What is the equation of the line of best fit for the following data? Round the
slope and y-intercept of the line to three decimal places.

[tex]\\ \sf\longmapsto \frac{5}{ \sqrt{7} - \sqrt{3} } + \frac{1}{ \sqrt{7} + \sqrt{3} } \\ \\ \sf\longmapsto \frac{5( \sqrt{7} + \sqrt{3} ) + 1 (\sqrt{7} - \sqrt{3} )}{( \sqrt{7} - \sqrt{3} )( \sqrt{7} + \sqrt{3} )} \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + 5 \sqrt{3} + \sqrt{7} - \sqrt{3} }{( { \sqrt{7} )}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + \sqrt{7} + 5 \sqrt{3} - \sqrt{3} }{7 - 3} \\ \\ \sf\longmapsto \frac{6 \sqrt{7} + 4 \sqrt{3} }{4} [/tex]

Answer:

[tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Step-by-step explanation:

Given

[tex]7n - (4n - 3)[/tex]

Required

Simplify

To simplify the given expression, you start by opening  the bracket

[tex]7n - (4n - 3)[/tex]

[tex]7n - 4n + 3[/tex]

Next, you perform arithmetic operations on like terms

[tex]3n + 3[/tex]

The answer can be further simplified;

Factorize [tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Hence;

[tex]7n - (4n - 3)[/tex] when simplified is equivalent to [tex]3n + 3[/tex] or [tex]3(n+1)[/tex]

Answer:

3n+n

Step-by-step explanation:

Answer:

Step-by-step explanation:

(D). The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

The location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

The dilation of a line segment is longer or shorter in the ratio given by the scale factor. If the scale factor is greater than 1, the image of line segment will be larger than the original line, and if the scale factor is less than 1 , the image will be smaller than the original line.

The original line segment is given in the figure with points A and B as A(0,2) and B(2,0) .

When the line segment is dilated by a scale factor of 3, we can draw a parallel line which will be larger than the pre-image of the original line segment.

Also, the new coordinates of the points A and B will also increase by a factor of 3.

Therefore, we have A'(0,6) and B'(6,0) as the new coordinates of the line segment.

Thus, the location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

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Answer:

B. The vectors v and w are orthogonal because their dot product is 0

Step-by-step explanation:

Given that :

v=  - i - j  

w= - i + j

Therefore;

vw = ( - i - j )  ( - i + j )

Taking each  set of integer of the vector into consideration:

vw = ( -1 × - 1) ( -1 × 1)

vw = 1 - 1

vw = 0

Hence, we can conclude that :

The vectors v and w are orthogonal because their dot product is 0  

We know

Sum of two interior angles =exterior angle

[tex]\\ \sf\longmapsto 2x+x=3x[/tex]

[tex]\\ \sf\longmapsto 3x=3x[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Answer:

true

Step-by-step explanation:

Answer:

1023.75

Step-by-step explanation:

The sum of a geometric sequence is

sum = a( 1 - r^n) / (1-r)

where a is the first term  r is the common ratio and  r^n is the nth term

We need to find the common ratio

r = 256/512 = 1/2

sum = 512 ( 1 - 1/2^12) / ( 1-1/2)

       =512( 1-.000244141) / (.5)

       =512(.999755859) /.5

     =1023.75

Answer:

1023.75

Step-by-step explanation:

sum = a( 1 - r^n) / (1-r)

a1 = 512

n = 12

r = 256 / 512 = 1/2

                              512 (1 - 1/2¹²)

therefore.. sum =  ------------------ = 1023.75

                                   1 - 1/2

Answer:

d. all of the above

Step-by-step explanation:

A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used

Answer:

1 = C

2 = A

3= B

4 = B

Step-by-step explanation:

Answer:

15 squares

Step-by-step explanation:

60/100 * 25 = 15

Answer:

Step-by-step explanation:

Hello, this is pretty straight forward. Let me remind you the following.

The standard equation of a parabola is

[tex]y=ax^2+bx+c[/tex]

But the equation for a parabola can also be written in "vertex form":

[tex]y=a(x-h)^2+k[/tex]

In this equation, the vertex of the parabola is the point (h,k) .

So, here the vertex is the point (2, -25) and the axis of symmetry is x = 2

Thank you

Answer:

if anyone still needs the answer I added a pic

Step-by-step explanation:

Answer:

The value of x is 30°

Step-by-step explanation:

We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.

If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.

[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,

[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],  

[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]

Solution : x = 30°

Answer:

The answer is 0.267949192

Step-by-step explanation:

I hope that is enough numbers.

Answer: 20 ft³

Step-by-step explanation:

volume of triangular pyramid = [tex]\frac{1}{3} bh[/tex]

Therefore, the volume is:

[tex]\frac{1}{3} *10*6=\frac{1}{3}*60=\frac{60}{3}=20[/tex]

Answer:

Length:8

Width:5.5

Step-by-step explanation:

We're given area = 44m^2, and the formula for the area of a rectangle is the length multiplied by the width. So,

A = L * w = 44

We're given that the length is 3m shorter than 2 times the width, which is 2w - 3. "2w" is the same as "2 times the width", and the 3 is subtracted because it says 3m shorter than 2 times the width. So L = 2w - 3, and we can substitute that into our equation above.

(2w - 3)(w) = 44

2w^2 - 3w - 44 = 0

Use the quadratic formula here.

x = {3 ± √(-3)^2 - 4(-44)(2)}/2(2)

= {3 ± √9 + 352}/4

= (3 ± 19)/4

You'll get two answers, but remember, we're measuring the length of the sides of shapes, so it has to be positive. It's impossible to have negative lengths, so we're going to stick with the (3 + 19)/4 answer, which is 22/4, which is 5.5. However, we are not finished yet. This is just the width. Now we need to plug it into the equation for length, which was 2w - 3

2(5.5) - 3 = 11 - 3 = 8

The length is 8m and the width is 5.5m.

Answer:

Step-by-step explanation:

1 km = 0.621 mi

1 hr = 60 min

(5 km)/(4.5 hr) × (0.621 mi)/km × (1 hr)/(60 min) = (0.0115 mi)/min

Answer:

x = 1/2

Step-by-step explanation:

8(-2x+1) =0

Divide each side by 8

-2x+1 = 0

Add 2x to each side

-2x+1+2x = 2x

1 = 2x

Divide by 2

1/2 = 2x/2

1/2 =x

Answer:

1/2

Step-by-step explanation:

8(-2x+1)=0

Use distributive property first

-16x+8=0

Subtract 8 on both sides

-16x=-8

Divide both sides by -16 to get x by itself

x=0.5

Which is also equal to 1/2

Therefore, x is equal to 1/2

[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]

Answer:

60.36 steps West from centre

85.36 steps North from centre

Step-by-step explanation:

Refer to attached

Musah start point and movement is captured in the picture.

or 360°, so bearing of 315° is same as North-West 45°.

Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.

How far West Is Musah's final point from the centre?

How far North Is Musah's final point from the centre?

Answer:

[tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Step-by-step explanation:

Given the differential equation [tex](x+2y)y'=2x-y[/tex], this can also be written as;

[tex](x+2y)\frac{dy}{dx} =2x-y[/tex]

On simplification

[tex](x+2y)\frac{dy}{dx} =2x-y\\\\\frac{dy}{dx} = \frac{2x-y}{x+2y} \\\\let \ y = vx\\\frac{dy}{dx} = v+x\frac{dv}{dx}[/tex]

The differential equation becomes;

[tex]v+x\frac{dv}{dx} =\frac{ 2x-vx}{x+2vx}\\\\v+x\frac{dv}{dx} = \frac{ x(2-v)}{x(1+2v)}\\\\v+x\frac{dv}{dx} = \frac{2-v}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v}{1+2v} - v\\\\x\frac{dv}{dx} = \frac{(2-v)-v(1+2v)}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v-v-2v^2}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-2v-2v^2}{1+2v}[/tex]

[tex]\frac{dx}{x} = \frac{1+2v}{2-2v-2v^2}dv\\\\integrating\ both \ sides\\\\[/tex]

[tex]\int\limits \frac{dx}{x} = \int\limits \frac{1+2v}{2-2v-2v^2}dv\\\\lnx = \frac{1}{2} \int\limits \frac{1+2v}{1-v-v^2}dv\\\\lnx + C = -\frac{1}{2}ln(1-v-v^2)[/tex]

[tex]C = -\frac{1}{2}ln(1-v-v^2) - lnx \\\\ -ln(1-v-v^2) - 2lnx = 2C\\\\-[ln(1-v-v^2) + lnx^2] = 2C\\\\-[ln(1-v-v^2)x^2] = 2C\\since\ v = y/x\\\\- [ln(1-y/x-y^2/x^2)x^2] = K\\\\-[ln(x^2-yx-y^2)] = K\\[/tex]

Hence the solution to the differential equation is [tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Step-by-step explanation:

I assume the length that got cut off is 18.

Use Pythagorean theorem:

x² + 36² = (x + 18)²

x² + 1296 = x² + 36x + 324

972 = 36x

x = 27

Answer:

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that 28% do not fail in the first 1000 hours of their use.

At the null hypothesis, we test that at least 28% do not fail, that is:

[tex]H_0: p \geq 0.28[/tex]

At the alternative hypothesis, we test if the proportion is of less than 28%, that is:

[tex]H_1: p < 0.28[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.28 is tested at the null hypothesis:

This means that [tex]\mu = 0.28, \sigma = \sqrt{0.28*0.72}[/tex]

Sample of 1800 computer chips revealed that 25% of the chips do not fail in the first 1000 hours of their use.

This means that [tex]n = 1800, X = 0.25[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.25 - 0.28}{\frac{\sqrt{0.28*0.72}}{\sqrt{1800}}}[/tex]

[tex]z = -2.83[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.25, which is the p-value of Z = -2.83.

Looking at the z-table, z = -2.83 has a p-value of 0.0023.

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

Answer:

y<(x-2)^2

Step-by-step explanation:

To graph this inequality, we first identify the function.

This is a quadratic function y=x^2

The function is translated horizontally to the right two. (x-2)^2

It is also a dotted line, <.

Answer:

>

Step-by-step explanation:

the less negative the greater the number

Answer:

27.5

Step-by-step explanation:

3 = 7.5

4 = 10

5*7.5=37.5-10=27.5

Seriously. 2=5 contradicts.

Answer:

Option a is the correct answer

Answer:

[tex]thank \: you[/tex]

Answer:

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Step-by-step explanation:

Given

[tex]log_{17}(52.875)[/tex]

Required

Convert to base 10

To do this, we make use of the following logarithm laws;

[tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

In the given parameters;

[tex]a = 52.875[/tex]

[tex]b = 17[/tex]

Substitute these values in [tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

[tex]log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}[/tex]

Represent as a ratio

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Hence;

[tex]log_{17}(52.875)[/tex] is represented as [tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Expression  [tex]log_{17} 52.875[/tex] can be written as in form of ratio of log  [tex]\frac{log_{10} 52.875}{log_{10} 17}[/tex] .

Any logarithmic expression [tex]log_{a} b[/tex] can we written as in form of ratio of log on base 10.

                   [tex]log_{a} b=\frac{log_{10} b}{log_{10} a}[/tex]

Here logarithmic expression is,  [tex]log_{17} 52.875[/tex] comparing with above expression.

We get,    [tex]b=52.875,a=17[/tex]

Substitute values of a and b in above expression.

 We get,      [tex]log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}[/tex]

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