Which principle helps us to determine the total number of outcomes in a sample space?

Answers

Answer 1
The principle that helps us to determine the total number of outcomes in a sample space is the counting principle.

The Fundamental Counting Principle: If there are “a” ways for one event to happen, and “b” ways for a second event to happen, then there are “a * b” ways for both events to happen.

Related Questions

Choose the product. 4p^3 3(p 2^ + 8p - 3)

4p^5 + 12p^4 + 7p^3
4p^6 + 44p^3
4p^3 - 12p^2 +32p^4
4p^5 + 32p^4 -12p^3

Answers

The answer would most likely be D.
I hope this helps.

Answer:  The correct option is

(D) [tex]4p^5+32p^4-12p^3.[/tex]

Step-by-step explanation:  We are given to choose the correct expression for the following product :

[tex]P=4p^3(p^2+8p-3)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the above product, we need to multiply 4p³ with every term within the bracket.

The required product (i) is

[tex]P\\\\=4p^3(p^2+8p-3)\\\\=4p^{3+2}+32p^{3+1}-12p^3\\\\=4p^5+32p^4-12p^3.[/tex]

Thus, the required product is [tex]4p^5+32p^4-12p^3.[/tex]

Option (D) is CORRECT.

The sum of two integers is 9 their difference is 5 what are the two integers

Answers

x+y=9     x=9-y
solve for x     
x-y=5   so substitute x by 9-y
9-y-y=5
9-2y=5 isolate 
9-2y-9=5-9
-2y=-4 divide both sides by -2
-2y/-2=-4/-2
y=2 and x=9-2=7
check for x+y=9
               7+2=9 
check for x-y=5
                7-2=5      so x=7 and y=2 

            

The values of the two integers are 7 and 2 respectively.

Let the two integers be a and b respectively.

In this exercise, you're required to determine two integers from the given word problem.

Thus, we would write a mathematical (algebraic expression) for the sentence.

Translating the word problem into an algebraic expression, we have;

The sum of two integers is 9;

[tex]a + b =9[/tex]    ....equation 1.

The difference between the two integers is 5;

[tex]a - b = 5[/tex]    equation 2.

Solving the systems of linear equations by using the elimination method, we have:

[tex]2a = 14[/tex]

Dividing both sides by 2, we have:

[tex]a = \frac{14}{2}[/tex]

a = 7

To find the value of y:

[tex]a + b =9\\\\7 +b=9\\\\b =9-7[/tex]

b = 2  

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The stores below each have the same snowboard for an original price of $189.59. At which store can you get the snowboard for the lowest price?

Answers

Answer:

D. You can get the lowest price at Store C.

Step-by-step explanation:

Edge 2021

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh 68.7 cm2 161.7 cm2 381.3 cm2 450.0 cm2

Answers

it A ( 68.7 cm2 ) hope that help guys

Answer:

Option B is the correct answer.

Step-by-step explanation:

We have one side = 27.6 cm

Hypotenuse = 30 cm

Length of remaining side [tex]=\sqrt{30^2-27.6^2}=11.76cm[/tex]

Area of right angled triangle [tex]=\frac{1}{2}\times \texttt{Product of lengths of 2 sides other than hypotenuse}[/tex]

Area [tex]=\frac{1}{2}\times 27.6\times 11.76=161.7cm^2[/tex]

Option B is the correct answer.

The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
A) The function has one imaginary zero.
B) The function has one real zero and two imaginary zeros.
C) The function has one real zero and one imaginary zero.
D) The function has one imaginary zero and two real zeros.

Answers

If a polynomial function with real coefficients has any complex roots, then the complex roots come in pairs of complex conjugates.
Your polynomial has real coefficients and is of degree 3.
It can have 0 complex roots, or it can have 2 complex roots.
It cannot have only 1 complex root.

The correct answer is

D) The function has one imaginary zero and two real zeros.


x = 3, 4i, -4i



Is the sequence geometric? If so, identify the common ratio.

