If a random variable is characterized by (infinitely) uncountable values within any interval, it is known as ________ variable

Answer:

[tex]y = -\frac{2}{3}x + 490[/tex]

gradient = = [tex]-\frac{2}{3}[/tex]

y-intercept = [tex]490[/tex]

Step-by-step explanation:

• The slope-intercept form of an equation takes the general form:

[tex]\boxed{y = mx + c}[/tex],

where:

m = slope,

c = y-intercept.

• We are given the equation:

[tex]2x + 3y = 1470[/tex]

To change this into the slope-intercept form, we must make y the subject:

[tex]3y = -2x + 1470[/tex]          [subtract [tex]2x[/tex] from both sides]

⇒ [tex]y = -\frac{2}{3}x + \frac{1479}{3}[/tex]        [divide both sides by 3]

⇒ [tex]y = -\frac{2}{3}x + 490[/tex]

• Comparing this equation with the general form equation, we see that:

m = [tex]-\frac{2}{3}[/tex]

c = [tex]490[/tex].

This means that the gradient is [tex]\bf -\frac{2}{3}[/tex], and the y-intercept is [tex]\bf 490[/tex].

Answer:

D. 195

Step-by-step explanation:

Answer:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x[/tex]

Rewrite 9 as 3²  and rewrite the 3/2 exponent as square root to the power of 3:

[tex]\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x[/tex]

Integration by substitution

[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]

[tex]\textsf{Let }x=3 \sin \theta[/tex]

[tex]\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}[/tex]

Find the derivative of x and rewrite it so that dx is on its own:

[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta[/tex]

[tex]\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta[/tex]

Substitute everything into the original integral:

[tex]\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}[/tex]

Take out the constant:

[tex]\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]

[tex]\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}[/tex]

[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:[/tex]

[tex]\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}[/tex]

[tex]\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:[/tex]

[tex]\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

Learn more about integration by substitution here:

https://brainly.com/question/28156101

https://brainly.com/question/28155016

The sum of the length of the overall pattern in the given cartesian coordinate is calculated as; 44

We are told that The final line on the plan is parallel to the y-axis and passes through x = -10

Now, looking at the pattern, the lengths of each side are as follows;

1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5

Thus, the sum of the length of the overall pattern is calculated as;

1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 = 44

Therefore we can conclude from all the deductions and calculations above that the sum of the length of the overall pattern in the given cartesian coordinate is calculated to be; 44

Read more about Cartesian plane at; https://brainly.com/question/2141683

#SPJ1

Answer:

read below or other answer

Step-by-step explanation:

2 [{2-2(2÷2-2)} ÷2]÷2​

2 [ { 2 - 2 ( 1 - 2 ) } ÷ 2 ] ÷ 2

2 [ { 2 - 2 ( - 1 ) } ÷ 2 ] ÷ 2

2 [ { 2 + 2 } ÷ 2 ] ÷ 2

2 [ 4 ÷ 2 ] ÷ 2

2 ( 2 ) ÷ 2

4 ÷ 2

2 divided by 2

Answer: 2

Step-by-step explanation:

Answer:

Area = (a² -5a) in²

Perimeter = (4a -10) in

Step-by-step explanation:

Let the length of the rectangle be a.

Given that, its width is 5 in less than the length.

So,

length ⇒ a

width ⇒ (a - 5)

First, let's find the area of the rectangle.

Area = length × width

Area = a ( a - 5 )

Solve the brackets.

Area = (a² -5a) in²

Now, let us find the perimeter of the rectangle.

Perimeter = 2 ( l + w )

Perimeter = 2 ( a + a - 5 )

Perimeter = 2 ( 2a - 5 )

Perimeter = (4a -10) in

The number of bags of candy and cookies sold by the drama club is 4 and 10 respectively

let

The equation:

8.50x + 4.50y = 79

y = x + 6

Substitute x = y + x into

8.50x + 4.50y = 79

8.50x + 4.50(x + 6) = 79

8.50x + 4.50x + 27 = 79

8.50x + 4.50x = 79 - 27

13x = 52

x = 52/13

x = 4

Recall,

y = x + 6

y = 4 + 6

y = 10

Therefore, the number of bags of candy and cookies sold by the drama club is 4 and 10 respectively.

Learn more about simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

Answer:

140°

Step-by-step explanation:

The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)

20 + 120 = 140

Answer:

y= 140

Step-by-step explanation:

first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.

In this situation, the cases are the bags or each piece of baggage.

In statistics, the word case is used to refer to the individual from which data is collected. For example, in a study about students' performance, the cases are each of the students.

Considering the administrators will need to weight and record each bag, the cases are each piece of baggage.

Note: This question is incomplete; here are the missing options:

A. Number of bags weighing more than 75 pounds.

B. Average weight of the bags.

C. Each piece of baggage.

D. The airport administrators.

Learn more about statistics in https://brainly.com/question/8058700

#SPJ1

Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.

Then substitute the values of p and q into p+2q to get -10

❄ Hi there,

let us revise the two rounding rules before getting down to the actual process of rounding.

[tex]\sf{Rules:}[/tex]

Let's see these rules in action!

The number is – [tex]219.2[/tex].

Nearest whole number – [tex]219[/tex], which is followed by a number between 0 and 4, so we just drop that number :

[tex]\sf{219.2- > > 219}[/tex]

❄

Answer:

3:10

10:1

8:1

100:7

Step-by-step explanation:

900:3000

300:1000

3:10

80:8

10:1

2000:750

8:1

100:7

Since this is the result of the second function, hence equations I and II are inverse of each other.

Inverse of a function

Inverse of a function is s a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

Given the function f(x) = 3x

Find its inverse

Replace with y with x

y = 3x

x =3y

Make y the subject of the formula

3y = x

y = x/3

Since this is the result of the second function, hence equations I and II are inverse of each other.

Learn more on inverse of a function here: https://brainly.com/question/2873333

#SPJ1

The smaller number that we can take is x = 14, and in that case, the value of the other number is y = 34

First, we have two numbers, x and y, such that:

y = 6 + 2*x

"the first number is 6 more than 2 times another number".

Now we know that the sum of these two numbers is smaller than 50, then we can write:

x + y < 50

Replacing y by the above equation we get:

x + 6 + 2x <  50

3x + 6 < 50

Now we can solve that inequality for x:

3x < 50 - 6 = 44

x < 44/3 = 14.6

And x can only be a whole number, then:

x ≤ 14

The smaller number that we can take is x = 14, and in that case, the value of the other number is:

y = 6 + 2*14 = 34

If you want to learn more about inequalities:

https://brainly.com/question/25275758

#SPJ1

Answer:

16u²

Step-by-step explanation:

It is a regular parallelogram

we have points (3, 4) and (4, 0).

we also have the origin which is (0, 0) and the difference between (0, 0) and (4, 0) on the x axis is 4 and since it is a regular shape, that means the top right corner = (3, 4) + (4, 0), so it is (7, 4). we know the base is 4 now. the vertical height = (7, 4) - (1, 0) which is (6, 4). now we are looking at difference in y. which is between (4, 0) and (6, 4), so the difference is 4.

now we just do 4 x 4 since it is bh and you get 16 units ²

Answer:

We note that,

x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³

now we can use binomial series on (1+x²)²ᐟ³

(1+x²)²ᐟ³ = ( 1+2x²/3+((2/3)*(2/3 -1)/2) x⁴ + ((2/3)*(2/3 -1)(2/3–2)/6) x⁶ +o(x⁶) =

= 1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶)

The last step is to differentiate,

x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³

= (3/4) d/dx (1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶) )

= (3/4) ( 0 + (4/3)x - 4/9 x³ + 24x⁵/81 + o(x⁵))

= x - x³/3 + 2x⁵/9 + o(x⁵)

The complete Question is- How do I find the Maclaurin series using binomial series in the function f(x) = x/³√1+x^2?

Learn more about binomial series here:

https://brainly.com/question/14004514

#SPJ4

Step-by-step explanation:

every single person will do 1/4 of each job.

divide into 2 group and each person will do half of one job and half of another.

10 meters away is the bus from the bus stop after 10 seconds.

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

A bus moves away from bus stop in a straight line. After 1 second it was 10 meters away, after 2 seconds it was 20 meters and after 3 seconds it was 30 meters away.

In this way bus forms an arithmetic sequence

10, 20, 30, 40........up to 10 terms.

nth term of an arithmetic sequence is represented by

[tex]T_{n}[/tex] = a+ (n - 1)d

Here a = 10 and d = common difference = 10

Therefore 10th term = 10 + (10-1)10

                                  = 10 + 90

                                  = 100

Therefore after 10 seconds bus will be 10 meters away from the bus stop.

To know more about arithmetic sequence visit:

https://brainly.com/question/2512128

#SPJ4

Answer:

Step-by-step explanation:

since we know that the 50 degrees is one side of the line then the angle that is strait opposite from this angle is 50 degrees, so 50+60=110degrees and 180-110=70, so x=70 degrees

The indicated sum for the geometric series is 121.5

The series is given as:

162 − 54 + 18 − 6 + .....

Start by calculating the common ratio of the geometric series.

