jogger runs around a circular track of radius 70 ft. let (x,y) be her coordinates, where the origin is the center of the track. when the jogger's coordinates are (42, 56), her x-coordinate is changing at a rate of 18 ft/s. find dy/dt.

The slope of linear graph is 4 which means the rate of prinitng program copies is 4 copies per minute.

What is formula for slope?

The slope of the line between two points (x₁, y₁) and (x₂, y₂) is

m = (y₂ - y₁)/(x₂ - x₁)

Slope of a line signifies rate of change between two quantities.

According to the given question:

(Check the graph attached below)

From the graph the two points we can consider for finding the graph are (0,0) and (3, 120)

Putting these values in the formula for slope

m = (y₂ - y₁)/(x₂ - x₁)

   = (120 -0)/(30 - 0)

   = 4

Hence slope of the line in the situation tells that the rate of printing program is 4 copies per minute.

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The correct relation is that both the angles are corresponding angles.

Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.

Given is an arrangement of streets in the form of two parallel lines and a street acting as a transversal.

The angle of library and angle of school are corresponding angles, and corresponding angles between parallel lines are congruent.

Since,  angle of library = 42°

angle of school =  angle of library

Therefore, angle of school = 42°

Hence, The correct relation is that both the angles are corresponding angles.

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A random selection of an Endure All battery has a 10.56% probability of lasting more than 550 hours.

The Z score is utilized to calculate how far the raw score deviates from the mean.

The Z score is calculated as follows:

z = (x - μ)/σ

Given that x > 550 and μ = 500, σ = 40:

z = 550 - 500 / 40

z = 1.25

Following the normal distribution chart,

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Therefore, there is a 10.56% chance that a randomly chosen Endure All battery would survive longer than 550 hours.

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Answer: 13.33

Step-by-step explanation: I could be wrong

(C) A parabola is the best representation of the situation that a second-degree polynomial regression equation would be used to mimic.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

A parabola can be described using a point and a line.

The situation that a second-degree polynomial regression equation would be used to simulate is best described by a parabola.

The phrase "parabolic move" originated as trader jargon.

It describes when a stock experiences an increase in price that resembles the right side of a parabolic curve: A parabolic move happens when the stock's price rises at an exponentially faster rate.

Therefore,(C) a parabola is the best representation of the situation that a second-degree polynomial regression equation would be used to mimic.

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Answer:



Step-by-step explanation:

GraphA shows the quadratic equation with complex roots.

Answer:

Step-by-step explanation:

The area of the triangle is 31.54 square units

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

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Pareto distribution is a member of a scale family referring fixed values of the shape parameter, it is trivially closed under scale transformations.

The Pareto distribution is a power-law probability distribution used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena. It was initially applied to demonstrate the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population. The pareto principle or 80-20 rule states that 80% of outcomes are due to 20% of causes. Pareto distribution is a member of the scale family distribution which is parameterized by a scale parameter. The larger the scale parameter, the more spread out the distribution.

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Answer:

y = -3x + 13

Step-by-step explanation:

Assuming the line is linear, you can use the point-slope equation of a line.

(y - y) = m (x - x)

The y and x variables come from the points on the line. Points are written in the form (x, y). In the point (2,7), 2 is x and 7 is y.

1. Plug your points in.

(7 - - 2) = m (2 - 5)

2. Solve for m (the slope)

(7 + 2) = m (2 - 5)

(9) = m (-3)

9 = -3m

m = -3

3. Write an equation of the line with the slope you found.

You can write this equation in different forms, but I'll use the slope-intercept form.

y = mx + b

You'll have to find b, the y-intercept. You can plug one of your points in for x and y as well as your slope, m, and solve for b.

7 = -3(2) + b

7 = -6 + b

b = 13

Therefore, the equation is y = -3x + 13

The square root of open paren x negative 3 close paren squared =

3 negative x​  negative x times the absolute value of x is greater than 0.

Let the equation be: |x−3|=3−x|x−3|=3−x

When x>3x>3, then RHS is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.

