Find the missing value so that the two points have a slope of 2/7. (-1, -1) and (x, 1)

Thirteen people on a softball team show up for a game. a)How many ways are there to choose 10 players to take the field? b)How m

marishachu [46]

Answer:

a) 286

b) 1,037,836,800

c) 285

Step-by-step explanation:

a) Since order is not important, the total possible number of ways to choose 10 players out of 13 is the following combination:

$C(13,10)=\frac{13!}{(13-10)!10! } \\C(13,10)=\frac{13*12*11*10!}{(3*2*1)10! }\\C(13,10) = 286$

b) The total number of possibilities to assign positions by the selecting 10 players is the permutation of 13 players for 10 positions:

$P(13,10) = \frac{13!}{(13-10)!}\\P(13,10) = 13*12*11*10*9*8*7*6*5*4\\P(13,10) =1,037,836,800$

c) The number of ways to pick 10 players including at least one woman is equal to the total number of ways to pick 10 players (found in item a) minus the the number of ways to pick 10 players without picking a single woman.

Since there 10 male players for 10 positions, there is only one possible way to pick a team without women, therefore:

$P=286-1 =285$

6 0

3 years ago

Create a proportional ratio to the given ratio:<br> 2/4 is equal to what?

sladkih [1.3K]

Answer:

4/8, 6/12, 7/14,etc.

Step-by-step explanation:

Multiply 2/4 by any number(like 4) and you can find a equal ratio

5 0

3 years ago

Given the following exponential function, identify whether the change represents

siniylev [52]

Hello there!

Using the given exponential function of y = 64(0.97)^x, we can tell that it is a decaying exponential function since the rate is less than 1.

The percent of decrease is 3% since 97% of the value is retained per x time.

8 0

3 years ago

A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10sin( t ) N(newtons) and moves in a mediu

yKpoI14uk [10]

Answer:

A) C1 = 0.00187 m = 0.187 cm, C2 = 0.0062 m = 0.62 cm

B) A sample of how the graph looks like is attached below ( periodic sine wave )

C) w = $\sqrt[4]{3}$ is when the amplitude of the forced response is maximum

Step-by-step explanation:

Given data :

mass = 5kg

length of spring = 10 cm = 0.1 m

f(t) = 10sin(t) N

viscous force = 2 N

speed of mass = 4 cm/s = 0.04 m/s

initial velocity = 3 cm/s = 0.03 m/s

Formulating initial value problem

y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m

spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m

f(t) = 10sin(t/2) N

using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion

the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)

A) finding the solution of the initial value

attached below is the solution and

B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like

C attached below

3 0

3 years ago

A _______ is a group of people who agree to save their money together and to make loans to each other at a relatively low rate o

Law Incorporation [45]

A Credit union is a group of people who agree to save their money together and to make loans to each other at a relatively low rate of interest. <span />

7 0

3 years ago

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