Which of the following best describes the slope of the line below?

A paper clip is dropped from the top of a 144‐ft tower, with an initial velocity of 16 ft/sec. Its position function is s(t) = −

hoa [83]

To calculate the velocity, we use the given expression above which is s(t) = −16t^2 + 144. First, we calculate the time it takes to reach the ground. Then, differentiate the expression and substitute time to the differentiated expression.

s(t) = −16t^2 + 144
0 = -16t^2 + 144
t = 3

s'(t) = v = -32t
v = -32(3)
v = -96

Note: negative sign signifies that the object is going down

5 0

2 years ago

Read 2 more answers

Customer account numbers for a certain company consists of 3 letters followed by 5 numbers how many different account numbers ar

Arturiano [62]

Answer:

1,757,600,000

Step-by-step explanation:

company consists of 3 letters followed by 5 numbers how many different account numbers are possible if repetitions of letters and digits are allowed.

We have 26 lettrs and 10 digits

So, the possible out comes for each one of the letters = 26

And the possible out comes for each one of the numbers = 10

∵ repetitions of letters and digits are allowed.

So, the possible accounts are = 26³ * 10⁵ = 1,757,600,000

5 0

3 years ago

Somebody please help me with this !!!

Damm [24]

Step-by-step explanation:

Case 1 :

$3x + 2y = 6 \\ 4x + y = 2 \\ 3x = 6 - 2y \\ x = \frac{6 - 2y}{3} = \\ x = 2 - \frac{2y}{3} \\ 4(2 - \frac{2y}{3} ) + y = 2 \\ 8 - \frac{8y}{3} + y = 2 \\ - 1.67y = - 6 \\$

$y = 3.59 \\ x = 2 - \frac{2y}{3} \\x = 2 - \frac{2 \times 3.59}{3} \\ \\ x = - 0.39$

Case 2 :

$3x + 2y = 6 \\ 4x - y = 2 \\ x = 2 - \frac{2y}{3} \\ 4(2 - \frac{2y}{3} ) - y = 2 \\ 8 - \frac{8y}{3} - y = 2 \\ - 3.67y= - 6 \\ y = 1.63$

$x = 2 - \frac{2y}{3} \\ x = 2 - \frac{2 \times 1.63}{3} \\ x = 2 - 1.087 \\ x = 0.913$

7 0

3 years ago

A scale model of a tower is 24 inches tall and 18 inches wide. If the height of the actual tower is 60 feet, what is its width?

alex41 [277]

Answer:

45 feet

Step-by-step explanation:

To find the width of the model, we need to find the scale of the model to the actual tower.

Since we know the height of both towers, we can use that as the basis.

24 inches : 60 feet

12 inches : 30 feet

6 inches : 15 feet

So the width of the tower is 18 inches wide.

18 inches will then be equal to 12 + 7 inches : 30 + 15 feet

18 inches : 45 feet

6 0

3 years ago

A recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with

tia_tia [17]

Answer:

Probability that deliberation will last between 12 and 15 hours is 0.1725.

Step-by-step explanation:

We are given that a recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours.

Let X = length of time that juries deliberate on a verdict for civil trials

So, X ~ N( $\mu = 12.56, \sigma^{2} = 6.7^{2}$ )

The z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 12.56 hours

$\sigma$ = standard deviation = 6.7 hours

So, Probability that deliberation will last between 12 and 15 hours is given by = P(12 hours < X < 15 hours) = P(X < 15) - P(X $\leq$ 12)

P(X < 15) = P( $\frac{X-\mu}{\sigma}$ < $\frac{15-12.56}{6.7}$ ) = P(Z < 0.36) = 0.64058

P(X $\leq$ 12) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{12-12.56}{6.7}$ ) = P(Z $\leq$ -0.08) = 1 - P(Z < 0.08)

= 1 - 0.53188 = 0.46812

Therefore, P(12 hours < X < 15 hours) = 0.64058 - 0.46812 = 0.1725

Hence, probability that deliberation will last between 12 and 15 hours is 0.1725.

7 0

3 years ago