what is the probability that a random point on AK will be on BE

Answer:

\(\displaystyle y=\frac{1}{2}x-7\)

Step-by-step explanation:

Perpendicular Lines

Two lines of slopes m1 and m2 are perpendicular if their slopes meet the condition:

\(m_1\cdot m_2=-1\qquad \qquad [1]\)

The slope-intercept form of a line with slope m and y-intercept of b is:

\(y=mx+b\)

The point-slope form of a line with slope m that passes through the point (h,k) is:

\(y-k=m(x-h)\)

We are given the line

\(y=-2x+4\)

From which we can know the value of the slope is m1=-2

The slope of the required line m2 can be calculated from [1]

\(\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{-2}=\frac{1}{2}\)

Now we know the slope and the point (8,-3) through which our line goes, thus:

\(\displaystyle y-(-3)=\frac{1}{2}(x-8)\)

To find the slope-intercept form, operate:

\(\displaystyle y+3=\frac{1}{2}x-\frac{1}{2}\cdot 8\)

\(\displaystyle y=\frac{1}{2}x-4-3\)

\(\mathbf{\displaystyle y=\frac{1}{2}x-7}\)

Step-by-step explanation:

the value of x= 3

.............

Answer:270

Step-by-step explanation:

Length:

U = 3 inches

W = 7 inches

Y = 8 inches

Add them up: 18 inches all together.

Width:

V = 4 inches

X = 7 inches
Z = 4 inches

Add them up: 15

A= L x W —>  15 x 18 = 270

The values of x are = 0, -2, -3

\(x^3 + 5x^2 + 6x = 0\)

\(x^3 + 5x^2 + (2 * 3)x = 0\)

\(x (\frac{x^3}{x} + \frac{5x^2}{x} + \frac{2*3x}{x}) = 0\)

\(x(x^{3-1} +5x^{2-1}+2*3) = 0\)

\(x(x^2+5x+6)=0\)

\(\left \{ {{x=0} \atop {x^2+5x+6=0}} \right.\)

\(\left \{ {{x=0} \atop {x(\frac{x^2}{x} + \frac{2x}{x}) + 3(\frac{3x}{3} + \frac{2*3}{3}) =0 }} \right\)

\(\left \{ {{x=0} \atop {x(x^{2-1} +2) + 3(x+2)=0}} \right.\)

\(\left \{ {{x=0} \atop {x(x+2)+3(x+2)=0}} \right.\)

\(\left \{ {{x=0} \atop {(x+2) (\frac{x(x+2)}{x+2}+ \frac{3(x+2)}{x+2})=0 } \right.\)

\(\left \{ {{x=0} \atop {(x+2) (x+3) =0}} \right.\)

\(\left \{ {{ x=0} \atop {x+2=0}} \atop {x+3=0}} \right.\\\\\)

\(\left \{ {{ x=0} \atop {(x+2) + (-2) = -2}} \atop {(x+3) + (-3)=-3}} \right.\\\\\)

\(\left \{ {{ x=0} \atop {x+2 -2 = -2}} \atop {x+3 -3 = -3}} \right.\\\\\)

\(\left \{ {{ x=0} \atop {x=-2}} \atop {x=-3}} \right.\\\\\)

\(x = (0, -2, -3)\)

Answer: The values of \(x=[0], [-2], [-3]\)

Answer:

We can factor out a 4x from the numerator and a 2 from the denominator, which gives:

(4x(x+1)) / 2( x^2 - 1)

We can then factor the denominator further using the difference of squares formula, which gives:

(4x(x+1)) / 2(x+1)(x-1)

Simplifying this expression further, we can cancel out the (x+1) terms in the numerator and denominator, which gives:

2x / (x-1)

Therefore, 4x^2 + 4x / 2x^2 - 2 simplifies to 2x / (x-1).

Answer:

x+115=180 x=65

90+65+y=180 y=25

Step-by-step explanation:

Answer:

8/27.

