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3 years ago

What is 7.65% of $509.25

Mathematics

2 answers:

OverLord2011 [107]3 years ago

7 0

Answer:

38.96

Step-by-step explanation:

Change from percent to decimal form

.0765 * 509.25

38.957625

Rounding to the nearest cent

38.96

harina [27]3 years ago

6 0

Answer:

38.957625 US$

Step-by-step explanation:

38.957625 US$

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Which logarithmic equation is equivalent to the exponential equation below?

aleksandr82 [10.1K]

Option B: $\ln 6=5 x$ is the correct answer.

Explanation:

The exponential equation is $e^{5 x}=6$

If $f(x)=g(x)$ , then $\ln (f(x))=\ln (g(x))$

Thus, the equation becomes

$\ln \left(e^{5 x}\right)=\ln (6)$

Applying log rule, $\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)$ and thus the equation becomes

$5 x \ln (e)=\ln (6)$

Since, we know that, $\ln (e)=1$ , using this we get,

$5 x=\ln (6)$

Hence, the logarithmic equation which is equivalent to the exponential equation $e^{5 x}=6$ is $\ln 6=5 x$

Thus, Option B is the correct answer.

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3 years ago

The hypotenuese of an isosceles right triangle is 13 inches. The midpoints of its sides are connected to form an inscribed trian

Georgia [21]

Answer:

The Sum of the areas of theses triangles is 169/3.

Step-by-step explanation:

Consider the provided information.

The hypotenuse of an isosceles right triangle is 13 inches.

Therefore,

$x^2+x^2=169\\2x^2=169\\x=\frac{13}{\sqrt{2} }$

Then the area of isosceles right triangle will be: $A=\frac{1}{2} x^2$

Therefore the area is: $A=\frac{169}{4}$

It is given that sum of the area of these triangles if this process is continued infinitely.

We can find the sum of the area using infinite geometric series formula.

$S=\frac{a}{1-r}$

Substitute $a=\frac{169}{4} \ and\ r=\frac{1}{4}$ in above formula.

$S=\frac{\frac{169}{4}}{1-\frac{1}{4}}$

$S=\frac{\frac{169}{4}}{\frac{3}{4}}$

$S=\frac{169}{3}$

Hence, the Sum of the areas of theses triangles is 169/3.

7 0

2 years ago

Who can answer this question

Anarel [89]

34 just look at your number and you get it

3 0

2 years ago

How do you do this?

Sholpan [36]

put the first equation in the graphic calculator in y= #1 then in y=#2 put one of the answer choices, if the y1 & y2 match that will be your answer

4 0

2 years ago

Read 2 more answers

Plz help me!!!

Nadya [2.5K]

To solve this we are going to use the exponential function: $f(t)=a(1(+/-)b)^t$
where
$f(t)$ is the final amount after $t$ years
$a$ is the initial amount
$b$ is the decay or grow rate rate in decimal form
$t$ is the time in years

Expression A
$f(t)=624(0.95)^{4t}$
Since the base (0.95) is less than one, we have a decay rate here.
Now to find the rate $b$ , we are going to use the formula: $b=|1-base|$ *100%
$b=|1-0.95|$ *100%
$b=0.05$ *100%
$b=$ 5%
We can conclude that expression A decays at a rate of 5% every three months.

Now, to find the initial value of the function, we are going to evaluate the function at $t=0$
$f(t)=624(0.95)^{4t}$
$f(0)=624(0.95)^{0t}$
$f(0)=624(0.95)^{0}$
$f(0)=624(1)$
$f(0)=624$
We can conclude that the initial value of expression A is 624.

Expression B
$f(t)=725(1.12)^{3t}$
Since the base (1.12) is greater than 1, we have a growth rate here.
To find the rate, we are going to use the same equation as before:
$b=|1-base|$ *100%
$b=|1-1.12|$ *100
$b=|-0.12|$ *100%
$b=0.12$ *100%
$b=$ 12%
We can conclude that expression B grows at a rate of 12% every 4 months.

Just like before, to find the initial value of the expression, we are going to evaluate it at $t=0$
$f(t)=725(1.12)^{3t}$
$f(0)=725(1.12)^{0t}$
$f(0)=725(1.12)^{0}$
$f(0)=725(1)$
$f(0)=725$
The initial value of expression B is 725.

We can conclude that you should select the statements:
- Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every fourth months.

- Expression A has an initial value of 624, while expression B has an initial value of 725.

8 0

2 years ago