Charles has rolled a 6-sided die three times and it landed on 3 each time. What is the probability of getting a 3 on the 4th roll?

Answer choices: A) 1, B) [tex]\frac{1}{36}[/tex], C) [tex]\frac{1}{216}[/tex], D) [tex]\frac{1}{6}[/tex]

Write f(x) above g(x), as shown below:

 f(x)=2x^2 + 3

- g(x) = x^2 - 7

---------------------   Next, combine the givens in three columns:

(f-g)(x) = x^2 + 10 (answer)

The arithmetic operation of the functions f(x) and g(x) is x² + 10 if  arithmetic operation is (f-g)(x) option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

f(x) = 2x² + 3

g(x) = x² - 7

To find the (f-g)(x)

(f-g)(x) = f(x) - g(x)

Plug the function f(x) and g(x):

The above expression is representing an arithmetic operation of the functions:

(f-g)(x) = f(x) - g(x) = (2x² + 3) - (x² - 7)

(f-g)(x) = 2x² + 3 - x² + 7

(f-g)(x) = x² + 10

Thus, the arithmetic operation of the functions f(x) and g(x) is x² + 10 if  arithmetic operation is (f-g)(x) option (D) is correct.

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Amount of soup in each container = 18 ounces

Total number of containers of soup = 6 containers

So, total amount of soup in 6 containers = [tex]6 \times 18[/tex]

= 108 ounces

Total amount of soup for 9 people = 108 ounces

So, amount of soup for 1 people = [tex]108 \div 9[/tex]

= 12

So, each person will get 12 ounces of soup.

big oof uh

Russel D Bag

8192, 16 x 8 x 64,  24 = 16, 26= 64, 23= 8

Hey there!

[tex]2^4[/tex] [tex]= 16[/tex]

[tex]2^3[/tex] [tex]= 8[/tex]

[tex]2^6[/tex] [tex]= 64[/tex]

____________________________________________________________

[tex]16(8)[/tex] [tex](64)[/tex]

[tex]16(8)[/tex] [tex]= 128[/tex]

[tex]128(64)[/tex] [tex]= 8192[/tex]

Answer: [tex]8,192[/tex]

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

Answer:

The answers are: A and D (for anyone else looking for answers)

I will meet my friends at the park if I complete my chores. If I meet my friends at the park, we will go to the duck pond. Therefore, if I complete my chores, we will go to the duck pond.

If Bob reads the book, then he will be prepared for the test. If Bob is prepared for the test, then he will get a good grade. Therefore, if Bob reads the book, he will get a good grade.

I just took the test and my correct answers are in the screenshot below :-)

Hopefully its not too late for brainliest!

Hello...

What creates the convection current inside Earth?

A. Rising and sinking of material

Answer: A. Rising and sinking of material.

Step-by-step explanation:

Convection currents are caused by the cooling of material as it rises up, which leads to the same material to sink. This material then warms as it sinks to rise again. This is why we call them convection currents. Because they both rise, and sink, in a circular motion we call the convection current.

The decimal expansion of 1/9 is 0.1111..., which continues indefinitely. This is achieved by dividing the numerator (1) by the denominator (9). The decimal expansion of a fraction is the expression of that fraction in base 10 notation.

The decimal expansion of the fraction 1/9 is 0.1111.... This is achieved by dividing the numerator (1) by the denominator (9). The process of long division would show you that 9 doesn't go into 1, so you add a decimal point and a zero, making the dividend 10. 9 goes into 10 once, so you put a 1 in the quotient above the line. This process repeats itself due to the nature of the divisor 9 and the decimal 0.1111... continues indefinitely.

It's important to note that the decimal expansion of a fraction is an expression of that fraction in base 10 notation. In other words, it is the fraction expressed as a decimal.

For some numbers, this can be a finite number of digits long, and for others, like 1/9, it can be infinitely repeating.

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Sand  

Because as you may be able to see it just goes through your fingers.

For example if you go to the beach and pick up a handful of sand, then let go. It will most likely fall out of your hands.

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Answer:

[tex]y = \frac{1}{3}x - 1[/tex]

Step-by-step explanation:

Let the gradient be calculated as follows:

slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

         = [tex]\frac{-7-(-3)}{6-(-6)}\\ = -\frac{1}{3}[/tex]

to find the equation passing through the point we calculate as follows:

[tex]- 3= \frac{1}{3} (-6) + b\\ -1 = b[/tex]

Therefore, the equation of the line is:

[tex]y = \frac{1}{3}x - 1[/tex]

An equation of this graphed line in slope-intercept form is [tex]y=-\frac{1}{3} x-5[/tex].

