3. Consider drawing a hand of five cards. What is the probability that:
a. The first card is a king.

0.030 is the probability that three students chosen at random all study History.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty. Mathematics' discipline of probability investigates potential outcomes of events as well as their relative likelihoods and distributions.

Given Data

12 students who study Geography(G),

11 students who study History(H)

10 students who study Economics(E)

Probability that three students chosen at random all study History

[tex]\frac{11}{3}[/tex] ÷ [tex]\frac{33}{3}[/tex]

[tex]\frac{11}{3}[/tex] ×[tex]\frac{3}{33}[/tex]

0.030

0.030 is the probability that three students chosen at random all study History.

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Answer: $2500

Step-by-step explanation:

Let the amount she sells in dollars be x. Then,

[tex]450+0.06x \geq 600\\\\0.06x \geq 150\\\\x \geq 2500[/tex]

Given:

The number of faces =8.

Required:

We need to find the polyhedron with 8 faces.

Explanation:

Recall that the tetrahedron is a polyhedron composed of four triangular faces

The number of faces in tetrahedron =4.

Recall that the octahedron is a polyhedron with 8 faces.

The number of faces in the octahedron= 8.

Recall that the dodecahedron is a polyhedron with 12 faces.

The number of faces in the dodecahedron = 12.

Recall that the icosahedron is a polyhedron with 20 faces.

The number of faces in icosahedron =20.

Final answer:

octahedron

After 18 hours the remaining quantity of the radioactive sample will be (A) 4.68 grams.

So, original radioactive substance = 3000 grams.

So, a number of half-lives in 18 hours:

Then, after 18 hours:

Therefore, after 18 hours the remaining quantity of the radioactive sample will be (A) 4.68 grams.

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The correct question is given below:
300 grams of a radioactive sample has a half-life of 3 hours. After 18 hours, the remaining quantity will be:

(A) 4.68 gm

(B) 2.34 gm

(C) 3.34 gm

(D) 9.37 gm

A = votes to Abe

G = votes to George

we know that all votes together were 539, so A + G = 539, we also know that George got 23  more than Abe, so "G = A + 23"

[tex]\stackrel{Abe's}{A}~~ + ~~\stackrel{George's}{(A+23)}~~ = ~~\stackrel{total}{539}\implies 2A+23=539\implies 2A=516 \\\\\\ A=\cfrac{516}{2}\implies \boxed{\stackrel{Abe}{A=258}}\hspace{12em}\boxed{\underset{George}{\stackrel{258~~ + ~~23}{281}}}[/tex]

Answer:

one tenth of 100.5 is 10.05 so 10.05$

Step-by-step explanation:

First take 100.5 multiply by one tenth=10.05$ or ten dollars and 5 cents

The quadratic expression when ( x - 2) ( x - 7 ) is multiplied is x² - 9x + 14.

A polynomial of degree two or a quadratic polynomial that has two as the highest exponent of the variable. A quadratic polynomial will typically have the following form: p(x): ax² + bx + c, a ≠ 0.

A coefficient is a multiplicative factor in a polynomial term, a series term, or an expression; it often has the form of a number but can also take the form of any expression.

When an expression ( x - r )( x - s ) is multiplied, where r and s are integers, we obtain a quadratic polynomial.

Therefore, when ( x - 2 )( x - 7 ) is multiplied we get:

( x - 2 )( x - 7 ) = x( x - 7 ) - 2( x - 7 )

( x - 2 )( x - 7 ) = x² - 7x - 2x + 14

( x - 2 )( x  - 7 ) = x² - 9x + 14

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[tex]\frac{x^{2} - 9}{3x^{2} + 8x - 3 } : \frac{x - 3}{x + 2} =\frac{(x^2 - 9)(x + 2)}{(3x^2 +8x - 3)(x - 3)} =\frac{x^3 + 2x^2 - 9x - 18}{3x^3 - 9x^2 + 8x^2 - 24x - 3x + 9} =\frac{ x^3 + 2x^2 - 9x - 18}{3x^3 - x^2 - 27x + 9} = \frac{0}{3 - 3x} = 0[/tex]

Answer:

0

Step-by-step explanation:

when you multiply, and add and subtract it all up, you eventually get 0 over 3-3x. what is 0 divided by 3-3x? 0

Answer:

h(x) = 9x-18 is the correct inverse function

Step-by-step explanation:

f(x) -> y (first we need to rewrite the equation with y)

y= 1/9x+2 (next we need to solve for x)

y=1/9x

-2 -2  (subtract 2 from both sides)

y-2= 1/9x (multiply 9 on both sides

9y-18= x (and lastly switch back x and y)

y = 9x - 18 (if a real equation than write h(x) or [tex]f(x)^{-1}[/tex], if not real equation keep it in y)

h(x) = 9x-18

Hope this helps!

