On which of these policies will an insurer pay if there’s a loss

Absolute value of -12 and -15

kvasek [131]

Absolute value- the amount a number is away from zero. With this information, we can conclude,

|-12| = 12

|-15| = 15

5 0

2 years ago

Read 2 more answers

Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

Dvinal [7]

Answer:

1.692 m/min

Step-by-step explanation:

Let $\theta$ be the angle between the two sides and x be the length of the third side. By cosine rule,

$x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta$

$x= \sqrt{340 - 336\cos\theta}$

We differentiate x with respect to $\theta$ by applying chain rule.

$\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}$

Rate of change of $\theta$ is 2

$\dfrac{\theta}{dt} = 2$

Rate of change of x is

$\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}$

$\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}$

At 60°,

$\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}$

4 0

1 year ago

A bicycle is traveling at 20 feet per minute. What is the bicycle's speed expressed in inches per second?

Vikentia [17]

Answer:

4 inches per second

Step-by-step explanation:

Speed = distance/time

Given

Distance = 20 feet

12 inches = 1 foot

X inches = 20 feet

X = 20 x 12 = 240 inches

Time = 1 minute = 60 secs

Therefore

Speed = 240/60

= 4 inches per second

7 0

2 years ago

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his brea

Novosadov [1.4K]

The answer is 141.35 ft²

Before the first break, it was painted:
150 ft² ÷ 2 = 75 ft²
Now it's left:
150 ft² - 75 ft² = 75 ft²

Before the second break, it was painted:
75 ft² ÷ 2 = 37.5 ft²
Now it's left:
75 ft² - 37.5 ft² = 37.5 ft²

Before the third break, it was painted:
37.5 ft² ÷ 2 = 18.75 ft²
Now it's left:
37.5 ft² - 18.75 ft² = 18.75 ft²

Before the fourth break, it was painted:
18.75 ft² ÷ 2 = 9.375 ft²
Now it's left:
18.75 ft² - 9.375 ft² = 9.375 ft²

Before the fourth break, it was painted:
9.375 ft² ÷ 2 = 4.6875 ft²
Now it's left:
9.375 ft² - 4.6875 ft² = 4.6875 ft²

Now, we will sum what he painted for now:
75 ft² + 37.5 ft² + 18.75 ft² + 9.375 ft² 4.6875 ft² = 141.3125 ft² ≈ 141.35 ft²

When the painter takes his fifth break, there will be 141.35 ft² of the wall painted.

6 0

1 year ago

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A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.Let B = t

pentagon [3]

Answer:

$P(R\ and\ B) = 0.0256$

Step-by-step explanation:

Given

$Red = 22$

$Yellow = 38$

$Green = 20$

$Purple = 28$

$Blue = 26$

$Orange = 16$

Required

Determine the probability of red then blue jelly? i.e. P(R and B)

From the question, we understand that the red jelly bean was not replaced. This means that the number of jelly beans reduced by 1 after the picking of the red jelly bean

So, we have:

$P(R\ and\ B) = P(R)\ and\ P(B)$