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3 years ago

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4 quarts of lemonade using 13 cup of sugar. Which expression could be used to determine the amount of sugar needed to make 1 qua

rt of lemonade?

1 answer:

Alecsey [184]3 years ago

3 0

Answer:

I think (4x13)+1 I'm just guessing Hope helps;)

Step-by-step explanation:

You might be interested in

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

3 years ago

Suppose a random sample of 50 college students are asked to measure the length of their right foot in centimeters. A 95% confide

hichkok12 [17]

Answer:

A 99% confidence interval will be wider than a 95% confidence interval

Step-by-step explanation:

From the question we are told that

The 95% confidence interval for for the mean foot length for students at the college is found to be 21.709 to 25.091 cm

Generally the width of a confidence interval is dependent on the margin of error.

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

From the above equation we see that

$E \ \ \alpha \ \ Z_{\frac{\alpha }{2} }$

Here $Z_{\frac{\alpha }{2} }$ is the critical value of the half of the level of significance and this value increase as the confidence level increase

Now if a 99% confidence level is used , it then means that the value of

$Z_{\frac{\alpha }{2} }$ will increase, this in turn will increase the margin of error and in turn this will increase the width of the confidence interval

Hence a 99% confidence interval will be wider than a 95% confidence interval

5 0

3 years ago

Write the equation of the line that passes through the points

sesenic [268]

Answer:

$y+5=2(x-3)$ or $y+9=2(x-1)$

Step-by-step explanation:

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the ordered pairs

(3,-5) and (1,-9)

substitute the values

$m=\frac{-9+5}{1-3}$

$m=\frac{-4}{-2}$

$m=2$

step 2

Find the equation in point slope form

$y-y1=m(x-x1)$

Analyze two cases

<em>First case</em>

we have

$m=2$

$point\ (3,-5)$

substitute

$y+5=2(x-3)$

<em>Second case</em>

we have

$m=2$

$point\ (1,-9)$

substitute

$y+9=2(x-1)$

Note: The equation of the line in point slope form varies according to the point you choose, in contrast to the slope-intercept form

6 0

3 years ago

Here goes another question lol oops

Murrr4er [49]

Student 1 and 3.
$- (5r - 3s + 1) = - 5r + 3s - 1$
Move the negative into the brackets,
positive becomes negative while two negatives make a positive.

3 0

4 years ago

Read 2 more answers

If you add 1 to half of 1, then half of 1 to the previous number, and so on, will you ever get to 2?

lisov135 [29]

Answer:

no

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers