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3 years ago

Use order of operations to make this true 7 11 4 2 = 10

Mathematics

1 answer:

Keith_Richards [23]3 years ago

5 0

Answer:

$7 + 11 - 4 \times 2 = 10$

Step-by-step explanation:

Using order of operations, the first thing to be calculated would be $4 \times 2$ .

That would turn our equation into this:

$7 + 11 - 8 = 10$

You can then calculate left-to-right as usual to get the answer 10.

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In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C an

Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

$P(x)=Ca^{x-2000}$

So, the population in 2000,

$P(2000)=Ca^{2000-2000}$

$=Ca^{0}$

$=C$

According to the question,

$P(2000)=1$

$\implies C=1$

(b) Similarly,

The population in 2025,

$P(2025)=Ca^{2025-2000}$

$=Ca^{25}$

$=a^{25}$ (∵ C = 1)

Again according to the question,

$P(2025)=1.2$

$a^{25}=1.2$

Taking ln both sides,

$\ln a^{25}=\ln 1.2$

$25\ln a = \ln 1.2$

$\ln a = \frac{\ln 1.2}{25}\approx 0.00729$

$a=e^{0.00729}=1.00731$

Thus, the function that shows the population in year x,

$P(x)=(1.00731)^{x-2000}$ ...... (1)

The population in 2010,

$P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555$

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

$1.4=(1.00731)^{x-2000}$

$\ln 1.4=(x-2000)\ln 1.00731$

$0.33647 = (x-2000)0.00728$

$0.33647 = 0.00728x-14.56682$

$0.33647 + 14.56682 = 0.00728x$

$14.90329 = 0.00728x$

$\implies x=\frac{14.90329}{0.00728}\approx 2047$

Therefore, the country's population might reach 1.4 billion in 2047.

3 0

3 years ago

How much would $200 invested at 7% compounded continuously be worth after 5 years

Norma-Jean [14]

Answer:

$280.51

Step-by-step explanation:

F= 200(1 + 07)^5

The future worth (F) of the investment at present (P) with a compound interest i after n years is calculated through the equation, F=P x (1 + i)^n

6 0

3 years ago

Read 2 more answers

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of pape

jenyasd209 [6]

Answer:

C. About 75 in²; Aubrey found the surface area of the cone and included the base.

Step-by-step explanation:

In the questions above we were given the following:

Cone with

Diameter(D) = 6 inches

Slant height (l) = 8 inches.

Aubrey made an error in her calculation.

She found the Total Surface area of the cone using the formula:

Total Surface Area of a cone = πrl + πr²

= πr(l + r)

The Total surface area of a cone is the calculated as Sum of the curved surface area of a cone and the base of the cone.

Where:

Curved surface area of the cone is calculated as = πrl

Base of a cone is calculated as = πr²

Where r = radius of the cone

l = slant height of the cone

In the question, we were given

slant height(l) = 8 inches.

radius = Diameter ÷ 2 = 6÷2 = 3 inches.

Using π = 3.14

Surface area = 3.14 × 3(8+3)

= 9.42 × 11

Surface area = 103.62 in²

Approximately to the nearest inch = 104 in² or 104 square inches.

But this answer is WRONG.

The RIGHT FORMULA Aubrey should have used is

Curved Surface Area or the Lateral Area of a Cone = πrL

slant height(l) = 8 inches.

radius = Diameter ÷ 2 = 6÷2 = 3 inches.

Using π = 3.14

Curved Surface Area of a Cone = πrL

= 3.14 × 3 inches × 8 inches

= 75.36 square inches or 75.36in²

Approximately to the nearest inch = 75 square inches or 75 in².

This is the correct answer.

The error Aubrey made was she calculated the Total surface area of the cone which includes the base of the cone instead of calculating the curved surface area of the cone only.

Hence, from the above calculation , we can see that Option C "About 75 in²; Aubrey found the surface area of the cone and included the base" is the correct option.

5 0

3 years ago

!!HELP ASAP!! What is the surface area of the rectangular pyramid below?

creativ13 [48]

Answer:

D. 507 square units

Step-by-step explanation:

surface area of the rectangular pyramid

$= area \: of \: base + 4 \times area \: of \: one \: \triangle \\ \\ = {13}^{2} + 4 \times \frac{1}{2} \times 13 \times 13 \\ \\ = 169 + 2 \times 169 \\ \\ = 169 + 338 \\ \\ = 507 \: {units}^{2} \\$

8 0

3 years ago

It take Zoe 12.5 minutes to swim 20 laps around the pool what is Zoe's unit rate

allochka39001 [22]

1.6 min. per lap
All you have to do is divide 20 by 12.5

6 0

3 years ago

Read 2 more answers