The rent for an apartment goes down by $35 per month.<br><br> What integer represents the situation?

Briony invests some money. Interest is paid on the money at a rate of 2% per annum for the first year and 1% per annum for the s

nalin [4]

Answer:

Brionny invested £8400.

Step-by-step explanation:

Simple Interest

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$T = E + P$

In this question:

We divide in two intervals, the first year and the second year. We have to know that the amount after the end of the first year is the principal at the start of the second year.

First year:

Amount of 2% interest, during 1 year.

So the interest earned is:

$E = P*I*t = P*0.02*1 = 0.02P$

The total amount at the end of the first year is:

$T = E + P = 0.02P + P = 1.02P$

Second year:

We have that:

$P = 1.02P$

The interest earned is of:

$E = P*I*t = 1.02P*0.01*1 = 0.0102P$

The total amount is:

$T = E + P = 0.0102P + 1.02P = 1.0302P$

After two years, the investment is worth £8653.68 How much did Briony invest?

So

$1.0302P = 8653.68$

$P = \frac{8653.68}{1.0302}$

$P = 8400$

Brionny invested £8400.

3 0

3 years ago

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces

nadya68 [22]

Answer:

a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less

b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours

d) 86 should have a battery life of at least 9 hours.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

The probability of being higher than x is:

$P(X > x) = \frac{b - x}{b-a}$

The probability of being between c and d is:

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

This means that $a = 8.5, b = 12$

a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

$P(X \leq x) = \frac{x - a}{b-a}$

$P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286$

0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.

b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

$P(X > x) = \frac{b - x}{b-a}$

$P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857$

0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

$P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714$

0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.

d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

Proportion of iPad Minis with a battery life of at least 9 hours.

$P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571$

Out of 100:

0.8571*100 = 85.71

To the nearest whole number

86 should have a battery life of at least 9 hours.

5 0

3 years ago

A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 4 standard deviat

Doss [256]

Answer:

more than 15.40 cm and less than 14.60 cm

Step-by-step explanation:

A manufacturer of bolts has a quality control policy that requires it destroy any bolts that are more than 4 standard deviations from the mean.

mean length= 15 cm

standard deviation= 0.10 cm

4 standard deviation from mean= 15±(4×0.10)

therefore, bolts of length more than 15+0.4, and less than 15-0.4 will be destroyed

= 15.40 cm and 14.60 cm

4 0

3 years ago

HELP PLEASE. For parallelogram LMNO, if m∠L = 3x - 25 and m∠N = 2x - 10, find m∠M.

Dvinal [7]

In a parallelogram opposite angles are congruent, that means:

Angle L = Angle N, replace L & N by they respective value, then

3x-25 = 2x-10 ==> x=15 , Now plug the value of x in any of the 2 sides
3(15) -25 =20°

hence Angle L =- Angle N = 20°

Now let's calculate Angle M. In a parallelogram the adjacent angle are supplementary, that means their sum = 180°, then

Angle N + Angle N = 180°==> Angle M = 180°-20° = 160°

5 0

3 years ago

At Supply World, 4 pens cost $10.00. How much do 3 pens cost if the price per pen is the same?

Romashka-Z-Leto [24]

Answer:

$7.50

Step-by-step explanation:

3 0

3 years ago

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The rent for an apartment goes down by $35 per month. What integer represents the situation?