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3 years ago

Write the equation of a linear function for which f=(-4)=0 and f=(0)=-2

Mathematics

1 answer:

densk [106]3 years ago

6 0

Answer:

y = -0.5x - 2

Step-by-step explanation:

equation: f(x) = mx + b

f(-4) : -4m + b = 0 ...(1)

f(0): 0m + b = -2 b = -2 ... plug in (1)

-4m - 2 = 0

m = - 1/2 = - 0.5

linear equation: y = -0.5x - 2

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Two planes leave an airport at noon. If the eastbound plane flies at 660 mph and the westbound plane flies at 600 mph, at what t

Eddi Din [679]

I'm guessing that they took of in the same airport.

Each hour they will separate by 1260 miles or 21 miles each minute

2,000/21 = 95.23 minutes which is 1 hour and 35 minutes

Hope this helps :)

6 0

3 years ago

An example problem in a Statistics textbook asked to find the probability of dying when making a skydiving jump.

MArishka [77]

Answer:

(a) 0.999664

(b) 15052

Step-by-step explanation:

From the given data of recent years, there were about 3,000,000 skydiving jumps and 21 of them resulted in deaths.

So, the probability of death is $\frac{21}{3000000}==0.000007$ .

Assuming, this probability holds true for each skydiving and does not change in the present time.

So, as every skydiving is an independent event having a fixed probability of dying and there are only two possibilities, the diver will either die or survive, so, all skydiving can be regarded as is Bernoulli's trial.

Denoting the probability of dying in a single jump by $q$ .

$q=7\times 10^{-6}=0.000007$ .

So, the probability of survive, $p=1-q$

$\Rightarrow p=1-7\times 10^{-6}=0.999993.$

(a) The total number of jump he made, n=48

Using Bernoulli's equation, the probability of surviving in exactly 48 jumps (r=48) out of 48 jumps (n=48) is

$=\binom(n,r)p^rq^{n-r}$

$=\binom(48,48)(0.999993)^{48}(0.000007)^{48-48}$

$=(0.999993)^{48}=0.999664$ (approx)

So, the probability of survive in 48 skydiving is 0.999664,

(b) The given probability of surviving =90%=0.9

Let, total $n$ skydiving jumps required to meet the surviving probability of 0.9.

So, By using Bernoulli's equation,

$0.9=\binom {n }{r} p^rq^{n-r}$

Here, r=n.

$\Rightarrow 0.9=\binom{n}{n}p^nq^{n-n}$

$\Rightarrow 0.9=p^n$

$\Rightarrow 0.9=(0.999993)^n$

$\Rightarrow \ln(0.9)=n\ln(0.999993)$ [ taking $\log_e$ both sides]

$\Rightarrow n=\frac {\ln(0.9)}{\ln(0.999993)}$

$\Rightarrow n=15051.45$

The number of diving cant be a fractional value, so bound it to the upper integral value.

Hence, the total number of skydiving required to meet the 90% probability of surviving is 15052.

3 0

3 years ago

Wendy scores 24 points in a basketball game. If all of her baskets were 3-point shots, how many baskets did she make?

yarga [219]

Hello!

If all her shots were 3 pointers we will just divide

24÷3=8

Wendy made 8 baskets.

I hope this helps!

5 0

3 years ago

Read 2 more answers

The sum of n 2 more than n

Lena [83]

N+2 would be the correct answer... i think!!!!!!!!!!!!

Hope i helped!!!!!!!!

4 0

3 years ago

If the angle of elevation of the sun is 61.7° when a building casts a shadow of 56.5 feet, what is the height of the building ro

maksim [4K]

SOLUTION

Let us use a simple diagram to interprete the question

In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.

So we will use the right-angled triangle formed to find h

As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA

$\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}$

So we have

$\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}$

Hence the answer is 104.9 feet to the nearest tenth

4 0

10 months ago