When x≤3x≤3, then LHS=|x−3|=−x+3=3−x=RHSLHS=|x−3|=−x+3=3−x=RHS

x≠3x≠3

Thus,

−x|x|>0−x|x|>0, this inequality implies that x<0x<0, hence x<3x<3.

Hence option b becomes the correct option i.e, negative x times the absolute value of x is greater than 0.

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.

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The correct option is independent of, dependent on for the given sets of hypothesis H0: Pass/fail rates are _____ school. H1: Pass/fail rates are _____school.

A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis). A straightforward hypothesis is a claim that expresses the relationship between precisely two variables. a dependant and a single independent. Take the statement "Smoking is a significant cause of lung cancer" as an example. Smoking is an independent variable that influences the dependent variable, lung cancer.

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The definition of the gradient vector for point a to b is defined below.

Vector:

In math vector value consists of magnitude and direction.

Given,

Here we need to find the gradient vector of point a or point b.

According to the definition of vector, a multidimensional input have partial derivatives, you might wonder what the full derivative of such a function is. Here in the case of scalar-valued multivariable functions, meaning those with a multidimensional input but a one-dimensional output, the answer is the gradient.

Where as the gradient of a function f, denoted as ∇f,

Where f, is the collection of all its partial derivatives into a vector.

Here the point a and b is more horizontal because of the partial derivative nature of vector.

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Answer:

b

Step-by-step explanation:

Answer:

The answer should be (8,0)

The value of x is 122°.

The value of y is 130°.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

The figure has two parts.

One part is a triangle.

Another part is a heptagon.

We see that,

The three angles sum 180 degrees.

Two angles are equal inside the triangle.

2m + 80 = 180

2m = 180 - 80

2m = 100

m = 50

Now,

y + 50 = 180

y = 180 - 50

y = 130

Now,

The sum of the heptagon angles is 900.

Three angles are the same.

i.e 3x

Two angles are the same.

i.e 130 + 130 = 260

260 + 3x + 135 + 140 = 900

3x + 535 = 900

3x = 900 - 535

3x = 365

x = 365/3

x = 122

Thus,

The value of x is 122°.

The value of y is 130°.

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The statistic's bias is a quality that the statistic does not display, according to the Central Limit Theorem for proportions.

Central limit theorem:

According to the central limit theorem in statistics, samples will be normally distributed and their means will be roughly equal to those of the entire population when the big sample size has a finite variance.

Given,

A certain statistic The population parameter d is being estimated using the function d. D's predicted value is not the same as D.

Find the property that does d display in this case.

According to the Central Limit Theorem, the following is true for a proportion p in an n-person sample:

Value anticipated, μ = p

Standard deviation: s = √p(1 - p) /n

Therefore,

The statistic is biased because the expected value in this case differs from the expected.

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Answer: y = 16807

Step-by-step explanation:

7 * 7 * 7 * 7 * 7 * 7 = 117649

7^16807 = 117649

Answer: 5/3 or 1.67

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/6

The conversion factor you should use to adjust your recipe for the new amount is 6.

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.

Given: original serving = 50                        8-ounce serving            

required new serving = 200                     12-ounce serving

Original serving = 50×8 ounce = 400 ounce

Required serving = 200×12 ounce                          

 = 2400 ounce

As we know, conversion factor = {Required Yield} ÷ {Original Yield}

∴ Conversion factor =2400 ÷ 400

∴  Conversion factor = 6

Conversion factor is greater than 1 when required yield is supposed to be greater than original yield and conversion factor is less than 1 when required yield is less than original yield.

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The answer should be 18cm

Here is why I think that:

On the ruler, you should count from 9 to 26

9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26.

1,  2,   3,  4,   5,  6,   7,   8,   9, 10, 11, 12,  13,  14, 15, 16,  17,   18.

The total tick marks from 9 to 26 is = to 18

(I know that R is resting above the number eight, do not count that one, many people make that mistake)

Please let me know in the comments if

somehow my calculation is wrong.

