How many $0.12 pencils can Chloe buy for $4.80?

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the pro

Elanso [62]

Answer:

Choose the first alternative

$\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}$

Step-by-step explanation:

Probabilities

The requested probability can be computed as the ratio between the number of ways to choose two sophomores in alternate positions $(N_s)$ and the total number of possible choices $(N_t)$ , i.e.

$\displaystyle P=\frac{N_s}{N_t}$

There are 6 sophomores and 14 freshmen to choose from each separate set. There are 20 students in total

We'll assume the positions of the selections are NOT significative, i.e. student A/student B is the same as student B/student A.

To choose 2 sophomores out of the 6 available, the first position has 6 elements to choose from, the second has now only 5

$_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C} \text{ ways to do it}$

The total number of possible choices is

$_{2}^{20}\textrm{C} \text{ ways to do it}$

The probability is then

$\boxed{\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}}$

Choose the first alternative

7 0

3 years ago

Read 2 more answers

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=2−x2. What are the dimensions of su

Paul [167]

Answer:

Step-by-step explanation:

Given that a rectangle is inscribed with its base on the x-axis and its upper corners on the parabola

$y=2-x^2$

the parabola is open down with vertex at (0,2)

We can find that the rectangle also will be symmetrical about y axis.

Let the vertices on x axis by (p,0) and (-p,0)

Then other two vertices would be (p,2-p^2) (-p,2-p^2) because the vertices lie on the parabola and satisfy the parabola equation

Now width = $2-p^2$

Area = l*w = $2(2p-p^3)$

Use derivative test

I derivative = $2(2-3p^2)$

II derivative = $-12p$

Equate I derivative to 0 and consider positive value only since we want maximum

p = $\sqrt{\frac{2}{3} }$

Thus width= $\sqrt{\frac{2}{3} }$

Length = $2\sqrt{\frac{2}{3} }$

Width = $2-2/3 = 4/3$

3 0

3 years ago

30 points please answer honestly. Geometry help needed. D is 9.32

Vadim26 [7]

Answer:

7.75 m

Step-by-step explanation:

First find the circumference. Use the formula C = 2πr

C = 2(3.14)(3)

C = 18.84

148° is a fraction of the entire circle which is 360°

Multiply

18.84/1 x 148/360

2788.32/360

7.745

4 0

2 years ago

Which tools were used by ancient mathematicians to make geometric constructions?

ArbitrLikvidat [17]

The tools that were used by ancient mathematicians to make geometric constructions are compasses and straightedges. A compass is a drawing instrument used to draw circles and arcs. The straightedges on the other hand is a tool to check on the accuracy of a straight line.

The answer is first choice.

7 0

3 years ago

Read 2 more answers

F(x) = x + 2 g(x) = x-4 (f g)(x) =

Yanka [14]

Answer:

f(g(x))=(x-4)+2

Step-by-step explanation:

Plug in the equation from g(x) into the x in f(x) and solve.

3 0

3 years ago