Each letter of the alphabet is written on a piece of paper and put in a hat. If a piece of paper is chosen at random, what is the probability that it will be a vowel?

The number of favorable outcomes is .

The number of possible outcomes is .

So P(vowel) = , or about percent.

The person 64 feet above the water can see 9.84 miles.

It is given in the question that the distance to the horizon is directly proportional to the square root of the elevation of the observer.

if the elevation of the observer be h and distance to the horizon be x then:

[tex]x=k\sqrt{h}[/tex]  where k is the constant of proportionality

from the given data:

[tex]7.4= k\sqrt{36}\\\\7.4=6k\\\\k=1.23[/tex]

So, if h = 64 feet then,

[tex]x=k\sqrt{h}\\\\x=1.23\sqrt{64}\\\\x=9.84 miles[/tex] is how far the person 64 feet above the water can see.

Learn more:

https://brainly.com/question/16998607

Answer:

The answer is A

Step-by-step explanation:

sadly i dont have the work of it just by looking it up you can get the answer tho. Answer is A

Answer: B. 19.9

Step-by-step explanation: Set up an equation where sin and the degree angle is in the numerator, and the side length is in the denominator.

Sin65/8 = Sinx/3

Plug Sin65 into your calculator and you will get 0.9063. Divide this number by 8.

0.9063/8 = 0.1133

Your equation is now 0.1133 = sinx/3

Multiply by 3 on each side.

0.3399 = sinx

Put sin on the left side. It will look like:

Sin^-1(0.3399) = x

Press enter on your calculator. You will get

X = 19.9.

It should be regular octagon, regular hexagon, and square

By definition the interquartile range or IQR is obtained when the 25th percentile or [tex] Q_{1} [/tex] is subtracted from the 75th percentile or [tex] Q_{3} [/tex].

Thus, from the above definition, the formula for IQR is:

[tex] IQR=Q_{3}-Q_{1} [/tex]

As we can see from the provided options that the definition of IQR matches the expression provided in Option A and thus, Option A is the correct answer.

Quartile 3 (Q3) minus quartile 1 (Q1) is right for apex.

A polynomial function of nth degree with given zeros, use the form f(x) = a (x - x1)(x - x2)...(x - xn), which is [tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]

To write a polynomial function of the nth degree with given zeros, you can use the fact that a polynomial function f(x) with zeros at x1, x2, ..., xn can be expressed as:

f(x) = a (x - x1)(x - x2)...(x - xn)

Where 'a' is the leading coefficient, which can be any non-zero real or complex number, and (x - xi) are factors for each zero of the polynomial. If the polynomial is supposed to have a specific coefficient for the highest power term, then 'a' is that coefficient; otherwise, 'a' can be chosen freely to define the polynomial.

To illustrate with an example, if we had a polynomial of degree 3 with zeros at 1, -2, and 3, and we want the leading coefficient to be 1, our polynomial would be:

f(x) = (x - 1)(x + 2)(x - 3)

Expanding this product, we would get:

[tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]

This polynomial of third degree has the specified zeros and a leading coefficient of 1.

I think that it would be a linear model.

Answer:

Step-by-step explanation:

quadratic C

If you got 3 questions wrong on a 12 problem math paper, to figure out how many you got right you must subtract the number you got incorrect (3) from the total number (12).

12-3=9

To figure out your grade, you have to divide how many you got correct (9-see above) by the total number of questions (12).

9/12 = 0.75

If you multiply this decimal by 100, you get the equivalent percentage of 75%.

Therefore, you would have gotten a 75% on the paper.

Hope this helps!

We have been given that a bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons.

We need to find the probability of drawing a red balloon.

We know that probability is given by

[tex]\\ \text{Probability =} \frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

Since we know that there are 10 red balloons. Therefore, our number of favorable outcomes is 10.

In order to find the total number of outcomes, we will add balloons of all colors.

Therefore, total outcomes are  = [tex]10+12+15+8 = 45[/tex]

We can now substitute the values of favorable outcomes and total outcomes in order to find the required probability.

[tex]\\ \text{Probability =} \frac{\text{10}}{\text{45}} = \frac{2}{9}[/tex]

9/37  is the correct answer.

The surface area of the square pyramid is [tex]\(360 \, \text{mm}^2\)[/tex]

To calculate the surface area of a square pyramid, we need to find the area of its base and the area of its four triangular faces. Given the following:

The base side length [tex](\(s\))[/tex] is [tex]10\ mm[/tex].

The height of the pyramid [tex](\(h\))[/tex] is [tex]12 \ mm[/tex]

Step-by-Step Calculation:

1. Area of the base:

The base is a square with side length [tex]\(s = 10\) mm.[/tex]

[tex]\[\text{Area of the base} = s^2 = 10^2 = 100 \, \text{mm}^2\][/tex]

2. Slant height of the pyramid:

To find the slant height [tex](\(l\))[/tex], we need to use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle where one leg is half the side length of the base [tex](\(\frac{s}{2} = \frac{10}{2} = 5\) mm)[/tex] and the other leg is the height of the pyramid [tex](\(h = 12\) mm)[/tex].

[tex]\[l = \sqrt{\left(\frac{s}{2}\right)^2 + h^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \text{mm}\][/tex]

3 Area of the four triangular faces:

Each triangular face has a base of [tex]10\ mm[/tex] and a slant height of [tex]13 \ mm[/tex].

[tex]\[\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 10 \times 13 = 65 \, \text{mm}^2\][/tex]

Since there are four triangular faces:

[tex]\[\text{Total area of the four triangular faces} = 4 \times 65 = 260 \, \text{mm}^2\][/tex]

4. Total surface area:

The total surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:

[tex]\[\text{Total surface area} = \text{Area of the base} + \text{Total area of the four triangular faces} = 100 + 260 = 360 \, \text{mm}^2\][/tex]

Answer:

  15x^3·y

Step-by-step explanation:

The numbers 60, 45, 75 are all multiples of 15, so 15 is their greatest common factor.

The least power of the factor x is 3; the least power of the factor y is 1, so the GCF is ...

  GCF = 15·x^3·y

Answer:

X + (0.18 * X)

where X is the price of the bill without the tip

Step-by-step explanation:

The first thing you have to do is convert the percentage to a decimal value. For example, if it is 30%, its decimal value is 0.30. As simple as dividing that 300 by 100. Repeat the previous step with all the percentages you have to add.

In this case it is 18% therefore the decimal value will be 0.18. As we do not have the value of the account, we will call this value X .

Therefore the total price of the account, that is, with the addition of the tip is as follows:

X + 18% de X =

X + (0.18 + X)

Answer: 57

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

Explanation:

Convert each raw score to a z score

If x = 63.4, then

z = (x-mu)/sigma

z = (63.4-72.3)/8.9

z = -1

if x = 81.2, then 

z = (x-mu)/sigma

z = (81.2-72.3)/8.9

z = 1

So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)

Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words

P(-1 < z < 1) = 0.68 approximately (see note below)

Multiply 0.68 by the total 84 to get

0.68*84 = 57.12

which rounds to 57 people

Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough