Special right triangle need help pls

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 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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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

Answer:

y < 15

Step-by-step explanation:

Check attachment for explanation

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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To solve this equation for v, we need to get v by itself on one side of the equation. To do this, we can subtract 6 from both sides of the equation:

[tex]\displaystyle -\frac{5}{8} - 6= v \\\\-\frac{5}{8} - \frac{48}{8} =v\\\\-\frac{53}{8} =v[/tex]

To convert a fraction in the form of a/b to a mixed fraction, we can divide a by b and then write the quotient as the whole number part of the mixed fraction and the remainder as the numerator of the fractional part, with the denominator being the same as the denominator of the original fraction.

In this case, we have a/b = -53/8. To convert it to a mixed fraction, we can divide -53 by 8: -53/8 = -6 R 5

So, -53/8 as a mixed fraction is -6 5/8.

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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Answer:

To solve for x, we need to isolate x on one side of the equation. We can start by multiplying both sides of the equation by 8:

8 * (X/10) = 8 * (2/8)

Expanding and simplifying the right side:

8 * (X/10) = 2

And multiplying out the left side:

8X/10 = 2

Next, we can multiply both sides by 10 to isolate x:

8X = 20

Finally, dividing both sides by 8:

X = 2.5

Answer:

X = 2.5.

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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We can solve this equation by setting up a system of equations and solving for the constants a, b, and c. Hence, w = 2v1 - 3v2 + 4v3.

Yes, it can.

w = 2v1 - 3v2 + 4v3

We can express w as a linear combination of v1, v2, and v3 by writing the equation w = ax1 + bx2 + cx3, where x1, x2, and x3 are the vectors v1, v2, and v3, respectively, and a, b, and c are constants.

We can solve this equation by setting up a system of equations and solving for the constants a, b, and c.

The equations we need to solve are:

2 = a + b + c

-3 = a + b

4 = a

From this, we can solve for a, b, and c to get a = 2, b = -1, and c = 2.

Hence, w = 2v1 - 3v2 + 4v3.

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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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Answer: If she makes 15 skateboards she will make $250

Step-by-step explanation:

$20(15) - $50=

Multiply the $20 by the 15 skateboards: $20 x 15= 300

300 - $50 = $250

May or may not be correct

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:

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:

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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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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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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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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Two length of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. Given that the pool in this instance is 24 m long and has six loops, the wavelength is 4 m.

Wavelength = Length of Pool / Number of Loops

24 m / 6 loops

= 4 m

Wavelength

= 4 m

Two waves of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. A stationary wave pattern is produced when the two waves collide and interfere with one another. Six loops make up the 24 m-long pool in this instance. As a result, the standing wave's wavelength is equal to the pool's length divided by the number of loops, or 24 m / 6 = 4 m. This indicates that the standing wave's wavelength is 4 metres. Standing waves can be used to determine a wave's speed because they are equal to wavelength times frequency. Understanding how waves behave in various contexts, such as swimming pools, oceans, or other bodies of water, can be helped by this.

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The given polynomials are discussed and grouped into each given category as given below.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

We can now look into each polynomial.

a) x³ + 125

   125 is a cube of 5 and also  x³  is the power of x.

So this is a perfect cube.

b) 8p³ - 27

    8p³ is a perfect cube of 2p and 27 is a perfect cube of 3.

So it is a perfect cube.

c) 12x³-9

    This is neither a cube nor a square.

d) a²-100

   100 is a perfect square and so is a².

So this is a difference of perfect squares.

e) 4m² + 25

4m² is a square of 2m and 25 is a square of 5.

But the operator is +

So this is neither a cube nor a difference of a perfect square.

f) 16x²-9

16x² is a square of 4x and 9 is a square of 3.

Also, the operator is -

So this is a difference of perfect squares.

Therefore the above polynomials are discussed and grouped into each given category accordingly.

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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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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 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 cube of the largest number is < 19683

Step-by-step explanation:

let the three integers be :- x, x+1, x+2

x + (x+1) + (x+2) < 75  (given)

x + x + x + 1 + 2 = 75 (considering that the sum is 75)

3x + 3 = 75

3(x + 1) = 75

x + 1 = 75/3 = 25

x = 24

The largest number is x + 3

x + 3 = 27

(x + 3)^3 = 27^3

= 19683

Answer:

1:5 or in decimal terms 0.2

Step-by-step explanation:

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The value of function f(6) is (35.606, 5.283). Therefore, option D is the correct answer.

When something has a constant rate of change, one quantity changes in relation to the other.

We are given that, f(t) rate of change = df(t)/dt =r(t)

df(t)/dt =r(t) = <[tex]e^\sqrt{t}[/tex], 10cos(t+√t)>

Let us solve for x component as all options have different x components.

x component of r(t)

df(t)/dt =[tex]e^\sqrt{t}[/tex]

∫df(t) = ∫[tex]e^\sqrt{t}[/tex] dt

f(t) = ∫[tex]e^\sqrt{t}[/tex] dt

Let us substitute t=x^2  -----(1)

dt=2xdx

f(t)=∫eˣ × 2xdx

Using integration by parts formula

f(t)=2[x ∫eˣdx- ∫∫ eˣ dx d(x)/dx .dx ∫eˣ+c

f(t) =2[xeˣ-∫eˣdx]+c

f(t) = 2[xeˣ-eˣ]+c

f(t)=2eˣ[x-1]+c

From equation (1) we have x=rtt

f(t)=2[tex]e^\sqrt{t}[/tex][√t-1]+c   -----(2)

Substituting t=2

We have f(2)=<2e, π-7>

2e=[tex]2^\sqrt{t}[/tex][√t-1]+c

2e=[tex]2^\sqrt{t}[/tex]2[√2-1]+c

2e=8.226[0.414]+c

2e=3.407+c

c=2.029

Now solving for f(6) (x-component only)

f(6)=2[tex]e^\sqrt{t}[/tex]6(√6-1)+2.029

= (23.165×1.45)+2.029

= 33.589+2.029

= 35.618

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

The instantaneous rate of change of the vector-valued function f(t) is given by r(t)=<[tex]e^\sqrt{t}[/tex], 10cos(t+√t)>. If f(2)=<2e, π-7>, what is the value of f(6)?

a) <11.582, -5.609>

b) 12.906, 0.163>

c) <30.170, 9.141>

d) <35.606, 5.283>

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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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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