Simplify this expression

Sanya makes a pattern of values for x and a pattern of values for y which ordered pair continues the patterns and has an x value

Mama L [17]

Answer:

C. (6,9)

Step-by-step explanation:

If you look at the way the x is going up. It goes by two digits every time. 0 -> 2

and 2 -> 4. While the y goes up by three every two x. 0 -> 3 and 3 -> 6. Which means if you make x = 6 than you would have to multiply 3 by 3 to equal 9.

6 0

4 years ago

Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily,

Rudik [331]

Answer:

Part 1) 8.17 years

Part 2) 4.98 years

Part 3) 4.95 years

Part 4) 4.95 years

Step-by-step explanation:

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

Part 1) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% compounded annually

in this problem we have

$t=?\ years\\ P=\$p\\A=\$2p\\r=14\%=14/100=0.14\\n=1$

substitute in the formula above

$2p=p(1+\frac{0.14}{1})^{t}$

$2=(1.14)^{t}$

Apply log both sides

$log(2)=log[(1.14)^{t}]$

$log(2)=(t)log(1.14)$

$t=log(2)/log(1.14)$

$t=8.17\ years$

Part 2) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% compounded monthly

in this problem we have

$t=?\ years\\ P=\$p\\A=\$2p\\r=14\%=14/100=0.14\\n=12$

substitute in the formula above

$2p=p(1+\frac{0.14}{12})^{12t}$

$2=(\frac{12.14}{12})^{12t}$

Apply log both sides

$log(2)=log[(\frac{12.14}{12})^{12t}]$

$log(2)=(12t)log(\frac{12.14}{12})$

$t=log(2)/12log(\frac{12.14}{12})$

$t=4.98\ years$

Part 3) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% compounded daily

in this problem we have

$t=?\ years\\ P=\$p\\A=\$2p\\r=14\%=14/100=0.14\\n=365$

substitute in the formula above

$2p=p(1+\frac{0.14}{365})^{365t}$

$2=(\frac{365.14}{365})^{365t}$

Apply log both sides

$log(2)=log[(\frac{365.14}{365})^{365t}]$

$log(2)=(365t)log(\frac{365.14}{365})$

$t=log(2)/365log(\frac{365.14}{365})$

$t=4.95\ years$

Part 4) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% continuously

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=?\ years\\ P=\$p\\A=\$2p\\r=14\%=14/100=0.14$

substitute in the formula above

$2p=p(e)^{0.14t}$

Simplify

$2=(e)^{0.14t}$

Apply ln both sides

$ln(2)=ln[(e)^{0.14t}]$

$ln(2)=(0.14t)ln(e)$

Remember that ln(e)=1

$ln(2)=(0.14t)$

$t=ln(2)/(0.14)$

$t=4.95\ years$

4 0

3 years ago

Can someone please help I will give brainliest if answer is right and 30 points no links please

ss7ja [257]

Answer:

ASA

Step-by-step explanation:

As we can see from the two triangles there is a same side between two angles, it is called ASA angle side angle congruence

6 0

3 years ago

An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic ch

liraira [26]

The charging rate equation for the auto mechanic is C = 50 + 40h(50 for the initial fee and 40 times h for every hour). If he works 10 hours in one day we have to plug in 10 into the hours spot, h.

C = 50 + 40(10)

Now we solve for C

C = 50 + 400

C = 450

The auto mechanic charges $450 for 10 hours.

7 0

3 years ago

Read 2 more answers

A ball has a radius of 5 inches. What is the volume it can hold

Nataliya [291]

A ball is a Sphere sooooo......
$V=4/3 \pi r^{3}$
And when you enter the radius.....
The answer will be about 523.6 inches

5 0

3 years ago