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

Answer:

The 7 basic units of measurement in the metric system are:

- second (s), measuring time

- meter (m), measuring length/distance

- kilogram (kg), measuring the mass/weight

- ampere (A), measuring electric current

- kelvin (K), for temperature.  kelvin uses the Celsius scale, but kelvin is the measure in the metric system for temperature because it starts at the absolute 0 (-273° C).

- mole (mol), the amount of a substance, used mostly in chemistry

and

- candela (cd), to measure light intensity

Final answer:

The 7 basic units of measurement in the metric system include meter, kilogram, second, ampere, kelvin, mole, and candela, serving as the foundation for scientific measurements.

Explanation:

The metric system, also known as the International System of Units (SI), is comprised of 7 basic units of measurement. These units form the foundation of the metric system and all other units are derived from these. The SI system is advantageous because it's based on powers of 10, making conversions between units straightforward.

The 7 Basic SI Units are:

Units such as millimeter, centimeter, and kilometer are derived from the basic unit of length, the meter, emphasizing the metric system's coherence and simplicity.

The intersecting secants theorem says

[tex]PQ\cdot PR=PS\cdot PT[/tex]

[tex]\implies8(8+x)=4(24+4)[/tex]

[tex]\implies64+8x=112[/tex]

[tex]\implies8x=48[/tex]

[tex]\implies x=6[/tex]

It's clear from the image that [tex]PT=28[/tex], so the first option is correct.

###

Same as in the first problem; the intersecting theorems says

[tex]NM\cdot NL=NO\cdot NP[/tex]

[tex]\implies5(5+x)=3(3+17)[/tex]

[tex]\implies25+5x=60[/tex]

[tex]\implies5x=35[/tex]

[tex]\implies x=7[/tex]

so the third option is correct.

Answer:

x = 6; PR = 14; PT = 28

Step-by-step explanation:

ur welcome

Answer:

a x = 14.3 units

Step-by-step explanation:

The Pythagorean theorem is

a^2 +b^2 = c^2  where a and b are the sides and c is the hypotenuse

x^2 + 14^2 = 20^2

x^2 +196 = 400

Subtract 196 from each side

x^2+196-196 = 400-196

x^2 =204

Take the square root of each side

sqrt(x^2) = sqrt(204)

x =14.28285686

To the nearest tenth

x = 14.3 units

Answer:

4, 4, and 4.

The three positive numbers that satisfy the given conditions are

x = y = z = 4, and their sum is 12.

Given,

Sum of three numbers is 12.

Let the three positive numbers are x, y, and z.

1. To minimize the sum of their squares as

[tex]f(x, y, z) = x^2 + y^2 + z^2[/tex]

Subject to the constraint: Sum of three numbers is 12.

[tex]g(x, y, z) = x + y + z = 12[/tex]

2. Using Lagrangian function:

[tex]L(x, y, z, \lambda) = f(x, y, z) - \lambda(g(x, y, z) - 12)[/tex]

Substituting the value of f(x, y, z) = [tex]x^2 + y^2 + z^2[/tex] and g(x, y, z) = [tex]x + y + z - 12[/tex]  into Lagrangian function gives

[tex]L(x, y, z, \lambda) = (x^2+y^2+z^2) - \lambda (x+ y+ z - 12)[/tex]

3. Now, take partial derivatives of L with respect to x, y, z, and λ,

[tex]\(\frac{{\partial L}}{{\partial x}}[/tex] = [tex]2x - \lambda\)[/tex]

[tex]\(\frac{{\partial L}}{{\partial y}}[/tex] = [tex]2y - \lambda\)[/tex]

[tex]\(\frac{{\partial L}}{{\partial z}}[/tex] = [tex]2z - \lambda\)[/tex]

[tex]\(\frac{{\partial L}}{{\partial \lambda}}[/tex] = [tex]-(x + y + z - 12)[/tex]

4. Now, set each derivative to zero to find the critical points.

Equation 1:     [tex]\(\frac{{\partial L}}{{\partial x}}[/tex] = [tex]2x - \lambda\)[/tex] =0

