given the input in the table which function rule produces the output?

Answer:

AAAA

Step-by-step explanation:

I just took the test

Answer:

vm=( 57.1+66,6)/2≈ 61,5 km/h

Step-by-step explanation:

The mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.

The standard deviation is calculated using the following formula:

[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]

Given the range (374 to 380 milliliters):

(a) Mean[tex](\(\mu\))[/tex]:

[tex]\[ \mu = \frac{{\text{min} + \text{max}}}{2} \][/tex]

[tex]\[ \mu = \frac{{374 + 380}}{2} \][/tex]

[tex]\[ \mu = 377 \text{ milliliters} \][/tex]

(b) Standard Deviation:

[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]

[tex]\[ \sigma = \frac{{380 - 374}}{{\sqrt{12}}} \][/tex]

[tex]\[ \sigma \approx \frac{{6}}{{\sqrt{12}}} \][/tex]

[tex]\[ \sigma \approx \frac{{6}}{{3.464}} \][/tex]

[tex]\[ \sigma \approx 1.732 \text{ milliliters} \][/tex]

So, the mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.

Final answer:

1,200 millimeters (mm) is less than 12 meters (m). To compare, we convert 1,200 mm to 1.2 m and directly compare it with 12 m, clearly seeing that 1.2 m is less than 12 m.

Explanation:

To determine whether 1,200 millimeters (mm) is greater or less than 12 meters (m), we need to convert mm to meters. We know that 1 meter is equal to 1,000 millimeters. Therefore, we can convert 1,200 mm to meters:

1,200 mm ÷ 1,000 = 1.2 m

Now we can compare 1.2 m with 12 m directly. Since 1.2 is less than 12, we can conclude that 1,200 mm is less than 12 m.

To use an example for further clarification, imagine you are measuring the length of a room with a tape measure:

If the room is 1,200 mm (or 1.2 m) long, it is shorter than a room that is 12 m long.

The equation that represents the situation is x = 80.

To write an equation representing the situation, let's use the variable x to represent the number of correct answers on the test. Since each correct answer is worth 1 point, the total number of points earned is the same as the number of correct answers. Given that the student needs to earn 80 points to keep an A grade for the semester, the equation is:

x = 80

Therefore, if the student answers 80 questions correctly, they will maintain an A grade for the semester.

Answer with Step-by-step explanation:

since, DAC is a straight line

Hence, ∠BAD+∠BAC=180°

98°+∠BAC=180°

⇒ ∠BAC=180°-98°

             = 82°

Now, we know that sum of angles of a triangle=180°

Hence, ∠BAC+∠ABC+∠BCA=180°

           82°+32°+x=180°

                     x=180°-82°-32°

                     x= 66°

Hence, correct option is:

C. 66°

Answer:

She has read 70 %  of the book.

Step-by-step explanation:

Given  : Melanie is reading a book that is 300 pages long. If she has read 210 pages of the book,

To find :  what percent of the book has she read.

Solution : We have given

Total pages in book = 300 pages .

She read  = 210 .

Percentage she read (%) = [tex]\frac{She\ read\ pages}{total\ pages}*100[/tex].

Percentage she read (%) = [tex]\frac{210}{300}*100[/tex].

Percentage she read (%) = [tex]\frac{210}{3}[/tex].

Percentage she read (%) =  70 % .

Therefore, She has read 70 %  of the book.

Answer:

Step-by-step explanation:

Considering 'm' as the slope of a function y=f(x) we can have:

1. m=(y2-y1)/(x2-x1) which is the slope of a line based on two points from the line.

2. m=dy/dx which is the slope of the function y=f(x) in (x,y) by the derivative.

3. m=tan(Ф) which is the slope of a line when the angle (Ф) with respect x-axis is known.  

The chance of rolling a 5 on a six-sided dice is 1/6, and the probability of getting a tails in a coin toss is 1/2. The total probability of both these independent events occurring is (1/6) * (1/2) = 1/12 or approximately 0.0833 on a decimal scale.

The question is asking for the probability of rolling a 5 on a dice and then getting a tails on a coin toss. To get the total probability, we multiply the individual probabilities together.

