A student solved an equation for the unknown value of n as 0 =0. Which set represents all of the possible values of n?

In April, Senator Smith’s approval rating dropped from 62% to 57%. In May, the approval rating decreased by another 8 percentage

Keith_Richards [23]

Senator Smith's percentage rating must increase by 13% in other to undo the previous decreases.

Initial rating = 62%

April rating = 57%

May rating = 57% - 8% = 49%

Final rating after decrease = May rating = 49%

In other to return to initial rating :

Initial rating - Final rating

62% - 49% = 13%

Hence, in other to undo the decrease in April and May rating, Senator Smith's percentage rating must increase by 13%

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7 0

3 years ago

This chart shows the growth of a maple tree. If the tree's height increases in this same pattern, what will be the height of the

sveta [45]

Answer:

31 inches

Step-by-step explanation:

you can get this answer by 2 ways. one is using number patterns.

find the difference between each of the heights.

13-10=3

16-13=3

19-16=3

therefore the common difference is 3

now create a number pattern.

first term + common difference× (n-1)= nth term

a+(n-1)d

let's check this with the 2nd month

10+ 3× (2-1)

10+3=13

in second month 13 inches

so this pattern works

let's find the height in 8th month

10+ 3(8-1)

10+ 21=31 inches

height in 8th month is 31 inches.

you can find this by just adding too. but forming an equation is always good and safe

5 0

3 years ago

5.Richard Miyashiro purchased a condominium and obtained a 30-year loan of $196,000 at an annual interest rate of 8.20%. (Round

GREYUIT [131]

Answer:

5 a) PMT=$1,465.60

b) Total Payments=$527,616

c) Total Interest=$331,616

6a) Interest=$1,079.93

b) Principal=$584.07

Step-by-step explanation:

a. Given the loan amount is $196,000, annual rate is 8.2% and the loan term is 30 years.

-The monthly mortgage payment can be calculated as follows:

$PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})$

Where:

PMT is the monthly mortgage payment
r is the annual interest rate
n,t is the number of annual payments and time in years respectively

-We substitute to solve for PMT:

$PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})\\\\=196000[\frac{(0.082/12)}{1-(1+\frac{0.082}{12})^{-12\times30}}]\\\\=\$1,465.60$

Hence, the monthly mortgage payment is $1,465.60

b. The total number of payments is obtained by multiplying the total number of payments by the amount of each payment:

$\sum(payments)=PMT\times nt\\\\=1465.60\times 12\times 30\\\\=\$527,616.00$

Hence, the total amount of payments is $527,616

c. The amount of interest paid over the loan's term is obtained by subtracting the principal loan amount from the total payments made:

$Interest=Payments-Principal\\\\=527,616.00-196,000.00\\\\=\$331,616$

Hence, an interest amount of $331,616 is paid over the loan's term.

6 a) We first obtain the effective loan amount by subtracting the down-payment:

$Loan \ Amount= Regular \ Price -Downpayment\\\\=205700-0.1(205700)\\\\=\$185,130$

The interest paid on the first mortgage payment is calculated as below:

$I=\frac{r}{n}\times P\\\\I=Interest\\r=interest \ rate\\n=Payments \ per \ year\\P=Outstanding \ loan \ balance\\\\\therefore I=\frac{0.07}{12}\times 185130\\\\=\$1,079.93$

Hence, the amount of interest in the first payment is $1,079.93

b. The amount of principal repaid is obtained by subtracting the interest amount from the monthly mortgage payments;

$Principal \ Paid=PMT-Interest\\\\PMT=A[\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}}]\\\\=185130[\frac{(0.07/12)}{1-(1+\frac{0.07}{12})^{-180}}\\\\=1664.00\\\\\\Principal \ Paid=1664.00-1079.93\\\\=\$584.07$

Hence, the amount of principal applied is $584.07

7 0

3 years ago

Please help im stuck on this

posledela

Answer

The slope is 2

Step-by-step explanation:

6 0

4 years ago

Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each. Daniel has $20 to

grigory [225]

The system of inequalities are x + y ≥ 7 and 3.75x + 1y ≤ 20 The one possible solution is 4 cupcakes and 3 donuts.

<u>Solution:</u>

Given, Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each.

Daniel has $20 to spend and must buy a minimum of 7 cupcakes and donuts altogether.

⇒ "x" represents the number of cupcakes purchased

⇒ "y" represents the number of donuts purchased,

we have to write and solve a system of inequalities graphically and determine one possible solution.

Now, he should buy minimum 7 items, then x + y ≥ 7 ⇒ (1)

And, he has $20, so his maximum purchase is $20 then, 3.75x + 1y ≤ 20 ⇒ (2)

Now, suppose that he took 5 cupcakes, then he must take at least 2 donuts to satisfy (1)

So, substitute x and y values in (2)

⇒ 3.75(5) + 1(2) ≤ 20

⇒ 20.75 ≤ 20 ⇒ condition failed

So he can take maximum of 4 cupcakes only, and subsequently he has to take minimum of 3 donuts.

Hence, the one possible solution is 4 cupcakes and 3 donuts

7 0

3 years ago