Equation 2:     [tex]\(\frac{{\partial L}}{{\partial y}}[/tex] = [tex]2y - \lambda\)[/tex] = 0

Equation 3:     [tex]\(\frac{{\partial L}}{{\partial z}}[/tex] = [tex]2z - \lambda\)[/tex] = 0

Equation 4:     [tex]\(\frac{{\partial L}}{{\partial \lambda}}[/tex] = [tex]-(x + y + z - 12)[/tex] = 0

Solving equations (1), (2), and (3) we get

        x = λ/2

        y = λ/2

         z = λ/2.

5. Substituting the value x = y = z = λ/2 into equation (4) gives

[tex]-(x + y + z - 12) = 0[/tex]

- [tex](\lambda/2 + \lambda/2 + \lambda/2 -12)= 0[/tex]

[tex]-(3\lambda/2 - 12) = 0[/tex]

[tex]3\lambda/2 = 12[/tex]

[tex]\lambda = 8[/tex]

So, x = y = z = λ/2 = 4.

Therefore, the three positive numbers are 4, 4 and 4.

Learn more about Lagrangian function here:

https://brainly.com/question/33166274

#SPJ4

[tex]\( a = \frac{8}{5} \)[/tex] and  [tex]\( b = \frac{3}{8} \)[/tex].

To find the number asuch that the line x = a bisects the area under the curve [tex]\( y = \frac{1}{{x^2}} \)[/tex] for [tex]\( 1 \leq x \leq 4 \)[/tex], we first need to find the total area under the curve in that interval. Then, we'll find the value of a such that the area to the left of x = a is equal to the area to the right of x = a.

The total area under the curve [tex]\( y = \frac{1}{{x^2}} \)[/tex] from x = 1 to x = 4 is given by the definite integral:

[tex]\[ A = \int_{1}^{4} \frac{1}{{x^2}} \, dx \][/tex]

[tex]\[ A = \int_{1}^{4} x^{-2} \, dx \][/tex]

[tex]\[ A = \left[ -\frac{1}{x} \right]_{1}^{4} \][/tex]

[tex]\[ A = -\frac{1}{4} + \frac{1}{1} \][/tex]

[tex]\[ A = 1 - \frac{1}{4} \][/tex]

[tex]\[ A = \frac{3}{4} \][/tex]

So, the total area under the curve is [tex]\( \frac{3}{4} \)[/tex].

To bisect this area, the area to the left of x = a and the area to the right of x = a must each be [tex]\( \frac{1}{2} \)[/tex] of the total area.

Let's integrate from x = 1 to x = a to find the area to the left of \( x = a \), then set it equal to [tex]\( \frac{1}{2} \)[/tex] of the total area:

[tex]\[ \int_{1}^{a} \frac{1}{{x^2}} \, dx = \frac{1}{2} \cdot \frac{3}{4} \][/tex]

[tex]\[ \left[ -\frac{1}{x} \right]_{1}^{a} = \frac{3}{8} \][/tex]

[tex]\[ -\frac{1}{a} + \frac{1}{1} = \frac{3}{8} \][/tex]

[tex]\[ -\frac{1}{a} + 1 = \frac{3}{8} \][/tex]

[tex]\[ -\frac{1}{a} = \frac{3}{8} - 1 \][/tex]

[tex]\[ -\frac{1}{a} = \frac{3}{8} - \frac{8}{8} \][/tex]

[tex]\[ -\frac{1}{a} = \frac{-5}{8} \][/tex]

[tex]\[ \frac{1}{a} = \frac{5}{8} \][/tex]

[tex]\[ a = \frac{8}{5} \][/tex]

So, [tex]\( a = \frac{8}{5} \)[/tex].

Now, to find the number b such that the line y = b bisects the area, we need to find the value of b such that the area above the line y = b is equal to the area below the line y = b.

