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3 years ago

3. Quincy deposits $400 in a new bank account that earns 4% simple interest per year. What

Mathematics

1 answer:

Illusion [34]3 years ago

8 0

Answer:

$448

Step-by-step explanation:

We can use the simple interest formula for this:

$A = P (1 + rt)$

P = initial balance

r = annual interest rate

t = time

First, change 4% into its decimal form:

4% -> $\frac{4}{100}$ -> 0.04

Now, lets plug in the values:

$A=400(1+(0.04)(3))$

$A=448$

The total amount in the account after 3 years will be $448

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Estimate 1 13 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round your answers to six decimal

babunello [35]

Answer:

(a) 4.152698

(b) 3.215557

Step-by-step explanation:

(a)

$\int\limits^{13}_1 {cos(x^2)} \, dx =M_n=$\sum_{n=1}^{\infty} f(m_i)\Delta x $$

n=4, so :

Each subinterval has length :

$\Delta x= \frac{b-a}{n} =\frac{13-1}{4} =\frac{12}{4} =3$

Therefore the subintervals consist of:

$[1,5], [5,9], [9,13]$

Now, the midpoints of these subintervals are:

$\frac{1+5}{2} =3\\\\\frac{5+9}{2} =7\\\\\frac{9+13}{2} =11$

Hence:

$M_4= 3*(cos(3^2))+3*(cos(7^2))+3*cos((11^2))\approx 4.152698$

(b)

$\int\limits^{13}_1 {cos(x^2)} \, dx =T_n=\frac{\Delta x}{2} (f(x_o)+2f(x_1)+2f(x_2)+...+2f(x_n_-_1)+f(x_n))$

n=4, so :

Each subinterval has length :

$\Delta x= \frac{b-a}{n} =\frac{13-1}{4} =\frac{12}{4} =3$

Therefore the subintervals consist of:

[1,5], [5,9], [9,13]

The endpoints of the subintervals consist of:

5,9

Hence:

$T_4= \frac{3}{2}(cos(1^2)+2*cos(5^2)+2*cos(9^2)+cos(13^2)) \approx 3.215557$

8 0

2 years ago

In the solution of the equation 5 + 3x = -2x + 9, 2x is added to the equation first. Which of the following should be done next?

puteri [66]

You should subtract 5 from both sides next.

Adding 2x to both side will give you the following.

5 + 5x = 9

And since you got all the variable terms to the left, you want all the constant terms to the right. You do that by subtracting 5 from both sides. This gives you the below statement.

5x = 4

You can then divide to solve.

x = 4/5 or .8

5 0

2 years ago

What is 7/8 minus the fraction 2/3?

tatiyna

Answer: 5/24

Explanation: To subtract unlike fractions such as 7/8 - 2/3, first find a common denominator. The common denominator of 8 and 3 will be the least common multiple of 8 and 3 which is 24.

To get a 24 in the denominator of 7/8, we multiply both the numerator and the denominator by 3 to get 21/24.

To get a 24 in the denominator of 2/3, we multiply both the numerator and the deliminator by 8 and to get 16/24.

Now we are subtracting like fractions since both fractions have the same denominator or bottom number of 16.

To subtract like fractions, we simply subtract the numerators and keep the same denominator. So here, we have 21/24 - 16/24 which is 5/24.

Since 5/24 is in lowest terms, it's our final answer.

This means that 7/8 - 2/3 is 5/24.

3 0

2 years ago

Read 2 more answers

Martin thinks of two numbers. he says, "The HCF of my two numbers is 6. The LCM of my two numbers is 15" write down two possible

tigry1 [53]

Answer:

There is no possible answers

Step-by-step explanation:

We are told in the above question that:

"The HCF of my two numbers is 6.

This means the two numbers are factors of 6

"The LCM of my two numbers is 15"

LCM means the lowest common multiple.

This means the two numbers must be have 15 as one of its multiples.

From the above explanation above, there are no two numbers like that

8 0

2 years ago

Sarah lost 12 pounds over the summer by jogging each week. By winter time, she had gained 4 3/8 pounds. Represent this situation

ANTONII [103]

Assume sarah's weight is m.
first, she lost 12 pounds,
this means that her weight became: m - 12 pounds
then, she gained 4 3/8 pounds, therefore, her current weight is: m-12+4 3/8 pounds
the total change in her weight is:
-12+4 3/8 = -7.625 pounds
the negative sign refers to the loss.
this means that the overall change is losing 7.625 pounds

7 0

3 years ago