Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?

The average rate of change of [tex]f(x)[/tex] on [tex]12\le x\le36[/tex] is the difference quotient

[tex]\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}[/tex]

(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].

CuSO₄ flows into the tank at a rate

[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]

and flows out at a rate

[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]

and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation

[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]

(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.

[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]

The integrating factor is

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]

Distributing [tex]\mu[/tex] on both sides gives

[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]

and the left side is now the derivative of a product,

[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]

Integrate both sides. By the fundamental theorem of calculus,

[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]

The first term on the right vanishes since [tex]C(0)=0[/tex]. Then

[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]

[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]

The remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)

The expression is given as:

x^2y - 2xy - 24y

Factor out y from the expression

y(x^2 - 2x - 24)

Expand the equation

y(x^2 + 4x - 6x - 24)

Factorize

y(x - 6)(x + 4)

Hence, the remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)

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Answer:

option 4

Step-by-step explanation:

F = [tex]\frac{kxy}{z}[/tex]

k is the constant of variation

• if the variables are on the numerator they vary directly

• if the variables are on the denominator they vary inversely

In this case F varies directly with x and y ( variables on numerator ) and inversely with z ( variable on denominator )

By definition of perimeter, direct observation and Pythagorean theorem, the perimeter of kite OBDE is 38 units. (Correct choice: C)

In geometry, the perimeter is the sum of the lengths of the sides of a figure.  Herein we must determine the perimeter of a quadrilateral, the kite OBDE, that is, the sum of the lengths of its four sides:, which can be found both by direct observation or by the use of the Pythagorean theorem.

Please notice that the quadrilateral has an axis of symmetry passing through the points O and D, which implies that OB = OE and BD = DE. The length of sides BD and DE is 6 units and the length of the sides OB and DE are:

OB = DE = 0.5 · √(24² + 10²)

OB = DE = 13

Lastly, the perimeter of kite OBDE is p = 2 · 6 + 2 · 13 = 38 units.  

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Answer:  C. 38 units

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!!  :)

Just did it and got it correct!

Answer:

3, 1, - 1, - 3, - 5

Step-by-step explanation:

using the recursive formula and f(1) = 3 , then

f(2) = f(1) - 2 = 3 - 2 = 1

f(3) = f(2) - 2 = 1 - 2 = - 1

f(4) = f(3) - 2 = - 1 - 2 = - 3

f(5) = f(4) - 2 = - 3 - 2 = - 5

first 5 terms are 3, 1, - 1, - 3, - 5

To solve this question, we simply need to divide the total amount of students by 8% to find out how many students were absent and how many were present.

However, we can't simply multiply it by 8%, so we need to turn that into a decimal.

8% - 0.08

Multiply:

355 x 0.08

= 28.4

Round:

28 kids were absent

Subtract:

355 - 28

= 327

This means that 28 kids were absent, and 327 kids were present.

Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.

Given the data in the question;

Since angle ABD and angle DBC are adjacent angle, there addition will give us the value of angle ABC.

∠ABD + ∠DBC = ∠ABC

We substitute in the given values

61° + 59° = ∠ABC

∠ABC = 120°

Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.

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The angle the pole makes with the tent is 39.7°.

Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.

Let θ represent the angle the pole makes with the tent.

Using trigonometric ratios:

Therefore, the angle the pole makes with the tent is 39.7°.

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Cheetahs population will be more affected by genetic drift

Genetic drift is the change in a population's frequency of an existing gene variant brought on by chance. Gene variations may totally vanish due to genetic drift, hence reducing genetic variation. Additionally, it may lead to the considerably greater frequency and even fixation of previously rare alleles.

Random drift is a result of recurrently small populations, drastic population reductions known as "bottlenecks," and founder events in which a new population is created from a small number of individuals.

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Step-by-step explanation:

x:y=0.75:0.90

Here,

Dividing by the value of y=0.90,

x:y=0.75/0.90:0.90/0.90

=5/6:1

Similarly,

y:z=1/3:1/4

Dividing by 1/3,we get,

y:z=1:3/4

Now,

X:y:z=5/6:1:3/4

Multiplying by both value of y,0.90×1/3=3/10

x:y:z=5/6×3/10:1×3/10:3/4×3/10

By solving this,

The probability that the machine produces fewer than 5 defective widgets in a production run of 100 items is 0.10

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 5 widgets.

It has a 0.07 defective rate.

Defective rate fewer than 5

Total Probability = P of 4 defective + P for 3 defective + P for 2 defective + P for  1 defective.

Total Probability = 4/100 + 3/99 + 2/98 + 1/97

Total Probability ≈ 0.10

Therefore, the required probability for fewer than 5 defective rate is 0.10

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The 15th term in the given A.P. sequence is a₁₅ = 33.

According to the statement

we have given that the A.P. Series with the a = 5 and the d is 2.

And we have to find the 15th term of the sequence.

So, for this purpose we know that the

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

And the formula is a

an = a + (n-1)d

After substitute the values in it the equation become

an = 5 + (15-1)2

a₁₅ = 5 + 28

Now the 15th term is a₁₅ = 33.

So, The 15th term in the given A.P. sequence is a₁₅ = 33.

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By using what we know about right triangles, we conclude that the height is 11ft.

We can think of this as a right triangle.

