Create a function with roots x = 3 and x = 2 and x = -3

Final answer:

The odds against rolling a sum of 6 with the roll of two dice are 31:5, as there are 5 favorable outcomes for a sum of 6 and 36 total possible outcomes when rolling two dice.

Explanation:

The question is asking about the odds against rolling a sum of 6 with two dice. To calculate this, first, we need to find all the possible combinations of two dice that sum up to 6. Those combinations are (1,5), (2,4), (3,3), (4,2), and (5,1), therefore there are 5 ways to achieve a sum of 6.

The total number of possible outcomes when rolling two dice is 6 * 6 = 36, since each die has 6 faces. So, there are 36 - 5 = 31 ways to not roll a sum of 6. The odds against rolling a sum of 6 are therefore the number of ways not to roll a 6 to the number of ways to roll a 6, which is 31:5.

Odds against rolling a sum of 6 with two dice = 31:5.

Answer:

  f(0) = -1

Step-by-step explanation:

Any scientific or graphing calculator can help you do this. According to the Order of Operations, the exponent is evaluated first, then the sign is applied:

  f(0) = -2^0 = -(2^0) = -1

Answer:a=2A/p

Step-by-step explanation:

To find the original price of the book, we can set up an equation: 0.75x = $90.75. Solving for x, we find that the original price is $121.

To find the original price of the book, we can set up an equation. Let's denote the original price as x. The sale price is 75% of the original price, which can be expressed as 0.75x. We are given that the sale price is $90.75, so we can set up the equation:

0.75x = $90.75

To solve for x, we divide both sides of the equation by 0.75:

x = $90.75 / 0.75

Using a calculator, we can calculate that the original price of the book is $121.

Answer: 39,075 is the answer

Step-by-step explanation:

Answer:

The area of the clock face is [tex]79\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=5\ m[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(5^{2})=78.5\ m^{2}[/tex]

Round to the nearest square meter

[tex]78.5\ m^{2}=79\ m^{2}[/tex]

Answer is D Use the distributive property to simplify.  

Answer: Second Option is correct.

Step-by-step explanation:

Since we have given that

ΔSRT is a triangle with measures :

SR = 7 yd

∠T = 79°

∠R = 59°

We need to find the side ST say x.

We will use " Law of Sines " :

[tex]\frac{\sin T}{SR}=\frac{\sin R}{ST}\\\\\frac{\sin 79^\circ}{7}=\frac{\sin 59^\circ}{x}\\\\0.14=\frac{\sin 59^\circ}{x}\\\\x=\frac{\sin 59^\circ}{0.14}\\\\x=6.12\ yd[/tex]

Hence, the length of ST = 6.1 yd.

Therefore, Second Option is correct.

The answer is 7 on e2020.

The total number of eggs a bird laid is 6 eggs.

To solve this problem we need to break it down step by step:

Assuming 1/3 of the eggs hatch means 2 eggs hatch, so if two eggs hatch, this represents 1/3 of the total eggs laid.

To find the total number of eggs the bird laid, we need to find the equivalent of 1 whole (the total). If 1/3 is equal to 2 eggs, then the whole (3/3 or 1) would be 6 eggs.

Mrs. Cunningham travels at a speed that is 20mph faster than Mr. Cunningham. Given that Mr. Cunningham has a 165-mile head start, Mrs. Cunningham would need 8.25 hours to cover this distance and catch up with him.

This question can be approached by analysing the relative speeds and the initial advantage Mr. Cunningham had. Mr. Cunningham travels for three hours at 55 mph before Mrs. Cunningham leaves, giving him a 165 mile head start. To determine how long it will take Mrs. Cunningham to overtake Mr. Cunningham, it's necessary to calculate how long it will take her to make up this 165-mile deficit at her faster speed.

Mrs. Cunningham travels 75mph, which is 20mph faster than Mr. Cunningham's speed. Thus, each hour, she closes the distance between them by 20 miles. To find out how many hours it takes her to close the 165 mile distance between them, divide this distance by her relative speed, so: 165miles / 20mph equals 8.25 hours.

Thus, it will take Mrs. Cunningham 8.25 hours to overtake Mr. Cunningham.

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The required expression is  (-3/2)a²b¹¹ which is equivalent to the given expression. which is the correct answer would be option (C)

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question as:

-18a⁻² b⁵/-12a⁻⁴ b⁻⁶

To find the equivalent expression for -18a⁻² b⁵/-12a⁻⁴ b⁻⁶, we need to combine the constants and factors that have the same base and exponent.

You can begin by combining the constants in the fraction: -18/-12 = -3/2.

Next, you can simplify the terms involving the variables. Recall that when you divide two powers with the same base, you subtract the exponents. Therefore, you can simplify the expression as follows:

(-3/2)(a⁻² ÷ a⁻⁴ (b⁵ ÷ b⁻⁶)

= (-3/2)(a⁻⁴ a⁴) (b⁵ b⁶)

= (-3/2)(a²)(b¹¹)

= (-3/2)a²b¹¹

This is the simplified form of the given expression.

Hence, the correct answer would be option (C)

Learn more about the algebraic expression here :

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Final answer:

Aaliyah ate 1/8 more of the mini-pizza than James after converting their consumed amounts to a common denominator and subtracting James's share from Aaliyah's.

Explanation:

To calculate how much more Aaliyah ate compared to James, we need to compare the fractions of the mini-pizzas they each consumed. Aaliyah ate 7/8 of her mini-pizza, while James ate 3/4 of his mini-pizza. To make a comparison, we have to ensure both fractions have the same denominator.

Since the least common denominator for 4 and 8 is 8, we convert James's fraction from 3/4 to 6/8 by multiplying both the numerator and the denominator by 2. Now we can compare the amounts:

To find out how much more Aaliyah ate, we subtract James's portion from Aaliyah's:

7/8 - 6/8 = 1/8

Therefore, Aaliyah ate 1/8 more of the mini-pizza than James.