ginny and carter are learning about probability and their teacher hands them a bag with 18 red marbles and 10 green marbles. ginny draws 2 red marbles and keeps them on her desk. carter wants to draw green marbles on his turn. how did the probability of drawing a green marble change from when ginny drew her marbles to when carter will draw?

Answer: 6(x - (23/2))² = 14x + 1044

Step-by-step explanation:

First, we need to move all the terms to one side of the equation:

6x² - 46x - 312 - 14x = 0

Next, we need to factor out the coefficient of the x² term:

6(x² - (46/6)x) - 312 - 14x = 0

Simplifying:

6(x² - 23x) - 312 - 14x = 0

To complete the square, we need to add and subtract the square of half the coefficient of the x-term inside the parentheses:

6[(x - (23/2))² - (23/2)²] - 312 - 14x = 0

Simplifying:

6(x - (23/2))² - 6(23/2)² - 312 - 14x = 0

Expanding the square term:

6(x - (23/2))² - 1044 - 14x = 0

Finally, adding 1044 to both sides and simplifying:

6(x - (23/2))² = 14x + 1044

The intermediate step after completing the square is:

6(x - (23/2))² = 14x + 1044

Carly will need to buy 27.05 gallons of gas for the trip, which will cost her $7.28.

To calculate the total cost of the road trip, we need to find out how many gallons of gas Carly will need and then multiply that by the cost per gallon.

First, we need to convert the distance from miles to gallons, using the truck's fuel efficiency of 21 miles per gallon

568 miles ÷ 21 miles per gallon = 27.05 gallons

So Carly will need approximately 27.05 gallons of gas for the trip.

Next, we need to convert the cost of gas from liters to gallons. There are 3.79 liters in 1 gallon, so the cost of gas is:

$1.02 per liter ÷ 3.79 liters per gallon = $0.269 per gallon

Finally, we can calculate the total cost of the road trip by multiplying the number of gallons of gas by the cost per gallon

27.05 gallons × $0.269 per gallon = $7.28

Therefore, the road trip will cost Carly approximately $7.28.

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Answer:

5 and 1/6 hours

Step By Step Explanation:

Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.

In mathematics, rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

Let's represent the number of books sold as "x". Then, the total amount of money that Mrs. Dundee will make from the first publisher is:

Total from first publisher = $80,000 + ($3 x x) = $3x + $80,000

Similarly, the total amount of money that she will make from the second publisher is:

Total from second publisher = $30,000 + ($5 x x) = $5x + $30,000

We want to find the range of values of x for which the total amount from the second publisher is greater than the total amount from the first publisher. In other words, we want to find the range of values of x for which,

$5x + $30,000 > $3x + $80,000

Simplifying this inequality, we get:

$2x > $50,000

x > $25,000

Therefore, Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.

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Alex will pay 13.8 for her lunch after adding a 15% tip.

We will calculate the amount she paid for her lunch by calculating the tip she paid and adding it to the original price of the lunch(i.e. 12).

[tex]\implies{\sf{15 \% \ of \ 12 \ = \ 12 \times \dfrac{\cancel{15}}{\cancel{100}} }}[/tex]

[tex]\implies{\sf{Tip = \cancel{12} \times \dfrac{3}{\cancel{20}}}}[/tex]

[tex]\implies{\sf{Tip = 3 \times \dfrac{3}{5}}}[/tex]

[tex]\implies{\sf{Tip = \dfrac{9}{5}}}[/tex]

[tex]\implies{\sf{ Tip = 1.8}}[/tex]

Now, add the amount of lunch and tip

[tex]\implies{\bf{ Total \ amount = 12 + 1.8}} \\ \implies{\bf{Total \ amount = 13.8}[/tex]

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The sums that prove that the wooden boards can create a triangular outline according to triangle inequality rule are:

The triangle inequality rule states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Testing each combination of sides, we get:

Case 1:

Let 5 feet be the third side

Then,

2.5 + 4 > 5

6.5 > 5

Case 2:

Let 2.5 feet be the third side

Then,

4 + 5 > 2.5

9 > 2.5

Case 3:

Let 4 feet be the third side

Then,

5 + 2.5 > 4

7.5 > 4

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Answer:

14

Step-by-step explanation:

28 mm is the diameter of the button, so we have to find the radius, which is half of the diameter.

28/2=14

So, the radius of this button is 14 mm

Answer: 3. is 13

4. is 36

5. is 21

6. is 15

7. is 21

8. is 2

9. is 6

10. is 45

Step-by-step explanation:

the letters are there to just confuse you. i promise its all right <-- the answers

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Answer: The formula for the volume of a cone is V=1/3hπr²

Step-by-step explanation: The volume or capacity of a cone is one-third of its corresponding cylinder. This means that when a cone and a cylinder have the same base dimension and height, the volume of the cone is one-third of the volume of the cylinder.