First, let's consider a fair six-sided die. The chance of rolling a 5 (or any specific number between 1 and 6) is 1/6.

Next, we consider a fair coin, which has two outcomes: heads or tails. So, the probability of getting tails is 1/2.

The total probability of both these events occurring is (1/6) * (1/2) = 1/12. So, the probability of rolling a 5 and then tossing a tail is 1 in 12 or approximately 0.0833 on a decimal scale.

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Answer: The measure of the third angle of a triangle is 64°.

Step-by-step explanation:

Since we have given that

First angle = 44°

Second angle = 72°

Let the third angle be x.

As we know that the sum of all three angles of a triangle is supplementary.

[tex]44^\circ+72^\circ+x=180^\circ\\\\116^\circ+x=180^\circ\\\\x=180^\circ-116^\circ\\\\x=64^\circ[/tex]

Hence, the measure of the third angle of a triangle is 64°.

John has 51 cards.

Paul has 32 cards.

George has a number of cards greater than either Paul or John.

This means, George does have number of cards greater than both Paul and John.

Number of Cards with John is 51 and number of cards with Paul is 32 cards.

Therefore the number of cards that George may have is in between 33 and 51

If George has any number of cards greater than 32 and less than 52, then this number of cards is greater than cards with Paul but less than the cards with John.

Number of cards George has is > 32 but < 52

Hope this helps..!!

Thank you:)

The answer is B 10x56 Sq 6xy

Answer:

B

Step-by-step explanation:

edgen 2020

Answer:

A. Yes, because each of the two outcomes are equally likely.

Step-by-step explanation:

A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newborn child is a boy or a girl.

The representative uses a 1 for a girl and a 2 for a boy when running a simulation.

Yes, the simulation will be a fair representation of possible survey results.

A. Yes, because each of the two outcomes are equally likely.

Cora's GPA, considering the weighted AP classes and grades achieved, calculates to be 3.875.

To calculate Cora's GPA with her AP and regular classes, we need to account for the weight of her AP classes.

Therefore, Cora's GPA is 3.875.

Answer:

The juice left at the end of the day is 1.085 liters.

Step-by-step explanation:

Juice at the beginning of the day: 3.875 liters

Juice drink by Mario during the day: 2.79 liters

Juice left at the end of the day = Juice at the beginning of the day - Juice drink by Mario during the day

                                                  = 3.875 - 2.79

                                                  = 1.085 liters

A polynomial is an expression of more than one term. An expression is considered a polynomial when is has more than one term, otherwise, it would be called a monomial. These can be combined together through multiplication, addition and subtraction only. (Meaning no division or fractions)

Ex.

[tex]3 x^{2} + 3x - 3[/tex]

 x is a variable (There can be more than 1 variable in a term. Ex. 3xy, 4xyz, 4ab)

*A variable may be represented by letters.

2 is an exponent

3 is a constant

Those are the parts of a polynomial.

Polynomials can be categorized depending on the number of terms and their degree.

A polynomial with two terms is called a binomial. If it has three terms it is called a trinomial. If the expression has more than 3 terms, they are generally called polynomials.

A polynomial can be categorized by degree as well. You can determine the degree of a polynomial by looking at the term that has the highest exponent.

Using the example above, you can categorize the polynomial as a 2nd degree trinomial because 2 is the highest exponent and it has three terms.

When you add and subtract polynomials you need to take note of the variables. You can only subtract and add like terms, which means that the variables and the exponents are the same.

Ex.

[tex]( 2x^{3} + 2 y^{2} + x + 1) + (4 x^{2} - y^{2} + y + 2)[/tex]

When you add these two polynomials, you can disregard the parentheses because according to the associative property of addition, no matter how you group the terms, the answer will be the same.

Like mentioned before you can only add and subtract like terms. It would be easier if you just group like terms together by rearranging the expression. Do not forget that the sign or operation comes along with them.

[tex]2 x^{3} + 2 y^{2} - y^{2} + 4 x^{2} + x + y + 2 + 1[/tex]

Now combine the like terms.