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 - (-3))/(6 - (-6))

Slope (m) = -1/3.

At data point (6, -7) and a slope of -1/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

[tex]y-(-7)=-\frac{1}{3} (x-6)\\\\y+7=-\frac{1}{3} (x-6)\\\\y=-\frac{1}{3} x-5[/tex]

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Answer:

9/28

Step-by-step explanation:

There are a total of 18+6+32 = 56 spectators.

Out of this total number, 18 cheered for Luca; this gives us the ratio

18/56.

Both of these are even numbers.  This means we can divide both by 2:

(18÷2)/(56÷2) = 9/28

Given that the revenue for each jumbo biscuit sold is $1

Given that the cost to make each jumbo biscuit is $0.20

Then profit on each jumbo biscuit =$1 - $0.20 = $0.80

Since positive profit occurs so producing jubo biscuit is good idea.

Given that the revenue from each regular biscuit is sold at $0.65

Given that the cost to make each regular biscuit is $0.15

Then profit on each regular biscuit =$0.65 - $0.15 = $0.50

Since positive profit occurs so producing regular biscuit is good idea.

As in both business, we are getting positive profit. Infact more profit on jumbo biscuits so YES, bakery can produce 10 regular biscuits and 55 jumbo biscuits.

The bakery can produce 10 regular biscuits and 55 jumbo biscuits. This conclusion is based on calculations showing that the revenue generated from selling these biscuits is higher than the cost to produce them. There are no clear limitations violated.

The bakery can indeed produce 10 regular biscuits and 55 jumbo biscuits, as long as it accounts for the cost associated with making each biscuit. We can calculate this through simple multiplication. The cost to make 10 regular biscuits would be 10 * $0.15 = $1.50, and the cost to make 55 jumbo biscuits would be 55 * $0.20 = $11.00.

The revenue from selling 10 regular biscuits would be 10 * $0.65 = $6.50, and the revenue from selling 55 jumbo biscuits would be 55 * $1 = $55. Hence, the total cost of producing these biscuits is $1.50 (for regular biscuits) + $11 (for jumbo biscuits) = $12.50, while the total revenue generated is $6.50 (from regular biscuits) + $55 (from jumbo biscuits) = $61.50.

The revenue generated ($61.50) is clearly higher than the cost of production ($12.50), so it would be financially feasible for the bakery to produce these biscuits. There are no apparent limitations violated.

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So, just divide:

52.50 / 6 = 8.75

This means that she earns $8.75 an hour.

If this is her hourly salary, then multiply 8.75 x 11

8.75 x 11 = 96.25

So, if Paula works for 11 hours,  she will earn $96.25!

Remark

I think you can only do this either as a 2 step question or as a proportion. The easiest way is the proportion.

Proportion

6 hours / 52.50 = 11/x      Cross multiply

6*x = 52.50 * 11                Combine the factors on the right

6x =  577.5                       Divide both sides by 6

6x/6 = 577.5/6

x = 96.25                        Answer

because the square root of 4 is 2 and the square root of 9 is 3 which means 2x3=6 and 9x4=36 and the square root of 36 is 6 because 6x6=36

-1/32ac2

You want to cancel out the -32 on the top with the 64 on the bottom leaving -1. Then do the same with the variables.

Answer:

75

Step-by-step explanation:

Number of foul shots made by the girl first time = 12

Number of shots missed by the girl first time = 8

Total number of shots played first time = 12 + 8 = 20

Let the number of foul shots made by the girl second time be x

The total number of shots played by the girl second time = 125

Let's set up a proportion,

[tex]\frac{Number of foul shots made by the girl first time}{Total number of shots played first time}[/tex] = [tex]\frac{number of foul shots made by the girl second time}{total number of shots played by the girl second time}[/tex]

=> [tex]\frac{12}{20} = \frac{x}{125}[/tex]

Flip the sides of the equation

[tex]\frac{x}{125} = \frac{12}{20}[/tex]

Multiplying both the sides by 125

[tex]\frac{x}{125}*125 = \frac{12}{20}*125[/tex]

Cancelling out the 125's on the top and bottom from the left side

x = [tex]\frac{12}{20}*125[/tex]

=> x =  [tex]\frac{1500}{20}[/tex]

=> x = 75

Number of foul shots made by the girl if she played 125 foul shots = 75

To find out how many shots the girl made, set up a proportion using the ratio of shots made to shots missed. The girl made 187 shots.

To find out how many shots the girl made, we can set up a proportion using the ratio of shots made to shots missed. The ratio is 12:8. Let's assume the number of shots made is x. We can create the proportion: 12/8 = x/125. Cross-multiplying gives us 8x = 12 * 125. Solving for x gives us x = (12 * 125) / 8. Evaluating this expression gives us x = 187.5. Since we can't have a fraction of a shot, we round down to the nearest whole number. Therefore, the girl made 187 shots.

the answer is

2.25 it is right

it is 2∪ 1/4...............

Answer:

the two integers are 17 and 18

Step-by-step explanation:

Let x represent the smaller integer. Then x+1 is the larger. The problem statement tells us

... 2 × larger = -15 + 3 × smaller

... 2(x+1) = -15 + 3x . . . substitute variable expressions for 'larger' and 'smaller'

... 2x +2 = 3x -15 . . . . . eliminate parentheses

... 17 = x . . . . . . . . . . . . .add 15-2x

The smaller integer is 17, so the larger is 18.

_____

Check

2×18 = 36 = 3×17 -15 = 51-15

Let's take the first number as 'x' ( This would be the smaller number )

Let's take the second number as 'x+1' ( This would be the larger number )

I have taken x and x+1 because both these numbers are consecutive.

Twice the larger number :-

... 2 ( x + 1 )

... 2x + 2

15 less than thrice the smaller number :-

... 3x - 15

The question states that these both values are equal. Hence,

... 2x + 2 = 3x - 15

... 2 + 15 = 3x - 2x

... 17 = x

The value of 'x' is 17

( The smaller number is 17 )

Larger number :-

... x + 1

... 17 + 1

... 18

Hence, the numbers are 17 and 18.

Hope my answer helps!!

Patrick initially has 600 meters of yarn. After using some to make a hat, he only has 351.1 meters of yarn left, which is not enough to make a scarf that requires 354.03 meters.

To answer this question, we have to perform a subtraction operation on the total lengths of yarn. Initially, Patrick has a 600-meter skein of yarn. After making a hat, he uses 248.9 meters of yarn. To find out how much yarn is left, we subtract the amount used from the total: 600 - 248.9 = 351.1 meters. You then need to check if 351.1 meters are enough to make a scarf that consumes 354.03 meters of yarn. In this case, we can see that Patrick does not have enough yarn left to make the scarf because 351.1 meters is less than 354.03 meters.

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Add 8y+3y=11y

Divide 44/11y=4

Answer= 4

The solution to the equation 8y + 3y = 44 is y = 4.

To solve the equation 8y + 3y = 44, we can combine like terms and solve for y:

Combine like terms on the left side:

8y + 3y = 44

Simplify:

11y = 44

Divide both sides by 11:

11y/11 = 44/11

Simplify: y = 4

Therefore, the solution to the equation 8y + 3y = 44 is y = 4.

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Answer:30

Step-by-step explanation:

20+10=30

Your answer is A. The sum of x and y is a rational number .

Answer:

A) The sum of x and y is a rational number.

Step-by-step explanation:

We will first prove that the given values of x and y are rational and then we will prove the fact that the sum of two rational numbers is a rational number.

A rational number is a number which is in the form [tex]\frac{p}{q}[/tex], where p and q are integers and q ≠ 0.

We can write - 5 as [tex]\frac{-5}{1}[/tex] and clearly 1 ≠ 0.

So, x = -5 is a rational number.

Similarly, y = -4 is also a rational number.

For the second part of the proof, consider any two rational numbers [tex]\frac{p}{q}[/tex] and [tex]\frac{r}{s}[/tex].

Now,

[tex]\frac{p}{q} +\frac{r}{s} =\frac{ps+rq}{qs}[/tex]

Since p, q, r and s are integers, ps + rq is also an integer.

Moreover, since q ≠ 0 and s ≠ 0, qs ≠ 0.

Therefore, [tex]\frac{ps+rq}{qs}[/tex] is also a rational number.

Hence, sum of two rational numbers is also a rational number.

Since x = -5 and y = -4 are rational numbers, x + y = (-5) + (-4) = -9 is also a rational number.

Remark

You have to read this carefully to know what way to write it.

One way you could write it would be

20 * x = 18 where x is  the fraction. Now all you need do is divide.

Divide both sides by 20

20/20 * x = 18/20

[tex]\text{x = } \dfrac{18}{20}[/tex]

But you should reduce this fraction. The way to do that is to factor 18 and 20 into primes.

18: 2 * 3 * 3

20: 2 * 2 *5

Cancel out the Highest common factor or 2.

You are left with

[tex]\text{x = } \dfrac{18}{20} =\dfrac{2*3*3}{2*2*5}=\dfrac{3*3}{2*5} = \dfrac{9}{10}[/tex] <<<< Answer

★ What fraction of 20 is 18?

In questions like these, when you see the word "of", it is usually used for the denominator. In your question, it says "of 20". That means the denominator will be 20.

Here is your current fraction:

[tex]\frac{x}{20}[/tex]

After that phrase, it says "is 18". The word "of" is used for the numerator. That means the numerator is 18.

Here is your fraction:

[tex]\frac{18}{20}[/tex]

You have your complete fraction, but it can be simplified. Both numbers are even(numbers that end with 2, 4, 6, 8, or 0) and every even number is divisible by 2. You can just divide both numbers by 2.

[tex]\frac{18 \div 2}{20 \div 2} = \frac{9}{10}[/tex]

You have your simplified fraction, which is [tex]\frac{9}{10}[/tex], and it cannot be simplified any further.

Your answer is [tex]\frac{18}{20}[/tex] which becomes [tex]\frac{9}{10}[/tex] when simplified.

If you have any questions, feel free to ask in the comments! :)

The sequence is adding by three

your answer is multiplying by 2

Given:

monthly deposit, A=100

rate of interest, i = 1% per month = 0.01 per period

compounding period = 1 month (assumed).

Total payments :

n=60 payments of $100 at the end of the month (beginning of the next month) +

1 payment at the beginning of the first month.

Future value after 60 months

= amount due to 60 monthly payments at end of month + value of first payment

= A((1+i)^n-1)/i  + A*(1+i)^60

=100(1.01^60-1) + 100(1.01^60)

= 8166.967 + 181.670

= 8348.64 (to the nearest cent)

Answer:

8348.64

Step-by-step explanation:

Answer:1) B. 240(0.92)^t < 115; 9 days  is the inequality which represents the situation.

2)After t=9 days the amount of the sample be less than 115 milligrams.

Step-by-step explanation:

The amount of sample which Jordan had in starting a =240 milligrams

rate of decreasing it r =8%=0.08

let t be the number of days the amount of sample took to become 115 milligrams then by the exponential decay  function

[tex]f(t)=a(1-r)^t[/tex] where f(t) =115

[tex]115=240(1-0.08)^t....(1)\\\Rightarrow\frac{115}{240}=(0.92)^t\\\Rightarrow0.479=(0.92)^t\\\text{taking log on both sides ,we get}\\log(0.479)=log((0.92)^t)\\\Rightarrow\ log(0.479)=t\ log(.092)\\\Rightarrow\ -0.735=t(-0.0833)....\text{after solving log values}\\\Rightarrow\ t=\frac{-0.735}{-0.833}\approx8.82 days[/tex]or 9 days(approx ).

therefore, after t=9 days the amount of the sample be less than 115 milligrams.

So ,the right inequality which represent the situation is

B. 240(0.92)^t < 115; 9 days (from (1))

Answer:

B.  240(0.92)t < 115

9 days.

Step-by-step explanation:

We are told that Jordan works in a science lab where he is studying the behavior of a certain unstable isotope. He has 240 milligrams of the sample, and the amount of the substance remaining in the sample decreases at a rate of 8% each day. After t days, there are less than 115 milligrams of the substance remaining. We  are asked to write an inequality to represent this situation.

An exponential function representing decay will be our inequality.Let us write an inequality for this situation.

[tex]240(1-0.8)^{t} <115=240(0.92)^{t} <115[/tex], where 240 is our initial amount of substance, 0.8 is decrease factor.

Now let us solve our inequality to find out number of days.

[tex](0.92)^{t} <\frac{115}{240}[/tex]

Upon taking natural log of both sides of inequality,

[tex]ln(0.92)^{t} <ln\frac{115}{240}[/tex]

[tex]t\ln \left(0.92\right)<ln(\frac{115}{240})[/tex]

[tex]-0.08338160t < -0.73570679[/tex]

[tex]t>8.82[/tex]

Upon rounding up our answer to nearest integer we can see that option B is correct. Therefore, our answer will be option B.

Answer:

Step-by-step explanation:

Answer is 72 cm2.For step by step explanation please find the attachment.