What is the y intercept?

Using integrals, the desired probabilities and measures are given as follows:

a) P(X < 6) = 0.84375 = 84.375%.

b) P(X < 13) = 1 = 100%.

c) P(6 < X < 8) = 0.15625 = 15.625%.

d) P(X > 5) = 0.31641 = 31.641%.

e) x = 6.434.

The distribution is given as follows, simplifying the operations:

f(x) = 0.09375x - 0.01171875x², 0 ≤ x ≤ 8.

Hence the density function is:

[tex]\int_{a}^{b} f(x) dx[/tex]

[tex]\int_{a}^{b} (0.09375x - 0.01171875x^2) dx[/tex]

[tex]0.046875x^2 - 0.00390625x^3|_{x=a}^{x = b}[/tex]

Applying the Fundamental Theorem of Calculus:

P(a < X < b) = 0.046875b² - 0.00390625b³ - 0.046875a² + 0.00390625a³

Hence, for item a:

P(X < 6) = 0.046875(6)² - 0.00390625(6)³.

P(X < 6) = 0.84375 = 84.375%.

For item b, the entire distribution is below 13, hence:

P(X < 13) = 1 = 100%.

For item c:

P(6 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(6)² + 0.00390625(6)³.

P(6 < X < 8) = 0.15625 = 15.625%.

For item d:

P(5 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(5)² + 0.00390625(5)³.

P(X > 5) = 0.31641 = 31.641%.

For item e:

We have to find b when a = 0 and P(X < b) = 0.9, hence:

0.046875b² - 0.00390625b³ = 0.9.

Using a calculator, the solution in the range of the distribution is given by:

b = x = 6.434.

More can be learned about integrals and probabilities at brainly.com/question/15109629

#SPJ1

Answer:

39 is the sum of their ages

Step-by-step explanation:

Hope this helps :)

Answer:

c) 1

Step-by-step explanation:

Solving for the value of s,

→ 3s - 12 = -9

→ 3s = -9 + 12

→ s = 3/3

→ [ s = 1 ]

Thus, option (c) is correct.

The value of the integer number is -1

The statement is given as:

The sum of an integer and 7 times the next consecutive odd integer is 6

Let the integer value be x

So, the next consecutive odd integer is x + 2

When represented as an equation, we have

x + 7(x + 2) = 6

Open the bracket

x + 7x + 14 = 6

Evaluate the like terms

8x = -8

Divide both sides by 8

x = -1

Hence, the value of the integer number is -1

Read more about consecutive integers at

https://brainly.com/question/10853762

#SPJ1

Answer:

  {-2}

Step-by-step explanation:

You want the solution set for the inequality 4(x +2)² ≤ 0.

The expression on the left cannot be negative, but it can be zero when ...

  x +2 = 0   ⇒   x = -2

The only solution to this inequality is x = -2.

Expressed as a set of solutions, we have ...

  x ∈ {-2}

Answer:

Step-by-step explanation:

97

Answer:

$97 per/tire

Step-by-step explanation:

         [tex]Borrow\:8\\4 \cdot 9 = 36\\= 38 - 36\\= 2\\4 \cdot 7 = 28\\28 - 28 = 0\\\\= 97\:\mathrm{R0}[/tex]

The number of columns is in the title floor before the change in layout is 10

Given that A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each columns and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular asked to find the number of columns in  the tile floor before the change in layout.

Let's assume the number of rows is x

The number of columns will be [tex]\frac{70}{x}[/tex]

After the changing, the rows can be x+4

The number of columns will be  [tex]\frac{70}{x}[/tex]-2

The equation will be (x+4)([tex]\frac{70}{x}[/tex]-2)=70

⇒[tex]x^{2} +4x-140=0[/tex]

⇒x=10

Therefore,The number of columns is in the title floor before the change in layout is 10

Learn more about columns here:

https://brainly.com/question/3642260

#SPJ9

A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex] kg and the earth has a mass of 5.972 x [tex]10^{24}[/tex] kg,26x[tex]10^{5}[/tex] earths would it take to equal the mass of the sun.

A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex]kg

earth has a mass of 5.972 x [tex]10^{24}[/tex]kg

Let x number of earths equal the mass of the sun

x (5.972 x [tex]10^{24}[/tex]) =  1.55272 x [tex]10^{31}[/tex]

x=  1.55272 x [tex]10^{31}[/tex] / 5.972 x [tex]10^{24}[/tex]

x= 26x[tex]10^{5}[/tex]

The wavelength of light emitted by a far-off galaxy extends and is "redshifted" toward the infrared region of the electromagnetic spectrum as it moves away from us. This means that by the time the light from a very distant galaxy that emits mostly visible or ultraviolet light reaches Earth, it will appear as infrared light.

