The relationship between ttt and rrr is expressed by the equation 2t+3r+6=02t+3r+6=02, t, plus, 3, r, plus, 6, equals, 0. If rrr increases by 444, which of the following statements about ttt must be true?

Answers

Answer 1

Question:

The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?

Answer:

The value of t is reduced by 6 when the value of r is increased by 4

Step-by-step explanation:

Given

$2t + 3r + 6 = 0$

Required

What happens when r is increased by 4

$2t + 3r + 6 = 0$ -------- Equation 1

Subtract 2t from both sides

$2t + 3r + 6 - 2t = 0 - 2t$

$3r + 6 = - 2t$ --- Equation 2

When r is increased by 4, equation 1 becomes

$2T + 3(r+4) + 6 = 0$

Note that the increment of r also affects the value of t; hence, the new value of t is represented by T

Open bracket

$2T + 3r+12 + 6 = 0$

Rearrange

$2T + 3r+6 +12 = 0$

Substitutr -2t for 3r + 6 [From equation 2]

$2T -2t +12 = 0$

Make T the subject of formula

$2T = 2t - 12$

Divide both sides by 2

$\frac{2T}{2} = \frac{2t - 12}{2}$

$T = t - 6$

This means that the value of t is reduced by 6 when the value of r is increased by 4

Related Questions

Quinn bought a bouquet of flowers as a surprise for her grandfather. She had expected it would cost $15 but her prediction was 50% more than the actual cost of the flowers. What was the actual cost of the flowers?

Answers

The actual cost of the flowers was $7.50.

To find 50% of 15, you multiply. 15*50% equals 7.5.

This is due in like a hour please help!

Answers

Answer:

i think the fourth one is equvilent ratio

Step-by-step explanation:

Question 46 of 50
Congruent figures are:

figures that are exactly the same size and shape.

figures that are the same shape.

figures that are the same size.

Answers

Congruent figures are figures that are exactly the same size and shape, option A.

What make a figure congruent?

A figure is considered congruent when it is exactly the same size and shape as another figure. In other words, two figures are congruent if they can be superimposed on each other perfectly, without any stretching or distortion.

Congruence can also be defined as: if one of the figures can be obtained after a series of rigid motions of the other, the figures are said to be congruent. They both have congruent sides and angles.

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find the area, pls and ty

Answers

its

Step-by-step explanation:

for square ,length=8cm we know that area of square=l2 then we can write area of square=(8)2 which is 64 cm2 . as it is the combination of two figure to find its total area we have to find the area of both figires.now,for triangle base=6cm as 14 cm is the base of all the figure but for now we only need base of triangle and we know that the length fo base of square is 8cm so by substracting to it we get base as 6cm,height =10cm now area of triangle =1/2*b*h=1/2*6*10 =30cm2 now total area= area of square +areaof triangle= 64+30=94cm2

6x = 52 − 2y 5x + 7y = 70 Question 1 What is the first step when solving the given system by the elimination method?

Answers

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

What is the solution to the equation?

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26 ...1

5x + 7y = 70

(5/7)x + y = 10 ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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6x^2=-3x+1 to the nearest hundredth

Answers

The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.

What are the solutions to the quadratic equation?

Given the quadratic equation in the question:

6x² = -3x + 1

To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:

6x² + 3x - 1 = 0

Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:

$x = \frac{-b \±\sqrt{b^2-4ac} }{2a}$

Here; a = 6, b = 3, and c = -1.

Let's substitute these values into the quadratic formula:

$x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23$

Therefore, the values of x are -0.73 and 0.23.

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1. Match each inequality to the meaning of a symbol within it.a. h > 50o less than or equal tob.h <20º greater thanC. 30 hgreater than or equal to2. Is 25 a solution to any of the inequalities? Which one(s)?3. Is 40 a solution to any of the inequalities? Which one(s)?4. Is 30 a solution to any of the inequalities? Which one(s)?

Answers

Definition

Inequality is the relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than', or < ‘less than'.

a. h > 50

Answer: greater than

b. h <= 20

less than or equal to

c. 30 >= h

greater than or equal to

Is 25 a solution to any of the inequalities?

Yes. 25 is a solution to the inequality 30 >= h

We can rewrite this inequality as:

$h\text{ }\leq\text{ 30}$

The inequality means that h can take values that are less than 30 or equal to 30

3. Is 40 a solution to any of the inequalities?

No. 40 is not a solution to any of the inequalities

4. Is 30 a solution to any of the inequalities?

Yes. 30 is a solution to the inequality 30 >= h

Cameron wants to buy a skateboard. he has $89, Which is $17 more than he needs. Which equation can be used to determine how much the skateboard costs

Answers

Answer:

The answer to this question is $72. The equation is x + 17 = 89

Step-by-step explanation:

Equation: x + 17 = 89

Cameron has $89 so 89 would go behind the equal sign.

He has 17 dollars more than he needs. Whenever more is used that usually indicates that it will be a plus sign. So we will do + 17 = 89.

Finally we need to add the x to complete the equation. This will be shown as x + 17 = 89.

If you solve this equation it will equal x = 72.

If this helped you please subscribe to The Game Rater. Thank you.

Answer:

89-17

Step-by-step explanation:

To find how much Cameron’s skateboard costs you need to take away 17 from your starting amount as you have more. Meaning we subtract the 17 to find how much the skateboard costs.

8.498 ? 8.478 use >,<,=

Answers

The inequality equation is 8.498 > 8.478

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the first number be represented as = p

Let the second number be represented as = q

Now , the value of p = 8.498

The value of q = 8.478

And , the hundredths value in the number 8.498 is greater than the hundredths value in the number 8.478

So , the value of p is greater than q

Therefore , 8.498 > 8.478

Hence , the inequality is 8.498 > 8.478

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Which expression represents the phrase ""the product of x and the quantity ‘10 minus x’""?

Answers

I think it is (10-x)=x pls correct me if I’m wrong

please please please help me my teacher has no idea how to reach and i desperately need to know this :D

Answers

The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray $\overleftrightarrow{EF}$ maps unto ray $\overleftrightarrow{GH}$

Ray $\overleftrightarrow{GH}$ maps unto ray $\overleftrightarrow{FE}$x

$\overleftrightarrow{FG}$ maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

What is the measure of an angle?

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line $\overleftrightarrow{EF}$ is equidistant from both the line $\overleftrightarrow{GH}$ which is parallel to the line $\overleftrightarrow{EF}$, the image of the line $\overleftrightarrow{EF}$ maps to the line $\overleftrightarrow{GH}$ following a 180° rotation about the point O, and the rotation of the line $\overleftrightarrow{FG}$ about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

m∠x = 40°

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There are 3 types of PercentProblems.
a) Number compared to the Base is unknown: x/100 = ?/b
b) Base Number is unknown: a/?= x/100
c) Percent is unknown: a/b = ?/100
Solve the following percent problems using the appropriate percent equation. Describe
the steps used to calculate each answer.
1) What distance is 24% of 710 miles?
2) 62 hours is what percent of 3 days?
3) 16% of what number is 8?

Answers

Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

Let X and Y be discrete random variables and let a and b be constants Which of the following is. FALSE? (a) mean (X + Y) = mean (X) + mean (Y).

Answers

Mean (X + Y) = Mean (X) + Mean (Y).

The above statement is false.

Discrete Random Variable:

A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.

Probability Distributions of Discrete Random Variables:

Probability distributions of discrete random variables list the probabilities associated with each possible outcome. Also called probability function or probability mass function.

The probability of a discrete random variable is between 0 and 1. Also, the sum of the probabilities of a discrete random variable is equal to 1. The probability distribution of discrete random variables resembles the normal distribution.

Example:

Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X goes from result 1 + 1 = 2 to 2 and the maximum value goes from result 6 + 6 = 12 to 12. Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.

Discrete random variables should not be confused with algebraic variables. Algebraic variables represent the values of unknown quantities in computable algebraic equations. However, a discrete random variable can have a range of possible values that result from experimentation.

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Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?

Answers

Let's analyze each scenario:

1. A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?

In this case, the spinner's outcome of landing on region three is independent of landing on region six. Each spin is unrelated to the previous spin, and the outcome of one region does not affect the outcome of the other region. Therefore, the events are independent. The probability of landing on both region three and region six is the product of their individual probabilities: 1/8 * 1/8 = 1/64.

2. A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?

In this scenario, the events are overlapping. A jersey can be both purple and have a number greater than 5 at the same time. Therefore, the probability of it being purple or having a number greater than 5 is the sum of their individual probabilities, minus the probability of the overlapping event (purple jerseys with a number greater than 5). There are 4 purple jerseys out of 10 total jerseys, and there is 1 jersey with a number greater than 5 out of 10. However, there is one jersey that satisfies both conditions (purple and number greater than 5), so we need to subtract it from the sum. So the probability is (4/10 + 1/10) - (1/10) = 4/10 = 2/5.

3. A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?

In this scenario, the events are mutually exclusive. A chocolate cannot be both a milk chocolate and have no peanuts inside at the same time. Therefore, the probability of it being a milk chocolate or having no peanuts inside is the sum of their individual probabilities. There are 6 milk chocolates out of 10 total chocolates, and there are 7 chocolates without peanuts out of 10. So the probability is 6/10 + 7/10 = 13/10, which is greater than 1. However, probabilities cannot exceed 1, so we need to take the maximum value of 1. Therefore, the probability is 1.

4. You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?

In this case, the events are independent. The outcome of the coin flip does not affect the outcome of the die roll. The probability of the coin landing heads up is 1/2, and the probability of the die showing an even number is 1/2. To find the probability of both events occurring, we multiply their individual probabilities: 1/2 * 1/2 = 1/4.

I hope this clarifies the nature of each event. Let me know if you have any further questions!

The first question:

"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"

Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.

To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:

P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.

Therefore, the probability of landing on both region three and region six is 1/64.

The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.

--------------------------------------------------------------------------------------------------------------------------

The second question:

"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"

To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.

The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.

The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.

To find the probability of either event occurring, we add the probabilities together:

P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.

Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.

The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.

--------------------------------------------------------------------------------------------------------------------------

The third question:

"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"

To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.

The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.

The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.

To find the probability of either event occurring, we add the probabilities together:

P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.

Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.

The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.

--------------------------------------------------------------------------------------------------------------------------

The fourth question:

"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"

The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.

The probability of rolling an even number on the die is 3

/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:

P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.

Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.

The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.

$\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}$

♥️ $\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}$

Graph the inequality.

-6 ≤y+ 2x <15

Answers

Answer:

Look Below Hope It Helps

Step-By-Step Explanation:

Answer:

Graph C.

Step-by-step explanation:

a bricklayers assistant starts building a wall laying 50 bricks per hour. Two hours later the master bricklayer joins the assistant and both lay bricks. The master bricklayer lays 80 bricks per hour. write an equation stating that the assistant and the master have laid the same number of bricks. how long has each one worked when they have laid the same number?

Answers

Answer:

80t = 50(t+2)master: 3 1/3 hoursassistant: 5 1/3 hours

Step-by-step explanation:

Given an assistant bricklayer laying 50 bricks an hour has worked 2 hours longer than a master bricklayer laying 80 bricks an hour, you want an equation stating they have laid the same number of bricks. You also want to know how long each has worked.

Rate and output

The output of each bricklayer is the product of the rate at which they lay bricks and the time for which they do it. If t is the time spent by the master bricklayer, their output will be 80t. The time spent by the assistant will be (t+2) hours, and their output will be 50(t+2).

Here is the equation that says their output is the same:

80t = 50(t+2)

Time

Solving the equation for t, we have ...

80t = 50t +100

30t = 100 . . . . . . . . . subtract 50t

t = 3 1/3 . . . . . . . divide by 30

The master bricklayer has worked 3 1/3 hours when they have laid the same number of bricks.

The assistant bricklayer has worked 5 1/3 hours at that time.

Additional comment

Each will have laid (80)(3 1/3) = 266 2/3 bricks.

Find the volume of the cylinder. Round your answer to the nearest tenth.
3ft.
10 ft.
Enter only the numerical value with the units of measure.

Answers

V=pi(radius)^2*height so the answer is 282.7 feet cubed

Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool?

Answers

The circumference of the pool is 26.38 meters

How to determine the circumference?

The radius, r is given as:

r = 4.2

The circumference, C is calculated using:

$C =2\pi r$

This gives

C =2 * 3.14 * 4.2

Evaluate

C = 26.38

Hence, the circumference of the pool is 26.38 meters

Answers

Answer:

x=-1/3

x=7

Step-by-step explanation:

Not sure if this correct tho

Answer:

x=2

y=-5

Step-by-step explanation:

substitute y=-3x+1 in y=x-7

$-3x+1=x-7$

$-3x-x=-7-1$

$-4x=-8\\x=2$

Substitute x=2 in any one of the given equations

y=x-7=2-7=-5

Determine whether each ordered pair is a solution of the equation y=2x+6

Answers

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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A laptop is bought for $1380 VAT inclusive. If VAT was charged at 15%, what
is the price of the laptop exclusive of VAT?

Answers

Answer:

vat=15%

selling price with vat=$1380

selling price with out vat=?

we have

selling price with vat=$1380

selling price with out vat+vat%of selling price with out vat =$1380

selling price with out vat(1+15/100)=$1380

selling price with out vat=$1380/1.15=$1200

What is the volume of this cone? Use 3.14 and round your answer to the nearest hundredth. 38 mm cubic millimeters

Answers

ANSWER

$V=7179.09\operatorname{mm}$

EXPLANATION

We are given the height of the cone as 19 mm and the diameter of its base as 38 mm.

The volume of a cone is given as:

$V=\frac{1}{3}\pi\cdot r^2h$

where r =radius; h = height

The diameter of a circle (the base of a cone) is twice the radius. Therefore:

$\begin{gathered} D=2r \\ r=\frac{D}{2} \\ r=\frac{38}{2} \\ r=19\operatorname{mm} \end{gathered}$

Therefore, the volume of the cone is:

$\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot19^2\cdot19 \\ V=7179.09\operatorname{mm}^3 \end{gathered}$

For which indicated domain are both the inequalities x > 2 and
x < 4 true?

Answers

Answer:

2 must be less than x if x is greater than 2, and x must be less than 4 if 4 is greater than x.

What is (−116)(51)(−2)?

1,392
−1,392
11,832
−11,832

Answers

Answer:

11832 ............

Step-by-step explanation:

Y = (-116)(51)(-2)

Y = (-116) × (51) × (-2)

Let's multiply the +- symbols first ...... So ,. (-) × (+) × (-) = (+)

NOTE :- (+) × (+) = (+) (+) × (-) = (-) (-) × (+) = (-) (-) × (-) = (+)

After we multiply the numbers ......

(116) × (51) × (2) = 11832

so combined the number and symbol ...... That's the Answer ...

Answer : + 11832 = 11832

WILL GIVE BRAINLIEST FOR FIRST ANSWER!
In some sparsely populated areas of the United States, the speed limit on highways can be as high as 80 miles per hour (mph).
What is this speed in meters per second (m/s)?

Answers

Answer:

Divide the speed value by 2.237

80/2.237=35.76

Answer:

35.76

Step-by-step explanation:

Chandler decided to go cliff jumping into the lake at his cottage. He started on the cliff at 32 ft above sea level. He jumped for 40 feet! How far below sea level did Chandler end up?

Answers

Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.

Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.

Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):

32 feet - 40 feet = -8 feet

It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level

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Answer:

-8 feet

Step-by-step explanation:

Which of the following sets of numbers could not represent the three sides of a triangle?

\{4,16,17\}{4,16,17}
\{8,20,25\}{8,20,25}
\{13,16,30\}{13,16,30}
\{8,20,25\}{8,20,25}

Answers

Answer:

Step-by-step explanation:

In order for the sides lengths to form a triangle, the sum of the shortest two must exceed the longest.

That will not be the case for ...

{13, 16, 30}

because 13 +16 = 29 < 30.

(13, 16, 30} could not form a triangle

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4
You draw five cards from a standard deck of 52 cards. P(heart) =
What type of probability is illustrated and why?
5
O A. theoretical; the result is based on the number of possible outcomes
O B. theoretical; the result is found by repeating an experiment
OC. experimental; the result is based on the number of possible outcomes
O D. experimental; the result is found by repeating an experiment
vered

Answers

Answer: The type of probability illustrated here is theoretical probability, and option A correctly identifies it as such.

Theoretical probability is based on mathematical reasoning and analysis of possible outcomes. In this case, we know that there are 52 cards in a deck, and 13 of them are hearts. So, the probability of drawing a heart on the first card is 13/52. After the first card is drawn, there are 51 cards remaining in the deck, including 12 hearts. So, the probability of drawing a heart on the second card is 12/51. Continuing this process, we find the probability of drawing five hearts in a row to be:

P(heart) = (13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.0104 or about 1.04%

This probability is based purely on mathematical reasoning and analysis of possible outcomes, and does not involve any actual experimentation. Therefore, it is an example of theoretical probability.

Step-by-step explanation:

Determine the largest power of 10 that is a factor of the following numbers (equivalently, the number of terminal 0's, using ordinary base 10 representation):(a) 50!.
(b) 1000!.

Answers

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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khalil is working two summer jobs, making $18 per hour tutoring and $9 per hour landscaping. last week khalil worked a total of 14 hours and earned a total of $180. graphically solve a system of equations in order to determine the number of hours khalil worked tutoring last week, x,x, and the number of hours khalil worked landscaping last week, yy.

Answers

10 number of hours khalil worked tutoring last week and 3 the number of hours khalil worked landscaping last week

given that

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.

khalil is working two summer jobs, making $18 per hour tutoring

$9 per hour landscaping

last week khalil worked a total of 14 hours and earned a total of $180.

let x be number of hours khalil worked tutoring last week

y be the number of hours khalil worked landscaping last week

we can form equation by given information

x + y $\leq$ 13 - (1)

18x + 9y > 180 - (2)

the numbers that satisfy the above equations is (10,3)

10 number of hours khalil worked tutoring last week and 3 the number of hours khalil worked landscaping last week

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