -4 at the same time. This is not allowed in a function. For a function to be possible, each input x must lead to exactly one y output.

Therefore, this given relation is not a function.

-----------

Domain = set of possible x inputs

Range = set of possible y outputs

The statement "An element from the domain is paired with more than one element from the range" basically means we have an x value paired with more than one y value. Therefore, this statement is true since I mentioned (4,5) and (4,-4) earlier.

Answer:

This answer is correct!

The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The equation of line passing through (5, 2) and (-4, -16) is:

y - 2 = [(-16-2)/(-4-5)](x - 5)

y - 2 = 2(x - 5)

y = 2x - 8

y + 16 = 2(x + 4)

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Probability of x successes given the probability p of success on a single trial is 0.0154.

When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes." In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.

Given Data

n = 6

X = 3

p = [tex]\frac{1}{6}[/tex]

Binomial distribution

P(X = x) = ₙCₓ(pˣ)(qⁿ⁻ˣ)

ₙCₓ =[tex]\frac{n!}{(n-x)!x!}[/tex]

P(X = 3) = ₃C₄(0.1667³)(1-0.1667)¹

P(X=3) = 0.0154

Probability of x successes given the probability p of success on a single trial is 0.0154.

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Given:

Charge for each repair = $75

Additional charge per hour = $42

The expression is used to calculate the total charge, in dollars, for each repair appointment:

75 + 42h

Let h represent the number of hours Susna works during an appointment.

To find the total charge if Susan works for 6 hours, substitute 6 for h in the expression and evaluate.

Thus, we have:

h = 6

75 + 42h

75 + 42(6) = 75 + 252 = 327

Therefore, the total charge in dollars if Susan works for 6 hours is = $327

ANSWER:

$327

The solution to the inequality shows that the circle will be on 10 and pointing to the left.

Inequality are expressions not separates by an equal sign.

Given the inequality expression below:

2(b + 2) < 24

Expand

2b + 4 < 24

2b < 24 - 4

2b < 20

Divide both sides by 2

2b/2 < 20/2

b < 10

Hence the number line with open point at 10 with arrow pointing left.

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Answer:

The dinner costs $18

Step-by-step explanation:

30x0.40=discount

discount=12

30-12=dinner price

dinner price=$18