2, -4, -16, -36, ...

A. Yes; -2
B. Yes; 2
C. Yes; -3
D. No

Answers

Answer:

No this is not the sequence geometric.

Step-by-step explanation:

Given : 2, -4, -16, -36, ...

To find : Is the sequence geometric? If so, identify the common ratio.

Solution : We have given that 2, -4, -16, -36, ...

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Geometric Sequence like this:

{a, ar, ar², ar³, ... }

On comparing

2, -4, -16, -36, ...

{ 2 , 2 ×-2, 2×(-2)², 2×(-2)³..

So we get { 2, -4, -8, -16...

Therefore , No this is not the sequence geometric.

Since the quotient between consecutive terms is different, the sequence is not geometric, and the correct option is:

D. No

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio.

In this problem, the sequence is: {2, -4, -16, -36, ...}

[tex]-\frac{4}{2} = -2[/tex]

[tex]\frac{-16}{-4} = 4[/tex]

Different quotients, hence not geometric, and option D is correct.

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The measure of an angle is 1/4 the measure of its complement. Find the measure of each angle

Answers

lets name the 1/4 the measure of its complement x .
complement means they add up to 90.

so both angles add up to 90 and one is 1/4 the other.
so if we set x = 1 the complement is 4x. together they make 5.
90/5=18

so one angle is 18 and the other is 72.

Final answer:

The two angles are 18 degrees and 72 degrees. The smaller angle is one-fourth of the larger, and they add up to 90 degrees because they are complementary.

Explanation:

In mathematics, complementary angles are two angles whose measures add up to 90 degrees. Based on the question, let's denote the smaller angle as x and the larger angle (its complement) as y.

Given that x is 1/4 of y, we can write the equation x = y/4.

Also, since they're complementary, their measures add to 90 degrees, giving the equation x + y = 90.

From x = y/4, it can be inferred that y = 4x. Substituting y in the second equation we get x + 4x = 90, which simplifies to 5x = 90. Dividing both sides by 5, we have x = 18.

To find y, substitute x = 18 into the equation y = 4x, giving y = 4*18 = 72. Therefore, the measures of the two angles are 18 and 72 respectively.

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Please help me

True or false. In order for a disjunction statement to be false, both of its component statements must be false. Explain.

Answers

The answer will be true.

The answer is true. This was just on my quiz and I know its correct.

The sum of two numbers is 28. one number is 14 more. find the numbers

Answers

The numbers are:  "7 " and "21 " .
_______________________________________
Explanation:
_______________________________________
The numbers are:  "x"  and "x + 14" .

x + (x + 14) = 28 .  Solve for "x" ; and then solve for "x + 14" .
_______________________________________
 → x + (x + 14) = 28 ;

Rewrite as:

 →  x + x + 14 = 28 ;

 →  1x + 1x + 14 = 28 ;

 →  2x + 14 = 28 ; 
  
 Subtract "14" from each side of the equation;
 
 →  2x + 14 − 14 = 28 − 14 ;

 →  2x = 14  ;

Divide EACH SIDE of the equation by "2" ;
     to isolate "x" on one side of the equation; & to solve for "x" ;

 →  2x / 2 = 14 / 2 ;

 →  x = 7 . 
_________________________________________
So;  one of the numbers is:  " 7 " .

The other number is:  " x + 14 " ; which equals: " 7 + 14 = 21".

The other number is:  "21 " .
_________________________________________
The numbers are:  "7 " and "21 " .
_________________________________________

The table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward.

Answers

A) The ball is at the same height as the building between 8 and 10 seconds after it is thrown.

C) The ball reaches its maximum height about 4 seconds after it is thrown

Answer:

A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.

C. The ball reaches its maximum height about 4 seconds after it is thrown

Step-by-step explanation:

edg.

A group of friends share slices of pizza.If each person gets 5 slices there will be 4 slices short.How many slices of pizza are there to share?

