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3 years ago

A line has a slope of-1 and passes through the point (1, -8) .What is its equation in slope -intercept form?

1 answer:

6 0

M = -1

Passes through (1, -8)

Slope intercept form : y = mx+b

Where m = slope, and b = y-intercept.

-8 = y-intercept

Simply plug in the values for the slope and y-intercept into the slope-intercept form.

y = mx + b

y = -x - 8

~Hope I helped!~

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The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room

Alexandra [31]

Answer:

$\bar x = 260.1615$

$\sigma = 70.69$

The confidence interval of standard deviation is: $53.76$ to $103.25$

Step-by-step explanation:

Given

$n =20$

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}$

$\bar x = \frac{5203.23}{20}$

$\bar x = 260.1615$

$\bar x = 260.16$

Solving (b): The standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

$\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}$ $\sigma = \sqrt{\frac{94938.80}{19}}$

$\sigma = \sqrt{4996.78}$

$\sigma = 70.69$ --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

$c =0.95$

So:

$\alpha = 1 -c$

$\alpha = 1 -0.95$

$\alpha = 0.05$

Calculate the degree of freedom (df)

$df = n -1$

$df = 20 -1$

$df = 19$

Determine the critical value at row $df = 19$ and columns $\frac{\alpha}{2}$ and $1 -\frac{\alpha}{2}$

So, we have:

$X^2_{0.025} = 32.852$ ---- at $\frac{\alpha}{2}$

$X^2_{0.975} = 8.907$ --- at $1 -\frac{\alpha}{2}$

So, the confidence interval of the standard deviation is:

$\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }$ to $\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }$

$70.69 * \sqrt{\frac{20 - 1}{32.852}$ to $70.69 * \sqrt{\frac{20 - 1}{8.907}$

$70.69 * \sqrt{\frac{19}{32.852}$ to $70.69 * \sqrt{\frac{19}{8.907}$

$53.76$ to $103.25$

8 0

2 years ago

150 centimeters is equivalent to

Elina [12.6K]

<span>150 centimeters is equivalent to 1 1/2 meters </span>

6 0

3 years ago

Read 2 more answers

What is the result of the calculation of 89.332 + 1.1 without adjusting for the correct number of significant figures?

Orlov [11]

The answer is 90.432.

7 0

3 years ago

PLEASE HELP! WILL MARK BRAINLIEST!!

Alecsey [184]

Answer:

The y-intercept is (0,1). The x values at the horiz. intercepts are:

{ (-3+√5)/2, (-3-√5)/2 }. Graph is that of a parabola that opens down.

Step-by-step explanation:

It'd be helpful to rewrite f(x) = 3-x2+3x-2 with the powers of x in descending order and using " ^ " to denote exponentiation:

f(x) = -x^2 + 3x -2 + 3, or

f(x) = -x^2 + 3x + 1

y-intercept: let x = 0. Then f(0) = 1. The y-intercept is (0,1)

x-intercepts: let y = f(x) = 0 = -x^2 + 3x + 1. Let's use the quadratic formula with a = -1, b = 3 and c = 1 to determine the roots of this polynomial. The discriminant, b^2-4ac, is 9-4(1)(1), or 5.

Thus, there are two real, unequal roots. They are:

-3 plus or minus √5

x = ---------------------------------

or { (-3+√5)/2, (-3-√5)/2 }

These are your two horizontal intercepts, where the function is zero.

Because the coefficient -1 of the x^2 term is negative, the parabola representing this function opens down.

8 0

3 years ago

Factorise the following 5y^2-20y-8z+2yz

andre [41]

Answer:

$(5y+2z)(y-4)$

Step-by-step explanation:

$5y^2-20y-8z+2yz=\\5y^2-20y+2yz-8z=\\5y(y-4)+2z(y-4)=\\(5y+2z)(y-4)$

8 0

2 years ago