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3 years ago

Write an exponential function to describe the given sequence of numbers.

Mathematics

1 answer:

andriy [413]3 years ago

5 0

Answer:

a(n) = 9·6^(n-1)

Step-by-step explanation:

The general term a(n) of a geometric sequence with first term a(1) and common ratio r is given by ...

a(n) = a(1)·r^(n-1)

Your sequence has first term 9 and common ratio 54/9 = 6, so the function describing it is ...

a(n) = 9·6^(n-1)

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Ellie, the elephant, eats 4 times as much as Popcorn, the pony. Zac, the zebra, eats twice as much as Popcorn. Altogether, they

Ierofanga [76]

Ellie requires 280 kg, Popcorn requires 70 kg and Zac requires 140 kg each week

Step-by-step explanation:

The given is:

Ellie, the elephant, eats 4 times as much as Popcorn, the pony
Zac, the zebra, eats twice as much as Popcorn
Altogether, they eat 490 kilograms of feed per week

We need to find how much feed each of them requires each week

Assume that Popcorn eats x kg each week

∵ Popcorn eats x kg each week

∵ Ellie eats 4 times as much as Popcorn

- Multiply x by 4 to find how much Ellie eats

∴ Ellie eats = 4 × x = 4 x kg

∵ Zac eats twice as much as Popcorn

- Multiply x by 2 o find how much Zac eats

∴ Zac eats = x × 2 = 2 x kg

- Add all of them to find how much they eat altogether

∴ Altogether eats = x + 4 x + 2 x = 7 x kg

∵ Altogether, they eat 490 kilograms of feed

- Equate the sum of their eat by 490

∴ 7 x = 490

- Divide both sides by 7

∴ x = 70

∵ Ellie eats 4 x

∴ Ellie eats = 4(70) = 280 kg

∵ Popcorn eats x

∴ Popcorn eats = 70 kg

∵ Zac eats 2 x

∴ Zac eats = 2(70) = 140 kg

Ellie requires 280 kg, Popcorn requires 70 kg and Zac requires 140 kg each week

Learn more:

You can learn more about the the word problems in brainly.com/question/3950386

#LearnwithBrainly

8 0

4 years ago

3. Machine A packs 4, cartons in 5 hour.

grigory [225]

Answer:

Machine B is the faster machine because it packs 4 cartons in an hour while the other machine takes 5 hours to pack 4 cartons. The faster machine can pack 4 cartons in an hour.

Step-by-step explanation:

3 0

3 years ago

A corner store sells two kinds of baked goods: cakes and pies. A cake costs $4 and a pie costs $6. In one day, the store sold 9

Troyanec [42]

Answer:

the number of cakes sell is 5

Step-by-step explanation:

The computation of the number of cakes sold is shown below;

Let us assume

The cake be C

And, the pie cost be P

Given that

There is two types of baked goods sold

The cost of the cake is $4

And, the cost of the pie cost is $64

Now the store sold 9 baked goods for a total of $44

So, the equation would be

C + P = 9

P = 9 - C ...... (1)

4C + 6P = 44............(2)

Now put the value of P in equation 2

4C + 6(9 - C) = 44

4C + 54 - 6C = 44

-2C = -10

C = 5

And, P = 4

hence, the number of cakes sell is 5

8 0

3 years ago

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines

slava [35]

Answer:

we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7 psi

Step-by-step explanation:

Let's first define the hypothesis;

Null hypothesis: H0: μ = 4.7

Alternative hypothesis: Ha: μ ≠ 4.7

We have;

Sample size; n = 110

Sample mean; x¯ = 4.6

Variance: σ² = 0.64

Standard deviation; σ = √0.64 = 0.8

Formula for test statistic is;

z = (x¯ - μ)/(σ/√n)

z = (4.6 - 4.7)/(0.8/√110)

z = -0.1/0.0763

z = -1.31

From online p-value from z-score calculator attached, using; z = -1.31, two tailed hypothesis, significance value of 0.1, we have;

P-value = 0.190196

The p-value is greater than the significance value and thus we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7

σ μ

8 0

3 years ago

I HAVE ANOTHER QUESTION PLEASE HELP

morpeh [17]

Answer:

136 cubic feet

Step-by-step explanation:

2x2x2= 8

4x4x8 = 128

128 + 8 = 136

4 0

2 years ago

Read 2 more answers