Answers

there would be 9 to share in total

How do I write the interval(s) for which f(x) is greater than or equal to 0 (interval notation)

Answers

We are looking for the set of values for which y is greater than 0. This would be negative infinity to -2, but not including
-2. This could be expressed as (-infinity, -2). Also, all x values greater than 0 also lead to a y-value greater than 0. Thus, another interval would be (0, infinity). Thus, the answer is (-infinity, -2) and (0, infinity).

To write intervals where f(x) is greater than or equal to 0, solve the equation f(x) >= 0 for x. The solutions are then expressed in interval notation. For instance, x >= 3 is written as [3, infinity).

To write the interval for which f(x) is greater than or equal to 0 in interval notation, you first need to establish where the function is above or touching the x-axis. With algebraic functions, you simply solve the equation f(x) >= 0 for x to find where the function is non-negative. You then write these solutions in interval notation. For example, if your solution was x >= 3, you would write this in interval notation as [3, infinity). Also, keep in mind that round brackets ( ) are used when the number is not included in the interval while square brackets [ ] are used when the number is included.

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A cyclist rides her bike at a speed of 12 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 5 minutes? Do not round your answers.

Answers

The cyclist will go 1 km in 5 minutes. You get the proportion 12/60 and turn in into 12/60=x/5, and when you solve for x, you get 1.

How can you find a unit rate when given a rate?

Answers

To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate.

Hope this helped :)
Set up a proportion.

The ratio of the angle measures of the acute angles in a right triangle is 1:2 . What is the measures of these angles a. 30 and 60 b. 45 and 90 c. 60 and 120 d. 10 and 20

Answers

a triangle has 3 angles, together they add up to 190 degrees. in a right triangle there is one angle that is 90 degrees, meaning the other two add up to 90 degrees. the ratio between them is 1:2 a 1/3 of 90 is 30 degrees meaning one angle is 1*30= 30 and the second is 2*30=60 -> the correct answer is "a"

Answer:

30 & 60

Step-by-step explanation:

The tutor is correct, besides the fact that the interior angles would equal 180, not 190. Typos happen.

Jack's overtime wage is $3 per hour more than his regular hourly wage. He worked for 5 hours at his regular wage and 4 hours at the overtime wage. He earned $66. Find his regular

Answers

Jack's regular wage is $6 per hour.

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.


A coat hanger is in the shape of isosceles triangle ABC shown in the figure. Sides AB and BC are congruent.

if m<BAC=22, then m<ABC= ?

Answers

m<BAC = m<BCA = 22
m<ABC = 180 - 2(22)
m<ABC = 180 - 44
m<ABC =136

Answer: m∠ABC=136°

Step-by-step explanation:

In the given figure we have a coat hanger is in the shape of isosceles triangle ABC.

Sides AB and BC are congruent.

The isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.

Therefore, in ΔABC, we have

m∠BAC=m∠BCA

If m∠BAC=22°, then m∠BCA= 22°

By angle sum property , we have

m∠BAC+m∠BCA+m∠ABC=180°

⇒22°+22°+m∠ABC=180°

⇒m∠ABC+44°=180°

⇒m∠ABC=180°-44°=136°

⇒m∠ABC=136°

Therefore, If m∠BAC=22°, then m∠ABC=136°

assume that y varies inversely with x. if y=27 when x=12, find x when y=-12.

Answers

y varies inversely with x, means y=k/x
27=k/12 => k=27*12=324
so the equation is y=324/x
when y=-12, -12=324/x => x=324/(-12)=-27

Solve for the variable: 12.9 = x + 7.1 5.8 -5.8 20 -20

Answers

12.9 = x + 7.1
subtract 7.1 from both sides to isolate the variable, x.

5.8 = x

5.8 is your answer.

Suppose g(x) = f(x + 2) – 3. Which statement best compares the graph of g(x) with the graph of f(x)?

