$490 at 2.1% compounded quarterly for 6 months

Vlada [557]

78 qt = y = max+b to the equation.

6 0

3 years ago

kareem deposits $5000 into an account that pays simple interest at a rate of 5% per year. how much interest will be paid in the

Ostrovityanka [42]

$4999.70 - $5000

.30 i believe it is 30 cents

7 0

4 years ago

Help please 50 points!

uranmaximum [27]

Answer:

A and B

Step-by-step explanation:

we would like to solve the following equation:

$\rm\displaystyle 5 - 2x = \sqrt{ {2x}^{2} + x - 1 } - x$

to do so isolate -x to the left hand side and change its sign:

$\rm\displaystyle 5 - 2x + x = \sqrt{ {2x}^{2} + x - 1 }$

simplify addition:

$\rm\displaystyle 5 - x = \sqrt{ {2x}^{2} + x - 1 }$

square both sides:

$\rm\displaystyle (5 - x {)}^{2} = (\sqrt{ {2x}^{2} + x - 1 } {)}^{2}$

simplify square of the right hand side:

$\rm\displaystyle (5 - x {)}^{2} = {2x}^{2} + x - 1$

use (a-b)²=a²-2ab+b² to expand the left hand side:

$\rm\displaystyle {x}^{2} - 10x + 25= {2x}^{2} + x - 1$

swap the equation:

$\rm\displaystyle {2x}^{2} + x - 1 = {x}^{2} - 10x + 25$

isolate the right hand side expression to the left hand side and change every sign:

$\rm\displaystyle {2x}^{2} + x - 1 - {x}^{2} + 10x - 25 = 0$

simplify:

$\rm\displaystyle {x}^{2} + 11x - 26= 0$

rewrite the middle term as 13x-2x:

$\rm\displaystyle {x}^{2} + 13x - 2x - 26= 0$

factor out x:

$\rm\displaystyle x({x}^{} + 13)- 2x - 26= 0$

factor out -2:

$\rm\displaystyle x({x}^{} + 13)- 2(x + 13)= 0$

group:

$\rm\displaystyle (x- 2)(x + 13)= 0$

by Zero product property we obtain:

$\displaystyle \begin{cases}x- 2 = 0\\ x + 13= 0 \end{cases}$

solve for x:

$\displaystyle \begin{cases}x = 2\\ x = - 13 \end{cases}$

to check for extraneous solutions we can define the domain of equation recall that a square root of a function is always greater than or equal to 0 therefore

$\rm\displaystyle 5 - x \geq0$

solve the inequality for x:

$\rm\displaystyle x \leqslant 5$

since 2 and -13 is less than 5 both solutions are valid for x hence,

$\displaystyle \begin{cases}x _{1} = 2\\ x_{2} = - 13 \end{cases}$

and we're done!

4 0

3 years ago

Read 2 more answers

Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negati

Anon25 [30]

Answer:

The one in the table on the left

Note that for the given values of x all of the y values are 2

This indicates a horizontal line, parallel to the x- axis with a slope of zero.

The equation of the line is y = c where c is the value of the y- coordinates the line passes through, in this case 2, thus

y = 2 is the equation of the line with zero slopeation

one of them is an undefined slope the other is a positive slope (Neither of them are a zero slope)

5 0

4 years ago

Read 2 more answers

In a random sample of 200 engineers, 137 have a master's degree. what is the sample proportion, p-hat, of engineers who have mas

Blababa [14]

The sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.

p-hat proportion:

In this proportion, "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.

The general form for calculating p-hat proportion is,

$\hat{p}=\frac{x}{y}$

where

x is the number of successes in the sample, and

y is the size of the sample.

Given,

In a random sample of 200 engineers, 137 have a master's degree.

Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees

According to the question,

x = 137 (number of successes in the sample)

and y = 200 (size of the sample)

Now apply the value on the formula then we get,

$\hat{p}=\frac{137}{200}$

So, the value of p-hat is

$\hat{p}=0.685$

The results are usually reported as a percentage, which in this case would be

=> 0.685 x 100 = 68.5%

Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.

To know more about p-hat proportion here

brainly.com/question/1597320

#SPJ4

3 0

2 years ago