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inessss [21]
2 years ago
14

What is the final amount if 1102 is increased by 2% followed by a further 1% increase? Give your answer rounded to 2 DP.

Mathematics
1 answer:
Lemur [1.5K]2 years ago
6 0
To increase by 2% you multiply to get 1102*0.02=22.04. You then add that to 1102, getting 1124.04. To then decrease it by 1% you multiply to get 1124.04*0.01=11.24. Subtract 11.24 from 1124.04 to get a final answer of 1112.8
You might be interested in
The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
2 years ago
If h(x)=(fog)(x) and h(x) = sqrt x+5, find g(x) if f(x) = sqrtx+2
Katen [24]

Answer: The value of g(x) is x+3.

Step-by-step explanation:

Since we have given that

h(x)=f\circ g(x)

Here,

h(x)=\sqrt{x+5}\\\\and\\\\f(x)=\sqrt{x+2}

We need to find the value of g(x):

f(x)=\sqrt{x+2}\\\\f(g(x))=\sqrt{g(x)+2}\\\\h(x)=\sqrt{g(x)+2}\\\\\sqrt{x+5}=\sqrt{g(x)+2}\\\\x+5=g(x)+2\\\\g(x)=x+5-2=x+3

Hence, the value of g(x) is x+3.

3 0
3 years ago
Joanie watched 1 out of three of a movie in the morning
Archy [21]

Answer:

7/15

Step-by-step explanation:

Determine how much she has watched.

1/3 + 1/5 The common denominator of 3 and 5 is 15. Multiply each fraction by an amount that will make the denominator 15

1/3 = 1*5/(3*5) = 5 / 15

1/5 = 1*3 / (5*3) = 3/15

Now add the two fractions together.

5/15 + 3/15 = 8/15

What is left of the movie? The whole movie = 1 so that which is left is

1 - 8/15

15/15 - 8/15

7 / 15

She has just a bit under 1/2 to go.

8 0
3 years ago
Answer asap please ​
sergeinik [125]

Answer:

t = 0

If the loan is to be paid in 0 months, the amount is very large

m = 50

Of the loan is to be paid in an indefinite amount of time, monthly payment would be 50

Step-by-step explanation:

(12000 + 600t)/12t

1000/t + 50

Asymptotes:

t = 0

If the loan is to be paid in 0 months, the amount is very large

m = 50

Of the loan is to be paid in an indefinite amount of time, monthly payment would be 50

3 0
3 years ago
1. The diameter of a sphere is 21.6 cm. The volume of the sphere is __
sveta [45]
Detailed Answers:

Volume of a Sphere (V) = 4/3 πr^3

1. Diameter (d) = 21.6 cm
Radius (r) = 21.6/2 = 10.8 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (10.8)^3
= 4/3 * 22/7 * 1259.712
= 88/21 * 1259.712
=> 5278.79

Volume (V) = 5278.79 cm^3

2. Diameter (d) = 16 cm
Radius (r) = 16/2 = 8 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (8)^3
= 4/3 * 22/7 * 512
= 88/21 * 512
=> 2145.52

Volume (V) = 2145.52 cm^3

3. Diameter (d) = 24 cm
Radius (r) = 24/2 = 12 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (12)^3
= 4/3 * 22/7 * 1728
= 88/21 * 1728
=> 7241.14

Volume (V) = 7241.14 cm^3

4. Diameter (d) = 6 cm
Radius (r) = 6/2 = 3 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (3)^3
= 4/3 * 22/7 * 27
= 88/21 * 27
=> 113.14

Volume (V) = 113.14 cm^3
6 0
1 year ago
Read 2 more answers
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