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2 years ago

The explicit rule for a sequence is

Mathematics

2 answers:

Sphinxa [80]2 years ago

6 0

The rule should be a(n)=a(1)+(n-1)d
d=-11 in this case, so a(n)=a(1)-11(n-1)
a(n)=a(1)-11n+11
a(n)=a(1)+11-11n
a(1)+11=48,
a(1)=37
B is the correct answer.

pishuonlain [190]2 years ago

3 0

For an explicit formula in its simplified form, we must evaluate the first two terms.

For $a_n=48-11n$ , $a_1=48-11=37$ , and $a_2=48-22=26$ . We see that the common difference is $37-26=-11$ , and $a_1=37$ , so we write,
$a_1=37, \ \ \ a_n=a(n-1)-11$ .

The correct answer is B.

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I need help with number 9: h, i, k and l

lozanna [386]

But i really need a name of this book and authors :)

7 0

3 years ago

A gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than

Neko [114]

Answer:

The probability that no more than 70% would prefer to start their own business is 0.1423.

Step-by-step explanation:

We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let $\hat p$ = sample proportion of people who prefer to start their own business

The z-score probability distribution for the sample proportion is given by;

Z = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, p = population proportion who would prefer to start their own business = 72%

n = sample of 18-29 year-olds = 600

Now, the probability that no more than 70% would prefer to start their own business is given by = P( $\hat p$ $\leq$ 70%)

P( $\hat p$ $\leq$ 70%) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ $\leq$ $\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }$ ) = P(Z $\leq$ -1.07) = 1 - P(Z < 1.07)

= 1 - 0.8577 = 0.1423

The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.

3 0

3 years ago

A man hits a baseball when it is 4 ft above the ground with an initial velocity of 120 ft/sec. The ball leaves the bat at a 30 d

Sauron [17]

et us assume that the origin is the floor right below the 30 ft. fence

To work this one out, we'll start with acceleration and integrate our way up to position.

At the time that the player hits the ball, the only force in action is gravity where: a = g (vector)
ax = 0
ay = -g (let's assume that g = 32.8 ft/s^2. If you use a different value for gravity, change the numbers.

To get the velocity of the ball, we integrate the acceleration
vx = v0x = v0cos30 = 103.92
vy = -gt + v0y = -32.8t + v0sin40 = -32.8t + 60

To get the positioning, we integrate the speed.
x = v0cos30t + x0 = 103.92t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + 60t + 4

If the ball clears the fence, it means x = 0, y > 30

x = 0 -> 103.92 t - 350 = 0 -> t = 3.36 seconds

for t = 3.36s,
y = -16.4(3.36)^2 + 60*(3.36) + 4
= 20.45 ft

which is less than 30ft, so it means that the ball will NOT clear the fence.

Just for fun, let's check what the speed should have been :)

x = v0cos30t + x0 = v0cos30t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + v0sin30t + 4

x = 0 -> v0t = 350/cos30
y = 30 ->
-16.4t^2 + v0t(sin30) + 4 = 30
-16.4t^2 + 350sin30/cos30 = 26
t^2 = (26 - 350tan30)/-16.4
t = 3.2s

v0t = 350/cos30 -> v0 = 350/tcos30 = 123.34 ft/s

So he needed to hit the ball at at least 123.34 ft/s to clear the fence.

You're welcome, Thanks please :)

6 0

3 years ago

The point (-3/5,y) in the third quadrant corresponds to angle θ on the unit circle.

romanna [79]

Sec(theta) = 1 / cos (theta) = hypotenuse / x -coordinate

hypotenuse = 1 (because it is the radius of the unit circle)

sec (theta) = 1 / (-3/5) = - 5/3

cot (theta) = 1 / tan(theta) = x-coordinate / y - coordinate

cot (theta) = -3/5 / y

y^2 + (-3/5)^2 = 1 => y^2 = 1 - 9/25 = 16/25 = y = +/- 4/5

Third quadrant => y = -4/5

=> cot (theta) = (-3/5) / (-4/5) = 3/4

7 0

3 years ago

120 is the same as 394 fewer than Z

SpyIntel [72]

Answer:

z=514

Step-by-step explanation:

120=z-394

+394. +394

514=z

Hope this helps

8 0

3 years ago