line of best fit - scatter plot questions

Answer:

4x + y = 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 4 , then

y = - 4x + c ← is the partial equation

to find c substitute (2, 7 ) into the partial equation

7 = - 4(2) + c = - 8 + c ( add 8 to both sides )

15 = c

y = - 4x + 15

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

then

y = - 4x + 15 ( add 4x to both sides )

4x + y = 15 ← in standard form

Answer:

14/26

Step-by-step explanation:

a fraction that is equivalent to 7/13 is 14/26 because to make the fraction equivalent the numerator and denominator have to be multiplied by the same number so another fraction that would be equivalent would be 21/39

i hope this helps

\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

The value is 896π/3

The spheres x² + y² + z² = 9 and x² + y² + z² = 16.

Convet into shperical coordinate

x2+y2+z2≤2z⟹ρ≤2cosϕ.

Then the volume of the element will be

Then we have

Cylindrical coordinates:

The distance from a chosen reference axis (axis L in the illustration opposite), the angle from the axis to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis are the three dimensions of a cylindrical coordinate system (plane containing the purple section). Whichever side of the reference plane faces the point determines whether the latter distance is expressed as a positive or negative value.

The location where all three coordinates may be specified as zero is the origin of the system. The reference plane and axis come together at this point. To distinguish it from the polar axis, the axis is often referred to as cylindrical or longitudinal axis.

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Based on the data from 191 credit card statements, the auditor calculated the fraction defective in each sample, estimated the true fraction defective, determined the mean and standard deviation of the sampling distribution, and established control limits for the process. With a known long-term fraction defective of 2 percent, a control chart was constructed using two-sigma control limits.

a. To determine the fraction defective in each sample, you divide the number of items with errors by the total sample size. The results are as follows:

Sample 1: Fraction Defective = 4/191 ≈ 0.0209

Sample 2: Fraction Defective = 2/191 ≈ 0.0105

Sample 3: Fraction Defective = 4/191 ≈ 0.0209

Sample 4: Fraction Defective = 10/191 ≈ 0.0524

b. To estimate the true fraction defective for the process, you can take the average of the fraction defective in each sample. Therefore, the estimate is (0.0209 + 0.0105 + 0.0209 + 0.0524)/4 = 0.0262, rounded to 1 decimal place.

c. To estimate the mean and standard deviation of the sampling distribution of fractions defective, you can use the following formulas:

Mean = Estimated True Fraction Defective = 0.0262

Standard Deviation = √[(Estimated True Fraction Defective * (1 - Estimated True Fraction Defective)) / Sample Size]

For each sample, the sample size is 191. Plugging in the values, we get:

Standard Deviation = √[(0.0262 * (1 - 0.0262)) / 191] ≈ 0.0154

Therefore, the estimate of the mean is 0.0262, and the estimate of the standard deviation is 0.0154.

d. To find the control limits that would give an alpha risk of 0.03 for this process, you need to calculate the z-value corresponding to an alpha risk of 0.03 (one-sided test). The formula for the z-value is:

Z = -InvNorm(Alpha Risk)

Plugging in the value, we have:

Z = -InvNorm(0.03) ≈ -1.8808

The control limits are calculated using the formula:

Control Limits = Estimated True Fraction Defective ± (Z * Standard Deviation)

Control Limits = 0.0262 ± (-1.8808 * 0.0154)

The upper control limit is approximately 0.0531, and the lower control limit is approximately -0.0008. Since the lower control limit cannot be negative, it is set to zero. Therefore, the control limits are 0.0531 (upper) and 0 (lower).

e. To determine the alpha risk for control limits of 0.0470 and 0.0054, you need to calculate the corresponding z-values using the formula:

Z = (Control Limit - Estimated True Fraction Defective) / Standard Deviation

For the upper control limit:

Z = (0.0470 - 0.0262) / 0.0154 ≈ 1.3442

For the lower control limit:

Z = (0.0054 - 0.0262) / 0.0154 ≈ -1.3442

The alpha risk can be calculated using the formula:

Alpha Risk = 1 - NormCDF(Z)

For the upper control limit, the alpha risk is approximately 0.0891, and for the lower control limit, the alpha risk is also approximately 0.0891.

f. Since the alpha risk for control limits of 0.0470 and 0.0054 is 0.0891, which is greater than the desired alpha risk of 0.03, the process is not in control.

g. If the long-term fraction defective of the process is known to be 2 percent (0.02), the mean of the sampling distribution would still be equal to the estimated true fraction defective, which is 0.02. The standard deviation can be calculated using the same formula as before:

Standard Deviation = √[(Estimated True Fraction Defective * (1 - Estimated True Fraction Defective)) / Sample Size]

Plugging in the values, we get:

Standard Deviation = √[(0.02 * (1 - 0.02)) / 191] ≈ 0.0149

Therefore, the mean of the sampling distribution is 0.02, and the standard deviation is 0.0149.

h. To construct a control chart for the process assuming a fraction defective of 2 percent (0.02) and using two-sigma control limits, you can calculate the control limits as follows:

Control Limits = Estimated True Fraction Defective ± (2 * Standard Deviation)

Control Limits = 0.02 ± (2 * 0.0149)

The upper control limit is approximately 0.0498, and the lower control limit is approximately -0.0098. Since the lower control limit cannot be negative, it is set to zero. Therefore, the control limits are 0.0498 (upper) and 0 (lower).

