What is the probability that a randomly chosen student prefers rap or sings in the shower 3-4 times a week

The probability that precisely two of the sampled people utilized a discount broker is 0.2668.

A discount broker was employed by 30% of individual investors.

p = 30 ÷ 100 = 0.3

q = 1 - p

q = 1 - 0.3

q = 0.7

n = 9

P(x) = [tex]{}^{n}C_{x}p^{x}q^{n - x}[/tex]

Only two of the people polled had utilized a broker.

x = 2

P(2) = [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex]= 0.2668

Only three persons have used a deal broker.

= P(3) + P(2) + P(1) + P(0)

= [tex]{}^{9}C_{3}[/tex](0.3)³[tex](0.7)^{6}[/tex] +  [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] + [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] + [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex]

= (84 × 0.027 × 0.1176) + (36 × 0.09 × 0.0823) + (9 × 0.3 × 0.0576) + (1 × 1 × 0.0403)

= 0.7291

Probability of a broker has been employed by at least three of them.

= P(2) - P(1) - P(0) - 1

= -([tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] -  [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] -  [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex]  - 1)

= -((36 × 0.09 × 0.0823) - (9 × 0.3 × 0.0576) - (1 × 1 × 0.0403) - 1)

= 0.9291

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The product of the HCF and LCM of 12 ,18,30 can be written as 1080.

The H.C.F.  can be described as the greatest factor  that can be found when expressing given two or more numbers, on the other hand the LCM can be described as the least factor that exist between a two given number.

factors of 12 are: 3, 4, 2, 6, 12.

factors of 18 are: 2, 3 , 6 9 , 18

factors of 30 are ; 2, 3, 6, 5, 10

HCF; The factor that is greatest among the factors of the numbers = 6

To calculate the LCM, we need to find to find the prime factor of the three numbers as:

Prime factor of 12 are ;  2*2*3

Prime factor of 18 are ; 2*3*3

Prime factor of 12 are ; 2*3*5

LCM is now the multiplication of the prime factors which is the highest occurrence of them in either numbers as ; 2*2*3*3*5 =180

From the given numbers we can see that the HCF = 6 and LCM = 180, then if we find the product as (6*180)=1080 which is the number of the product of the lowest common factor as well as the highest common factor.

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The radical form  ∛ is 1/3.

The radical form of the expression [tex]15^{\frac{1}{3}[/tex] is ∛15.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

Example: 3 + x, 3x, √4, ∛27 are all expressions.

We have,

[tex]15^{\frac{1}{3} }[/tex]

We need to write it in radical form.

This means we must remove the power 1/3 in the given expression.

Some of the expressions in the radical form are:

∛ = 1/3

√ = 1/2

We know that,

∛ = [tex]\frac{1}{3}[/tex]

So,
Since ∛ is 1/3 we can write the expression as ∛15.

[tex]15^{\frac{1}{3} }[/tex] = ∛15.

Thus,

The radical form of the expression [tex]15^{\frac{1}{3}[/tex] is ∛15.

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If a caterer needs 21 pounds of pasta and a local store sells 8 pounds of pasta for $12, then the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta, calculated using the unitary method.

As per the question statement, a caterer needs 21 pounds of pasta to cater a wedding, while a local store sells 8 pounds of pasta for $12.

We are required to calculate the total amount which the caterer will have to pay at the store for their 21 pounds of pasta.

To solve this question, first we will need to calculate the price of 1 pound of pasta at the local store, from their rate provided in the question statement, and then multiply the cost of unit pound of pasta with the number of pounds the caterer needs, to obtain our desired answer, that is,

Using the unitary method, we get,

The local store sells 8 pounds of pasta for $12,

Or, it then sells 1 pound of pasta for $(12/8)

Or, the cost of 21 pounds of pasta at this store will $[(12/8) * 21] = $31.5

Hence,  the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta.

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Answer:2.10971436E14

Step-by-step explanation:

Answer:

Step-by-step explanation:

1,747,544,165,078,382 is the answer.

Answer:

Your answer is 1649 miles.

Step-by-step explanation:

[tex]5^{4} + 4^{5} = 1649[/tex]

Because we have a closed dot at (4, 17), we conclude that when x = 4 the value of the function is 17, so the correct option is the third one.

Here we have the graph of a piecewise function, and we want to see which value the function takes when x = 4.

To do so, we need to find x = 4 on the horizontal axis, and then move until we hit the graph.

For x = 4 we can see two points on the graph.

One open point at y = 7, where the open dot means that this value does not belong to the function.

A closed point at y = 17, where the closed dot means that this value belongs to the function.