Where the length of the escalator is the hypotenuse

We know that the angle of depression is 42.51°, then the top angle of our right triangle is:

90° - 42.51° = 47.49°

Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Replacing what we know:

cos(47.49°)  = height/16ft

cos(47.49°) *16ft = height = 10.8ft

Rounding to the nearest foot, we get:

height = 11ft

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Answer:

cashier needed to divide by 1000, not 3.

Step-by-step explanation:

there are 1000ml in one liter. in order to find the amount of liters, youd have to divide the milliliters by 1000. its only after then that you can multiply by $2. answer would be $36

Answer:

-3

Step-by-step explanation:

If you reflect over the y-axis and then move 2 units to the left(x-2), then ABCD will be 3 units above EHGF. Since you need to move it down 3 units to map ABCD onto EHGF, you will need to do y-3, which is the same as y+-3

Answer:

Step-by-step explanation:

Answer:

i think no 3 hasexactly one 0

The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.

Note that this is simple probability.

Hence probability of the 75% football starts selected randomly where the chance is 93% =

75% x 93%

= 69.75%

The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:

Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.

Recall that the total population is 100%.

From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.

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correct answer is 28.

If the mean of four numbers is 25 and three numbers are 36, 12 and 24 then fourth number is 28.

given terms are:

first number =36

second number=12

third number=24

fourth number=?

let us assume the fourth number be x.

we know the formula to find mean is:

Mean=addition of given terms / total number of terms

According to given statement, we put the values in above equation and we get,

25=(36+12+24+x) / 4

By rearranging, we get

36+12+24+x=100

72+x=100

x=100-72

x=28

so, the fourth number is 28.

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Answer:

a^2+b^2=c^2

Step-by-step explanation:

leg1=a

leg2=b

hypotenuse=c

a^2+b^2=c^2

Answer:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Step-by-step explanation:      

Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  [tex]\frac{1}{3}[/tex].

A linear equation o line can be expressed in the form y = mx + b.

where

Perpendicular lines are lines that intersect at right angles or 90° angles.

Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -3. So:

(-3)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-3)

slope perpendicular line=  [tex]\frac{1}{3}[/tex]

Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  [tex]\frac{1}{3}[/tex].

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Step-by-step explanation:

1. Entrance of Head of State and IOC President

2. Playing of the national anthem

3. The parade of the athletes

4. The symbolic release of doves

5. Olympic Laurel Award

6. Official Speeches

7. Opening of the Games

8. Raising the Olympic flag and playing the Olympic Anthem

9. Athletes, judges and coaches’ oath

10. Lighting of the Olympic flame

11. The artistic programme

The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.

Hence, f(-3/5) = 101/25.

Given the function; f(x) = ( 8x² - 2x + 4 ) / 2

To determine the value of the function when x = -3/5, we simply replace the variable x with -3/5 in the function.

f(x) = ( 8x² - 2x + 4 ) / 2

f(-3/5) = ( 8(-3/5)² - 2(-3/5) + 4 ) / 2

Divide each term by 2

f(-3/5) = 4(-3/5)² - (-3/5) + 2

f(-3/5) = 4(9/25) - (-3/5) + 2

f(-3/5) = 36/25 +3/5 + 2

f(-3/5) = ( 36 + 3×5 + 2×25 ) / 25

f(-3/5) = ( 36 + 15 + 50 ) / 25

f(-3/5) = 101/25

The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.

Hence, f(-3/5) = 101/25.

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Answer:

168 square inches

Step-by-step explanation:

A = BH

or

Area = Base x Height

In other words multiply 12 and 14.

The grid of numbers with a row and column sum of 30 is

3   15  12

17   11   2

10  4   16

The grid in the question has a row sum and column sum of 15

The question implies that we create a similar grid with a row sum and column sum of 30

Represent the grid as follows:

a    b   c

d    e    f

g   h    j

So, we have the following sum of rows

a + b + c = 30

d + e + f = 30

g + h + j = 30

And, we have the following sum of rows

a + d + g = 30

b + e + h = 30

c + f + j = 30

Using trial by error, we have:

3 + 15+ 12  = 30

17 + 11 + 2 = 30

10 + 4 + 16 = 30

When the columns are added, we have

3 + 17 + 10 = 30

15 + 11 + 4 = 30

12 + 2 + 16 = 30

Hence, the grid of numbers is

3   15  12

17   11   2

10  4   16

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Answer:

600

Step-by-step explanation:

since it is a right triangle based pyramid, 2 of them will make a cube. so, it is bwh / 2.

base = 24

width = 10

height = 5

volume = 1200

volume of pyramid = 600

Z = 1.555 should be used

If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.

Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.

the zα/2 value of z0.06.

This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.

The standard score (more commonly referred to as a z-score) is a very useful statistic because it

(a) allows us to calculate the probability of a score occurring within our normal distribution and

(b) enables us to compare two scores that are from different normal distributions.

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Answer:

The scale factor is 1/5.

Step-by-step explanation:

You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached.  I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15.  What do I need to multiple 3 by to get 15?  5.  That is the scale factor from the little triangle to the big triangle.  If I go the other way, the scale factor is the reciprocal of 5 or 1.5

Answer:

120

Step-by-step explanation:

seema 150 marbles

rani 20 more marbles

alok 50 less marble

150+20=170_rani

170-50=120_alok