The second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

An expression is a grouping of figures, symbols, and algebra (such as addition, reduction, multiply, and division) that expresses a value. Variables, that are symbols for unknowable values, are symbols that can be included in expressions. The statement can be evaluated to give a specific value after the contents of the variables are assigned. An expression using a variable x, for instance, is 3x + 5. When we give x a number of 2, the expression is evaluated to: 3(2) + 5 = 6 + 5 = 11 . As a result, the expression's value at x = 2 is 11.

given

a. Assume that "S" represents the number of field goals Suzy scores each minute and "J" represents the number of field goals Joshua scores each minute.

The calculation for the total number of field goals Suzy and Joshua score in their 30-minute workout is as follows:

[tex]Field goals total = (9 + 10 S) + (20 (S + J)[/tex]

The first term (9 + 10S) denotes Suzy's total number of field goals in the first 10 minutes, while the second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

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The correct statements for the given probability are-

The following are the key concepts for probability problems to understand:

Given condition:

Total number of card in deck = 52

Total black cards = 26

Total diamonds = 13

So,

probability ( black card ) = total black card / total cards

probability ( black card ) = 26 /52

probability ( black card ) = 1/2

probability (diamond )  = total number of diamond cards / total cards

probability (diamond )  = 13/ 52

probability (diamond ) = 1/4

probability (compound event) = probability (black  and diamond)

probability (compound event) =  1/2 * 1/4

probability (compound event) = 1/8

Thus, The correct statements for the given probability are-

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Complete question:

From a standard deck of cards, your first draw is a black card. You replace the card, and the second draw is a diamond. Which THREE statements are correct for the outcome of the event?

A) The probability of drawing the black card is 1/2

B) The probability of drawing the diamond is 1/4

C)The probability of the compound event is 1/6

D) The probability of the compound event is 1/8

E) The probability of the compound event is 3/4 ​

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

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Answer:

x=4 y=3

Step-by-step explanation:

because y=3 and x=4

1) Note that the rates of change (slope) are 4 and 30 respectively over (0,3).  This mean that the slope of y=1+4^x is much higher. This is also evidenced in the graph.

It is crucial to compare the slopes of linear equations because it can disclose vital information about how the dependent variable varies in relation to the independent variable.

It may also be used to find patterns or trends in data and forecast future behavior.

Note that to get the y values of each function, we just plugged in the value of x into the equation to solve. See the attached sheet showing the formula .

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Answer:

y = - 9x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )

m = [tex]\frac{-31-50}{5-(-4)}[/tex] = [tex]\frac{-81}{5+4}[/tex] = [tex]\frac{-81}{9}[/tex] = - 9 , then

y = - 9x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 31 )

- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )

14 = c

y = - 9x + 14 ← equation of line

One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:

$4a^5 - 3a^4 + 2a^3 - 7a^2$

A polynomial expression is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. The term "polynomial" comes from the fact that the expression can be thought of as a sum of many terms, each of which is a product of one or more variables raised to a non-negative integer power.

For example, the expression 3x^2 + 4x - 1 is a polynomial in one variable, x, with three terms. The first term is 3x^2, the second term is 4x, and the third term is -1. The highest power of the variable in this expression is 2, which makes it a polynomial of degree 2.

Polynomial expressions can be written in standard form, where the terms are arranged in descending order of degree and the coefficients are written with the highest power of the variable first. For example, the expression above could be written in standard form as 3x^2 + 4x - 1.

One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:

$4a^5 - 3a^4 + 2a^3 - 7a^2$

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the probability that no two people of the same sex sit next to each other is 2/7.

One way to solve this problem is to use the principle of inclusion-exclusion. Let A be the event that the boys sit next to each other, and let B be the event that the girls sit next to each other. Then, we want to find the probability of the complement of (A or B), which is the probability that neither A nor B occurs.

The probability of A occurring is the same as the probability of the 5 boys sitting in a row, which is 5! (since each order is equally likely). Similarly, the probability of B occurring is 5!. However, we need to subtract the probability of A and B occurring simultaneously. This can be seen as follows: once the boys are seated in a row, there are 6 spaces (between or on the ends) where the girls can be seated. Thus, the probability of A and B occurring is 2*5!*6.

Therefore, the probability of neither A nor B occurring (i.e., the probability that no two people of the same sex sit next to each other) is:

P(neither A nor B) = 1 - P(A or B) = 1 - [P(A) + P(B) - P(A and B)]

= 1 - [(25!) / 10! - (25!6) / 10!]

= 1 - [25!*(1 - 6/9!)]

= 2/7

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Answer:

b + 17

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 3(6 + b) - (2b + 1)

Let's simplify the expression,

→ 3(6 + b) - (2b + 1)

Applying Distributive property:

→ 3(6) + 3(b) - (2b) - (1)

→ 18 + 3b - 2b - 1

Combining the like terms:

→ (3b - 2b) + (18 - 1)

→ (1b) + (17)

→ b + 17

Hence, the answer is b + 17.

They should mix 16 pounds of City Roast Columbian coffee with 4 pounds of French Roast Columbian coffee to make their blend.

Let x be the number of pounds of City Roast Columbian coffee.

Let y be the number of pounds of French Roast Columbian coffee.

The total cost of the blend is 7.80x + 8.10y

The total weight is x + y = 20.

We can write an equation for the cost per pound:

(7.80x + 8.10y) / 20 = 7.86.

We will multiply both sides by 20 which gives:

7.80x + 8.10y = 157.20.

We can use this equation along with the total weight equation to solve for x and y:

x + y = 20

y = 20 - x (subtract x from both sides)

7.80x + 8.10(20 - x) = 157.20 (substitute y = 20 - x into the cost equation)

7.80x + 162 - 8.10x = 157.20 (distribute)

-0.30x = -4.80

x = 16

Solve for the equation (x + y = 20):

y = 20 - x

y = 20 - 16

y = 4.

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The main advantage of an independent measures design is that it reduces the risk of order or practice effects and minimizes the influence of individual differences between participant

An independent measures design, also known as a between-subjects design, is a type of research study in which different groups of participants are used for each condition being tested.

In other words, each participant is only exposed to one condition, and the data from each group is analyzed and compared to determine if there are any significant differences between the groups.

The main characteristics of an independent measures design are:

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Answer:

We can start by calculating the total amount of money earned per week:

$12.50/hour x 25 hours/week = $312.50/week

To find out how many weeks it will take to earn $3,437.50, we can set up a proportion:

Total amount earned / Amount earned per week = Number of weeks

$3,437.50 / $312.50/week = 11 weeks

Therefore, it will take 11 weeks to earn $3,437.50 working 25 hours per week at a rate of $12.50 per hour.

Answer:

100ft²

Step-by-step explanation:

to find the area of the figure you must do the area of the small rectangle plus the area of the large rectangle

area = length* width

so the area of the small rectangle equals

7ft * 4ft = 28ft²

then the large rectangle

9ft*8ft=72ft²

28ft²+72ft²=100ft²

Answer:

To find out how many gallons of paint are needed to cover the walls, we need to first find the total area of the walls.

The four walls are rectangles with a length of 20 feet and a height of 12 feet. So, the area of one wall is:

20 feet x 12 feet = 240 square feet

Since there are four walls, the total area of the walls is:

4 x 240 square feet = 960 square feet

We know that one gallon of paint can cover approximately 320 square feet. To find how many gallons of paint are needed, we can divide the total area of the walls by the area covered by one gallon of paint:

960 square feet ÷ 320 square feet per gallon = 3 gallons of paint

Therefore, you need approximately 3 gallons of paint to cover the walls.

Taking the quotient between the total volume and the flow rate, we can see that the correct option is D.

We know that water flows at a rate of 1.5*10^4 gallons per second. We know that 6.525*10^6 gallons flowed while Jeremy was watching, then the time that he has been watching is the quotient between these values, we will get:

time = ( 6.525*10^6)/(1.510^4) seconds =  (652.5/1.5) second = 435 seconds

We know that 60 secons = 1 minute, then:

435/60  = 7 + 15/60

So he has been watching for 7 minutes and 15 seconds, the correct option is D.

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the amount of paint required is dependent on the size of the area that needs to be painted.

In an equation or algebraic expression, an uncertain amount is denoted by a symbol in algebra, which is often a letter. A variable is, in the simplest terms, a quantity that can change and is not fixed. The two primary categories of variables are categorical and numerical. Then, for both categorical and numerical variables, discrete or continuous subcategories are created for each category. In this section, a summary of several categories is provided. a measure that can take many different forms. Something that can alter; the sign of a variable; a variable in a scientific experiment.

Because it is the variable which the homeowner may alter or control, the area of the house that needs to be painted in this scenario is the independent variable. Because it depends on the portion of the home that needs to be painted, the overall quantity of paints that need to be obtained is a variable that is dependent. To put it a different way, the amount of paint required depends on the size of the area that needs to be painted.

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Answer:

f(x) C= x+50 x=17.50$/h

Step-by-step explanation:

I might not be sure about it, but it might be a function that is f(x) C= x + 50 dollars

x=17.50 dollars /hour

so that means if it is 1 hour, then 17.50$ +50$ which is 67.50$, if it's 2 hours then 17.50$/h = n$/2h so n=17.50$ *2 = 35$ + 50$ = 85$

The 99.9% confidence interval for the mean weight is (14.042, 14.202).

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To construct a 99.9% confidence interval for the mean weight, we can use the formula:

CI = X ± Zα/2 * (σ/√n)

where X is the sample mean, Zα/2 is the critical value from the standard normal distribution corresponding to a 99.9% confidence level (which is 3.291), σ is the population standard deviation (which we don't know, so we will use the sample standard deviation as an estimate), and n is the sample size.

First, we need to calculate the sample mean and sample standard deviation:

X = (14.07 + 13.99 + 14.16 + 14.17 + 14.15 + 14.11 + 14.24 + 13.99 + 14.14 + 14.13 + 14.20 + 14.21 + 14.06 + 14.05) / 14 = 14.122

s = sqrt((1/(n-1)) * ∑(xᵢ - X)²) = 0.072

where n is the sample size and ∑(xᵢ - X)² is the sum of squared deviations from the sample mean.

Plugging in the values, we get:

CI = 14.122 ± 3.291 * (0.072/√14) = (14.042, 14.202)

Therefore, the 99.9% confidence interval for the mean weight is (14.042, 14.202).

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