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3 years ago

Someone please help me with this

Mathematics

1 answer:

vodomira [7]3 years ago

8 0

1. Independent. 2. Dependent because the marble was not replaced. 3. However, there is a “dependency” in which that the coach determines the batting order, and there’s only so many players left on the team. So dependent because there’s only so many other players on the team that can up to the plate, similar to the marble problem. 4. Independent. 5. Dependent because there is no replacement. 6. 0.5 because there are 3 even numbers on a 6-sided die. 7. 0.5 because there are 13 clubs and 13 spades (all back) which is 26 black cards. 26 out of 52 cards in a standard deck are black. 8. 1/8 because of the chance of getting heads in one event is 1/2, in 2 events 1/4, and 3 it’s 1/8. 9. 1/6 because 4 is one number of the six-sided die.

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The length of a swimming pool is 22 ft. The width is 40 ft. If the volume of the pool is 2,500 ft³, which equation below could b

AURORKA [14]

The equation best used would be 2500=22*40*d

5 0

3 years ago

Read 2 more answers

Find the general term of sequence defined by these conditions.

disa [49]

Answer:

$\displaystyle a_{n} = (2)^{2n -1} - (3) ^{n-1 }$

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

$\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0 \: \: where : \: \:a_1 = 1 \: ,a_2 = 5,$

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

${x}^{n} = c_{1} {x}^{n - 1} + c_{2} {x}^{n - 2} + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}$

the steps for solving a linear homogeneous recurrence relation are as follows:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

${x}^{2} - 7x+ 12= 0$

Step-2:Solve the polynomial by factoring

factor the quadratic:

$( {x}^{} - 4)(x - 3) = 0$

solve for x:

$x = \rm 4 \:and \: 3$

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

$\displaystyle a_{n} = c_{1} {x} _{1} ^{n } + c_{2} {x} _{2} ^{n }$

so substitute the roots we got:

$\displaystyle a_{n} = c_{1} (4)^{n } + c_{2} (3) ^{n }$

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

$\begin{cases}\displaystyle 4c_{1} +3 c_{2} = 1 \\ 16c_{1} + 9c_{2} = 5\end{cases}$

solve the system of equation which yields:

$\displaystyle c_{1} = \frac{1}{2} \\ c_{2} = - \frac{1}{3}$

finally substitute:

$\displaystyle a_{n} = \frac{1}{2} (4)^{n } - \frac{1}{3} (3) ^{n }$

$\displaystyle \boxed{ a_{n} = (2)^{2n-1 } - (3) ^{n -1}}$

and we're done!

7 0

3 years ago

11. Which could be the table of values that was used to graph the function of x shown below?

frutty [35]

Answer:

Step-by-step explanation:

Here, we want to select the possible table of the given line

Let us look at the intercepts

On the x-axis, we have an intercept at x = 2

On the y-axis, we have an intercept at y = -4

This means that when y = 0, x = 2 and when x = 0, y = -4

Looking at the options, the table that supports this answer is the table of option D

8 0

3 years ago

samuel needs to estimate the product of 24 x 395. Explain two different methods Samuel can use to estimate.

JulsSmile [24]

Samuel needs to estimate the product of 24 x 395.

First method

We round the number to nearest tens

24 can be rounded to 20 because we have 4 on ones place

395 can be rounded to 400 because we have 5 in ones place so we add 1 with 9 and it becomes 10 . so we add 1 with 3 and got 400

20 * 400 = 8000

Second method:

We round the number to nearest hundreds place

24 have no number in hundreds place so it remains 24

395 can be rounded to 400 because we have 9 in tens place.

24 * 400 = 9600

4 0

3 years ago

Todd has twice as many songs in his playlist as Vlad. Becca has three times as many songs in her playlist as Todd. If all three

nikitadnepr [17]

Answer:

Todd has 540540 songs in his playlist.

Vlad has 270270 songs in his playlist.

Becca has 162162 songs in her playlist.

Step-by-step explanation:

# of songs Todd has = T

# of songs Vlad has = V

# of songs Becca has = B

1) Todd has twice as many songs in his playlist as Vlad:

T=2V

2) Becca has three times as many songs in her playlist as Todd:

B=3T

3) All three people have a total of 243243 songs in their playlists:

T+V+B=243243

Because T=2V then you can substitute T as 2V in the second equation:

B=3(2V)

B=6V

Now in the final equation, you can substitute everything for V:

2V+V+6V=243243

9V=243243

V=27027

Now substitute for T:

T+1/2T+3T=243243

9/2T=243243

T=54054

Now substitute for B:

1/3B+1/6B+B=243243

3/2B=243243

B=162162

Check answers:

27027+54054+162162=243243

243243=243243

3 0

3 years ago