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3 years ago

You use 4 gallons of water on 30 plants in your garden at that rate how much water will it take to water 45 plants

Mathematics

1 answer:

harina [27]3 years ago

7 0

Answer 6 gallons

Step-by-step explanation:

Use proportion to solve problem:

4:30=x:45

45*4=30x

x=45*4/30

x=6

You might be interested in

To which subset does the following number belong? √7

marishachu [46]

Irrational numbers. √7 is an irrational number.

4 0

3 years ago

A particular concentration of a chemical found in polluted water has been found to be lethal to 40% of the crayfish that are exp

Jet001 [13]

Answer:

a) $P(X=13)=(24C13)(0.4)^{13} (1-0.4)^{24-13}=0.0608$

$P(X=17)=(24C17)(0.4)^{17} (1-0.4)^{24-17}=0.0017$

$P(X=13 U X=17) = 0.0608+0.0017=0.0624$

b) $P(X \geq 17)=0.000427$

c) $P(X \geq 16)= 1-0.000427=0.9996$

d) $E(X)= np = 22*0.4=8.8$

e) $Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=24, p=0.4)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

3) Part a

$P(X=13)=(22C13)(0.4)^{13} (1-0.4)^{22-13}=0.0336$

$P(X=17)=(22C17)(0.4)^{17} (1-0.4)^{22-17}=0.00035$

$P(X=13 U X=17) = 0.0336+0.00035=0.0340$

4) Part b

$P(X \geq 17)=P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)$

$P(X=17)=(22C17)(0.4)^{17} (1-0.4)^{22-17}=0.00035$

$P(X=18)=(22C18)(0.4)^{18} (1-0.4)^{22-18}=0.0000651$

$P(X=19)=(22C19)(0.4)^{19} (1-0.4)^{22-19}=0.00000914$

$P(X=20)=(22C20)(0.4)^{20} (1-0.4)^{22-20}=0.000000914$

$P(X=21)=(22C21)(0.4)^{21} (1-0.4)^{22-21}=5.81x10^{-8}$

$P(X=22)=(22C22)(0.4)^{22} (1-0.4)^{22-22}=1.76x10^{-9}$

$P(X \geq 17)=0.000427$

5) Part c

$P(X \leq 16)=1-P(X>16)=1-P(X\geq 17) = 1-[P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)]$

$P(X \geq 16)= 1-0.000427=0.9996$

6) Part d

The expected value is:

$E(X)= np = 22*0.4=8.8$

7) Part e

The variance is given by:

$Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

3 0

3 years ago

Need help with geometric sequences <br> 30 points

NeTakaya

Answer:

$a_{n}$ = 6 $(5)^{n-1}$

Step-by-step explanation:

The n th term of a geometric sequence is

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

Here a = 6 and r = 30 ÷ 6 = 5, thus

$a_{n}$ = 6 $(5)^{n-1}$

8 0

3 years ago

A rock is thrown upward from a bridge that is 57 feet above a road. The rock reaches its maximum height above the road 0.76 seco

bekas [8.4K]

answer:

$f(t) = -9.9788169(t -0.76)^2 +57$

Step-by-step explanation:

On this question we see that we are given two points on a certain graph that has a maximum point at 57 feet and in 0.76 seconds after it is thrown, we know can say this point is a turning point of a graph of the rock that is thrown as we are told that the function f determines the rocks height above the road (in feet) in terms of the number of seconds t since the rock was thrown therefore this turning point coordinate can be written as (0.76, 57) as we are told the height represents y and x is represented by time in seconds. We are further given another point on the graph where the height is now 0 feet on the road then at this point its after 3.15 seconds in which the rock is thrown in therefore this coordinate is (3.15,0).

now we know if a rock is thrown it moves in a shape of a parabola which we see this equation is quadratic. Now we will use the turning point equation for a quadratic equation to get a equation for the height which the format is $f(x)= a(x-p)^2 +q$ , where (p,q) is the turning point. now we substitute the turning point