Webb's ability to detect infrared light and the cosmos' expansion, which extends light to redder wavelengths, make it a good tool for identifying galaxies that originated at the beginning of the Universe's existence.

To learn more about this visit distant galaxy https://brainly.com/question/5368237

#SPJ9

Answer:

below

Step-by-step explanation:

25)-ab

=-(-1/2)(3/4)

=3/8

26)b÷c

=(3/4)×1/-6

=3/-24

=-1/8

27)c÷a

=-6÷-1/2

=6×2/1

=12

Answer:

3

Step-by-step explanation:

i think its 3 because 28 divided by 9 is 3

Answer: I'm pretty sure its a verb

Step-by-step explanation:

The sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11

(6.9 × 10^6) and (5.9 × 10^5)

Sum

= (6.9 × 10^6) + (5.9 × 10^5)

= (6.9 + 5.9) × 10^(6+5)

= 12.8 × 10^11

Therefore, the sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11

Learn more about scientific notation:

https://brainly.com/question/27862246

#SPJ1

Check the picture below.

Answer:

4

Step-by-step explanation:

the coefficient is usually a constant factor for a variable.

so, the answer here is 4.

Answer: 2.1606

Step-by-step explanation:

36.01 x 0.06 =

3601/100 x 6/100=

3601 x 6/(100 x 100)=

21606/10000=2.1606

Answer: ann is 69 and beth is 138

Step-by-step explanation:

Answer:

  1000

Step-by-step explanation:

You want the next number after 222 in base 3.

In any useful number base, the counting at any given integer position is ...

  0, 1, 2, 3, ..., (base -1), 0 and add 1 to the next number position

For base 3, this is ...

  0, 1, 2, 10

When the digit in the next higher position is also (base -1), then it gets incremented to 0 and the carry is propagated to the left.

In base 10, the equivalent is ...

  999 +1 = 99(9+1) = 99(10) = 9(9+1)0 = 9(10)0 = (9+1)00 = 1000

In base 3, your incremented value is ...

  222 +1 = 22(2+1) = 22(10) = 2(2+1)0 = 2(10)0 = (2+1)00 = 1000

The next whole base 3 number after 222 is 1000.

Answer:

This point would affect the mean more because the median is less sensitive to outliers.

Step-by-step explanation:

Hope this helps!

Answer:

See explanation

Step-by-step explanation:

Selected theme park admission prices has the lower standard deviation.

Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.

specific home stereo system: 3.99/59=0.0676.

selected theme park admission prices: 4/1499=0.002668

0.0676>0.002668

Answer:

The theme park ahs the lower standard deviation

4 × 10 then put a 6 by the 10 as an exponent.

There is no number which is satisfying the given conditions.

The first condition is that the number has seven digits.

The second condition is that the number lies between 1000 and 10000.

From these two conditions, we can conclude that there is no number which satisfies all the given conditions. Because there is no seven-digit number which is less than 10000.

Let us assume that the second condition is the number lies between 1000000 and 10000000.

And let the required number be "abcdefg".

The third condition is the digit in the tenth place is 150% of the digit in the thousandth place.

⇒ f = 150 × (d) / 100 = 1.5 × d

The fourth condition is the digit in the hundredth place is the sum of the digit in the tenth place and the digit in the thousandth place.

⇒ e = f + d = 1.5d + d = 2.5d

The fifth condition is the sum of all the digits in the number is 17.

⇒ a + b + c + d + e + f + g = 17

⇒ a + b + c + d + 2.5d + 1.5d + g = 17

⇒ a + b + c + 5d + g = 17

And the last condition is none of the digits is zero.

Using the last condition the possible values for d are either 1 or 2.

Because, if d is 3, then if we take the least possible digit(1) for others, the sum on the LHS is 19, which is greater than 17.

And d can not be 1. Because, if d is 1, then f and e are 1.5 and 2.5 respectively. 1.5 and 2.5 are not valid digits.