Answers

Answer:

B. the graph of g(x) is shifted 2 units right and 3 units up

Step-by-step explanation:

just got it right

We conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. Option D is the correct answer.

The given function is g(x) = f(x + 2) – 3.

What is a function?

A function is a relation for which each value from the set of the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

To shift a function right:

Subtract inside the function's argument. For example, f(x)-b is basically f(x) shifted b units to the right.  

Subtracting inside the function's argument moves you to the right.

So, g(x) = f(x – 2) means f(x) is shifted two units to the right.

To move a function down:

Subtract outside the function. For example,  f(x)-b is basically f(x) moved down 3 units.

So, g(x) = f(x – 2) + 3 means, f(x) is moved 3 units down.

Therefore, we conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. So, option D is the correct answer.

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a 12000-gallon pool is being filled at a rate of 40 gallons per minute. at this rate, how many minutes will it take to fill this pool 3/4 full?

Answers

First figure out what 3/4 of the pool is. 

12000* 3/4 
=9000 gallons 

If the rate is 40 gallons per minute, 
9000/40 
=225 minutes 

It would take 225 minutes to fill up 3/4 of the pool.

Hope I helped :) 

The number of minutes taken to fill the pool in three-fourths full is 225.

Given that,

There is a 12,000-gallon pool filled at the rate of 40 gallons per minute.And, there is three-fourths full.

Based on the above information, the calculation is as follows:

[tex]= (12000 \times \frac{3}{4}) \div 40[/tex]

= 225 minutes

Therefore we can conclude that the number of minutes taken to fill the pool in three-fourths full is 225.

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Julio's father is 4 times as old as Julio. The sum of their ages is no less than 55.

What is the youngest age Julio can be?


Enter your answer in the box.

years

Answers

Julio = j, father = f
f = 4j, j+f = 55, j + 4j = 55, 5j = 55, j = 11
So youngest Julio can be is 11 years old.

karen has 12 apples. she gives 3 to john, 4 to lennard, and 2 to tracy. she then takes away 2 from john, 1 from lennard, and 1 from tracy. how many apples does she have now?

Answers

She has 12 apples
Let's calculate how many apples the other people have and subtract how many she took away
John; 3-2=1
Lenard; 4-1=3
Tracy; 2-1=1
Now let's add the answers up to know how many she has given out
1+3+1=5
So that means she has lost 5 apples. To find how many she has left will be the total minus the apples given out.
12-5=7
She has 7 apples left
Hope that helped. Have a nice day
she has seven apples

What is the approximate value of x? Round to the nearest tenth.

A) 3.1 cm
B) 3.9 cm
C) 4.6 cm
D) 5.4 cm

Answers

x = 6cm * sin(50) = 4.59

 rounded to 4.6

 Answer is C

Answer:

option C is correct    

The approximate value of x is, 4.6 cm(nearest to tenth)

Step-by-step explanation:

In the given figure; the triangle is right angle triangle:

Label the figure:

then, the triangle XYZ is right angle triangle.

Using trigonometric ratio:

The ratio of the opposite side of a right triangle to the hypotenuse is called  the sine. i.e,

[tex]Sine=\frac{opposite}{Hypotenuse}[/tex]

using sine ratio in triangle XYZ:

[tex]\sin 50^{\circ} = \frac{XY}{XZ}[/tex]

Substitute the value of XY = x cm and XZ = 6 cm in above ratio:

[tex]\sin 50^{\circ} = \frac{x}{6}[/tex] or

[tex]0.76604444247801 = \frac{x}{6}[/tex]

Simplify:

[tex]x= 4.59626665[/tex] cm

Therefore, the approximate value of x nearest to tenth is, 4.6 cm




What is the common difference for the sequence shown below? coordinate plane showing the points 1, 5; 2, 2; and 3, negative 1?

Answers

The correct answer to this problem would be -3. Based on the points you've provided on the graph, -3 would be the correct common difference. :)

Answer:

the common difference of the sequence (d) = -3

Step-by-step explanation:

Given sequence is 1st term, 2nd term, 3rd term

= 5, 2, -1

It is an arithmetic sequence.

The common difference (d) = second term - first term

d = 2 - 5

d = -3

Therefore, the common difference of the sequence (d) = -3

Hope this will helpful.

Thank you.

What is the reason for each step in the solution of the equation? −5(x−6)=10x Drag and drop the reasons into the boxes to correctly complete the table.

Answers

First, you have to distribute the -5 on the left side only to make the equation simpler to solve.
-5x+30=10x

Second, you add 5 to both sides which is kind of like combining like-terms.
30=15x

Finally, you divide by 15 on both sides to get x by itself which will leave you with the solution to the equation.
2=x

That’s it.

Answer:

Step-by-step explanation:

-5(x -6) = 10x . . . . . given

-5x +30 = 10x . . . . distributive property of multiplication over addition

30 = 15x . . . . . . . . addition property of equality (5x was added to both sides)

2 = x . . . . . . . . . . . division property of equality (both sides were divided by 15)

hope this helped

Arliss has two pieces of carpet runner. One is2/13 yards long and the other3/13
is yards long. She needs 10 yards of carpet runner altogether. How much more does she need to buy?

Answers

Solution steps:

1. Add the two given fractions.

2. Subtract the sum from 10 to find your answer.

Answer:

5 2/3

Step-by-step explanation:i thought this problem was literally impossible to do and its stopped me from progressing but i finally found out the answer and here it is

Write a number that is greater than 1 in scientific notation. explain how you know it is greater than 1

Answers

To write a small number (between 0 and 1) in scientific notation, you move the decimal to the right and the exponent will have to be negative. You may notice that the decimal point was moved five places to the right until you got the number 4, which is between 1 and 10. The exponent is −5.

The positive power of 10 shows that the number is greater than 1.

What is scientific notation?

A given number, equation, or expression is written in a format known as a scientific notation, which adheres to a set of principles. Large numbers like 8.6 billion are difficult to write in their numerical form since they are not only unclear but also time-consuming, and there is a potential that we may write a few zeros more or less.

Given:

number that is greater than 1 in scientific notation.

So, to get know the number is greater than 1 we can tell it by seeing the power of 10.

If the powers of 10 is positive then the number is also greater than 10.

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What is the value of the expression? ( 5/2 ) ^2 +3/4 ^3

Answers

5/2 ^2 =  6 1/4 = 6.25

3/4^3 =  27/64 = 0.4201875

6 1/4 + 27/64 = 6 43/64  (mixed number)

6.25 +0.421875 = 6.671875 (decimal)


 not sure what format you need, since the question was in fraction form, I think you need to answer using a mixed number though.


Please check and correct the following answers:

What decimal is equivalent to 72/100?
Is the answer 0.72?

Express 0.72 as a fraction in simplest form.
Is the answer 18/25?

What makes the statement true? 9^-2 = ?
Is the answer 1/81

Answers

Alright, so this is quite simple really. 

A: What decimal is equivalent to 72/100?
Well, 72/100 means you have 72 out of 100. Meaning it's not a whole number, so this means as a decimal, your answer would be behind the decimal point. 
Behind the decimal, you have 3 main places. Tenths, Hundredths, and Thousandths. It goes much further than that, of course, but most don't have to worry about those. 72/100 is represented as 72-hundredths, or .72
You are correct.

B: .72 as a fraction is 72/100. Simply divide by 2 until you simply can't anymore, this saves you time. 72/100 divided by 2 equally is 36/50. This divided by 2 equally is 18/25. This is the lowest form, you are correct.

C: Well, also simple. We know that when you have an exponent, you multiply the number by itself. 9^2 is 81, because 9*9=81. HOWEVER, this applies to only positive exponents. With negative exponents, you have to make it a fraction as 1. So, your answer is indeed 1/81

You are correct on all! Great job!

~Hope this helps!
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