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2 years ago

12

The bird house in your friend's yard casts a shadow that is 14 feet long. Your friend is 5 feet tall and casts a shadow that is

3.5 feet long. What is the height of the bird house?

1 answer:

astra-53 [7]2 years ago

3 0

3.5/5=14/x 20ft tall

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At a desert resort, the temperature at 7 a.m. was 3°C. The temperature increased by an average of 3.4°C each hour until it reach

11Alexandr11 [23.1K]

Answer: It will take 8 hours to reach this temperature.

Step-by-step explanation:

Given: At a desert resort, the temperature at 7 a.m. was 3°C.

The temperature increased by an average of 3.4°C each hour until it reached 30.2°C.

Let x be the number of hours taken to reach 30.2°C..

As per given ,

Initial temperature +(average increase in temperature) (Number of hours) = 30.2

⇒3+3.4x=30.2

⇒3.4x=30.2-3

⇒3.4x=27.2

⇒ x=8 [Divide both sides by 3.4]

Hence, it will take 8 hours to reach this temperature.

6 0

1 year ago

Which statement identifies how to show that j(x) = 11.6ex and k(x) = In (StartFraction x Over 11.6 EndFraction) are inverse func

Vadim26 [7]

Answer:

<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>

Step-by-step explanation:

Given the function j(x) = 11.6 $e^x$ and k(x) = $ln \dfrac{x}{11.6}$ , to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,

For j(k(x));

j(k(x)) = j[(ln x/11.6)]

j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}

j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)

j[(ln x/11.6)] = 11.6 * x/11.6

j[(ln x/11.6)] = x

Hence j[k(x)] = x

Similarly for k[j(x)];

k[j(x)] = k[11.6e^x]

k[11.6e^x] = ln (11.6e^x/11.6)

k[11.6e^x] = ln(e^x)

exponential function will cancel out the natural logarithm leaving x

k[11.6e^x] = x

Hence k[j(x)] = x

From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 $e^x$ and k(x) = $ln \dfrac{x}{11.6}$ are inverse functions.

4 0

2 years ago

In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that

attashe74 [19]

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let <em>X</em> = number of soldiers killed by horse kicks in 1 year.

The random variable $X\sim Poisson(\lambda = 0.62)$ .

The probability function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,...$

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

= 1 - P (X = 0) - P (X = 1)

$=1-\frac{e^{-0.62}(0.62)^{0}}{0!}-\frac{e^{-0.62}(0.62)^{1}}{1!}\\=1-0.54335-0.33144\\=0.12521\\\approx0.1252$

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: $\lambda=7\times0.62=4.34$

Compute the probability of no deaths in a corps over 7 years as follows:

$P(X=0)=\frac{e^{-4.34}(4.34)^{0}}{0!}=0.01304\approx0.0130$

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

6 0

2 years ago

Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australia. While booking her family's plan

Shkiper50 [21]

Answer:

Step-by-step explanation:

According to the graph, the amount of gasoline after 16 hours is 0 gallons. ⇒ Jet has to land to refuel after 15 hours of flying.

3 0

2 years ago

Nikki drew a rectangle with a perimeter of 18 units on a coordinate grid. Two of the vertices were (4, –3) and (–1, –3). What co

Talja [164]

Answer:

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)

Step-by-step explanation:

Geometrically speaking, the perimeter of a rectangle ( $p$ ) is:

$p = 2\cdot b + 2\cdot h$ (1)

Where:

$b$ - Base of the rectangle.

$h$ - Height of the rectangle.

Let suppose that the base of the rectangle is the line segment between (4, -3) and (-1, -3). The length of the base is calculated by Pythagorean Theorem:

$b = \sqrt{[(-1)-4]^{2}+[(-3)-(-3)]^{2}}$

$b = 5$

If we know that $p = 18$ and $b = 5$ , then the height of the rectangle is:

$2\cdot h = p-2\cdot b$

$h = \frac{p-2\cdot b}{2}$

$h = \frac{p}{2}-b$

$h = 4$

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)

8 0

2 years ago