Answer:

9x–18

you can ask questions for clarification

Answer: 20 children’s tickets and 47 adult’s tickets

20 children's tickets were sold and 47 adult tickets were sold.

People bought tickets at the theater and $704 was collected.

charge - $7 for children and $12 for adults.

let, x number of children and y number of an adult take admission,

then, according to question ->

7*x+12*y=704; said eq. 1

and, given 67 people bought tickets at the theater.

x + y=67; said eq. 2

now, on solving these equations,

we get,

multiply eq.2 by 7 then subtract with eq. 1

then we get, y=47 then put the value of y in eq. 2 we get x=20;

so,

20 children's tickets were sold and 47 adult tickets were sold.

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Answer:

15

Step-by-step explanation:

Divide it into triangles, then solve for area.

Answer:

Standard deviation measures the dispersion of a dataset relative to its mean

Step-by-step explanation:

Answer:

[tex]a\:\dfrac{\sqrt{a^3}}{a^4} =\dfrac{\sqrt{a}}{a^2}[/tex]

Step-by-step explanation:

I believe this question is wrongly or part of it has been truncated in the screenshot

I have simplified the original expression and checked my answer.

[tex]\mathrm Simplify \;\;a\dfrac{\sqrt{a^3}}{a^4}\\\\\sqrt{a^3} = a^{\dfrac{3}{2}} = a^{(1 + \frac{1}{2})} = a \cdot a^\frac{1}{2} = a \sqrt{a} \\\\a\dfrac{\sqrt{a^3}}{a^4}\\\\ = \dfrac{a\cdot a\cdot \sqrt{a}}{a^4}\\\\= \dfrac{a^2\sqrt{a}}{a^4}\\\\= \dfrac{\sqrt{a}}{a^{(4-2)}}\\\\\\=\dfrac{\sqrt{a}}{a^2}[/tex]

The graph of the given points form the rectangle is attached below.

Graph:

The graph is defined as the pictorial representation or a diagram that represents data or values in an organized manner.

Given,

The points are (2, 1),(2, 5), (7, 1), and (7, 5).

Here we need to plot the graph and we have to identify whether it will form the rectangle.

First, we have to do the following in order to solve it,

Therefore, the resulting graph is attached below.

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Answer:

Bro x =21

Step-by-step explanation:

X=21 and AM=14

As all the lines are same so all will be 7 and x will be 3 times 7 which is 21 and in the AM case there 7 is 2 times thus multiply 7 by 2 for 14

The area of the composite figure is 58. 71 square units.

It is important to note that the area of the composite figure is given as;

Area of a rectangle + area of a semi circle

The formula for area of a rectangle is expressed as;

Area = lw

Where;

Now, let's substitute the values, we have;

Area = 6 × 9

Area = 54 square units

The formula for area of a semicircle is expressed as;

Area = πr²/2

Where;

Given diameter = 6, radius = 6/2 = 3

Substitute the value

Area = 3. 14(3)/2

Area = 4. 71 square units

But area of the composite figure = 54 + 4. 71 = 58. 71 square units.

Hence, the area is 58. 71 square units.

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n = - 3

How is the given equation  [tex]5^{n} =\frac{1}{125}[/tex]   solved to find n ?

Converting the fraction to negative exponential form,

[tex]5^{n} ={125}^{-1} \\\\5^{n} ={(5^{3})}^{-1} \\\\\text{We know } (a^{n} )^{m} =a^{nm} \\\\\text{Applying this exponent power rule in the above expression},\\\\5^{n} = 5^{-3} \\\\\text{As the corresponding exponents are equal}\\\\n= -3[/tex]

What are laws of exponents?

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The value of x in this geometric sequence is equal to √2.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

For this exercise, we would formulate an equation from the common ratio of this geometric sequence as follows:

r = a₂/a₁ = a₃/a₁

Substituting the given parameters into the common ratio formula, we have;

1/√X + 1 = √x - 1/1

Next, we would take the square of both sides, we have:

1/x + 1 = x - 1/1

Cross-multiplying, we have:

(x + 1)(x - 1) = 1

x² - x + x - 1 = 1

x² - 1 = 1

Adding 1 to both sides, we have:

x² - 1 + 1 = 1 + 1

x² = 1 + 1

x² = 2

x = √2

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Based on the line and the points that it goes through, the equation with the same proportional relationship as the graph is y = three-fifths x.

To find the relationship of the points on the line in the coordinate plane, you need to find the slope of the line. The slope can be found by the formula:

= Change in y / Change in x

Solving for the slope gives:

= (3 - 0) / (5 - 0)

= 3 / 5

For equations to be proportional, they need to have the same slope. With the slope of the line being 3/5, the equation that would have the same proportional relationship is:

y = 3/5x

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After completing 6 week and 8 days, the amount in the bank account will be $280.

