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9 days ago

P(t)P(t)P, left parenthesis, t, right parenthesis models the distance of a swinging pendulum (in \text{cm}cmstart text, c, m, en

d text) from the place it was released ttt seconds after it starts to swing. Here, ttt is entered in radians. P(t) = -5\cos\left(2\pi t\right) + 5P(t)=−5cos(2πt)+5P, left parenthesis, t, right parenthesis, equals, minus, 5, cosine, left parenthesis, 2, pi, t, right parenthesis, plus, 5 What is the first time the pendulum reaches 3.5\text{ cm}3.5 cm3, point, 5, start text, space, c, m, end text from the place it was released? Round your final answer to the nearest hundredth of a second.

Mathematics

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If a and b are integers,what conditions would make a×b > 0?

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Both a and b must be positive whole numbers.

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2 months ago

A local PTA runs a fundraiser, selling lottery tickets for $5, offering 1 first prize of $100 and 5 second prizes worth $20 each

Inessa [12570]

The expected value is calculated by subtracting the expected cost from the anticipated income.

The expected cost is fixed at $5.

The anticipated income arises from the probability associated with each outcome multiplied by its respective reward.

=> For the first prize: probability * prize = (1 / 100) * $ 100 = $1

=> For the second prize: probability * prize = (5 / 100) * $20 = $1

Thus, the expected value comes out to $1 + $1 - $5

This gives us an expected value of - $3

Final answer: - $ 3

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2 months ago

12x+7<−11 AND5x−8≥4012

Svet_ta [12734]

Answer:

No solution

Step-by-step explanation:

Given: $12x+7$ and $5x-8\geq 40$

Handle each inequality separately.

$12x+7$ Utilizing the subtraction property of inequalities

$12x$

$x$

and

$5x-8\geq 40$ Utilizing the addition property of inequalities

$5x\geq 40+8$

$5x\geq 48$

$x\geq \dfrac{48}{5}$

Thus, the solution to the combined inequality is the overlap of both solutions.

Refer to the attached image for the number line representation.

No solution

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3 months ago

Read 2 more answers

Jean lives about 10 miles from the college where she plans to attend a 10-week summer class. There are two main routes she can t

PIT_PIT [12445]

Answer:

We would recommend the Country Route as its travel time is consistently estimated between 15 and 18 minutes.

Step-by-step explanation:

Jean lives approximately 10 miles away from the college where she plans to attend a summer class lasting ten weeks. She has two primary routes available, one that traverses the city and another that goes through the countryside.

Jean has set up a randomized trial in which she flips a coin each day to determine her travel route, collecting data from five days for both.

Country Route - 17, 15, 17, 16, 18 (in minutes)

City Route - 18, 13, 20, 10, 16 (in minutes)

Next, we need to evaluate which route is superior for Jean.

The data indicates that the Country route has timing ranging from 15 to 18 minutes, suggesting she will typically arrive within this timeframe.

Conversely, the City route timings show significant variation with a minimum of 10 minutes and a maximum of 20 minutes, indicating uncertainty regarding her arrival time.

Hence, it is advisable for her to select the Country route.

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2 months ago

An arena receives $1,700 per event for 12 concerts. If the costs for this sponsorship total $14,000, what is the profit margin f

Zina [12379]

Answer:

The profit margin associated with the concert sponsorship is 31.3725 %

Step-by-step explanation:

The arena earns $1700 for a single event

Consequently, for 12 events, the arena gains $12 \times 1700$

The total for 12 events equals 20400

The expenses for this sponsorship amount to $14,000

Thus, profit = 20400-14000

This calculates to profit =6400

To find the profit margin = $\frac{6400}{20400} \times 100$

Profit margin is defined as $31.3725\%$

Thus, the profit margin for the concert sponsorship is 31.3725 %

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2 months ago