Step-by-step explanation:

To find out which class had the greatest fraction of students who preferred vanilla ice cream, we need to compare the ratios of students who preferred vanilla to the total number of students in each class.

For second period class:

Number of students who preferred vanilla = 725

Total number of students = unknown

Ratio of students who preferred vanilla to total number of students = unknown/unknown = undefined

For fourth period class:

Number of students who preferred vanilla = 8

Total number of students = 27

Ratio of students who preferred vanilla to total number of students = 8/27

For sixth period class:

Number of students who preferred vanilla = 30% of total number of students

Total number of students = unknown

Ratio of students who preferred vanilla to total number of students = 0.3*unknown/unknown = 0.3

Therefore, the fourth period class had the greatest fraction of students who preferred vanilla ice cream, with a ratio of 8/27.

Answer:

849x²+109x+24615

Explanation:

Total electricity produced:

→  -17x² +181x + 14453+866x²-72x+10162

group the term like this ↓

→ - 17x²+866x²+181x-72x+14453+10162

same thing here ↓

→ 17x²+866x²+181x-72x+24615

add and subtract terms ↓

→ 849x²+181x-72x+24615

final result will appear like this ↓

→ 849x²+109x+24615

Answer:

tape

Step-by-step explanation:

tape is tape

Hello !

Answer:

\(\boxed{\sf Option\ C \to A=155ft}\)

Step-by-step explanation:

To calculate the area of this figure, we will divide it into three smaller figures as shown in the attached file.

Now that we have three rectangles A, B, and C.

The formula to calculate the area of a rectangle is:

\(\sf A_{rec} = Length\times Width\)

Let's calculate the area of the 3 rectangles using the previous formula :

\(\sf A_A=12\times 5=60ft\)

\(\sf A_B = 7\times5=35ft\)

\(\sf A_C=12\times 5 =60ft\)

Now we can calculate the total area of the figure.

\(\sf A=A_A+A_B+A_C\\A=60+35+60\\\boxed{\sf A=155ft}\)

Have a nice day ;)

Answer:

$3.15

Step-by-step explanation:

Divide the total amount of money Marisa earned by the number of days.

Hope this is helpful!!! :)

Answer:

Marisa earned $3.15 a day.

Step-by-step explanation:

To find this, first we must identify our info. We know that the total for the 5 days of walking a dog was $15.75. So, to find out how much money she earned each day, simply divide $15.75 by 5.

You will get $3.15. That means that Marisa earned $3.15 a day for walking the dog.

Answer:

Distance is 566.21 ft

Step-by-step explanation:

sin 26=h/d

(1)step:0.438=248/d

(2)step:d=248/0.438

(3)step:d=566.21 ft

Answer:

508 ft

Step-by-step explanation:

See attachment.

We need to use trigonometry to solve this, specifically, tangent, which is opposite divided by adjacent.

Here, our angle is 26 degrees, and our opposite side is 248 feet. Let's denote the adjacent side as x. Now, write the equation:

tan(26) = 248 / x

Multiply both sides by x and divide both sides by sin/tan(26):

x = 248 ÷ tan(26) ≈ 508.47 ≈ 508 ft

Answer:

0.075 kJ

Step-by-step explanation:

To calculate the energy used by a 75 Watt light bulb when turned on for one second, we can use the formula:

Energy = Power x Time

where power is measured in watts and time is measured in seconds.

In this case, the power is 75 watts and the time is 1 second, so we can calculate the energy as:

Energy = Power x Time

Energy = 75 watts x 1 second

Energy = 75 joules

Note that joules (J) are the standard unit of energy in the International System of Units (SI). To convert joules to kilojoules (kJ), we divide by 1000. Therefore, the energy used by the 75 watt light bulb when turned on for one second is:

Energy = 75 joules = 0.075 kJ (to the nearest thousandth)

So the answer is 0.075 kJ.

Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

y can be written as the sum of two orthogonal vectors, one in the span of {u} and one orthogonal to u: y = (-2.5, 2.5) + (3.5, 3.5)

To write y as the sum of two orthogonal vectors, we need to find the projection of y onto u (which will be in the span of {u}) and the difference between y and this projection (which will be orthogonal to u).

First, let's find the projection of y onto u:
proj_u(y) = (y·u / ||u||^2) * u

where "·" represents the dot product and "|| ||" represents the magnitude.

y·u = (1)(5) + (6) (-5) = 5 - 30 = -25
||u||^2 = (5) ^2 + (-5) ^2 = 25 + 25 = 50

proj_u(y) = (-25 / 50) * u = -0.5 * (5, -5) = (-2.5, 2.5)

Now, we find the difference between y and this projection:
y - proj_u(y) = (1 - -2.5, 6 - 2.5) = (3.5, 3.5)

Thus, y can be written as the sum of two orthogonal vectors, one in the span of {u} and one orthogonal to u:
y = (-2.5, 2.5) + (3.5, 3.5)

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Answer:

Oh easy...

Step-by-step explanation:

Multiply the numerator on the left by the denominator on the right, and the numerator on the right by the denominator on the left, to solve a proportion. Cross multiplying is the term for this. Simplify the equation, then solve for the variable using the inverse operation, division.

Answer:

I dont see the graphs

Step-by-step explanation:

But thanks for the point lol

It is sampled at a rate 25% higher than the Nyquist rate and quantized into L levels. The maximum acceptable error in sample amplitudes is limited to 0.1% of the peak signal amplitude.

To sketch the amplitude spectrum of g(t), we observe that sinc functions centered at 16 kHz and 10 kHz contribute amplitudes of 16x10³ and 10x10³, respectively, while the cosine component centered at 30 kHz has an amplitude of 20x10³. The horizontal axis represents the frequency (f).

The amplitude spectrum of the sampled signal, within the range -50 kHz to 30 kHz, will exhibit replicas of the original spectrum centered at multiples of the sampling frequency. The amplitudes and frequencies should be labeled according to the replicated components.

The minimum required bandwidth for binary transmission can be determined by considering the highest frequency component in g(t), which is 30 kHz. Therefore, the minimum required bandwidth will be 30 kHz.

For M-ary multi-amplitude signaling within a channel bandwidth of 50 kHz, we need to find the minimum value of M. It can be determined by comparing the available bandwidth with the required bandwidth for each amplitude component of g(t). The minimum M will be the smallest number of levels needed to represent all the significant amplitude components without violating the bandwidth constraint.

To minimize M, we need to select a pulse shape that achieves the narrowest bandwidth while maintaining an acceptable level of distortion. Different pulse shapes can be considered, such as rectangular, triangular, or raised cosine pulses.    

If a raised cosine pulse is used, the roll-off factor determines the pulse shape's bandwidth efficiency. The roll-off factor is defined as the excess bandwidth beyond the Nyquist bandwidth. The required M can be calculated based on the available channel bandwidth, the roll-off factor, and the distortion tolerance.

When using delta modulation with a sampling rate of five times the Nyquist rate, the number of levels (L) and corresponding bit rate can be determined by considering the quantization error and the maximum acceptable error in sample amplitudes. The bit rate will be determined based on the number of bits required to represent each level and the sampling rate.  

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The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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Answer:

The answer would be 80.

Step-by-step explanation:

First you want to add 16 and 24.

Next you want to multiply that answer by 2.

Then you have your answer and I hope this helps

Answer:

b. The quadratic is expressed in standard form; a=8, b= -5, and c=3.

1) Rewrite the given differential equation: The given differential equation is y dx - 6(x + y^8) dy = 0. We can rewrite it as: y dx = 6(x + y^8) dy

2. Separate variables:
Now, separate the variables x and y:
(y/6) dx = (x + y^8) dy

3. Integrate both sides:
Integrate both sides of the equation with respect to their corresponding variables:

∫(y/6) dx = ∫(x + y^8) dy

(1/12)xy = (1/2)xy + (1/9)y^9 + C

4. Solve for x(y):
To find the general solution in form x(y), rearrange the equation: x(y) = 3y^8 + Cy^6

5. Find the largest interval:
To find the largest interval over which the general solution is defined, consider the domain of y.

The general solution is defined for all y except y = 0 (since this would result in a division by zero). Therefore, the largest interval is: (-∞, 0) ∪ (0, ∞)

6. Determine transient terms:
Since the general solution does not contain any terms that tend to zero as y approaches infinity, there are no transient terms. So the answer is: NONE

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Answer:

12+x

Step-by-step explanation:

=-6+1/4x+3(1/4x+6)

=-6+x/4+3(x/4+6)

=-6+x/4+3×(x+24/4)

=-6+x/4+3x+72/4

=-24+x+3x+72/4

=48+4x/4

=4(12+x) /4

=12+x.

hence, answer is 12+x..

Answer:

1x + 12

Step-by-step explanation:

-6 + 1/4x + 3(1/4x + 6)

-6 + 1/4x + 3/4x + 18

-6 + 1x + 18

1x + 12

Answer:

x=1.5 y=-1/3

Step-by-step explanation:

2x-3y=4

2x+8=11

Let's subtract 8 from both sides of the second equation:

2x=3

x=1.5

Substituting this into the first equation, we get:

2(1.5)-3y=4

3-3y=4

-3y=1

y=-1/3

To build a multiple regression model to forecast per capita fuel consumption in gallons (fuelcon) from the given predictors, we can use the fuelcon4 data provided. The model equation can be written as follows:

fuelcon = β0 + β1*drivers + β2*hwymiles + β3*gastax + β4*income + ε

where β0 is the intercept, β1 to β4 are the coefficients for each predictor variable, and ε is the error term.

We can use statistical software like R or Python to estimate the coefficients and obtain the diagnostic statistics. Here is the R code to fit the multiple linear regression model:

# load the data

data <- read.csv("fuelcon4.csv")

# fit the multiple regression model

model <- lm(fuelcon ~ drivers + hwymiles + gastax + income, data = data)

# print the model summary

summary(model)

```

The output of the `summary` function will provide us with the estimates of the coefficients, standard errors, t-values, p-values, and R-squared value, among others. We can use these statistics to evaluate the goodness of fit of the model and check for any potential problems such as multicollinearity or heteroscedasticity.

It is important to note that before building the model, we should check for outliers, missing values, and nonlinearity in the data. We should also assess the assumptions of the regression model, such as normality of errors, constant variance, and independence.

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9514 1404 393

Answer:

  x → 4x

Step-by-step explanation:

Isolate the right-side 'x' and reverse the arrow.

  x → x/4 . . . . . given

  4x → x . . . . . multiply by 4 to get x by itself on the right

  x → 4x . . . . . reverse the arrow

Answer:

yes. They both equal [20]=20

The sweets Candy Bars 1 through 3 and Each individual will get a one - third of a candy bar as  each candy bar is cut into three equal pieces .

A fraction is a percentage or ratio between two numbers that is expressed numerically. Typically, it is expressed as a/b, where a stands for the numerator and b for the denominator. The denominator is the total number of equal parts that make up the whole, while the numerator is the number of equal parts that are being taken into account. Three out of four equal portions, or three-fourths of the entire, are represented by the fraction 3/4, for instance. Mathematicians frequently use fractions, particularly in the areas of algebra, geometry, and arithmetic.

given

Each individual will get a one - third of a candy bar.

A visual representation of this might be the following, where each candy bar is cut into three equal pieces and presented to a different friend:

\(| 1/3 | | 1/3 | | 1/3 |\)

The sweets Candy Bars 1 through 3 and Each individual will get a one - third of a candy bar as  each candy bar is cut into three equal pieces .

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Answer:

A.) 93

B.) 77

C.) 369

Step-by-step explanation:

Answer:

Its the same one that I answered lol

Step-by-step explanation: