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3 years ago

6

the height in feet above the ground of an arrow after it is shot can be modeled by y=-16r^2+63r+4.Can the arrow pass over a tree

that is 68 feet tall? Explain.

1 answer:

miss Akunina [59]3 years ago

7 0

Answer:

yes

Step-by-step explanation:

y=-16r^2+63r+4

maximum value of y :

y'=0

-32r +63=0

r= 63/32

y = -16(63/32)²+63(63/32)+4

= -4 + 124 + 4 = 124 ft

124 > 68

the Arrow can pass over the tree

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Sever21 [200]

Answer:

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3 years ago

If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? how many if each school must rece

DaniilM [7]

Alright, so we'd use the combinations with repetition formula, so we choose from 4 schools to distribute to and distribute 8 blackboards. It's then

( 8+4-1)!/8!(4-1)!=11!/(3!*8!)=165

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8 0

3 years ago

Recent census data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. A random sample of 125

kicyunya [14]

Answer:

The probability is $P(14 < X < 20 ) = 0.5354$

Step-by-step explanation:

From the question we are told that

The proportion that live with their parents is $\r p = 0.142$

The sample size is n = 125

Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution

i.e

$X \ \~ \ B( \mu , \sigma )$

Now the mean is evaluated as

$\mu = n * \r p$

$\mu = 125 * 0.142$

$\mu = 17.75$

Generally the proportion that are not staying with parents is

$\r q = 1 - \r p$

= > $\r q = 0.858$

The standard deviation is mathematically evaluated as

$\sigma = \sqrt{n * \r p * \r q }$

$\sigma = \sqrt{ 125 * 0.142 * 0.858 }$

$\sigma = 3.90$

Given the n is large then we can use normal approximation to evaluate the probability as follows

$P(14 < X < 20 ) = P( \frac{ 14 - 17.75}{3.90}$

Now applying continuity correction

$P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < \frac{ X - \mu }{\sigma } < \frac{ 19.5 - 17.75}{3.90} )$

Generally

$\frac{ X - \mu }{\sigma } = Z ( The \ standardized \ value \ of X )$

$P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < Z< \frac{ 19.5 - 17.75}{3.90} )$

$P(14 < X < 20 ) = P( -1.0897 < Z< 0.449 } )$

$P(14 < X < 20 ) = P( Z< 0.449 ) - P(Z < -1.0897)$

So for the z - table

$P( Z< 0.449 ) = 0.67328$

$P(Z < -1.0897) = 0.13792$

$P(14 < X < 20 ) = 0.67328 - 0.13792$

$P(14 < X < 20 ) = 0.5354$

6 0

3 years ago

A jogger goes 1.5km west and then turns south.If the jogger finishes 1.7 km from the starting point,how far south did the jogger

kakasveta [241]

Hello!

You can use the Pythagorean Theorem to solve this

$a^{2} + b^{2} = c^{2}$

c is the hypotenuse
a and b are the legs

Put in the values you know

$1.5^{2} + b^{2} = 1.7^{2}$

Square the numbers

$2.25+ b^{2} =2.89$

Subtract 2.25 from both sides

$b^{2} =0.64$

Take the square root of both sides

b = 0.8

The answer is 0.8km

Hope this helps!

6 0

3 years ago