In a survey of 97 resorts, it was found that

chet needs to buy 4 work shirts,all costing the same amount .the total cost before chet appplies a $25 gift certificate can be n

Rashid [163]

So for this problem, let us use x as the cost before Chet would apply a $25 gift certificate. Based on the problem, we can see that the original cost of the product cannot be more than 75 which means that it can be equal to 75 or less than 75. We can actually express the inequality as x< or = 75 since we are looking for the cost before Chet applied the $25 gift certificate. This means that we do not need to add in the 25 yet since the question asks for the cost before the application of the discount.

5 0

2 years ago

How to simplify the ratio 30ml:45ml

svlad2 [7]

Since 30 and 45 can both be divided by 5, just divided them and is 6:9 and 6 and 9 can be both divided by 3,so the final answer should be 2ml:3ml

4 0

3 years ago

Read 2 more answers

Experimental data are collected as:

aliina [53]

Answer:

$y = 1.00114x + 1.75243$

Step-by-step explanation:

Given

The x and y values

Required

The regression line equation

Because of the length of the given data, I will run the analysis using online tools, then analyze the result.

From the analysis, we have:

$\sum x = 5050$

$\sum y = 5231.1011$

$\bar x = 50.5$

$\bar y = 52.311$

$SSX = 83325$ --- Sum of squares

$SP = 83419.7626$ --- Sum of products

The regression equation is calculated as:

$y = ax + b$

Where:

$a = \frac{SP}{SSX}$

So, we have:

$a = \frac{83419.76}{83325}$

$a = 1.00114$

$b = \bar y - a * \bar x$

$b = 52.31 - (1.00114*50.5)$

$b = 1.75243$

So:

$y = ax + b$ becomes

$y = 1.00114x + 1.75243$

6 0

2 years ago

Find the integral using substitution or a formula.

Nadusha1986 [10]

$\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx$

Derivative of the denominator:
$\rm (x^2+2x+5)'=2x+2$

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

$\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx$

and then split the fraction,

$\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx$

Based on our previous test, we know that a simple substitution will work for the first integral: $\rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx$

So the first integral changes,

$\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx$

integrating to a log,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx$

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

$\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2$

So we have this going on,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx$

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx$

Bringing all that stuff together as a single square,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx$

Making the substitution: $\rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx$

giving us,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du$

simplying a lil bit,

$\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du$

and hopefully from this point you recognize your arctangent integral,

$\rm ln|x^2+2x+5|+\frac52arctan(u)$

undo your substitution as a final step,
and include a constant of integration,

$\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c$

Hope that helps!
Lemme know if any steps were too confusing.

8 0

3 years ago

What percent of 2000 is 204

Darina [25.2K]

204 is 10.2% of 2000

Working Out

204/2000 x 100 = 10.2%

3 0

2 years ago