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3 years ago

Tom rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a factor of 21.

Mathematics

1 answer:

Ber [7]3 years ago

5 0

The probability of getting a total that is a factor of 21 is 0.22

<u>Explanation:</u>

Factor of 21 is = 1, 3, 7, 21

Out of all the factors of 21, we cannot get 21 when the two die are rolled as the maximum sum that can be obtained is 12

The possible combinations are:

(1,2) (1,6)

(2,1) (2,5)

(3,4)

(4,3)

(5,2)

(6,1)

Total outcome = 6 X 6

= 36

Number of outcomes that is the factor of 21 is 8

The probability of getting a total that is a factor of 21 is $\frac{8}{36}$

p(21) = 0.22

Therefore, the probability of getting a total that is a factor of 21 is 0.22

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The product of the square of a number x and 2 subtracted from 3 is y.

lozanna [386]

The algebraic expression for the given statement is: 2x² - 3 = y.

<h3>How to Write an Algebraic Expression?</h3>

To wrote an algebraic expression is translate a statement using numbers, variables, and mathematical sign into a mathematical statement.

Square of x is: x²

Product of x² and 2 is: 2x²

Thus, we would have:

2x² - 3 = y

The algebraic expression is: 2x² - 3 = y.

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5 0

2 years ago

A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an

slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Horizontal distance from the start line, measured in meters.

$y$ - Height of the long jumper, measured in meters.

$a$ , $b$ , $c$ - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m)$ , $(x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m)$ , this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0$ (Eq. 1)

$81\cdot a + 9\cdot b + c = 0$ (Eq. 2)

$64\cdot a + 8\cdot b + c = 0.05$ (Eq. 3)

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}$ , $b = \frac{3}{25}$ , $c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}$ .

But we need $y$ measured in centimeters, then, we use the following conversion:

$y = 100\cdot y'$

Then, we get that:

$y = -x^{2}+12\cdot x -27$

Where $x$ and $y$ are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

4 0

3 years ago

A moving company had one sixth of a ton weight to move across town. If they wanted to split it equally amongst 4 trips, how much

Vlad [161]

1/24 of a ton.
Hope this helps

3 0

3 years ago

Help me . With work to plz

Zepler [3.9K]

Answer:

57°

Step-by-step explanation:

Angles EGB and EHD are corresponding angles of two parallel lines cut by a transversal; therefore, they are congruent.

m<EGB = m<EHD = 57°

7 0

3 years ago

For the right triangle shown, the lengths of two sides are given. Find the third side. Leave your answer in simplified, radical

KATRIN_1 [288]

The Pythagorean theorem tells you

... a² + b² = c²

... a² = c² - b² = 16² - 9² = 256-81 = 175

... a = √175 = √(25·7)

... a = 5√7

4 0

3 years ago