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Ugo
4 months ago
5

1.How much taller Porter is than Henry, given that Porter is n inches tall and Henry is m inches tall. 2.How many times as tall

Porter is than Henry, given that Porter is n inches tall and Henry is m inches tall.
Mathematics
1 answer:
lawyer [12.5K]4 months ago
3 0

Answer:

Porter is n-m inches taller than Henry.

Porter is \frac{n}{m} times taller than Henry.

Step-by-step explanation:

To find the height difference, subtraction is used.

As Porter is taller than Henry, Henry's height will be drawn from Porter's height. This calculation will reveal only the height difference.

n = Porter's height

m = Henry's height

Thus, the height difference can be represented as:

n-m

Answer: Porter measures n-m inches taller than Henry.

To determine how many times Porter is taller than Henry, division comes into play.

For example, if Porter's height is 200cm and Henry's is 100cm, Porter is evidently 2 times taller.

If we perform the division of Porter's height by Henry's height...

\frac{200}{100}=2

..the result will be 2, because Henry's height "fits in twice" within Porter's height. 100 fits twice into 200.

Using our notations, n and m, we perform n divided by m.

\frac{n}{m}

Answer: Porter is \frac{n}{m} times taller than Henry.

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Brenda is cooking couscous. The recipe says she requires 480 grams of couscous for 4 people. How many will she need for 14?
AnnZ [12381]
1,680 grams

To determine this, we can set up a proportion as follows:

grams/people=grams/people

The recipe requires 480 grams for 4 individuals and we need to find how many grams (x) are necessary for 14 individuals.

480 grams/4 people=x grams/14

480/4=x/14

Now, let's isolate x, the grams necessary for 14 people. Currently, x is divided by 14, so we will multiply both sides by 14 as multiplication is the inverse of division.

14(480/4)=(x/14)14

14(480/4)=x

14*120=x

1680=x

Thus, she requires 1,680 grams of couscous to serve 14 individuals.

8 0
3 months ago
The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting
Svet_ta [12734]

a) The sequence is geometric.

b) The subsequent term is 486

c) The rule is: a_n=6(3)^{n-1}

The 20th term will be: a_{20}=6973568802

Step-by-step explanation:

The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.

Part a) Is this sequence arithmetic or geometric?

An arithmetic sequence has a constant difference between consecutive terms.

In the given series 6, 18, 54, 162,

18-6 = 12

54-18= 36

The differences are not constant, thus it isn’t arithmetic.

A geometric sequence maintains a constant ratio between consecutive terms.

In this series 6, 18, 54, 162,

18/6 = 3

54/18 = 3

162/54 = 3

The ratios remain constant; therefore, the sequence is geometric.

The sequence in question is geometric.

Part b) How can you determine the next number in the series?

The next number can be calculated using the following formula:

a_n=a(r)^{n-1}

where a_n= nth term

a= first term

r= common ratio

The next number represents the 5th term of the sequence.

To find the 5th term:

a_n=a(r)^{n-1}\\a_5=6(3)^{5-1}\\a_5=6(3)^4\\a_5=6*81\\a_5=486

Thus, the next term in the sequence is 486

Part c) What is the rule for determining the 20th week? Calculate the 20th week.

The rule for determining the 20th week is:

a_n=6(3)^{n-1}

Here n=20

Calculating the 20th week

a_n=6(3)^{n-1}\\a_{20}=6(3)^{20-1}\\a_(20)=6(3)^{19}\\a_{20}=6973568802

5 0
4 months ago
Christina has $103 earned from babysitting saved at home, and the amount is modeled by the function h(x) = 103. She reads about
AnnZ [12381]
s(x)=1.03x−1

so be sure to place parentheses around (x-1)

This indicates that her investment is increasing by 3% each time period as defined by the bank (e.g., monthly, annually...).

7 0
2 months ago
Read 2 more answers
ali's tyre pressure gauge shows a reading witch is 8 % lower than the actual pressure when the gauge shows 33.58
AnnZ [12381]

Answer:

The actual pressure is 31.09

Complete question:

What is the actual pressure when Ali's gauge indicates 33.58

Step-by-step explanation:

Given,

Ali's tire pressure gauge displays a reading that is 8% higher than the true pressure.

His gauge reads 33.58.

Let the actual pressure be denoted as x.

According to the problem,

x\times\frac{108}{100} =33.58 { [If 8% increase of a number ⇒ The number becomes = (\frac{100+8}{100})of the number}

x= \frac{33.58\times100}{108}

x=31.09

Thus, the actual pressure equals 31.09

5 0
3 months ago
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