JUANITA WANTS TO PARTICIPATE IN A 20 KILOMETER BICYCLE RACE. SHE IS CONSIDERING TWO TRAINING PROGRAMS BELOW.

Dovator [93]

$\displaystyle\sum_{n=1}^\infty\left(1+\frac5n\right)^n$

Notice that

$\displaystyle\lim_{n\to\infty}\left(1+\frac5n\right)^n=e^5\neq0$

which means the series is divergent. So if this is one of those "select all that apply" questions, then both (c) and (j) are the only choices that do.

7 0

2 years ago

The height of a wooden pole, h, is equal to 15 feet. Ataut wire is stretched from a point on the ground to the top of the pole.

Taya2010 [7]

The question is incomplete. Here is the complete question:

The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?

Answer:

Length of wire = 17 feet

Step-by-step explanation:

Given:

The height of the wooden pole is, $h=15\ ft$

The distance from the base of the pole to this point on the ground is, $b=8\ ft$

Let the length of the wire be 'l'.

Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.

Using Pythagorean theorem, we can find the hypotenuse.

$(Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2$

Plug in the given values and solve for 'l'. This gives,

$l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17$

As length can never be negative, we ignore the negative result.

Therefore, the length of the wire is 17 feet.

7 0

3 years ago

What happens to the standard deviation of the average of a sample as the sample size increases? Group of answer choices It gets

NeX [460]

Answer:

Gets smaller

Step-by-step explanation:

- The standard deviation is the quantification of spread of data. According to descriptive statistics the standard deviation s is given by:

s = Σ ( x - u ) / sqrt ( n )

Where, n : sample size

u : Mean value

- So we see that standard deviation (s) is inversely proportional to square root of sample size (n).

- We can see that as sample size (n) increases the standard deviation (s) decreases.

3 0

2 years ago

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

2 years ago

Find X and QT. The shape is a Rhombus

kompoz [17]

Answer:

See below ~

Step-by-step explanation:

Sides of a rhombus are equal.

⇒ QT = TS

⇒ x² - 4x - 10 = 6x + 14

⇒ x² - 10x - 24 = 0

⇒ x² + 2x - 12x - 24 = 0

⇒ x (x + 2) - 12 (x + 2) = 0

⇒ (x + 2)(x - 12) = 0

⇒ x = -2 or x = 12

Substitute both values and see which gives a positive value for QT :

<u>When x = -2</u> :

QT = (-2)² - 4(-2) - 10
QT = 4 + 8 - 10
QT = 2

<u>When x = 12</u> :

QT = (12)² - 4(12) - 10
QT = 144 - 48 - 10
QT = 86

The 2 possible answers are :

x = -2, QT = 2
x = 12, QT = 86

8 0

1 year ago