A store has 25% off sale on coats. With this discount the price of one coat is $34.50

The principal amount, $5500, earns 3.75% interest compounded continuously.

Eva8 [605]

Answer:

a)

The function that represents the value of the account at any time, t

$\:\:A=Pe^{rt}$

b)

The total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.

Step-by-step explanation:

a. Write the function that represents the value of the account at any time, t.

The function that represents the value of the account at any time, t

$\:\:A=Pe^{rt}$

where

A represents the Future Value

P represents the Principle (Initial Value)

r represents the Interest rate

t represents the time

b) What will the value be after 6 years?

Given

The principal amount P = $5500

Annual Rate r = 3.75% = 3.75/100 = 0.0375

Time Period t = 6 years

To Determine:

The total amount A = ?

Using the formula

$\:\:A=Pe^{rt}$

substituting the values

$A\:=\:5500\left(2.71828\right)^{\left(0.0375\right)\left(6\right)}$

$A=5500\cdot \:2.71828^{0.225}$

$A = $ 6,887.77$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.

8 0

3 years ago

Franco's Pizza is selling their pizzas 35% cheaper than usual if a pizza normally cost $12 how much is it now

avanturin [10]

Answer:

New or current cost = 12 - 4.2 = $7.8

Step-by-step explanation:

Franco's Pizza is selling their pizzas 35% cheaper than usual. This is a discount on the normal cost. To get the amount it costs now, we will find the percentage of the discount on the original cost and subtract what we get from the original cost.

Discount = 35℅

Original cost of pizza is $12 (if a pizza normally cost $12).

So the discount in terms of dollars

= ℅ discount / 100 × normal cost of pizza

= 35 / 100 × 12 =0.35 × 12 = $4.2

New or current cost of pizza would be normal or original cost - the discount in dollars.

New or current cost = 12 - 4.2 = $7.8

4 0

3 years ago

A machine used to regulate the amount of a certain chemical dispensed in the production of a particular type of cough syrup can

olchik [2.2K]

Answer:

The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml

Step-by-step explanation:

Standard deviation ( σ )= 0.250 ml

assume the required amount of chemical to be deposited in each syrup bottle to be X

Hence the distribution of X in each bottle can be represented as :

X Г N ( u , 0.250 )

for a bottle not to be rejected : P ( X ≤ 2 )

To determine the setting so that no more than 1% of the bottles of cough syrup prepared by this machine will be rejected we have to standardize the variable X

at X = 2 ml

$\frac{x - u }{std} = \frac{2 - u}{std}$

z = $\frac{2-u}{0.250}$ = z ----------- ( 1 )

probability for a bottle to be rejected : P( x >2 ) = 1 - P ( x ≤ 2 )

= 0.01

attached below is a normal distribution curve showing probability values

from the curve

p( 0 < Z < z ) = 0.5 - 0.01 = 0.49

Area = 0.49 hence from the Normal table where area = 0.49 the value of z = 2.33

Referring back to equation 1 above: z = $\frac{2-u}{0.250}$ = 2.33 --------- (2)

<em>u</em> = mean value that should be added so that the bottle will not be rejected

make <em>u</em> subject of the equation : u = 2 - ( 2.33 * 0.250 )

u = 1.41750

The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml

6 0

3 years ago

Write the word phrase for 0.3x + 5.

Debora [2.8K]

0.3x+5 is an expression. If we had an equation, then we would have solved for x. It looks like you need to translate this into a words. You can say "5 more than 30 percent of a number."

3 0

3 years ago

Complete the statement to describe the expression abc + defabc+defa, b, c, plus, d, e, f. The expression consists of terms, and

natita [175]

Answer:

The expression consists of 2 terms and each terms contains 3 factors.

Step-by-step explanation:

Given the expression (abc)+(def), the description of the expression is as shown:

The expression consists of 2 terms and each terms contains 2 factors.

Terms are expressions connected by mathematical signs such as addition and subtraction sign. As we can see from (abc)+(def), 'abc' and 'def' are separated by addition signs therefore both abc and def are the "terms" of the expression.

Factors are variables connected using the multiplication or bracket signs. As we can see, each term contains 3 factors. Looking at the first term 'abc', we can see that there are 3 variables/factors (a, b and c) multiplied together. This shows that they are connected by multiplication signs and same goes with 'def'.

Hence, the expression consists of 2 terms and each terms contains 3 factors.

3 0

2 years ago