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3 years ago

Before sunrise, the temperature was 22.4°F below zero. By noon, it had risen 12.8°F. What expression can be used to find the

Mathematics

2 answers:

mrs_skeptik [129]3 years ago

8 0

Answer:

-22.4+12.8

Step-by-step explanation:

If the temperature started at 22.4 below zero you would write that as -22.4 because it had risen 12.8 degrees you would add those 12.8 degrees to -22.4

MrMuchimi3 years ago

6 0

Answer:-22.4+12.8

Step-by-step explanation:

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Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, co

sineoko [7]

2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Step-by-step explanation:

The given is,

Initial investment - $5000

Future amount - $6000

Interest rate - 7.5% (compounded quarterly)

Step:1

Formula to calculate the Future amount with compound interest,

$F = P(1+\frac{r}{n} )^{nt}$ ...................................(1)

Where, F - Future amount

P - Initial amount

r - Rate of interest

n - No. of compounding in a year

t - Time period

From given,

F = $6000

P = $5000

r = 7.5%

n = 4 (compounded quarterly)

Equation (1) becomes,

$6000=5000(1+\frac{0.075}{4} )^{(t)(4)}$

$\frac{6000}{5000} =(1+0.01875)^{4t}$

$1.2 = (1.01875)^{4t}$

Take log on both sides,

$log 1.2 = 4(t) log 1.01875$

Substitute log values,

0.07918 = 4(t) (0.0080676)

= (t) (0.0322705)

$t = \frac{0.07918}{0.0322705}$

= 2.45

t ≅ 2.5 years

Result:

2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

3 0

3 years ago

The current population of a town is 10,000 and its growth in years can be represented by P(t) = 10,000(0.2)^t, where t is the ti

DiKsa [7]

Answer:

1) 20%

2) Choice a.

Step-by-step explanation:

$P(t)=10000(0.2)^t$

1) $P(0)$ is the population initially.

$P(1)$ is the population after a year.

$\frac{P(1)}{P(0)}$ represents the population increase factor.

So let's evaluate that fraction:

$\frac{P(1)}{P(0)}$

$\frac{10000(0.2)^1}{10000(0.2)^0}$

$\frac{0.2^1}{0.2^0}=\frac{0.2}{1}=0.2$

0.2=20%

2) Let's figure out the population growth in terms of months instead of years.

$P(t)=10000(0.2)^{t}$

We want t to represent months.

A full year is 12 months, in a full year we have that $P(1)=10000(0.2)^1=10000(0.2)=2000$

So we want a new P such that $P(12)=2000$ since 12 months equals a year.

Let's look at the functions given to see which gives us this:

a) $P(12)=10000(0.87449)^{12}=2000 \text{approximately}$

b) $P(12)=10000(0.87449)^{12(12)}=0 \text{ approximately}$

c) $P(12)=10000(0.87449)^{\frac{1}{12}}=9889 \text{approximately}$

d) $P(12)=10000(0.87449)^{12+12}=400 \text{approximately}$

So a is the function we want.

Also another way to look at this:

$P(t)=10000(.2)^t$ where $t$ is in years.

$P(t)=10000(.2^\frac{1}{12})^t$ where $t$ is in months.

And $.2^\frac{1}{12}=0.874485 \text{approximately}$

8 0

4 years ago

Find the equation of the line that passes through the following points. Write the equation in slope-intercept form.

ra1l [238]

Answer:

The equation in the slope-intercept form will be:

y = 1/4x - 7

Step-by-step explanation:

Given the points

(-4.-8)

(-8, -9)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-4,\:-8\right),\:\left(x_2,\:y_2\right)=\left(-8,\:-9\right)$

$m=\frac{-9-\left(-8\right)}{-8-\left(-4\right)}$

$m=\frac{1}{4}$

We know that the slope-intercept of line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

substituting m = 1/4 and the point (-4, -8) to find the y-intercept 'b'

y = mx+b

-8 = 1/4(-4)+b

-8 = -1 + b

b = -8+1

b = -7

so the y-intercept = b = -7

substituting m = 1/4 and b = -7 in the slope-intercept form of line equation

y = mx+b

y = 1/4x + (-7)

y = 1/4x - 7

Thus, the the equation in slope-intercept form will be:

y = 1/4x - 7

6 0

3 years ago

What is the perimeter of this hexagon?

Akimi4 [234]

The answer is A. 46.3 cm

4 0

3 years ago

Read 2 more answers

When b > 0 and d is a positive integer, the expression (3b)^2÷d is equivalent to what?

tensa zangetsu [6.8K]

9x squared over d
hope this helps:)

5 0

3 years ago