is area = ∫ β α f ( x ) d x as positive, negative or zero? note two vertical lines indicate α and β . select a for positive area, b for negative area and c for zero area.

Out of 100 observations, 10% of them were the number 3.

Percentage is a way of expressing a proportion or a fraction as a part of 100. It is a common method used in everyday life and in various fields, including finance, statistics, and education.

To determine the percentage of time a 3 was observed, you need to first find the number of occurrences of the number 3 in a given set of data. Let's say, you have a set of 100 observations and 10 of them are 3.

To find the percentage of time a 3 was observed, divide the number of occurrences of the number 3 (10) by the total number of observations (100) and multiply the result by 100.

Percentage = (10/100) * 100

Percentage = 10

Therefore, the percentage of time a 3 was observed is 10%.

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The ROE (Return on equity)  of the Roten Rooters, Inc., with following requirements is 16.46%

Given that,

If Roten Rooters Incll. has an equity multiplier of 1.59, a total asset turnover of 1.50 and a profit margin of 6.9%.

To find :  What is its ROE?

What is ROE ?

A metric of financial performance known as return on equity (ROE) is obtained by dividing net income by shareholders' equity. Since shareholders' equity is calculated by deducting a company's debt from its assets, ROE is also referred to as the return on net assets.

ROE = (PM)(TAT)(EM)

ROE = (0.069)(1.50)(1.59) = 0.1646, or 16.46%

Hence, the Roten Rooters, Inc.'s ROE (Return on equity) is 16.46% given the requirements shown below.

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No, because the slope of AB is 5/3 and the slope of CD is -3/4.

The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.

A line's steepness may be determined by its slope. In measuring slopes mathematically, "rise over run" is being used (change in y divided by change in x).

The vertical difference between two places, known as the rise, and the horizontal difference between those same two points, known as the run, is known as the slope. It is referred to as the slope-intercept version of the equation if the equation of a line is expressed as y = mx + b. Slope is indicated by "m". And b is the value in the y-intercept point (0, b).

The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.

Thus, the correct option is: C

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Answer: 42258

Step-by-step explanation:

multiply by 2 because if 1 hour is 21,189 feet 2 hours is 2 times more!

Hope this helps!

Answer:

Um, answer my recently asked question l ol It's called"Their eyes were watching god" and im on ch 5.

Step-by-step explanation:

Answer:

answer my recently asked question please.

If line L passes through point (1, 2, 3) and is perpendicular to the xy-plane,  the coordinates of the points on the line which are at a distance 7 from the point P(3,-1, 5) are (1, 2, 11) or (1, 2, -1).

Equation of the xy - plane is z = 0. So, direction ratio perpendicular to xy - plane is (0,0,1)

So, the equation of line passing point (1, 2, 3) and is perpendicular to the xy-plane is:

          x-1/0 = y-2/0 = z-3/1 = t (say)

x = 1, y = 2 and z = t + 3

Let, (1, 2, t+3) be any point on the line that is at a distance 7 units from the point (3, -1, 5)

Then, ( (1 - 3)² + (2 + 1)² + (t + 3 - 5)²)^1/2 = 7

                                          4 + 9 + (t - 2)² = 49

                                                      (t - 2)² = 36

                                                         t - 2 = ± 6

                                                              t = 8, -4

Hence, the coordinates of the points on the line which are at a distance 7 from the point P(3,-1, 5) are (1, 2, 11) or (1, 2, -1).

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In linear equation, $ 1300 is the cost for 80 employees.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.      

                             The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Given that cost of a company picnic varies directly as the number of employees attending the picnic

Let "c" be the company picnic cost

Let "n" be the number of employees attending the picnic

Therefore,

 cost ∝ number of employee attending picnic

       c ∝ n

   c = kn

Where "k" is the constant of proportionality

c = kn ---------- eqn 1

Given that company picnic costs $487.50 for 30 employees

Therefore substitute c = 487.50 and n = 30

   487.50 = k(30)

  k =   487.50/30

   k = 16.25

Substitute n = 80 and k = 16.25 in eqn 1

    c = 16.25(80)

    c = 1300

Thus $ 1300 is the cost for 80 employees.