From this, we conclude that when x = 4, the value of the function is 17.

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Answer:

6/4

Step-by-step explanation:

For a RIGHT triangle, Tan = opposite leg / adjacent leg  =  6/4 for angle F in this example

The area is 28.26 in²

The distance between the two boats is found as 21.60 m.

For the given question,

Let the distance of ship c from the bottom of the cliff is 'a'.

Let the distance between both ships is 'b' m.

The height of the cliff is 110 m.

The angle of depression by both the ship with the top of the cliff is 48° and  57°.

Data from the figure shown,

Consider right triangle ABD,

tan 48° = AB/BD

tan 48° = 110/(a+b)

a + b = 110/tan 48°

a + b = 99.04   .......eq 1

Now in  right triangle ACD,

tan 57° = 110/a

a = 110/tan 57°

a = 71.43 m

Put the value of in eq 1.

a + b = 99.04

b = 99.04 - 71.43

b = 21.60 m

Thus, the distance between the two boats is found as 21.60 m.

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Let:

x = Speed of the jet

y = Speed of jetstream

so:

and

Solve the system using elimination method:

Replace x into (1)

Answer:

Rate of the jet in still air: 726 mph

Rate of the jetstream: 65mph

The quadratic function of best fit for the data is given as follows:

h(t) = -0.004t² +1.032t + 5.667.

Using this function, the initial height of the shot is of 5.67 feet.

The input and the output of the data are given as follows:

As the input increases, the output increases and then it decreases. Since this behavior of increase/decrease is not uniform over the entire domain of the relation, a quadratic function best models this data.

To find the quadratic function of best fit, we insert the points (input,output) into a calculator, from point (20, 25) to point (200,64).

Inserting the points into the calculator, the function is defined as follows:

h(t) = -0.004t² +1.032t + 5.667

The height in which the shot started its flight is given by the height when t = 0, hence:

h(0) = -0.004(0)² + 1.032(0) + 5.667 = 5.667 feet = 5.67 feet (rounded to the hundredths place).

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10 is a natural number, whole number and an integer.

Natural numbers may be defined as the numbers which include all the positive integers that is non-negative integers, and the numbers will be from 1 to infinity. 10 is a natural number as it lies in the range from 1 to infinity. Whole numbers may be defined as the numbers which include all the positive integers as well as zero. So, the range of whole numbers is from zero to infinity and 10 is a whole number as it lies in this range. Integers may be defined as the collection of positive and negative numbers along with zero but no fractions. 10 lies in this range so 10 is an integer.

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The polynomial factors are (x -2)(x+ i)(x - i)

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

To find the factors of the given polynomial, we can proceed as

[tex]x^3 -2x^2 + x - 2[/tex]

Let's factor out a common term

[tex]x^3 - 2x^2 + x - 2 = x^2(x-2) + (x-2)\\x^2(x-2)+(x-2)\\(x-2)(x^2+1) = (x-2)(x+i)(x-i)[/tex]

The factors of the given polynomial is (x-2)(x+ i)(x- i)

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The arc marked in red is a quarter of the circle's circumference.

Hence the arc marked red subtends an angle of 90degrees.

In our case

Answer:

Step-by-step explanation:

The total for 12 oranges would be $8.28

We can say that the graph of 4x+5y = 3/7 is a line because it can be represented by the straight line equation.

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.

Given equation :   4x+5y = 3/7

The given equation can be written as

5y = -4x + 3/7

y = (-4/5)x + 3/35

This is a form of y = mx + c

It is a the equation of the straight line.

Therefore, we can say that the graph of 4x+5y = 3/7 is a line as it can be represented as the equation of the straight line.

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The value of the [tex]\lim_{x\to \ 0} h(x)[/tex] cannot be determined based on the given information.

Squeeze Theorem :

When standard algebraic techniques like factorization, conjugation, algebraic manipulation, etc. fail to solve a limit problem, the squeeze principle is utilized. It does, however, demand that you can "squeeze" your issue between two other, "simpler" functions whose bounds are quickly computed and equal.

It states that if [tex]g(x),f(x) and h(x)[/tex] are three functions such that,

[tex]g(x)\leq h(x)\leq f(x)[/tex]

and [tex]\lim_{x\to \ 0} f(x) = \lim_{x \to \ 0} g(x) =L[/tex] , Then

[tex]\lim_{x\to \ 0} h(x) = L[/tex]

Given Data :

[tex]g(x)=\frac{x^{2} }{3} +\frac{2}{5}[/tex]

Now, [tex]\lim_{x\to \ 0} g(x) =\frac{2}{5}[/tex]

and [tex]f(x) = x^{2} -2x+4\\[/tex]

and [tex]\lim_{x \to \ 0} f(x)=4[/tex]

Since,[tex]\lim_{x \to0} f(x) \neq \lim_{x\to \ 0} g(x)[/tex]

Thus, we cannot employ the Squeeze Theorem, Hence the data is insufficient to calculate the limit of h(x).

