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2 years ago

What single percentage change is equivalent to a 12% increase followed by a 13% increase?

Mathematics

1 answer:

lozanna [386]2 years ago

5 0

Answer:

A 26.56% increase.

Step-by-step explanation:

A 12% increase corresponds to a total of 112% of the original amount.

Hence, a 13% increase of the 112% of the original amount would be equal to 1.12*1.13 = 1.2656, which equates to 126.56% of the original amount.

Hence, the single percentage change would be a 26.56% increase.

Hope this helped!

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Help me with this 1,2,3. For each sequence, Determine with whether it appears to be arithmetic If it does find a common differen

pshichka [43]

Problem 1

<h3>Answer: Arithmetic, common difference = -4</h3>

-------------------

Explanation:

Pick any term of the sequence, and subtract off the previous term to find that,

term2 - term1 = -12 - (-8) = -12 + 8 = -4
term3 - term2 = -16 - (-12) = -16 + 12 = -4
term4 - term3 = -20 - (-16) = -20 + 16 = -4

Each time we get the same result, so that means we have an arithmetic sequence with common difference -4

This indicates that adding -4 to each term, or subtracting 4 from each term, will generate the next one.

Eg: term2 = term1 - 4 = -8-4 = -12.

==========================================================

Problem 2

<h3>Answer: Arithmetic, common difference = 5</h3>

-------------------

Explanation:

Similar to problem 1, this sequence is also arithmetic because we add on 5 to each term to get the next one

-6+5 = -1
-1+5 = 4
4+5 = 9

Or you could subtract adjacent terms as done in problem 1, to find that the common difference is 5.

==========================================================

Problem 3

<h3>Answer: Not arithmetic</h3>

-------------------

Explanation:

Unlike the previous two problems, this sequence is not arithmetic.

We can see that

term2 - term1 = 12 - 3 = 9
term3 - term2 = 48 - 12 = 36

The gaps of 9 and 36 aren't the same. We need the same common difference between any adjacent terms to have an arithmetic sequence.

This sequence is instead geometric because

term2/term1 = 12/3 = 4
term3/term2 = 48/12 = 4
term4/term3 = 192/48 = 4

Each quotient is 4, showing the common ratio is 4. To find the next term, we multiply the current term by 4. So the next term after 192 would be 4*192 = 768, then 4*768 = 3072 is next, and so on.

3 0

2 years ago

The client drank 6 ounces of orange juice and 4 ounces of coffee for breakfast, 8 ounces of tea and 6 ounces of ginger ale for l

algol13

Answer:

946.242 milliliters

Step-by-step explanation:

The client drank 6 ounces of orange juice and 4 ounces of coffee for breakfast. We need to convert ounces to milliliters

1 ounce = 29.574 milliliters

6 ounces of orange juice

= 6 × 29.574 = 177.444 milliliters

4 ounces of coffee = 4 × 29.574 = 118.296 milliliters

For lunch, he consumed 8 ounces of tea and 6 ounces of ginger ale.

8 ounces of tea = 8 × 29.574 =236.529 milliliters

6 ounces of ginger ale = 6 × 29.574 =177.444 milliliters

4 ounces of water at 10:00 a.m. and at 2:00 p.m. this means 8 ounces of water.

8 ounces of water = 8 × 29.574 =236.529 milliliters

Total consumption by the client =

177.444 + 118.296 + 236.529 + 236.529= 946.242 milliliters

5 0

3 years ago

Given the functions f(x) = 2x + 5 and g(x) = x2 + 8, which of the following functions represents f(g(x)] correctly?

lakkis [162]

Answer:

Choice 4.

Step-by-step explanation:

f(g(x))

Replace g(x) with x^2+8 since g(x)=x^2+8.

f(g(x))

f(x^2+8)

Replace old input,x, in f with new input, (x^2+8).

f(g(x))

f(x^2+8)

2(x^2+8)+5

Distribute:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

Combine like terms:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

2x^2+21

7 0

2 years ago

Match these similar triangles proof<br>

AlekseyPX

Answer:

Step-by-step explanation:

Ok. They are trying to reconstruct the smaller looking triangle in the bigger triangle using angle A as the common angle.

The first statement is always the given.

Second they constructed line segment XY into the bigger triangle so that XY is parallel to BC.

Third, from the construction of the parallel lines we can now find corresponding angles that are congruent. This would be the use of F.

Since we have all three angles in triangle AXY and triangle ABC, then the construction of the smaller triangle we made inside the bigger triangle is similar to the bigger triangle. So we have the triangles are similar. You could say E or D here in my opinion. This is choice D.

Fifth the creation of those fractions of sides being equal comes from us knowing the corresponding sides of similar triangles are proportional. This is choice H.

Things looked cut off for the sixth thing so I can't fully read it, but it is possible a substitution has occured.

The seventh thing is a congruence statement which can be proven by a congruence postulate. The only one listed is SAS. So that is G.

The last thing, since the triangle construction is congruent to the smaller triangle then we know the smaller triangle is also similar to the bigger triangle since the bigger one is also similar to the construction we made. I really think E and D is interchangeable. Choice E goes here.

7 0

2 years ago

A tank containing 2.85 cube of oil how many bottles of 300 ml capacity can be filled out of it

Ronch [10]

Answer:

9,500 bottles.

Step-by-step explanation:

1 cubic meter = 1000000 milli liters

We can convert (2.85 cubic meter) to (milli liters) as

1 cubic meter = 1000000 milli liters

2.85 cubic meter = X milli liters

If we Cross multiply and find X, we have

X milli liters = [(2.85 cubic meter × 1000000 milli liters) ] / 1 cubic meter

X= 2850,000 milli liters

Then (2.85 cubic meter) will be equal to ( 2850,000 milli liters)

Capacity of the Bottle = 300 ml

Number of bottles that 300 ml capacity can be filled out of it =

(2850,000 milli liters) / (300 ml)

= 9,500 bottles.

8 0

2 years ago