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22 days ago

10

An engineer is asked to design a playground slide such that the speed a child reaches at the bottom does not exceed 6.0 m/s. Det

ermine the maximum height that the slide can be

1 answer:

babunello [11.8K]22 days ago

4 0

Response:

1.8 m

Detailed explanation:

The slide’s descent is predominantly influenced by gravitational forces. It starts from a standstill. We apply the equation of motion

$v_f^2 = v_i^2 + 2as$

$v_f$ and $v_i$ indicate final and initial velocities, a is the acceleration, and s represents the distance travelled.

In this scenario, the initial velocity is 0 m/s, the final velocity is 6 m/s, a denotes gravitational acceleration (9.8 m/s2), and s signifies the height, h.

$v_f^2 = v_i^2 + 2gh$

$6^2 = 0^2 + 2\times9.8h$

$h=\dfrac{36}{19.6}=1.8 \text{ m}$

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According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult

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Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

b)

c)

d) $P(r = 15) = 3.2768 *10^{-11}$

Step-by-step explanation:

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

$P(r = n) = ^nC_r * p^r * q^{n-r}$

Here C signifies combination

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=>

=> $q = 1 - p$

Thus

$P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}$

$P(r = 15) = 3.2768 *10^{-11}$ Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

$P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}$

$P(r = 5) = 0.1032$

In relation to question d:

The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as

$P(r \ge 1 ) = 1 - P (r = 0 )$

$P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}]$

$P(r \ge 1 ) = 1 - 0.0352$

$P(r \ge 1 ) = 0.9648$

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1 month ago

On a coordinate plane, 2 trapezoids are shown. The first trapezoid has points A (negative 1, negative 2), B (1, negative 2), C (

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The translation rule can be expressed as T -3,1(x,y). The translation can also be indicated as (x,y)➡️(x-3,y+1).

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1 month ago

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How could Brent use a rectangle to model the factors of \large x^2-7x+6?

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Brent could represent a rectangle with the dimensions of x - 1 and x - 6, then demonstrate that the area equals the combination of x^2, -x, -6x, and 6.

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18 days ago

Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a

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Answer:

A. Combining one pound of pistachios with one pound of almonds costs $20.

C. Decreasing the almond quantity by one pound leads to a total price of $40.

E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let:

x = cost per pound of pistachios

y = cost per pound of almonds

We know that

x = y + 4 (Equation A)

2x + 3y = 48 (Equation B)

Substitute x from Equation A into Equation B:

2(y + 4) + 3y = 48

2y + 8 + 3y = 48

5y = 48 – 8

y = 8

Find x:

x = 8 + 4 = 12

Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.

Verify the statements:

Case A) One pound of each equals $20.

True, since 12 + 8 = 20.

Case B) Pistachios cost twice as much as almonds.

False, because 2 × 8 = $16 ≠ $12.

Case C) Reducing almond pounds by 1 yields $40 total.

True, as 2(12) + 2(8) = 24 +16 = 40.

Case D) The almond cost modeled by 2(a – 4) + 3a = 48.

False; it should be 2(a + 4) + 3a = 48.

Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.

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Answer:

Part 1) The algebraic expression can be represented as $1.10(n-1)$ or $1.10n-1.10$

Part 2) The algebraic expression is represented as $\frac{1.10}{n}$

Step-by-step explanation:

Part 1) The expression (n-1) raised by 110%

Recognizing that

110%=110/100=1.10

thus,

The algebraic representation of (n-1) increased by 110% translates to 1.10 multiplied by (n-1).

$1.10(n-1)$

Expanded

$1.10n-1.10$

Part 2) The expression n^(-1) raised by 110%

<pGiven that

110%=110/100=1.10

therefore, the representation of n^(-1) increased by 110% becomes 1.10 multiplied by n^(-1).

Remember that

$n^{-1}=\frac{1}{n}$

thus,

$1.10(n^{-1})=1.10\frac{1}{n}=\frac{1.10}{n}$

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