If the pressure is increased to 19 pounds per square inch, then the volume is 368.42 cubic inches

The volume of the gas = 500 cubic inches

The pressure = 14 pounds per square inch

The volume of a gas in a container varies inversely proportional with the pressure on the gas.

V ∝ 1/P

Where V is the volume and P is the pressure

Then,

V = k/P

Where k is the constant

500  = k/14

k = 500 × 14

k = 7000

The pressure of the gas = 19 pounds per square inch

Volume = 7000 /19

= 368.42 cubic inches

Therefore, the volume is 368.42 cubic inches

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Answer:

Temperature of ch4 will be 150K

given :-

[tex]\sqrt{2} speed of 02 = 448.8[/tex]

u.avg. = [tex]\sqrt{8rt/\pi m} \\[/tex]

u.avg ch4 = [tex]\sqrt{8rt1/\pi 16}[/tex]

hence , mass of ch4 = 12 +4 = 16

Methane (US: MEH-thayn, UK: MEE-thayn) is a chemical compound with the chemical formula CH4 (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas.

The molar mass of oxygen atom  O

O

 is 15.99

This is only the mass of 1 oxygen atom so the molar mass of oxygen molecule  O is 15.99

is double the number, i.e. approximately 32

u.avgO2 = [tex]\sqrt{8r(300)/\pi (32)}[/tex]

u.avgch4 = u.avgo2

[tex]\sqrt{8rt1/\pi 16}[/tex] = [tex]\sqrt{8r(300)/\pi (32)}[/tex]

==> t1/16 = 300/32

==> t1 = 150 K

They have same average velocity when the temperature of CH4 is 150 K

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Answer:

A) y=0.5x+10 C) 17.5 dollars (don't forget your units)

Step-by-step explanation:

a) 0.5 is the price paid per song, or x, and 10 is the price that does not change for a month, so we can say that y=0.5x+10

c) to download 15 songs, we substitute x by 15

y=0.5(15)+10

y=7.5 + 10

y=17.5

and for b, im sorry but I cannot graph here.

The slope of the line is going to be m = 163.

Here, we have been told that the sum of the numbers is going to be -

= ∑[tex]w _{k}[/tex]= 3 + 504i (i)

The other set of complex numbers is (z₁, z₂, ....[tex]z_{k}[/tex]) and their sum is going to be = ∑[tex]z_{k}[/tex]= 3 + 504i (ii)

If we write the number 3+504i in the standard form for complex numbers i.e., a+bi with respect to the summations, we get -

=  ∑[tex]a_{k}[/tex]= 3 (III)

= ∑[tex]b_{k}[/tex]= 504 (Iv)

The standard equation is of the form, y = mx+3. Substituting the polar coordinates, we get -

= [tex]b_{k}[/tex] = m[tex]a_{k}[/tex] + 3

Now, if we use all of the given values in equations (iii) and (iv) for k, we get -

= 504 = 3m + 15

Now, on simply solving for m, we get -

= 3m = 504 - 15 = 489

= m = 489/3

= m = 163

Henceforth, we find out that the slope of the line, m is 163.

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Answer:

Step-by-step explanation:

first, you have to divide the total cost of the passes by the number of teachers and students combined. Then you must multiply the individual cost of the pass by the number of students. Finally, you have to take the total cost for student passes and add it to the cost of the lunches, then you answer.

Applying the definition of an isosceles triangle, the measure of angle P = 10.5°.

If a triangle has two sides that are of the same length, then the triangle is an isosceles triangle. Thus, the angles that are opposite the two equal sides of an isosceles triangle are called the base angles, and they are therefore congruent to each other.

Given that triangle PQR has two equal sides, QR ≅ PQ, it means it is an isosceles triangle, therefore its base angles, ∠P ≅ ∠R.

Therefore:

m∠Q = 159° [given]

m∠P = 1/2(180 - 159)

m∠P = 1/2(21)

m∠P = 10.5°

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