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If a given point, P, exists on a great circle on the surface of a sphere, no line can be drawn on the sphere that is parallel to the great circle because each pair of great circles(parallel lines) will always intersect, regardless of how they are drawn.

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Answer:

2a

Step-by-step explanation:

when you have two of the same variable you can combine them. We know that all variables that do not have a coefficient by default have the constant 1 so 1a+1a equals 2a

Answer:h

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\sf -3\left(33b+65\right)=-95b-6b-87[/tex]

Combine like terms:

[tex]\sf -3\left(33b+65\right)=-101b-87[/tex]

Expand:-

[tex]\sf -99b-195=-101b-87[/tex]

Add 195 to both sides:-

[tex]\sf -99b-195+195=-101b-87+195[/tex]

Simplify:-

[tex]\sf -99b=-101b+108[/tex]

Add 101b to both sides:-

[tex]\sf -99b+101b=-101b+108+101b[/tex]

Simplify:-

[tex]\sf 2b=108[/tex]

Divide both sides by 2:-

[tex]\sf \cfrac{2b}{2}=\cfrac{108}{2}[/tex]

Simplify:-

[tex]\sf b=54[/tex]

Therefore, your answer is b = 54!!

___________________________

Hope this helps you!

Have a great day! :)

The balloon that was farther from the town at the beginning, and which traveled more quickly is Henry's balloon.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Henry's balloon is 48 miles after 2 hours.

Tasha's balloon after 2 hours will be:

= 8x + 20

= 8(2) + 20

= 32 miles

In this case, Henry's balloon is farther.

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IN THE PLACE OF Y PLUG IN 0

[tex] = \frac{( {0})^{2}}{5} \\ = \frac{0}{5} \\ = 0[/tex]

The answer is 0

Writing 1 trillion in scientific notation is 1 × 10^12.

A scientific notation simply means the way of expressing numbers that are either too large of too small. Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.

In this case, I trillion is written as 1,000,000,000,000.

Therefore, it has 12 zeros.

The scientific notation is 1 × 10^12.

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Area of Rectangles of the given values are 5/3inches², 20/3inches², 10/3inches² and 1 inches²

What is Area of Rectangle?

The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle called its area.

Since we know that,

Area of Rectangle = length x width

So, by the given values we can find the area of the following:

a) 5inch and 1/3inch

Let,

Length = 5inch

Width = 1/3inch

Since,

Area of Rectangle = length x width

                               = 5 x 1/3

                               = 5/3inches²

b) 5inch and 4/3 inch

Let,

Length = 5inch

Width = 4/3inch

Since,

Area of Rectangle = length x width

                               = 5 x 4/3

                               = 20/3inches²

c) 5/2inch and 4/3 inch

Let,

Length = 5/2inch

Width = 4/3inch

Since,

Area of Rectangle = length x width

                               = 5/2 x 4/3

                               = 5 x 2/3

                               = 10/3inches²

d) 7/6 inch and 6/7inch

Let,

Length = 7/6inch

Width = 6/7inch

Since,

Area of Rectangle = length x width

                               = 7/6 x 6/7

                               = 1 inches²

Hence, The following area of rectangles are 5/3inches², 20/3inches², 10/3inches² and 1 inches²

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19x/3+2/9 is the quotient and 50 is the remainder for the given equation (6x³+13x²-12x-6)÷(3x+2).

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three. Latin's "how many times" is the meaning of the word "quotient." That makes perfect sense: by dividing two numbers, you can determine "how many times" the second number enters the first.

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remainder is the name for this amount.

On dividing the equation,

The quotient will be 19x/3+2/9 and the remainder will be 50.

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The solution of the inequality expression given as 12 + 4y < 32 is y < 5

An inequality expression is an expression where both sides of the expression have unequal values and they make use of any of the symbols <, >, <=, >= and !=

The inequality expression is given as

12 + 4y < 32

Subtract 12 from both sides of the inequality

So, we have the following expression

12 - 12 + 4y < 32 - 12

Evaluate the like terms in the above inequality

So, we have the following expression

4y < 20

Divide both sides of the inequality by 4

So, we have the following expression

4y/4 < 20/4

Evaluate the quotient

y < 5

Hence, the solution is y < 5

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