Based on these control limits, the process is in control since the estimated true fraction defective falls within the control limits.

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Answer:

i believe its

6/14 or 3/7 which is the same

The limit for the given function as (x, y) approaches (0, 0) is DNE.

To find the limits as (x, y) approaches (0, 0) for the given function, let's evaluate them step by step:

Along the x-axis (y = 0):

Taking the limit as y approaches 0, we have:

lim(x,0)→(0,0) 5x^2/(x^2+5(0)^2) = 5x^2/x^2 = 5

The limit along the x-axis is 5.

Along the y-axis (x = 0):

Taking the limit as x approaches 0, we have:

lim(0,y)→(0,0) 5(0)^2/((0)^2+5y^2) = 0/5y^2 = 0

The limit along the y-axis is 0.

Along the line y = mx:

Substituting y = mx into the expression, we have:

lim(x,mx)→(0,0) 5x^2/(x^2+5(mx)^2)

Simplifying, we get:

lim(x,mx)→(0,0) 5x^2/(x^2+5m^2x^2)

Factoring out x^2 from the denominator, we have:

lim(x,mx)→(0,0) 5x^2/(x^2(1+5m^2))

Canceling out the x^2 terms, we have:

lim(x,mx)→(0,0) 5/(1+5m^2)

The limit along the line y = mx is 5/(1+5m^2), which depends on the value of m.

The overall limit:

Since the limits along different paths (x-axis, y-axis, and y = mx) are not equal, the limit as (x, y) approaches (0, 0) does not exist (DNE).

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Answer:

Step-by-step explanation:

a=0.5

Answer:

y = (x+5)/3

Step-by-step explanation:

Isolate y

x = 3y - 5

x + 5 = 3y

(x+5)/3 = y

Answer:

9

Step-by-step explanation:

Answer:

i belive the awnser is 9

Step-by-step explanation:

the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.

Lets take v1 = (1,0,0), v2 = (1,1,0) and v3 = (0,1,0). Neither of the vectors are a multiple of the other, however they dont generate R³ because for example the vector (0,0,1) is not a linear combination of v1, v2 and v3.

Not that, despite not being a multiple of v1 or v3, v2 is a linear combination of v1 and v3, because it is the sum of both of them. Therefore, the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.

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Answer:

I suggest that you use Socratic to solve this. It answers almost every question.

Step-by-step explanation:

Answer: \(g(x) = 3^{x-6}\)

Step-by-step explanation:

Think about it like doing

x - 6 = 0

x = 6

That is how you know that it will be shifted 6 units right (how you can tell the difference between right and left shift)

The cost of building a house with the area 5,425 square feet is $763,125.

The given function is C(x)=85,000+125x.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, x represents the area of a house is 5,425 square feet.

Put x=5425 in the given function, that is

The total cost = C(5425)=85,000+125 × 5425

= $763,125

Therefore, the cost of building a house with the area 5,425 square feet is $763,125.

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Answer:

La longitud de BC es 15 cm y la longitud AB es 45 cm

Step-by-step explanation:

Ecuaciones

Tenemos un segmento AC de longitud 60 cm, dividido en dos segmentos BC y AB tal que:

AB+BC=60 cm

También sabemos que AB=3BC. Reemplazando en la ecuación anterior, tenemos:

3BC+BC=60 cm

Reuniendo términos semejantes:

4BC=60 cm

Despejando BC:

BC=60/4 = 15 cm

Como AB=3BC, entonces

AB=3*15= 45 cm.

La longitud de BC es 15 cm y la longitud AB es 45 cm

Answer:

12 pieces

Step-by-step explanation:

Given the information:

=> total number of  size pieces of granola bar Adrian has is:

= Number of bars * Number of equal parts in each bars

= 3 * 4

= 12 pieces.

Please have a look at the attached photo (lines in the model to find the answer)

Therefore, the probability that 0 < X < 1 is approximately 0.3413, or 34.13%.

If a random variable X is distributed normally with zero mean and unit standard deviation (X ~ N(0, 1)), the probability that 0 < X < 1 can be calculated using the standard normal distribution table or a statistical software.

In this case, we need to find the area under the normal curve between 0 and 1 standard deviations from the mean. Since the standard deviation is 1, we are interested in finding the probability that the value of X falls between 0 and 1.

Using the standard normal distribution table, we can look up the cumulative probability associated with 1 standard deviation from the mean, which is approximately 0.8413. Similarly, we can look up the cumulative probability associated with 0 standard deviations from the mean, which is 0.5.