This is calculated using

r = -54/162

Evaluate

r = -1/3

The indicated sum for the geometric series is then calculated as:

S = a(1 - r^n)/1 - r

Substitute the known values in the above equation

S = 162(1 - (-1/3)^7)/1 + 1/3

Evaluate the exponent and the sum

S = 162(1 + 1/2187)/4/3

Evaluate the sum

S = 162(2188/2187)/4/3

Express as products

S = 162 * (2188/2187)* 3/4

Evaluate the product

S = 162 * 547/729

Evaluate the product

S = 121.5

Hence, the indicated sum for the geometric series is 121.5

Read more about geometric series at

https://brainly.com/question/24643676

#SPJ1

Answer:

9

Step-by-step explanation:

let the number be y

5×y - 7 = 3×y + 11

5y-7 = 3y+11

collect like terms

5y-3y = 11+7

2y = 18

y = 18/2

y = 9

Answer: Yes, the correlation coefficient is statistically significant

The correlation coefficient describes how one variable actions when it comes to every other. A high-quality correlation shows that the 2 circulate within the identical path, with a +1.zero correlation once they move in tandem. A poor correlation coefficient tells you that they as a substitute flow in opposite directions. A correlation of 0 shows no correlation in any respect.

where ρ corresponds to the population correlation.

The sample size is n = 17,

so then the number of degrees of freedom is df = n-2 = 17-2 = 15

The corresponding critical correlation value re for a significance level of a 0.05, for a two-tailed test is た= 0.482

Observe that in this case,

              the null hypothesis H0 : ρ-0 is rejected

                             if |r> re 0.482.

Based on the sample correlation provided, we have that lrl = 0.595 >=0.482,                            

which is concluded that the null hypothesis is rejected.

Learn more about correlation coefficient here:- https://brainly.com/question/4219149

#SPJ4

The general solution of the given higher-order differential equation. y''' − 9y'' 15y' 25y = 0 is Y= c1e^-x +c2e^5x + c3xe^5x

m^3 -9m^2+15m+25=0

Possible rational roots = 1,-1,5,-5,25

Now on putting these possible rational roots which have been found by the discriminant and hit and trial method,

we will check these roots.

m=-1 comes out to be a root of the equation.

m^2-10m+25=0

(m-5)(m+5)=0

(m-5)^2=0

m=5

So the general equation comes out to be

Y= c1e^-x +c2e^5x + c3xe^5x

For more information about differential equations, visit

https://brainly.com/question/1164377

#SPJ4

To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.

Herein we must prove that two circles are similar by taking advantage of two key characteristics: (i) Center, (ii) Radius. Based on such facts, we must apply the following rigid transformation:

Step 1 - Traslating the circle from A to B: Translation vector - (- 1, 1).

(x, y) = (2, 3) + (- 1, 1)

(x, y) = (1, 4)

Step 2 - Dilate the circle by a factor of 2.

r = 2 · 5

r = 10

To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.

To learn more on transformation rules: https://brainly.com/question/9201867

#SPJ1

Answer:

============================

Conditions we need to meet:

To get the smallest number we'd use all 10 digits in the ascending order:

Here we can't have zero in the beginning as the number becomes 9-digit.

So swapping zero with the closest digit, 1.

Our number should be even, so we should swap 9 with one even digit.

Again it should be the closest one to 9, so it is 8.

We get the following number as a result:

To test you may swap digits, any number you get will be greater than this number.

The statement; In western culture, 4 to 12 feet is considered public space whereas personal space is 1½ to 4 feet is false.

These refers to culture which is related to the people of the west.

Culture

This can be defined as the beliefs, values, behaviour and material objects that constitute a people's way of life.

Therefore, it is b false that in western culture, 4 to 12 feet is considered public space whereas personal space is 1½ to 4 feet.

Learn more about Western culture:

https://brainly.com/question/19800361

#SPJ1

Step-by-step explanation:

clearly divergent.

the elements of the series are getting bigger and bigger intercepted by some constant "1" (but they don't help here - after every intercepting "1" are 2 numbers that are larger by 1 than the 2 numbers before the intercepting "1", and that continues into infinity, so, the numbers will go to infinity, and that shows that the series is divergent).

The slope is (B) -5/4.

To find the slope:

Therefore, the slope is (B) -5/4.

Know more about slopes here:

https://brainly.com/question/3493733

#SPJ4

The complete question is given below:

What is the slope of a line that is parallel to the line whose equation is y=45x−3?

A. −4/5

B. −5/4

C. 5/4

D. 4/5

Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

Formular for the area of a kite is expressed as;

A = pq/2

Where p and q are the two diagonals of the kite.

Given the data in the question;

From the diagram, we can determine line AM and line MD using Pythagoras theorem.

c² = a² + b²

First, we find line AM

c² = a² + b²

5² = 3² + b²

25 = 9 + b²

b² = 25 - 9

b² = 16

b = √16

b = 4

Line AM = 4

Next, we determine Line MD

c² = a² + b²

(√58)² = 3² + b²

58 = 9 = b²

b² = 58 - 9

b² = 49

b = √49

b = 7

Line MD = 7

Now, we can find the area of the kite.

Diagonal p = BC = 6

Diagonal q = AD = AM + MD = 4 + 7 = 11

Area = pq/2

Area = [ 6 × 11 ]/2

Area = 66 / 2

Area = 33cm²

Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

Learn more about area of kite here: https://brainly.com/question/12286366

#SPJ1