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Answer:

So, Lake Erie is 3/8 the size of Lake Superior.

Step-by-step explanation:

To find the size of Lake Erie in comparison to Lake Superior, we need to first find the size of Lake Michigan in relation to Lake Superior. If Lake Michigan is about 7/8 the size of Lake Superior, we can say that:

Lake Michigan / Lake Superior = 7/8

Next, we need to find the size of Lake Erie in relation to Lake Michigan. If Lake Erie is about 3/7 the size of Lake Michigan, we can say that:

Lake Erie / Lake Michigan = 3/7

Now, we can use these two relationships to find the size of Lake Erie in relation to Lake Superior. To do this, we can cross-multiply and simplify:

Lake Erie / Lake Michigan = 3/7

(Lake Erie / Lake Michigan) * (Lake Michigan / Lake Superior) = (3/7) * (7/8)

Lake Erie / Lake Superior = (3/7) * (7/8) = 3/8

So, Lake Erie is 3/8 the size of Lake Superior.

positive value for a causes the fixed point to be unstable; a negative value for a makes it stable; and a value of zero places the fixed point at the origin and makes it stable On a graph.

The fixed point of the system occurs at x* = 3/a when an is positive. The system's eigenvalue is = a, while the system's Jacobian matrix is provided by J = [a]. The fixed point is said to be unstable if an is positive because small perturbations will cause larger departures from the fixed point. If an is positive, then is also positive. When an is low, the fixed point is stable and the eigenvalue is also low. The fixed point is at the origin (x* = 0) when an is zero and the eigenvalue is also zero. This indicates that the fixed point is stable and that the system won't deviate from its starting place. On a graph, the fixed point is at the origin if the slope is zero, unstable if the slope is positive, and stable if the slope is negative. Since positive slopes travel away from the fixed point and negative slopes go closer to the fixed point, the slope's sign reflects how stable the fixed point is. As a result, the fixed point is unstable if an is positive, stable if an is negative, and stable if an is zero, meaning the fixed point is at the origin.

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The mean temperature is excepted to be less than median and the value of 96.725 falls outside of an outlier.

The five number summary for the temperatures of students on a particular day is 96.6, 97.85, 98.25, 98.6, 101.8.

Min=96°

Q1=97.85

Median=98.25

Q2=98.6

Max=101.8°

Bowley skewness is a way to figure out if you have a positively-skewed or negatively skewed distribution One of the most popular ways to find skewness is the Pearson Mode Skewness formula. However, in order to use it you must know the mean, mode (or median) and standard deviation for your data.

=[tex]=\frac{98.6+97.85-2*98.25}{98.6-97.85} \\\\=-0.066[/tex]

The standard deviation of the temperatures measured in degree Fahrenheit will have higher standard deviation.

The data is negatively skewed

Therefore, Mean<Median<Mode.

Thus, the mean temperature is excepted to be less than median.

(b).

We can see the values 96.7, 98.4, 99.2

Inter quartile: The interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

=98.6-97.85

=0.75

=1.5 IQR=1.125

⇒[tex]Q_{1}-1.5*IQR=96.725[/tex]

⇒×[tex]Q_{3}+1.5*IQR=99.725[/tex]

Therefore, the value of 96.725 falls outside of an outlier.

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The required number of bacteria after 17 hours will be 99 bacteria.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
A researcher is studying the growth of bacteria. he starts with 60 of the bacteria. it grows continuously at a rate of 3%per hour.
Let the number of bacteria be y after x hours
y = 60 [1 + 0.03]ˣ
y = 60[1.03]ˣ

Now,
Put x = 17
y = 60[1.03]¹⁷
y = 99

Thus, the required number of bacteria after 17 hours will be 99 bacteria.

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Answer:

y < 15

Step-by-step explanation:

Check attachment for explanation

In order to solve for the missing sides of a right triangle, you need to use the Pythagorean Theorem.

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The measure of PRS is 70°, So correct option is D.

