Caleb invested $6,200 in an account paying an interest rate of 7 1/2% compounded

What is the slope of the line that passes through the points (−4,−1) and (18,−2) ?

Tatiana [17]

Answer:

D

Step-by-step explaination:

7 0

3 years ago

Molly can read four-fifths of a page in the time it takes kayla to read one page. how many pages will kayla read in the time it

aev [14]

Kaila will read 1 page and 2 fifths

3 0

3 years ago

You want to save $500 for a school trip. You begin by saving a penny on the first day. You save an additional penny each day aft

irga5000 [103]

Answer:

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

a = 1 penny = 1/100 = $0.01

d = 0.01

a) For 100 days, the sum of the first 100 terms, S100 would be

S100 = 100/2[2 × 0.01 + (100 - 1)0.01]

S100 = 50[0.02 + 0.99)

S100 = 50 × 1.01 = $50.5

b) when Sn = $500, then

500 = n/2[2 × 0.01 + (n - 1)0.01]

Multiplying through by 2, it becomes

500 × 2 = n[2 × 0.01 + (n - 1)0.01]

1000 = n[0.02 + 0.01n - 0.01]

1000 = n[0.01 + 0.01n]

1000 = 0.01n + 0.01n²

0.01n² + 0.01n - 1000 = 0

Applying the general formula for quadratic equations,

x = [-b±√(b² - 4ac)]/2a

n = - 0.01±√0.01²-4(0.01 × - 1000)]/2 × 0.01

n = (- 0.01 ± √40.001)/0.02

n = (- 0.01 + 6.32)/0.02 or

n = (- 0.01 - 6.32)/0.02

n = 315.5 or n = - 316.5

Since n cannot be negative, then n = 315.5

It will take approximately 316 days to save $500

6 0

3 years ago

The number of bacteria in a petri dish is 50,000 (on day 0) if the amount is doubling each day by when will the number of bacter

Drupady [299]

Answer:

f(x) = 50000*2^x
3 days

Step-by-step explanation:

<u>Given:</u>

Initial amount of bacteria = 50000
Growth rate = 2 times a day

<u>Required equation:</u>

f(x) = 50000*2^x

<u>Solve for x:</u>

400000 = 50000*2^x
2^x = 400000/50000
2^x = 8
2^x = 2^3
x = 3

After 3 days bacteria numbers will reach 400000

5 0

3 years ago

Which system of equations could be graphed to solve the equation below? log Subscript 0. 5 Baseline x = log Subscript 3 Baseline

Vanyuwa [196]

You can use the fact that two expressions in equality can be considered to be equal to a third variable(not used in given context).

The system of equations that could be graphed to solve the equation given is

$y = \log_{0.5}(x)\\\\$
$y = \log_3(2+x)$

<h3>How can we form a system of equations from an equation?</h3>

Suppose the equation be $a = b\\$

Let there is a symbol $c$ such that we have $a = b = c$

It is because a and b are same measure (that is exactly what a = b means)

and we gave another name c to that measure.

Thus, we have

$a = c\\b = c$

in addition to $a = b\\$

<h3>Using the above method to find the system of equations needed</h3>

Since the given equation is $log_{0.5}(x) = log_2(2+x)$

The 2d graphs are usually expressed as $y = f(x)$ on X-Y plane.

Taking the equation's expressions equal to y, we get

$log_{0.5}(x) = log_2(2+x) = y$

or, we get system of equations as

$y = log_{0.5}(x)\\\\y = log_3{(2 + x)}$

Their graph is plotted below. The intersection point of both curves is the solution to the given equation as it satisfies both the equations of the system of equations formed from the given equation.

Thus,

The system of equations that could be graphed to solve the equation given is

$y = \log_{0.5}(x)\\\\$
$y = \log_3(2+x)$

Learn more about solutions to system of equations here:

brainly.com/question/14550337

4 0

3 years ago