Solve the equation for the unknown quantity. 6y + 7 = 5y

Describe and correct the error(s) made in each of the problems below.

ladessa [460]

Answer:

$\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}$

$\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}$

Step-by-step explanation:

Errors in Algebraic Operations

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign
When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive.
Not to confuse product of fractions with the sum of fractions. Rules are quite different

The first expression is

$1-x / (5-x)(-x)=x-1 / x(x-5)$

Let's arrange into format:

$\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}$

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

$\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}$

Now for the second expression

$5/s+2/5=2/s$

Let's arrange into format

$\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}$

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

$\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}$

6 0

3 years ago

Which ordered pair is a solution to the equation y = 6x - 4?

Yuri [45]

Answer:

Here are 3 different pairs (0,4) , (1,2) , (2,8)

Step-by-step explanation:

Hope this helped

7 0

3 years ago

SOMEONE PLEASEEEE HELPPPP

andrew11 [14]

Answer:

The triangles are not similar

Step-by-step explanation:

6 0

2 years ago

The bad debt ratio for a financial institution is defined to be the dollar values of loans defaulted divided by the total dollar

Nimfa-mama [501]

Answer:

(a) NULL HYPOTHESIS, $H_0$ : $\mu \leq$ 3.5%

ALTERNATE HYPOTHESIS, $H_1$ : $\mu$ > 3.5%

(b) We conclude that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.

Step-by-step explanation:

We are given that a random sample of seven Ohio banks is selected.The bad debt ratios for these banks are 7, 4, 6, 7, 5, 4, and 9%.The mean bad debt ratio for all federally insured banks is 3.5%.

We have to test the claim of Federal banking officials that the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.

(a) Let, NULL HYPOTHESIS, $H_0$ : $\mu \leq$ 3.5% {means that the the mean bad debt ratio for Ohio banks is less than or equal to the mean for all federally insured banks}

ALTERNATE HYPOTHESIS, $H_1$ : $\mu$ > 3.5% {means that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks}

The test statistics that will be used here is One-sample t-test;

T.S. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean debt ratio of Ohio banks = 6%

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 1.83%

n = sample of banks = 7

So, test statistics = $\frac{6-3.5}{\frac{1.83}{\sqrt{7} } }$ ~ $t_6$

= 3.614

(b) Now, at 1% significance level t table gives critical value of 3.143. Since our test statistics is more than the critical value of t so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.

Hence, Federal banking officials claim was correct.

7 0

3 years ago

What is the equation in slope-intercept form of the line that passes through the points (0, −4) and (2, 0)?

Nastasia [14]

Answer:

$y = 2x -4$