A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, away from a given central point. Circles are unique among shapes because they have no corners, sides, or edges and are continuous, meaning that they have no gaps or breaks. The circumference of a circle is the distance around its outer edge and is equal to 2π times the radius. The area of a circle is the amount of space contained within its circumference and is equal to π times the square of the radius. Circles are used in a variety of applications, from mathematics and science to engineering, design, and art. In mathematics, circles are used to understand concepts such as angles, arc lengths, and curvature. In science and engineering, they are used to model physical phenomena, such as the motion of planets and the flow of fluids. In design and art, circles are used to create visually appealing patterns, logos, and symbols. The circle is considered a symbol of unity, wholeness, and completeness.

In triangle QRS, angle SQR is 20°, so angle QSR is 180° - 20° = 160°. Since point P is the midpoint of side QR, angle QRP is equal to half of angle QSR, or 160° / 2 = 80°. Therefore, angle PRS = 180° - 80° = 100°. So the measure of angle PRS is 100°, making the answer D. 70°.

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If the length, width, and height of a right rectangular prism are halved, the surface area will be reduced by a factor of four.

The surface area of a right rectangular prism can be calculated by adding up the areas of all six of its faces.

To see why, consider that each of the original face's area was given by the product of two of the original dimensions. If each of those dimensions is halved, the area of each face is reduced to one-fourth of its original size. Because there are six faces, the total surface area is reduced by a factor of four.

In other words, if the original surface area was 2 * (44 cm * 22 cm + 44 cm * 77 cm + 22 cm * 77 cm) = 6176 square cm, the surface area of the halved rectangular prism would be 6176 square cm / 4 = 1544 square cm.

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The required retail price is $44 for the markdown of 20% with an original price of $55.

The retail price is calculated by the formula,

retail price = original price - a markdown

Now markdown is calculated from the markdown percentage i.e.,

markdown = (original price) × markdown percentage

Calculation:

The given original price = $55

Markdown percentage = 20% = 0.2

So, the markdown value = $55 × 0.2 = $11

Then, the retail price = original price - a markdown

retail price = $55- $11 = $44

Therefore, the retail price is $44.

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The map scale is printed in the map legend. It is given as a ratio of inches on the map corresponding to inches, feet, or miles on the ground. For example, a map scale indicating a ratio of 1:24,000 (in/in), means that for every 1 inch on the map, 24,000 inches have been covered on the ground.

The function graphed in this problem is a secant/cosecant function.

The secant of an angle is given by the division of one and the cosine of the angle, as follows:

sec(x) = 1/cos(x).

As the cosine is a periodic function varying between -1 and 1, the secant function is periodic, with values with absolute value greater than 1.

The secant function has vertical asymptotes at the values of x for which

cos(x) = 0.

The cosecant of an angle is given by the division of one and the sine of the angle, as follows:

csc(x) = 1/sin(x).

With vertical asymptotes at the values of x for which

sin(x) = 0.

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The probability that 30% and 35% of adults will say that math is the most important subject is 0.618. Hence, option D is the correct answer.

We have been told that the sample is random. In order for this to be true both np = (400)(0.34) = 136 ≥ 10 and n(1 - p) = (400)(0.66) = 264 ≥ 10. Another thing to be noted is that the aforementioned sample is clearly less than 10% of all people. So the sampling distribution is approximately normal where the mean is 0.34 and the standard deviation is -

= σ = [tex]\sqrt{\frac{(0.34)(0.66)}{400} }[/tex] = 0.0237

The z-scores are going to be -

= 0.30 - 0.34 / 0.0237 = - 1.688

=  0.35 - 0.34 / 0.0237 = 0.422

Now, the probability that the sample proportion is -

= (-1.688,.422)= 0.618. Hence, the correct option is option D.

The complete question that you might be looking for is given below.

Thirty-four percent of Americans say that math is the most important subject in school. In a random sample of 400 Americans, what is the probability that between 30% and 35% will say that math is the most important subject?

A. 0.291

B. 0.337

C. 0.382

D. 0.618

E. 0.709

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The correct equation of the linear graph is; y = 1/2x - 3

Linear graph is usually represented in the form of a straight line. To show a relationship between two or more quantities we use a graphical form of representation.

