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3 years ago

14

You put $5,000 in a simple interest account at a bank. You will earn $1,200 in just 4 years. What is the annual interest rate fo

r the account?

1 answer:

Sav [38]3 years ago

4 0

<span>1200 = 5000*4r
1200/20000 = r = .06 0r 6%</span>

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What statement is true?

givi [52]

Answer:

$\frac{18}{32}>\frac{16}{32}$

Step-by-step explanation:

We need to find which statements are true.

Solution to find the same we will solve each statement and will conclude the same.

1. $\frac{14}{21}>\frac{17}{24}$

Now On solving we get;

$\frac{14}{21} = 0.66$

$\frac{17}{24}=0.70$

So we can see that 0.70 > 0.66

Hence The given statement is False.

2. $\frac{18}{32}>\frac{16}{32}$

Now On solving we get;

$\frac{18}{32}=0.5625$

$\frac{16}{32}= 0.5$

So we can see that 0.5625 > 0.5

Hence The given statement is True.

3. $\frac{20}{15}$

Now On solving we get;

$\frac{20}{15} = 1.33$

$\frac{28}{23}=1.2$

So we can see that 1.33 > 1.2

Hence The given statement is False.

4. $\frac{29}{35}$

Now On solving we get;

$\frac{29}{35}= 0.82$

$\frac{20}{30}= 0.66$

So we can see that 0.82 > 0.66

Hence The given statement is False.

7 0

3 years ago

Use the multiplier method to increase £258 by 43%<br>You must show your working.

raketka [301]

Hello there, to answer your question...

258, percentage increased by 43% (percent) of its value

<h2> = 368.94</h2>

<em>258 + 43% = 368.94</em>

<em></em>

I hope this information helps.

8 0

3 years ago

Uninhibited growth can be modeled by exponential functions other than A(t) =Upper A 0 e Superscript kt. For example, if an i

laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than $A(t)=A_{0}e^{kt}$ . for example, if an initial population P₀ requires n units of time to triple, then the function $P(t)=P_{0}(3)^{\frac{t}{n} }$ models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form $P(t)=P_{0}(3)^{\frac{t}{n} }$ that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form $A(t)=A_{0}e^{kt}$ .

Answer: a) $P(t)=50(3)^{\frac{t}{30} }$

b) P(t) = 280 insects

c) t = 74 days

d) $A(t)=50e^{0.037t}$

Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

$P(t)=50(3)^{\frac{t}{30} }$

b) In t = 47 days:

$P(t)=50(3)^{\frac{t}{30} }$

$P(47)=50(3)^{\frac{47}{30} }$

$P(47)=50(3)^{1.567}$

P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

$750=50(3)^{\frac{t}{30} }$

$\frac{750}{50}=(3)^{\frac{t}{30} }$

$(3)^{\frac{t}{n} }=15$

Using the property <u>Power</u> <u>Rule</u> of logarithm:

$log(3)^{\frac{t}{30} }=log15$

$\frac{t}{30}log(3)=log15$

$t=\frac{log15}{log3} .30$

t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

A(t) = 3A₀ and t = 30

$A(t)=A_{0}e^{kt}$

$3A_{0}=A_{0}e^{30k}$

$3=e^{30k}$

Use Power Rule again:

$ln3=ln(e^{30k})$

$ln3=30k$

$k=\frac{ln3}{30}$

k = 0.037

Equation for exponential growth will be:

$A(t)=50e^{0.037t}$

3 0

3 years ago

Factor x^3-4x^2-3x+18=0 given that 3 is a zero.

Mandarinka [93]

Answer:

B: (x + 2)(x - 3)^2

Step-by-step explanation:

This is only going to have 3 roots. One of them is (x - 3)

D does not look right. So let's solve it using synthetic division.

3 || 1 - 4 -3 18

3 -3 -18

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

1 -1 -6 0

So what you have is a quadratic

x^2 - x - 6 = 0 which will factor
(x - 3)(x + 2) = 0
x - 3 = 0
x = 3
x + 2 =0
x = - 2
(x - 3)(x - 3)(x + 2 ) = 0

The answer is B

3 0

3 years ago

60 is 5/6 of what number?

Stels [109]

If x = the number you are trying to find:
$60 = \frac{5}{6} * x$
$\frac{60}{ \frac{5}{6} } = x$
and when dividing by a fraction you can flip it and multiply instead:
60 * 6/5 = 72
The number is 72

4 0

3 years ago