Therefore, the value of d = 2.

f = 1.5d = 3

e = 2.5d = 5

If d = 2, then we get a + b + c + g + 10 = 17

⇒ a + b + c + g = 17 - 10

⇒ a + b + c + g = 7

⇒ The possible values for (a, b, c, g) are (4, 1, 1, 1), (1, 4, 1, 1), (1, 1, 4, 1), (1, 1, 1, 4), (2, 2, 2, 1), (2, 2, 1, 2), (2, 1, 2, 2), (1, 2, 2, 2), (2, 3, 1, 1), (3, 2, 1, 1), (1, 1, 2, 3), and (1, 1, 3, 2)...

Therefore there are more than 12 possible answers that satisfy the assumption made.

Learn more about number here:

https://brainly.com/question/28569835

#SPJ9

Answer:

[tex]x = \frac{2a}{a - 2} [/tex]

If the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019

The given parameters are:

Year Millionaire Households

2015 9,200,000

2016 9,350,000

2017 9,620,000

2018 9,970,000

From the question, we have

The percentage increase between 2017 and 2018 continued for 2018 and 2019

The percentage increase between 2017 and 2018 is calculated as

Percentage = (2018 - 2017)/2017 * 100%

So, we have

Percentage = (9,970,000 - 9,620,000)/9,620,000 * 100%

Evaluate

Percentage = 3.64%

The number of millionaire households in 2019 is calculated as

2019 = 2018 * (1 + percentage)

So, we have

Households = 9,970,000 * (1 + 3.64%)

Evaluate

Households = 10332908

Hence, if the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019

Read more about percentage increase at

https://brainly.com/question/11360390

#SPJ1

The perimeter of the equilateral triangle will be 27x - 48.

It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.

Therefore, the perimeter of the equilateral triangle will be:

= 3(9x - 16)

= 27x - 48

Therefore, the perimeter of the equilateral triangle will be 27x - 48.

Learn more about triangles on:

brainly.com/question/1058720

#SPJ1

Find the perimeter of the equilateral triangle.

9x - 16

Yes; The construction demonstrates how to bisect an angle correctly using technology because Circles D & E have the same radius

How to properly bisect an angle?

In construction of angles and lines, bisection means dividing either a given angle or line segment into two equal parts. This means after the construction, the two parts must have equal measure.

The steps to bisect a line segment are as follows;

1. Draw the required length of the line segment AB.

2. With point A and radius of the compass greater than half of AB, describe arcs above and below the segment.

3. With the same radius as in step 2 and point B, describe two arcs above and below the segment. These would intersect that of step 2 at C and D.

4. Join the points of intersection of the arcs with a straight line CD.

Now, in this given question with the circle, we can see that line AG is the line that bisects the angle EAD.

Now, we see that circles C and D have the same radius and as such the construction demonstrated is correct for that very reason.

Answer: yes

Step-by-step explanation: the construction correctly shows how to bisect an angle using technology because circles D and E have the same radius. 

The perimeter of the regular polygon is 232

The side lengths of the regular polygon are given as

4/3x - 1/3 and x + 7

The sides of regular polygon are equal

So, we have:

4/3x - 1/3 = x + 7

Multiply both sides by 3

4x - 1 = 3x + 21

Collect like terms

4x - 3x = 1 + 21

Evaluate the like terms

x = 22

Substitute x = 22 in x + 7

Side = 22 + 7

Side = 29

The perimeter of the regular polygon is calculated as:

Perimeter = Number of sides x Side length

So, we have

Perimeter = 8 * 29

Evaluate

Perimeter = 232

Hence, the perimeter of the regular polygon is 232

Read more about perimeter at

https://brainly.com/question/24571594

#SPJ1

Answer:

7/10

Step-by-step explanation:

Rewriting 0.7 as a fraction would be 7/10. 0.7 can also be 0.70, and 70/100

The circle has an area of 28.26 ft².

It is assumed that the circle's radius is 3 feet.

The circle's area must be determined.

What is radius of a circle ?

A line segment from a circle's center to its perimeter is known as the radius.

As per the question ;

Radius of circle , r = 3 ft

Area of the circle is given by ;

A = πr²

A = π × 3²

A = 9π

or

A = 9 × 3.14

or

A = 28.26 ft²

Thus , the area of the circle will be 28.26 ft².

To learn more about circle click here ;

https://brainly.com/question/704946

#SPJ1

3 houseplants will weigh 15 kg (Refer to the tape diagram below).

The weight of 3 household plants will be about 15 kg.

Therefore, the weight of 3 household plants will be about 15 kg (Refer to the tape diagram below).

Know more about tape diagrams here:

https://brainly.com/question/26354395

#SPJ1