The total area under the curve is [tex]\( \frac{3}{4} \)[/tex]. Since the curve is symmetric about the x-axis, the line y = b must pass through the midpoint of the total area, which is [tex]\( \frac{3}{8} \)[/tex] above the x-axis.

So, [tex]\( b = \frac{3}{8} \)[/tex].

Answer:

54.65m

Step-by-step explanation:

This is going to be extremely difficult to explain.  We have one large right triangle split up into 2 triangles:  the first one has a base angle of 57 with unknown base length (y) and unknown height (x), and the second one has a base angle of 27 with unknown base length of y + 43 and unknown height (x.  This is the same x from the first one and is what we are looking for...the height of the tower).  We can find the vertex angle of the first triangle because 180 - 90 - 57 = 33.  The side across from the 33 is y and the side adjacent to it is x so we have that tan33 = y/x.  Not enough yet to do anything with.  Our goal is to solve for that y value in order to sub it in to find x.  Next we have to use some geometry.  The larger triangle has a base angle of 27.  The angle within that triangle that is supplementary to the 57 degree angle is 180 - 57 = 123.  So now we have a triangle with 2 base angles measuring 123 and 27, and the vertex angle then is 180 - 123 - 27 = 30.  That vertex angle of 30 added to the vertex angle of the first triangle is 63 degrees total.  Now we can say that tan63 = (y+43)/x.  Now we have 2 equations with 2 unknowns that allows us to solve them simultaneously.  Solve each one for x.  If

[tex]tan33=\frac{y}{x}[/tex], then

[tex]x=\frac{y}{tan33}[/tex].

If

[tex]tan63=\frac{y+43}{x}[/tex], then

[tex]x=\frac{y+43}{tan63}[/tex]

Now that these both equal x and x = x, we can set them equal to each other and solve for y:

[tex]\frac{y}{tan33}=\frac{y+43}{tan63}[/tex]

Cross multiply to get

[tex]tan33(y+43)=ytan63[/tex]

Distribute through the parenthesis to get

y tan33 + 43 tan33 = y tan 63.

Now get the terms with the y in them on the same side and factor out the common y:

y(tan33 - tan63) = -43 tan33

Divide to get the following expression:

[tex]y=\frac{-43tan33}{(tan33-tan63)}[/tex]

This division gives you the fact that y = 64.264 m.  Now we add that to 43 to get the length of the large right triangle as 107.26444 m.  What we now is enough information to solve for the height of the tower:

[tex]tan27=\frac{x}{107.2644}[/tex]

and x = 56.65 m

Phew!!!!! Hope I didn't lose you too too badly!  This is not an easy problem to explain without being able to draw the picture like I do in my classroom!

Angle of elevation is the angle between a line of sight and the horizontal surface.

The height of the tower is [tex]32.74 m[/tex]

The question is illustrated with the attached image.

First, calculate distance BC (x)

This is calculated using the following tan ratio

[tex]\tan(57) = \frac{h}{x}[/tex]

Make h the subject

[tex]h = x\tan(57)[/tex]

Next, calculate distance CD using the following tan ratio

[tex]\tan(27) = \frac{h}{CD}[/tex]

Make h the subject

[tex]h = CD \times \tan(27)[/tex]

From the attached image:

[tex]CD = x + 43[/tex]

So, we have:

[tex]h = (x + 43) \times \tan(27)[/tex]

Substitute [tex]h = x\tan(57)[/tex]

[tex]x \tan(57) = (x + 43) \times \tan(27)[/tex]

[tex]1.5398x = (x + 43) \times 0.5095[/tex]

Open brackets

[tex]1.5398x = 0.5095x + 21.9085[/tex]

Collect like terms

[tex]1.5398x - 0.5095x = 21.9085[/tex]

[tex]1.0303x = 21.9085[/tex]

Solve for x

[tex]x = \frac{21.9085}{1.0303}[/tex]

[tex]x = 21.2642[/tex]

Recall that:

[tex]h = x\tan(57)[/tex]

[tex]h = 21.2642 \times 1.5398[/tex]

[tex]h = 32.74[/tex]

Hence, the height of the tower is [tex]32.74 m[/tex]

Read more about elevation and depression at:

https://brainly.com/question/9817377

Answer:

109 degrees is the answer

Answer:

96°

Step-by-step explanation:

The given quadrilateral is inscribed in a circle, so its opposite angles are supplementary, which means that the sum of their measures is 180∘.