To find the probability that 0 < X < 1, we subtract the probability associated with 0 from the probability associated with 1:

P(0 < X < 1) = P(X < 1) - P(X < 0) = 0.8413 - 0.5 = 0.3413

Therefore, the probability that 0 < X < 1 is approximately 0.3413, or 34.13%.

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The effect of seeing a square with alternating green and yellow stripes after looking at a square made up of alternating red and blue stripes is due to pairs of ganglion cells that work in opposition.

Ganglion cells are neurons located near the inner surface of the retina, whose axons form the optic nerve. They receive visual signals from bipolar cells and then send them to the brain via the optic nerve.

In order to understand why we see a square with alternating green and yellow stripes after looking at a square made up of alternating red and blue stripes, it's important to know that there are three types of cones in the retina that respond to different wavelengths of light: blue, green, and red.

When we look at the square made up of alternating red and blue stripes for several minutes, the cells that are responsible for perceiving red and blue colors become fatigued, while the green cones continue to respond normally. This creates an imbalance between the signals being sent to the brain, which then interprets the remaining signals as a mixture of green and red. This is why we see a square with alternating green and yellow stripes.

Pairs of ganglion cells work in opposition in this phenomenon because each ganglion cell receives input from both types of cones that are sensitive to a particular color. In the case of the square made up of alternating red and blue stripes, one group of ganglion cells is receiving more input from the red-sensitive cones, while the other is receiving more input from the blue-sensitive cones. When we look at the blank white sheet of paper, these ganglion cells continue to work in opposition, leading to the perception of green and yellow stripes.

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

bquyawvwj2kqko1k12b2b

sec²x

........Hope I helped!..................

Answer:

7× greater than or equal to 50

Step-by-step explanation:

it won't let me put the sign but I think that the correct answer

Step-by-step explanation:

Here,

diameter(d) of the cylinder is 16 yd.

radius of a cylinder is 16/2 yd= 8 yd.

height (h) of a cylinder is 18yd.

now, we use formula for surface area of cylinder,

a= 2.pi.r(r+h)

or, a= 2×3.14×8(8+18)

by simplifying it we get,

The surface area of cylinder is 1306.24 sq.yd.

Hope it helps...

Answer:

The surface area of this cylinder is:

1306.24 square yards

Step-by-step explanation:

  There are 2 types of surface:

then:

total  surface = 2 flat surface + circular surface

ts = 2(п r²) + (п*d*h)

ts = total suface

п ≈ 3.14

d = diameter = 16 yd

r = radius = diameter/2 = 16/2 = 8yd

h = high = 18yd

then:

ts = 2(3.14*8²) + (3.14*16*18)

ts = 2(3,14*64) + (904,32)

ts = 2(200.96) + 904.32

ts = 401.92 + 904.32

ts = 1306.24 yd²

The required, there are 8998912 possible license plates that can be generated using this format.

Here, we have,

There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.

Therefore, there are 8 choices for each of the three digits,

giving us 8 x 8 x 8 = 512 possible combinations for the digits.

Similarly, there are 26 letters that can be used for each of the three letters on the license plate.

Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.

Total number of license plates = number of choices for the digits x number of choices for the letters

= 512 x 17576

= 8998912

Therefore, there are 8998912 possible license plates that can be generated using this format.

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Michael took the return trip at a velocity 33.75 miles per hour.

Let suppose that Michael drove in straight line road and at constant velocity. Therefore, the speed of the vehicle (v), in miles per hour, can be defined as distance traveled by the vehicle (d), in miles, divided by travel time (t), in hours.

First trip

45 = s / 3     (1)

Second trip

v = s / 4       (2)

By (1) and (2):

45 · 3 = 4 · v

v = 33.75 mi / h

Michael took the return trip at a velocity 33.75 miles per hour.

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Answers

2x+3y=4

A=2 , B=3 , C=4

step by step:

2x+3y=2  the slope is -2/3

3y=-2x+2

y=-2/3 x+2

parallel line have the same slope: -2/3

the equation of parallel line that passes through point (2,0) y=mx+b

find b

2(2)+3(0)=b

4+0=b

b=4

the equation will be

2x+3y=4

to check : graph the equations:

Answer:my brother said 3.

Step-by-step explanation:

Answer:

x=1/2

Step-by-step explanation:

Step-by-step explanation:

Given,

D = ( 0 , 12 )

S = ( -4 , 6 )

we know,

x1 = 0 , y1 = 12

x2 = -4 , y2 = 6

and also,

\(d \: = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \)

so, after inserting the values we got,

\( \sqrt{ {(( - 4) - 0)}^{2} + {(6 - 12)}^{2} } \\ \sqrt{ {( - 4)}^{2} + {( - 6)}^{2} } \\ \sqrt{16 + 36} \\ \sqrt{52} = 7.2\)

so, according to the obtained result the ans is 7.2 and in nearest 10th it is 7.

hope this answer helps you dear! take care and may u have a great day ahead...take care!

Answer:

3/6

Step-by-step explanation:

1 2 and 3 are less than 4 so only 3 numbers