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4 years ago

yesterday, Jack drove 40 1/2 miles. he used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallons

Mathematics

1 answer:

Amanda [17]4 years ago

3 0

From the information we have, Jack drove 401/2 miles and used a total of 1 1/4 gallons of gasoline.

We need to find out how many miles he travelled per each gallon.

40 1/2 miles can be written as 40.5 miles

1 1/4 gallons can be written as 1.25 gallons.

So now we form an equation.

40.5 = 1.25

x = 1

Where x is the number of miles per gallon

We cross multiply the equation

40.5 * 1 = 1.25 * x

40.5 = 1.25x

40.5 / 1.25 = x

32.4 = x

x = 32 .4

So the unit rate for miles per gallons is 32.4 miles per gallon

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Keith_Richards [23]

Answer:

1. an = (-1)^(n-1)·(n+2)!/3^n

2. the sequence diverges

Step-by-step explanation:

Perhaps you're concerned with the sequence ...

{2, -24/9, 120/27, -720/81, ...}

1. This is neither arithmetic nor geometric. Ratios of terms are -4/3, -5/3, -6/3.

The alternating signs mean one factor of the general term is (-1)^(n-1). The divisors of 3 in the term ratios indicate 3^-n is another factor. The increasing multipliers suggest that a factorial is involved.

If we rewrite the sequence factoring out (-1)^(n-1)/3^n, we have ...

{6, 24, 120, 720, ...}

corresponding to 3!, 4!, 5!, 6!. This lets us conclude the remaining factor is (n+1)!.

The general term is ...

$\boxed{a_n=\dfrac{(-1)^{n-1}(n+2)!}{3^n}}$

2. The magnitude of the factorial quickly outstrips the magnitude of the exponential denominator, so the terms keep getting larger and larger.

The sequence diverges.

3. No series are provided.

3 0

3 years ago

A collection of 30 gems, all of which are identical in appearance, are supposedto be genuine diamonds, but actually contain 8 wo

levacccp [35]

Answer:

Step-by-step explanation:

From the given information:

There are 30 collections of gems, of which 8 are worthless;

Thus, the number of the genuine diamonds = 30 - 8 = 22.

Let X = random variable;

X consider the value as 0 (for 2 worthless stone selection),

X = 1200(1 worthless stone & 1 genuine stone)

X = 2400 (2 genuine stones selected)

However, the numbers of ways of selecting and chosen Gems can be estimated as:

$(^n_r) = (^{30}_2) \\ \\ \implies \dfrac{30!}{2!(30-2)!} \\ \\ \implies \dfrac{30!}{2!(28)!} \\ \\ \implies \dfrac{30*29*28!}{2!(28)!} \\ \\ \implies \dfrac{30*29}{2*1} \\ \\ \implies 435$

Thus;

$Pr (X = 0) = \dfrac{(^8_2)}{435}$

$Pr (X = 0) = \dfrac{\dfrac{8!}{2!(8-2)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7*6!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7}{2*1}}{435} \\ \\ Pr (X = 0) = 0.0644$

$P(X =1200) = \dfrac{(^{8}_{1})(^{22}_{1})}{435}$

$P(X =1200) = \dfrac{ \dfrac{8!}{1!(8-1)!}) ( \dfrac{22!}{1!(22-1)!}) }{435}$

$P(X =1200) = \dfrac{ (8) ( 22) }{435}$

$P(X =1200) =0.4046$

$Pr (X = 2400) = \dfrac{(^{22}_2)}{435}$

$Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(22-2)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(20)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22*21*20!}{2!(20)!}}{435} \\ \\ Pr (X =2400) = \dfrac{\dfrac{22*21}{2*1}}{435} \\ \\ Pr (X = 2400) = 0.5310$

To find E(X):

E(X) = (0 × 0.0644) + (1200 × 0.4046) + (2400 × 0.5310)

E(X) = 0 + 485.52 + 1274.4

E(X) = 1759.92

8 0

3 years ago

I need help ASAP, Will give brainliest

Kitty [74]

Answer:

D {1,3,5,7,9,11,14,16}

Step-by-step explanation:

1 is a vertical angle to 3

Then due to opposite inside angle therom and oposite outside

7 and 3

7 and 5

1 and 16

16 and 14

14 and 9

9 and 11

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3 years ago

20 points <br> Match the provided functions to a graphed function with the same zero(s).

Lelechka [254]

i am working on this atm.

to solve you find the horizontal (x) intercepts.

so example graph A int is +3

then you find the equation where instead of f(x) etc, 0= the equation with the X value plugged in.

IE: 0=x^3-3x^2+x-3

would fit because when you simplify 0=0

0=3^3- 3(3^2)+3-3

0=27-27+3-3

0=0+0

0=0

it matches. so A would be the equation with f(x)

and continue in the same way

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4 years ago

Four students get 90s on a test, three get 70s, 2 get 60s and one gets an 80. what is the mean test score in this group?

faltersainse [42]

The mean score will be given by:
mean=
mean=[90*4+70*3+2*60+80]/10
=[360+210+120+80]/10
=770/10
=77
the mean score is 77

8 0

3 years ago