MATHEMATICS COLLEGE

Jimmy purchased a government bond which has maturity value of $2500 after 9 months at 11 % simple interest. How much should he pay for this bond?

Answers

Answer 1

Answer:

Answer: he should pay $23095 for this bond.

Step-by-step explanation:

We would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the bond purchased.

P represents the principal or amount of bond purchased.

R represents interest rate

T represents the duration of the bond in years.

From the given information,

R = 11%

T = 9 months = 9/12 = 0.75

I = 25000 - P

Therefore

25000 - P = (P × 11 × 0.75)/100

25000 - P = 8.25P/100 = 0.0825P

P + 0.0825P = 25000

1.0825P = 25000

P = 25000/1.0825

P = $23095

Answer 2

Answer:

Answer:$2706.25

Step-by-step explanation:

Principal(t)=$2500

Time(t)=9months=9/12=0.75year

Rate(r)=11%

Simple interest(si)=?

Si=(pxrxt)/100

Si=(2500x11x0.75)/100

Si=20625/100

Si=$206.25

Total amount=p + si

Total amount=2500+206.25

Total amount=$2706.25

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Catherine's employer matches 25% of her 401(k) contributions — up to $2000. Catherine's salary is $50,000, and last year she contributed $10,000 to her 401(k) plan. What was her employer's contribution to the 401(k)?

Answers

We have been given that Catherine's employer matches 25% of her 401(k) contributions or a maximum of $2000. Further we are given that Catherine's salary is $50,000 and she contributed $10,000 to her 401(k) plan.

Let the contribution form her employer be $x. We are given that her employer matches 25% of Catherine's contribution under 401(k) plan. Therefore, contribution made by employer would be either 25% of 10,000 or 2000, whichever is lesser.

Let us find 25% of 10,000.

$25\% \text{ of 10000 } = 10,000 * (25)/(100) = \$2500$

Since 25% of 10,000 is more than 2000, therefore, Catherine's employer would make a contribution of $2000.

25% of $10,000 is $2,500

But because they only match "up to $2,000," her employers contribution was $2,000

Use the given level of confidence and sample data to construct a confidence interval for the population proportion p.n= 195, p^=p hat= 0.831, Confidence level=95%

a.) 0.777

Answers

Answer:

The 95% confidence interval for the population proportion is (0.778, 0.884).

Step-by-step explanation:

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.831.

The standard error of the proportion is:

$\sigma_p=\sqrt{(p(1-p))/(n)}=\sqrt{(0.831*0.169)/(195)}\n\n\n \sigma_p=√(0.00072)=0.027$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.027=0.053$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sisgma_p = 0.831-0.053=0.778\n\nUL=p+z \cdot \sisgma_p = 0.831+0.053=0.884$

The 95% confidence interval for the population proportion is (0.778, 0.884).

What is the greatest number that rounds to 500 when rounded to the nearest ten?

Answers

Answer:

504.999...

Step-by-step explanation:

505 rounds to 510, but a number that is infinitessimally smaller rounds to 500.

Unfortunately, for any number you can write that rounds to 500, there are an infinite number of numbers that are greater and still less than 505.

In short, there is no "greatest number" that is less than 505—unless you put additional restrictions on it, like the number of digits that can be used to express it, for example.

i believe the answer is 549.

What is the standard form of two hundred fifty three thousandths

Answers

We are given number in words " two hundred fifty three thousandths".

Let us write it in number form: First we would write the number form of "two hundred fifty".

Two hundred fifty = 253.

Now, we need to write three thousandths.

Three thousandths = .003

Now, we need to combine 253 and 0.003.

On combining we get 253.003.

Therefore, two hundred fifty three thousandths in standard form is 253.003.

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, ifc=2b, a=12?