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3 years ago

Solve the given inequality. Round to the nearest ten-thousandth, if necessary. e x > 14

Mathematics

1 answer:

Bess [88]3 years ago

8 0

Answer:

$x\in(1.146,\infty)$

Step-by-step explanation:

We are given an inequality

$e^x>14$

We have to solve the given inequality.

Taking both side ln of given inequality

Then, we get

$ln(e^x)>ln(14)$

$xlne>1.146$

We know that

lne=1

Using the value

$x>1.146$

$x\in(1.146,\infty)$

Hence, the value of x is given by

$x\in(1.146,\infty)$

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11. Mr Lee bought a second hand car for

Marrrta [24]

Answer :

Depends on the rate compound interest is accrued. See answers.

Step-by-step explanation:

We need the compound interest formula which is:

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

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

It doesn't say how frequently the interest is compounded, so we will do monthly, quarterly, and yearly.

MONTHLY

So we know the car costs $25,480 and he made a down payment of $10,000. By subtracting the down payment from the purchase price we find the loan amount.

$25,480 - $10,000 = $15,480

P = 15,480

r = 4.75% = .0475

n = 12 (12 months in a year)

t = 2

Plug everything into the compound interest formula.

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

$A = 15480(1+\frac{.0475}{12})^{12*2}$

$A = 15480(1+\frac{.0475}{12})^{24}$

$A = 15480(1+.00396)^{24}$

$A = 15480(1.00396)^{24}$

$A = 15480*1.0992$

$A = $17016.14$

Mr. Lee paid $17,016.14 when the bill came due at 2 years with interest compounded monthly.

QUARTERLY

P = 15,480

r = 4.75% = .0475

n = 4 (4 quarters in a year)

t = 2

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

$A = 15480(1+\frac{.0475}{4})^{4*2}$

$A = 15480(1+\frac{.0475}{4})^{8}$

$A = 15480(1+.0119})^{8}$

$A = 15480(1.0119)^{8}$

$A = 15480*1.099$

$A = 15480(1.099)$

$A = 17013.20$

Mr. Lee paid $17,013.20 when the bill came due at 2 years with interest compounded quarterly.

YEARLY

P = 15,480

r = 4.75% = .0475

n = 1

t = 2

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

$A = 15480(1+\frac{.0475}{1})^{1*2}$

$A = 15480(1+\frac{.0475}{12})^{2}$

$A = 15480(1+.0475})^{2}$

$A = 15480(1.0475)^{2}$

$A = 15480*1.0973$

$A = 16985.53$

Mr. Lee paid $16,985.53 when the bill came due at 2 years with interest compounded yearly.

4 0

3 years ago

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Nikitich [7]

The answer could be expressed as 2^8 because the product is 16!

4 0

2 years ago

Points C, D, and G lie on plane X. Points E and F lie on plane Y.

IrinaK [193]

Answ

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Step-by-step explanation:

7 0

2 years ago

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 132.

laiz [17]

Let a=price of adult ticket
let c=price of a child's ticket
start out by writing the following system of equations:
3a+4c=132
2a+3c=94
then, multiply the first equation by 2, and the second equation by 3 to get the following system of equations:
6a+8c=264
6a+9c=282
subtract the like terms to get the following equation:
-c=-18
divide both sides by -1 to get rid of the negative to get the price of a child's ticket to be $18. to find the price of an adult ticket, pick one of the original equations to substitute the 18 in for c to find a. for example:
2a+3c=94
2a+3(18)=94
2a+54=94
-54 -54
2a=40
2 2
a=20

or if you decide to use the other equation:
3a+4c=132
3a+4(18)=132
3a+72=132
-72 -72
3a=60
3 3
a=20
either way, you still get an adults ticket to be $20 and a child's ticket to be $18.

8 0

3 years ago

Eight more than the product of four and a number is twice the sum of the number and six. Write an equation that can be used to s

masha68 [24]

4n+8=2(n+6)
Now isolate the n on one side of the equation:
4n+8=2n+12(distribution of the 2)
4n=2n+4(combine like terms)
2n=4(combine like variables)
N=2(isolate the n)

The answer is 2
Good luck!

3 0

3 years ago