The measures of the opposite angles in the quadrilateral are given as      (6m + 1 3)∘ and (4m + 7)∘.

Equate the sum of the given measures to 180∘.

6m + 13 + 4m + 7 = 180

Combine like terms.

10m + 20 = 180

Subtract 20 from both sides.

10m = 160

Divide both sides by 10.

m = 16

Substitute 16 for m into the expression given for the measure of angle M and simplify.

6m = 6(16)

=96∘

Therefore, m∠M = 96∘.

Answer:

  A.  x = -2

Step-by-step explanation:

A spreadsheet is a suitable tool for making a chart like this.

The values of f(x) and g(x) are the same for x = -2. That is, f(-2) = g(-2), so x=-2 is the solution to f(x)=g(x).

ANSWER

[tex]882 \: {in}^{2} [/tex]

EXPLANATION

The area of the original rectangle is 72 in².

If the length and the width of the rectangle are changed by a scale factor of 3.5.

Then the area will change by

[tex]{3.5}^{2} = 12.25[/tex]

To get the area of the new rectangle is we multiply the area of the original rectangle by 12.25.

This implies that,the area of the new rectangle is

[tex]3.5 \times 72 = 882 \: {in}^{2} [/tex]

Therefore the area of the new rectangle is 882 square inches.

Answer:

2.) 437.50

Step-by-step explanation:

When doing the formula for interest and plugging in 5 for the value of time, this equation increases by approximately 437.50.

Answer with explanation:

When two coins are tossed

Total Sample Space ={T T,HT, TH, H H}=4

By getting , T T, total points won =1 Point

For, a fair game , you need to lose 1 point, so that sum of all the points

    =1 -1

   =0

The point = -1 , must be obtained from three outcomes which are {HT, TH, and H H}.

Sum of ,HT , TH and H H = -1

⇒S(H T) +S (TH) +S(H H)= -1, where S=Sum

If points obtained on each of three outcome are equal, then

[tex]S(HT)=\frac{-1}{3}\\\\S(TH)=\frac{-1}{3}\\\\S(HH)=\frac{-1}{3}[/tex]

Answer:

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:

BBBBBBBBBBBBBBB

Answer:

Joe is 9 years old

Step-by-step explanation:

We can start by creating two different equations, one for each fact that we know about their ages.

Say that J is Joe's age

Say that T is Tim's age

Our first equation would then be:

4J + 2T = 50

J - 2 = T

Now that we know that T is J - 2, we can plug that in to the first equation.

4J + 2(J - 2) = 50

We can simplify this equation to solve for J

4J + 2J - 4 = 50

6J = 54

J = 9

Joe is 9 years old

Answer:

Step-by-step explanation:

If two plygons are similar, then corresponding sides are in proportion.

Therefore we have the equation:

[tex]\dfrac{z}{9}=\dfrac{2}{6}[/tex]          cross multiply

[tex]6z=(9)(2)[/tex]

[tex]6z=18[/tex]          divide both sides by 6

[tex]z=3[/tex]

Answer:

Step-by-step explanation:

find the value of x and y

Answer:

Step-by-step explanation:

THE ANSWER IS C.

Answer: The answer is D.

Step-by-step explanation: Considering that the dots represent people, all you have to do is count the dots. Graph D is the only plot that has three in both 6 and 8.

Hope this helps & Good Luck,

Melodii

The answer is D

The last chart that has three dots on the numbers 8 and 6

To find 3 people that sleep for 8 hrs, there should be 3 dots on top of the number 8...

And to find 3 people that sleep ofor 6 hrs, there should be 3 dots on top of the number 6 too

Hope this helped,

have a blessed day :-)

Answer:

Sometimes

Step-by-step explanation:

By definition:

Isosceles triangle:Two equal sides and

Two equal angles

Acute triangle: All angles are less than 90°.

Because an angle of an isosceles triangle can be greater than 90° sometimes an acute triangle is not an isosceles.

ANSWER

A (-∞,-2)

B (0,4).

EXPLANATION

The portion of the graph that is above the x-axis is considered positive.

From the graph the curve is above the x-axis on the interval

(-∞,-2) and (0,4).

The first and second options are correct.

Answer:

AM = 4

Step-by-step explanation:

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, that is

AM = [tex]\frac{1}{3}[/tex] × 12 = 4

Answer:

3/4

Step-by-step explanation:

I'm not very good at understanding word problems but I'll try to help using the info I already have.

You bought 3/4 pounds and you need a total of 1 1/2 pounds.

Find the common denominator which in this case is 4. Multiply 1 1/2 by 2/2 to get 1 2/4

You leave 3/4 alone because the denominator is already 4.

Convert 1 2/4 to a mixed number by taking away the 1 and adding 4 to the numerator leaving you with 6/4

6/4 - 3/4 = 3/4

Therefore you need 3/4 pounds left

Hope I helped

The Center = (-1.5, 2) and radius is 2 of the equation  (x+1.5)^2 + (y-2)^2 = 4.

We have given that,

A manufacturer is designing a two-wheeled cart that can maneuver in tight spaces.

On one test model, the wheel placement and radius are modeled by the equation (x+1.5)^2 + (y-2)^2 = 4.

We have to determine the center and radius of the given equation.

The standard form for the equation of a circle is [tex](x-h)^2+(y-k)^2=r^2.[/tex]

The center is (h,k) and the radius measures r units.

Compare the given equation with the standard form of the equation so we get,

radius=4=(2)^2=2

center(h,k)=(-1.5,2)

Therefore, the Center = (-1.5, 2) and radius is 2 of the equation  (x+1.5)^2 + (y-2)^2 = 4.

To learn more about the standard form of the circle visit:

https://brainly.com/question/1506955

#SPJ2

Answer:

see explanation

Step-by-step explanation:

36

Since triangle is isosceles then AB = BC

Equate the 2 sides, that is

4x - 21 = 2x - 7 ( subtract 2x from both sides )

2x - 21 = - 7 ( add 21 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7, hence

AB = 2x - 7 = (2 × 7) - 7 = 14 - 7 = 7

BC = 4x - 21 = (4 × 7) - 21 = 28 - 21 = 7

AC = x - 3 = 7 - 3 = 4

--------------------------------------------------------------

37

Since the triangle is equilateral then all 3 sides are equal.

Equate any 2 sides and solve for x

6x + 1 = 3x + 10 ( subtract 3x from both sides )

3x + 1 = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

HF = 6x + 1 = (6 × 3) + 1 = 18 + 1 = 19 = FG = HG

A parabola is U shaped.

Answer:

C

The answer is c

Hope it helps

Answer:

5.6

Step-by-step explanation:

fr fr

Answer:

6.2

Step-by-step explanation:

The expected value is the sum of the each value times its probability.

X = (3×0.2) + (4×0.1) + (5×0.25) + (7×0.05) + (9×0.4)

X = 0.6 + 0.4 + 1.25 + 0.35 + 3.6

X = 6.2

Answer:

simplify -1(3/5)÷(-2/3) = 9/10

=90/100

= .90 and there's your answer

Answer:

12/5 = 2  2/5

Step-by-step explanation:

Convert -1  3/5 into an improper fraction:  -8/5.

Next, divide -8/5 by (-2/3).  Equivalently, invert (-2/3), obtaining (-3/2), and multiply:

(-8/5)(-3/2) = 24/10 = 12/5 = 2  2/5

Answer:

A and C

Step-by-step explanation:

I got the answers correct on edg.

Hope this helps :)

Answer:

AB is the shortest segment in △ABC

AC = 2AB

Step-by-step explanation:

Edge 2022

George's earnings from typing forty-five regular pages are $67.50. To calculate his total earnings, the charge per page for thirty-six technical papers is needed, which is not provided in the question.

To calculate how much George will earn for typing papers, we must know the charge per page for both regular and technical papers. For regular term papers, the charge has been provided: $1.50 per page. However, the charge for technical papers has not been specified. Thus, additional information is needed: the rate George charges per page for technical papers. Without this rate, we cannot accurately calculate his total earnings.

Given that George types forty-five regular pages, his earnings from regular papers can be calculated as:
45 pages *$1.50 per page = $67.50

As for the technical papers, we must have the rate per page to calculate his earnings from the thirty-six technical pages he typed. Once we have this rate, it would be a similar calculation to the one done for regular papers.

Answer:

[tex]\large\boxed{_6P_2=30}[/tex]

Step-by-step explanation:

[tex]_nP_k=\dfrac{n!}{(n-k)!}\\\\n!=1\cdot2\cdot3\cdot...\cdot n\\======================\\\\_6P_2=\dfrac{6!}{(6-2)!}=\dfrac{6!}{4!}=\dfrac{4!\cdot5\cdot6}{4!}\\\\\text{cancel}\ 4!\\\\=5\cdot6=30[/tex]

Answer:

The quotient contains a terminating decimal and The quotient is a whole number less than 11.

Step-by-step explanation:

To answer this one, it's mandatory to remember that quotient, is the outcome of a ratio: a number (r) over another (s) (different than 0). In this case:[tex]\frac{81}{918}[/tex]. So q is equal to =0.08823529411.

Analyzing the number: 0.08823529411

This is not a repeating decimal, but it is a terminating decimal for it has an end.

The quotient is also a whole number less than 11.

The Whole Set of numbers is made up of the following numbers W ={0,1,2,...} and 0 < 11. Therefore it is true.

The quotient of 81 divided by 918 is a decimal that contains repeating digits.

The question asks about the quotient of the division problem 81 divided by 918. To find out the nature of the quotient, we can perform the division. The result of this division is not a whole number since 81 cannot evenly divide 918. Therefore, we will be looking at a decimal result. When we carry out the division, we notice that the decimal will not terminate shortly; thus, we can infer that the pattern of digits will start to repeat at some point. This tells us that the quotient contains a repeating decimal. Therefore, the correct answer is that the quotient contains a repeating decimal. It is not a whole number, nor is it terminating, and the quotient will be less than 1 since 81 is less than 918.

Answer:

x =(6-√-12)/6=1-i/3√ 3 = 1.0000-0.5774i

x =(6+√-12)/6=1+i/3√ 3 = 1.0000+0.5774i

Step-by-step explanation:

Two imaginary solutions :  

x =(6+√-12)/6=1+i/3√ 3 = 1.0000+0.5774i

 or:  

x =(6-√-12)/6=1-i/3√ 3 = 1.0000-0.5774i

Two solutions were found :

x =(6-√-12)/6=1-i/3√ 3 = 1.0000-0.5774i

x =(6+√-12)/6=1+i/3√ 3 = 1.0000+0.5774i

Answer:

m<ADB = 25 degrees

Step-by-step explanation:

<ADB has two different intercepted arcs: AB and the unlabeled one that has a measure of 20. To find the actual measure of the angle, we must find the difference between these arcs and divide by 2.

70-20 = 50

50/2 = 25

Applying the angle of intersecting secants theorem, the measure of angle ADB in the diagram is: A. m∠ADB = 25°

When two secants meet at a point outside a circle, the measure of angle formed at that point is half the positive difference of the intercepted arcs, based on the angle of intersecting secants theorem.

m∠ADB = 1/2(70 - 20)

m∠ADB = 1/2(50)

m∠ADB = 25°

Learn more about the angle of intersecting secants theorem on:

https://brainly.com/question/1626547

#SPJ2