A science teacher needs to choose 4 students from a class of 20 to go to the library to do some research. How many different groups can he select?

Answer:

The value of the square root of 120 is 10.95

      What is square root ?

Square root of the number is the factor that we can multiply by itself to get that number .

     If square of a number is equal to another number than we can write

         m = n²

    And after taking root to both side

       √m = √n²

   We can cancel the square with root and

       √m = n

   We know the prime factor of 120

        120 = 2x2x2x3x5

   So the square root of 120 will be

       √(2x2x2x3x5)= 2 √(2x3x5)

                                = 2 √(30)

   And we know the value of √(30) = 5.477

     Root of 120 = 2x5.477

                           = 10.95

Hence , the square root of 120 is 10.95 .

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The distribution of the z-scores for the time it takes to solve a crossword puzzle that is strongly skewed to the right with a mean of 30 minutes and a standard deviation of 15 minutes can be calculated using the formula z=(x-mean)/standard deviation. Z-scores can be used to determine how far a data point is from the mean in terms of standard deviations.

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times can be calculated using the formula:

z = (x - mean)/standard deviation

For example, if a person takes 45 minutes to solve the puzzle, the z-score would be:

z = (45 - 30)/15 = 1

This means that the person's time is one standard deviation above the mean.

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1 yard = 3 ft

10/3 = 3 1/3 yards

3 1/3 x 4 = 13 1/3 square yards

Answer:

0.45x + 12.50

Step-by-step explanation:

To put the given equation of a sphere in standard form, complete the square for x, y, and z, and combine constant terms on the right side. The standard form of the sphere's equation is (x + 2)2 + (y - 3)2 + (z - 3)2 = 28, with a center at (-2, 3, 3) and a radius of √28.

To write the equation of the sphere in standard form, we will complete the square for the x, y, and z terms in the given equation x2 + y2 + z2 + 4x − 6y − 6z = −6.

First, we organize the variables and separate the constants:

x2 + 4x + y2 - 6y + z2 - 6z = -6

We then complete the square for each variable by adding and subtracting the square of half the coefficient of the linear term:

x2 + 4x + 4 - 4 + y2 - 6y + 9 - 9 + z2 - 6z + 9 - 9 = -6

Now we can rewrite this as:

(x + 2)2 - 4 + (y - 3)2 - 9 + (z - 3)2 - 9 = -6

Combining the constant terms on the right side we get:

(x + 2)2 + (y - 3)2 + (z - 3)2 = 4 + 9 + 9 + 6

Which simplifies to:

(x + 2)2 + (y - 3)2 + (z - 3)2 = 28

The sphere's center is located at (-2, 3, 3) and has a radius of √28. In standard form, the equation of the sphere is:

(x + 2)2 + (y - 3)2 + (z - 3)2 = 28

Answer:  The required value of c that makes the given statement true is 5.

Step-by-step explanation:  We are given to find the value of c that makes the following statement TRUE :

[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of c, we need to equate the coefficients of the same powers of the unknown variable x.

From equation (i), we have

[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5\\\\\Rightarrow -2cx^{3+3}-2x^{3+2}=-10x^6-2x^5\\\\\Rightarrow -2cx^6-2x^5=-10x^6-2x^5.[/tex]

Equating the coefficients of [tex]x^6[/tex] on both sides of the above equation, we get

[tex]-2c=-10\\\\\Rightarrow c=\dfrac{-10}{-2}\\\\\Rightarrow c=5.[/tex]

Thus, the required value of c that makes the given statement true is 5.

The simplified form of the expression (y^8)(y^2) is y^10, found by applying the laws of exponents that dictate adding the exponents when multiplying with the same base.

The simplified form of the expression (y8)(y2) can be found using the laws of exponents which state that when multiplying two powers with the same base, you add the exponents. Here, since the base is y, and we have exponents 8 and 2, we add them together:

y8 × y2 = y8+2

This simplifies to y10, which is the compressed form of the given expression.

Final answer:

To simplify the expression (y⁸)(y²), use the rule of exponents which says that you add the exponents when multiplying powers with the same base, resulting in y¹⁰.

Explanation:

The question requires simplifying an algebraic expression with exponents. The given expression is (y⁸)(y²). To simplify this, we use the rule of exponents which states that when multiplying two powers with the same base, you add the exponents. Therefore, y⁸ × y² = y⁸₊²} = y¹⁰

multiply 12 x 0.75

12 x 0.75 = 9

answer is B. 9 pounds

Answer:

Josh will need 9 pounds Option B.

Step-by-step explanation:

Josh wants to make a set of 12 ceramic cups.

For each cup he will need 0.75 pound of clay

We have to calculate how many pounds of clay does Josh need for 12 ceramic cups. So we have to multiply 12 cups by 0.75.

for 12 cups he will need = 12 × 0.75 = 9 pounds.

Josh will need 9 pounds to make a set of 12 ceramic cups.

y - y1 = m (x - x1)

where m is the slope and (x1 , y1) is the point given

We are given:

m= -1

the point is (2, 4)

Then:

Answer:

60 my vros                

Step-by-step explanation:

3x-6 = 2x+11

3x = 2x+17

x = 17

3(17)-6 = 45

2(17)+11 = 45

45+45 = 90

answer is C 90 degrees:right