What is the slope of the line represented by the following equation?
y= 1/3x + - 2/3
A) -1/3
B)-2/3
C)1/3
D)2/3

Answer:

2

Step-by-step explanation:

I think this is the answer not sure. Feel free to tell me if I'm wrong

Answer:

it might be 4.5

Step-by-step explanation:

im not sure sorry

Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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Answer:

Step-by-step explanation:

The root of the equation \(\(f(x) = x^3 - 3x - 1\)\) between -1 and 1, after the second iteration of the False Position method, is approximately -1.

The False Position method involves finding the x-value that corresponds to the x-intercept of the line passing through \(\((a, f(a))\)\) and \(\((b, f(b))\),\)where (a) and (b) are the endpoints of the interval.

Let's begin the iterations:

Iteration 1:

\(\(a = -1\), \(f(a) = (-1)^3 - 3(-1) - 1 = -3\)\)

\(\(b = 1\), \(f(b) = (1)^3 - 3(1) - 1 = -3\)\)

The line passing through (-1, -3) and (1, -3) is (y = -3). The x-intercept of this line is at (x = 0).

Therefore, the new interval becomes [0, 1] since the sign of f(x) changes between\(\(x = -1\) and \(x = 0\).\)

Iteration 2:

\(\(a = 0\), \(f(a) = (0)^3 - 3(0) - 1 = -1\)\)

\(\(b = 1\), \(f(b) = (1)^3 - 3(1) - 1 = -2\)\)

The line passing through\(\((0, -1)\) and \((1, -2)\) is \(y = -x - 1\)\). The x-intercept of this line is at (x = -1).

After the second iteration, the new interval becomes [-1, 1] since the sign of f(x) changes between (x = 0) and (x = -1).

Therefore, the root of the equation \(\(f(x) = x^3 - 3x - 1\)\) between -1 and 1, after the second iteration of the False Position method, is approximately -1.

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In the regression line y = a+ bx+ e, a is the slope of the regression line.

The above statement is False.

The correct Statement is :

The linear regression line has an equation of the form Y =a + bX

where, Y is called the dependent variable or response.

X means independent or predictor or explanatory variable.

a is the y-intercept and b is the slope of the line.

Regression Line:

A regression line is a statistical tool that shows the correlation between two variables. Specifically, it is used when the variation of one (the dependent variable) depends on changes in the value of the other (the independent variable).

Simple linear regression has two cases:

The formula for the least squares regression line (LSRL) from Y to X is:

                           Y=a + bX + ɛ

where,

Y is the dependent variable.

a is the Y intersection.

b is the slope of the regression line.

X is the independent variable.

ɛ is the residual (error).

and

b = (N∑XY-(∑X)(∑Y) / (N∑X2– (∑X)2) ;

and

a = (∑Y – b ∑X) / N

where, N is the total number of observations.

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Answer:

-13

Step-by-step explanation:

-5 + 2( 8 - 12 )

Distribute;

-5 + 2 ( 8 - 12 )

-5 + 16 - 24

Simplify;

-5 + 16 - 24

11 - 24

-13

Answer:

-13

Step-by-step explanation:

Follow the Order of Operations:

1. Parentheses

2. Exponents

3. Multiplication and Division

4. Addition and Subtraction

Parentheses:

-5+2(-4)

Exponents:

There is no exponents so we can skip that step

Multiplication and Division:

-5-8

Addition and Subtraction:

-13

Hope this helps! Have a safe and wonderful Thanksgiving!

Answer:

= 2 7/12

Step-by-step explanation:

We solve the above question using the operation of addition.

2 1/3 + 1/4

Lowest common denominator = 12

2 + ( 1/3 + 1/4)

2 + (4 × 1 + 3 × 1/12)

2 + (7/12)

= 2 7/12

98 square feet of glass were used to build the aquarium.

Given that the public library has an aquarium in the shape of a rectangular prism, which has a base of 6 feet by 2.5 feet and a height of 4 feet. We are to find out how many square feet of glass were used to build the aquarium.

The surface area of a prism is given as;S.A of the rectangular prism = 2(lw + lh + wh)Where l = 6 feet, w = 2.5 feet, and h = 4 feetSubstituting the given values;S.A of the rectangular prism = 2(6 × 2.5 + 6 × 4 + 2.5 × 4)S.A of the rectangular prism = 2(15 + 24 + 10)S.A of the rectangular prism = 2(49)S.A of the rectangular prism = 98

In order to construct the aquarium, 98 square feet of glass were utilised.

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(a) The y-intercept = 0, the slope = 25 and the equation representing Quinton’s scenario is y = 25x

(b) The independent variable is the hours worked and the dependent variable is the total amount earned

(c)

x        0        1      2       3     4

f(x)      0      25    50     75   100

(d) The domain and the range of the function are the set of whole numbers

From the question, we have the following parameters that can be used in our computation:

The consulation fee is 0

So, we have

y-intercept = 0

The amount charged per hour is $25

So, we have

Slope = 25

A linear equation is represented as

y = Slope * x + y-intercept

So, we have

y = 25x

Hence, the equation representing Quinton’s scenario is y = 25x

Using (a) as a guide:

Using the function y = 25x, we have the table of values to be

x        0        1      2       3     4

f(x)      0      25    50     75   100

The domain and the range of the function are the set of whole numbers

The graph of the function is attached

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Compared with the beam, the large cube has the same volume but a smaller surface area.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Given that, there are two sets of eight blocks, each with an edge measurement of 1 cm. Two blocks are placed on top of two other blocks to form a big cube. You assemble the second set into a 1-by-8-block straight beam.

Since the volume is the same.

The surface area of a cube,

=6a²

=6(2)²

=6×4

=24 cm²

The surface area of a beam,

=1 × 8

=8 cm²

Thus, compared with the beam, the large cube has the same volume but a smaller surface area.

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If the Thompsons need the movers for more than 6 hours, City movers would be the better deal. Therefore, option D is the correct answer.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Given that, the Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour.

Let the number of hours be x.

Now, 30+15x

Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal

72+8x

From the graph, both the movers have same charge at 6th hour and City movers charge is decreasing then compare to Town Movers.

Therefore, option D is the correct answer.

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Answer:

The width of the rectangular park is 40m.

Step-by-step explanation:

We are given that the area of a square has the same area as the rectangle (the fact that they're parks doesn't matter)

We are also given one length side of the square, and since squares have all equal sides, we know all the side lengths are 60m.

To find Area, we do L * W, so it would be 60 * 60 = 3600.

That means the area of the rectangle park is 3600m. One side of the rectangle is 90m, so the formula is L * W = A. So we plug in known values of the rectangle which would be 90 * W = 3600. To find W, we do 3600/90 which is 40.

Let me know if you have any questions

Answer:

D

Step-by-step explanation:

9514 1404 393

Answer:

  -x +2

Step-by-step explanation:

The expression can be simplified as follows.

  \(\sqrt{x^2-4x+4}=\sqrt{(x-2)^2}=|x-2|\)

For negative values of its argument, the absolute value changes the sign.

For x < 1, x-2 is negative, so the simplified form is ...

  -(x -2) . . . . . for x < 1

  -x +2 . . . . . for x < 1

The cost for 1 song is $0.99, then from the 150 songs 149 will cost $0.10, therefore, the total cost for the 150 songs is:

Answer: $15.89.

Part A

\(g(-1/3)=3(-1/3)-4=-5\\\\f(g(-1/3))=f(-5)=-5+2=\boxed{-3}\)

Part B

\(g(f(x))=g(x+2)=3(x+2)-4=3x+6-4=\boxed{3x+2}\)

Part C

Since \(g(f(x)) \neq x\), \(g(x)\) and \(f(x)\) are not inverses.

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Using the concepts of standard normal distribution,43 people height is in between 160 and 180 and 31 people height is taller than 165cm

The standard normal distribution is actually  of the forms of the normal distribution. It occurs when  normal random variable has a mean equal to zero and a standard deviation equal to one. Or a normal distribution with a mean 0 and standard deviation of 1 is known as the standard normal distribution. Also, the standard normal distribution is concentrated at zero, and the standard deviation gives the degree to which a given measurement deviates from the mean.

Now, we find the Z score of the given heights range

We know that Z score is given by formula

Z=(\(\frac{X-\alpha }{\beta }\))

where X is normal random variable,\(\alpha\) is mean of given sample and \(\beta\) is standard deviation of given sample.

Therefore, Z score is

z(160) = (170-160)/5 = 2

z(180) = (180-170)/5 = 2

P(160<= x <=180) = P(2<= z <=2) = 0.4772(from standard distribution table)

Therefore for 90 people=90×0.4772= 43 people after rounded up.

b) Similarly, we need to find Z value for people height greater than 165 cm.

Therefore, by using the above formula, we get

z(165) = (170-165)/5 = 1

P(x > 165) = P(z > 1) = 0.3438(from standard distribution table)

Therefore, for 90 people=0.3438×90=31 after rounded up

Hence, number of people whose height is in between 160 and 180cm is 43 and number of people whose height greater than 165cm is 31

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Answer:

Step-by-step explanation:

(see pic)

Answer:

3 more square feet.

Step-by-step explanation:

x = The amount Melinda can shovel in 1 minute

y = The amount Paula can shovel in 1 minute

So make two equations:

30(x + y) = 450       x + y = 15       x = 15 - y

20x + 25y = 345     4x + 5y = 69

Plug in:

4(15 - y) + 5y = 69

60 - 4y + 5y = 69

y = 9

x = 6

9 - 6 = 3

Answer:

Answer is A

Step-by-step explanation:

Took it on Edg.

Answer:

-1.5

Step-by-step explanation:

Hope this helps! :D

Answer:

-13-4=-17

Step-by-step explanation:

When you are subtracting more from a negative number, you can think of it as adding those numbers together. 13+4 would be 17, so if you flip the signs to negatives, it would be -17.

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Step-by-step explanation:

mass(m)= 3kg

height(h)= 2m

gravity(g)= 9.8 m/s^2

P.E.= mgh

=3*2*9.8

=58.8 Joule

Answer:

58.84 Joules

Step-by-step explanation:

3(Mass)*2(Height)*9.8=58.84J

Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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Answer:

First, set x equal to .93

x=.939393939393...

Then, since the repeating is by two digits, let's multiply x by 100

This would make 100x=93.9393939393...

Now, we can subtract 100x−x

This would leave us with 99x=93 because the repeating digits cancel out.

This looks much easier now right?

Just divide the 99 and isolate the x to get x=9399

Get the simplified fraction, and the final answer is x=3133

Answer:

x = 58°

Step-by-step explanation:

Label the point where the diagonals cross as T

Diagonals always meet at right angles

m∠SRT = 32

Sum of interior angles of ΔSRT = 180

x = 180 - 90 - 32 = 58

These lines will be parallel to the initial line and will intersect the final velocity line at the corresponding values (122 for the lower estimate and 298 for the upper estimate)

To sketch the velocity against time, you can take the following steps:

First, calculate the acceleration using the given data by using the formula;

acceleration = (final velocity - initial velocity)/time

Where; Initial velocity is the velocity before applying the brakes

Final velocity is the velocity at which the car comes to stop

Time is the time it takes to stop the car (6 seconds in this case)

Now, calculate the lower and upper estimates using the formula;

Lower estimate = initial velocity + (acceleration x time)

Upper estimate = initial velocity + (2 x acceleration x time)

Sketch the graph using the following steps;

On the vertical axis, plot the velocity of the car

On the horizontal axis, plot the time

Start from the initial velocity and draw a straight line with the calculated acceleration until the end of the time (6 seconds)This straight line will give you the final velocity (0 in this case)

Now, draw two more lines, one with the lower estimate and the other with the upper estimate

Finally, label the axes and the lines with their corresponding values.'

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We will apply the principle of similar triangles to solve this question

Given that

Method: Find side AC

We will use the Pythagoras theorem to evaluate AC

T