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given graph, we can tell that the y-intercept is c = -3

Now, the slope will be calculated with two coordinates using the formula;

m = (y2 - y1)/(x2 - x1)

Coordinates are (2, -2) and (4, -1)

m = (-1 - (-2))/(4 - 2)

m = 1/2

Thus, equation is;

y = 1/2x - 3

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If the sequence is aₙ = n/2n²+1 then the process to show the sequence is monotone decreasing for n≥1 is shown below .

To show that the Sequence "aₙ = n/2n²+1"  is monotone decreasing for n ≥ 1, we need to prove that for any two consecutive terms of the sequence, the next is always less than or equal to the previous one .

Let's compare two consecutive terms of the sequence, aₙ and aₙ+1:

⇒ aₙ = n / 2n² + 1  

So , aₙ₊₁ = (n + 1)/2(n + 1)² + 1

we have to show that aₙ₊₁ ≤ aₙ, we can subtract aₙ from both sides:

⇒ aₙ₊₁ - aₙ = [(n + 1)/2(n + 1)² + 1] - [n/2n² + 1]  ;

We can simplify this expression and get ;

⇒ aₙ₊₁ - aₙ = (n+1-n)/2(n+1)²+(1-1)

⇒ aₙ₊₁ - aₙ = 1/2(n + 1)²

the fraction ,  1/2(n + 1)² > 0 for all n ≥ 1,
that means ⇒ aₙ₊₁ - aₙ > 0 ; ⇒  aₙ > aₙ₊₁ ;

Therefore,  the sequence " aₙ " is monotone decreasing for n ≥ 1.

The given question is incomplete , the complete question is

A Sequence is given by the formula aₙ = n/2n²+1 . Show the sequence is monotone decreasing for n≥1.

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Considering Moses Road is 7 kilometres long, then that would take Moses roughly 21 minutes and 30 seconds to make the route at his top speed of 21 kilometres per hour.

Speed is referred to as the rate at which an object's location changes in any direction. Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no scale, speed is a scalar number.

Step 1: Determine the total distance travelled (7 km)

Step 2: Determine how long it takes to traverse the distance (7 km/21 km/h = 0.333 h = 20 min).

Step 3: Accounting for the half km/h, add 30 seconds to the overall time (20 minutes + 0.5 minutes = 20.5 minutes).

Step 4: To the closest minute, round the total time (20.5 minutes = 21 minutes).

As a result, at the maximum speed of 21 km/h, Moses will finish the route in around 21 minutes.

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The both integral and differential form of conservation law will be equivalent.

Differentiation and Integration are the two major concepts of calculus. Differentiation is used to study the small change of a quantity with respect to unit change of another.

On the other hand, integration is used to add small and discrete data, which cannot be added singularly and representing in a single value.

Integral and differential forms of the conservation law:

Both the farms are equivalent only. Integral form is applied to a region in spore (control volume). Differential form is formulated for an infinitesimal fluid particle.

Integral form:

for any control volume (Ω),

[tex]$$\begin{aligned}\frac{d}{d t} \int_{\Omega} u d v & =\text { Infher through } \partial \Omega \\& =\int_{\partial \Omega} \ \vec{f} (u) \cdot(-\vec{h}) d A+\int_{\Omega} g d \omega\end{aligned}$$[/tex]

Integrating and changing the above Equation,

We get,

[tex]\frac{\partial u}{\partial t}[/tex][tex]+\nabla \cdot f(u)=g[/tex]

By Divergence theorem,

[tex]$$\begin{gathered}\int_{\delta u} \frac{I}{f} \cdot \vec{n} d A=\int \nabla \cdot \bar{f} d v \\\frac{d}{d t} \int_{\Omega} u d w+\int_{\Omega} \nabla \cdot \bar{f} d v=\int_{\Omega} g d v \\\frac{\partial u}{\partial r}+\nabla \cdot \bar{f}(h)=g\end{gathered}$$[/tex](integral form)

Differential form: for can arbitrary control volume the integrand must be saw yielding the differential Equation.