The initial balance in the bank account = $60.

Allowance deposit per week = $7.

Paycheck deposit per week = $25.

Let 'w' be the number of week.

Th equation of the total amount 'b' after 'w' week becomes;

b = 60 + (25+7)w

As, the total amount becomes $280, after the week .

Put b = 280 in equation and find w.

280 = 60 + (25+7)w

Simplifying;

220 = 32w

w = 6.875

Thus, after completing 6 week and 8 days, the amount in the bank account will be $280.

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Answer: $860 this week.

Step-by-step explanation:

Paul worked 40 hours this week, and makes 21.50 dollars an hour. Gross pay means the amount of money paid before taxes.

So we don't need to calculate any taxes, which means all we need to do is multiply 21.50 by 40 hours, since he makes 21.50 an hour, and he worked 40 hours.

Answer:

n < - 1

Step-by-step explanation:

- 2(n - 4.5) > 11 ← distribute parenthesis on left side

- 2n + 9 > 11 ( subtract 9 from both sides )

- 2n > 2

divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

n < - 1

Answer:

n < -1

Step-by-step explanation:

-2(n -4.5) > 11 (multiply the contents within the bracket by -2.)

-2n + 9 > 11 (- × - = +)

-2n > 11 - 9 [ like terms have to be with each other (transposing); and when u transpose a number it changes signs.]

-2n > 2 (divide both sides by negative 2)

n < -1 (sign changes as a reslut of the negative division)

The properties of equality used in the equation are subtraction properties and multiplication properties of equality

The complete question is added at the end of the solution

From the complete question, the equation is given as:

(1/3d + 4 = 28)

Start by removing the bracket in the given equation

So, we have

1/3d + 4 = 28

Next, we continue by applying the subtraction properties of equality

This means that we subtract 4 from both sides of the equation.

So, we have:

1/3d + 4 - 4= 28 - 4

Evaluate the difference in the above equation

So, we have

1/3d = 24

Next, we continue by applying the product properties of equality

This means that we multiply both sides of the equation by 3

So, we have:

3 * 1/3d = 24 * 3

Evaluate the products in the above equation

So, we have

d = 72

By looking at the computations above, we can see that we apply the following properties:

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Possible question

Which properties of equality are used in the example shown on the left?

(1/3d + 4 = 28)

The integers in the solution set of 3p − 10 ≥ 7p + 6 are -4 and -5

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The set is given as

S: {−2, −3, −4, −5}

The inequality expression is given as

3p − 10 ≥ 7p + 6

We start by evaluating the inequality expression

So, we have

3p − 10 ≥ 7p + 6

Subtract 7p from both sides of the inequality expression

So, we have

-4p − 10 ≥ 6

Add 10 to both sides of the inequality expression

So, we have

-4p ≥ 16

Divide both sides of the inequality expression hy -4

So, we have

p ≤ -4

This means that the integers in the solution set are integers that do not exceed -4

These integers are -4 and -5

Hence, the solution is -4 and -5

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The given value 4.09 in digits can be written in words as four and nine hundredths.

The system of written number digits in words can be described as the system that enable the numbers to be breakdown in words for simplicity.

This can starts from the lowest which is the units as well as the tens , and also hundreds and thousands, however from the  given value 4.09 we can see that if we convert to the word system of naming numbers we can come into conclusion that it is  four hundred nine hundredths.

Therefore, option B is correct.

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Answer:

D

Step-by-step explanation:

The author shows that computer programs make it faster to make changes to blur prints.

A computer program is a set of instructions written in a programming language that a computer is supposed to obey.

Hence it is clear that the author shows that computer programs make it much faster to make changes to blue prints.

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The balloon's vertical distance above the ground is equal to 633.7 feet

What is angle of depression?
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.

Given data ,

we have Angle of depression = 35°

Base distance D = 905 ft

Let the vertical distance be H

To calculate the vertical distance H of the balloon above the ground , we use the angle of depression and the base distance.

Therefore , using the trigonometric identities ,

sin = Opposite / Hypotenuse

cos = Adjacent / Hypotenuse

tan = Opposite / Adjacent

So , tan  Ф = tan 35°

                  = H / D

      tan 35°= H / 905

H = tan 35° x 905 ft

H = 0.7002075 x 905

H = 633.7 ft

Hence ,  vertical distance is equal to 633.7 ft

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Answer:

I believe the answer is 2^3x3^2

Answer:

8, B

Step-by-step explanation:

[tex]-6(3-r)=30 \\ \\ -18+6r=30 \\ \\ 6r=48 \\ \\ r=8[/tex]

Answer:

667/45 or 14 37/45

Step-by-step explanation:

you have to convert 5 4/5 x 2 5/9 then you multiply those numbers but simply them which would be 29/5 x 23/9 then you get 667/45 or 14 37/45 as an alternative form

hope this helps