[tex]2 x^{3} + y^{2} + 4 x^{2} + x + y + 3[/tex]

Notice that we retained the terms [tex]2 x^{3} [/tex] , [tex]4 x^{2} [/tex], x and y, this is because they have no similar terms.

FOIL method is used when multiplying 2 BINOMIALS. Remember that a binomial is an expression with 2 terms.

FOIL means:

FIRST term: first terms of each binomial.

OUTSIDE term: The two outer terms when taking the equation as a whole.

INSIDE term: The two inner terms when taking the equation as a whole.

LAST term: Last term of each binomial (2nd term of each binomial)

To get the answer, you need to multiply them with their corresponding term.

Ex. (2x+3)(x-4)

F:  2x and x            (2x)(x) = [tex] 2x^{2} [/tex]     

O: 2x and -4    (2x)(-4) = -8x

I: 3 and x          (3)(x)   = 3x

L: 3 and -4           (3)(-4)   = -12

Resulting expression:

[tex]2 x^{2} - 8x + 3x -12[/tex]         -8x and 3x are similar or like terms, so you can combine them

[tex]2 x^{2} - 5x -12[/tex]

When doing multiplication with binomials, there are two special cases you can consider doing, which follow a pattern. The first is multiplying sum and difference.

The condition where you can apply the first special case is the first term needs to be the same and the second term are additive inverses.

(a+b)(a-b)

The resulting expression follows this pattern [tex] a^{2} - b^{2} [/tex]

Ex. (x+3)(x-3) = [tex] x^{2} - 3^{2} [/tex] or [tex] x^{2} -9[/tex]

You can use FOIL to check your answer:

F: (x)(x) = [tex] x^{2} [/tex]

O: (x)(-3) = [tex]-3x[/tex]

I: (3)(x) = [tex]3x[/tex]

L: (3)(-3) = [tex]-9[/tex]

Arrange the expression:

[tex] x^{2} - 3x + 3x - 9[/tex]      Combining -3x+3x = 0 

[tex] x^{2} -9[/tex]

The next special case is squaring a binomial and there are two scenarios that you can consider. 

[tex] (a+b)^{2} [/tex] and [tex] (a-b)^{2} [/tex]

The resulting expression follows a certain pattern for each:

[tex] (a+b)^{2} [/tex] = [tex] a^{2} + 2ab + b^{2} [/tex]

[tex] (a-b)^{2} [/tex] = [tex] a^{2} - 2ab + b^{2} [/tex]

Let's use an example of each to demonstrate this and check with FOIL:

[tex] (a+b)^{2} [/tex]

[tex] (2x+4)^{2} [/tex]

a = 2x     b = +4

Let's insert that into our pattern:

[tex] a^{2} + 2ab + b^{2} [/tex]

 [tex] 2x^{2} + 2(2x)(4) + 4^{2} [/tex]

Simplify the expression:

[tex] 2x^{2} + 16x + 4^{2} [/tex]

[tex] 4x^{2} + 16x + 16 [/tex]

Let's check with FOIL

[tex] (2x+4)^{2} [/tex] = [tex] (2x+4)(2x+4) [/tex]

F: (2x)(2x) = [tex] 4x^{2} [/tex]

O: (2x)(4) = [tex]8x[/tex]

I: (4)(x) = [tex]8x[/tex]

L: (4)(4) = [tex]16[/tex]

a = 2x     b = -4

Let's insert that into our pattern:

[tex] a^{2} - 2ab + b^{2} [/tex]

 [tex] 2x^{2} - 2(2x)(-4) + (-4)^{2} [/tex]

Simplify the expression:

[tex] 2x^{2} - 16x + (-4)^{2} [/tex]

Let's check with FOIL

[tex] (2x+4)^{2} [/tex] = [tex] (2x-4)(2x-4) [/tex]

F: (2x)(2x) = [tex] 4x^{2} [/tex]

O: (2x)(-4) = [tex]-8x[/tex]

I: (-4)(x) = [tex]-8x[/tex]

L: (-4)(-4) = [tex]16[/tex]

Answer:

2

Step-by-step explanation:

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