[tex]& \frac{\partial}{\partial t} \int f \hat{\jmath}+\int P \tilde{v} \cdot d \vec{A} \\[/tex]

[tex]& \int \rho \vec{v} \cdot d \vec{A}=\left(-\left|\rho u-y / \partial x\left(f(x) \frac{d_2}{x}\right) d_y d_z\right|\right. \ )[/tex]

[tex]& \frac{\partial f}{\partial t} d_x d_y d_z=\left(\frac{\partial \beta_u}{\partial x}+\frac{\partial e v}{\partial y}+\frac{\partial e w}{d z}\right) d{_x}d_ y d_z} \\[/tex]

[tex]& 0=\frac{\partial f}{d t}+\frac{\partial P_u}{\partial x}+\frac{\partial P v}{\partial y}+\frac{\partial P w}{\partial z} \\[/tex]

[tex]& \vec{\nabla} \cdot \vec{F}=\frac{\partial A_x}{\partial x}+\frac{\partial A_1}{\partial y}+\frac{\partial A_2}{\partial_2} \\[/tex]

[tex]& \nabla \cdot(P \vec{v})=\frac{\partial P_n}{\partial}+\frac{\partial P_v}{\partial u}+\frac{\partial P_w}{\partial 2} \\[/tex]

[tex]& \left.\frac{\partial s}{\partial t}+\nabla \cdot(A \vec{v})=9\right)[/tex] (Differential form)

From the hint of two equations, we can evaluate that both integral and differential form of conservation law will be equivalent.

Therefore, both integral and differential form of conservation law will be equivalent.

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The unit rate at which the barber cuts the hair is then 16:1.

What is meant by the ratio and rate?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

In contrast, a rate is a comparison of two quantities that may have different units. A rate is a unique ratio that differs somewhat from a ratio. It compares measures with other units. A rate having a denominator of 1 is known as a unit rate.

Given,

   number of haircuts in 2 days = 32

So the number of haircuts in 1 day = 32/2= 16

Therefore the unit rate at which the barber cuts the hair is then 16:1.

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Answer:

The formula d2 + hw could be for an area. The formula is the sum of two terms, d2 and hw. The first term, d2, is the area of a square with side length d. The second term, hw, is the area of a rectangle with length h and width w. Therefore, the formula is for the total area of the square and the rectangle combined.

Step-by-step explanation:

Answer:

If 3 brownies require 3/4 cups of flour, then 12 brownies will require 12/3*(3/4) = 3 cups of flour.

Step-by-step explanation:

Answer:

3 cups of flour

Step-by-step explanation:

We know

3/4 cups of flour = 3 brownies

? = 12 brownies

12 brownies are 4 times 3 brownies, so we take 3/4 cups of flour times 4

3/4 times 4 = 3 cups of flour

So, you need 3 cups of flour for 12 brownies

The polynomial function can be written as:

p(x)=  (x - 1)*(x + 6)

So the correct option is A.

Remember that a polynomial of degree N with the zeros {x₁, x₂, x₃, ...} can be written as:

p(x) = (x - x₁)*(x - x₂)*...

Here we can see that the zeros are x = 1 and x = -6, 2 zeros means that we will have two factors.

Then the polynomial can be written as:

p(x) = (x - 1)*(x - (-6))

p(x) = (x - 1)*(x + 6)

Then the correct option is A.

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The separation between a 6.8 kg particle and a 3.7 kg particle in order for their gravitational attraction to have a magnitude of 2.9 ✕ 10^−12 N will be 24 m.

m₁ = 6.8 kg

m₂ = 3.7 kg

F = 2.9×10^−12 N

We want to determine the distance r between both particles. The gravitational force on particle 2 due to particle 1 has the same magnitude as the force on particle 1 but in the opposite direction. If a distance r separates two masses, then the magnitude of the gravitational force acting on each due to the presence of the other is given by

F = Gm₁m₂/r²     Eqn(1)

Where G is the gravitational constant and equals 6.6×10^−11 N⋅m²/kg².

By solving equation (1) for r, we get

r = √(Gm₁m₂/F)

Now we can plug our values for m₁, m₂ and G into equation (2) to get the separated distance r

r = √(Gm₁m₂/F)

= √{[(6.6×10^−11 N⋅m²/kg²)(6.8 kg)(3.7 kg)]/(2.9×10^−12 N)}

​= 24 m

The gravitational force is very small due to the small masses where this force is indistinguishable.

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Answer:

1:5 or in decimal terms 0.2

Step-by-step explanation:

hope this help

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