a weighted die has probability 0.102 of landing on a 6. if you roll the die until you get a 6 for the first time, what is the expected number of rolls it will take?

The starting number of Michael's thought is 96

From the question, the given parameters are:

The above sequence of statements can be represented as

x * (100÷8) + 6.50 = 1206.5

Where x represents the number

So, we have

x * (100÷8) + 6.50 = 1206.5

Evaluate the quotient

x * 12.5 + 6.50 = 1206.5

Subtract 6.50 from both sides

x * 12.5 = 1200

Divide both sides by 12.5

x = 96

Hence, the initial number is 96

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The mean is 58.319 m/h and the standard deviation is 11.665 m/h of the vehicle speed if 5% of all vehicles travel less than 39.13 m/h and 10% travel more than 73.25 m/h.

The mean and standard deviation of the vehicle speed can be calculated by using the formula for z-score.

The z-score of measure X can be given as;

Z = X - μ / σ

In this case, 39.13 m/h is the 5th percentile; therefore when X = 39.13, Z has a p-value of 0.05, hence Z = -1.645

Z = X - μ / σ

-1.645 = (39.13 - μ) / σ

39.13 - μ = -1.645σ

μ = 39.13 + 1.645σ

Additionally, 73.25 m/h is the 90th percentile (100 - 10 = 90), therefore when X = 73.25, Z has a p-value of 0.9, hence Z = 1.28

1.28 = (73.25 - μ) / σ

73.25 - μ = 1.28σ

μ = 73.25 - 1.28σ

We can find the standard deviation by equalling both equations as follows;

39.13 + 1.645σ = 73.25 - 1.28σ

1.645σ + 1.28σ = 73.25 - 39.13

2.925σ = 34.12

σ = 34.12/2.925 = 11.665 m/h

Now the mean can be calculated as follows;

μ = 73.25 - 1.28σ

μ = 73.25 - 1.28(11.665)

μ = 58.319 m/h

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In this picture, we have the triangles with two common sides and one common angle. However, they are not congruent, as they do not follow any of the congruence theorems. The congruence theorem with two sides and an angle is the SAS(Side-Angle-Side). However, the angle has to be the angle between the two sides, which does not happen in this case.

Answer:

y = -1

Explanation:

The slope-intercept form of the equation of a line has the form:

y = mx + b

Where m is the slope and b is the y-intercept.

The slope can be calculated as:

Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.

So, replacing (x1, y1) by (1, -1) and (x2, y2) by (2, -1), we get:

On the other hand, the y-intercept is the point where the line crosses the y-axis. So, the y-intercept is -1.

Finally, the equation of the line in the slope-intercept form is:

y = 0x - 1

y = -1

So, the answer is y = -1

Answer :- Constant term

In p(x) = x - 12, 1 is the coefficient of x and -12 is the constant term.

Answer:

30

Explanation:

To know the output value of the function, we need to replace x by -5 and calculated f(x). So:

Therefore, if the input x is -5, the output f(x) is 30

So, the answer is 30.

Given:

The number sentence for 4 and n

Required:

We have to find the given sentence

Explanation:

4 and N, simply means you mixed them up, you sum them up

your result is 9, 4+N=9

Required solution :

4+N=9

W+(9+3) is the equivalent expression of  (w+9)+3 by using associate property

An expression is combination of variables, numbers and operators.

The given expression is (w+9)+3

The operator in given expression is plus and variable is W.

The associative property of addition states that Changing the grouping of addends does not change the sum.

(x+y)+z=x+(y+z)

Similarly (W+9)+3=W+(9+3)

W+(9+3) is the equivalent expression of  (w+9)+3 by using associate property

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Each bird would receive 1/9 cup of bird food.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given an area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds.

The dividend would be

⇒ 2/3

The divisor would be

⇒ 6

The division expression would be

⇒ 2/3

Divided by 6

Rewrite the division expression to get

⇒ 2/3 × 1/6

⇒ 2 / 18

⇒ 1/9

Therefore, each bird would receive 1/9 cup of bird food.

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⇒Mathematically this means

[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]

Attached is the solution.

The discount rate is 15% and the VAT rate is 13%

The following can be deduced:

MP = 2080

Discount = d%

VAT = (d-2)%

Cost = 1997.84

Apply discount:

2080 - d% = 2080*(1 - 0.01d)

Add VAT:

2080*(1 - 0.01d) + (d - 2)%

2080*(1 - 0.01d) * (1 + (d -2)/100)

2080*(1 - 0.01d) * (0.98 + 0.01d)

= 1997.84

(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080

0.98 + 0.01d - 0.0098d - 0.0001d²

= 0.9605

- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0

0.0001d²- 0.0002d - 0.0195 = 0

d² - 2d + 195 = 0

Solving the quadratic equation we get:

d = 15

Therefore discount is 15%

VAT rate = d - 2 = 15% - 2% = 13%

The concept shown above is the calculation for the discount and the amount of the value added tax.

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When Allison arrived, Austin still had 24 miles to go. Allison drive 116 miles per hour.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

As given, Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 46 mph.  Allison arrived, Austin still had 24 miles to go.

Let t be the time they drove.

Then you have this "distance" equation

58t = 46t + 24

saying that both parts of the equation represent the same distance.  Then

58t - 46t = 24

12t = 24

t = 2  hours.

Hence the distance is, 2 x 58 = 116 mph.

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At first, we multiply 5 by 4

Then multiply 5 by 3i

Then multiply -2i by 4

Then multiply -2i by 3i

Since i^2 = -1, then we will multiply -6 by -1

Now, we will add the terms

Then we will add the like terms

So the answer is b

Given:

To Determine: The percentage with greater than 24mpg

Solution

According to the theorem, the corresponding angles, formed by a transversal on a pair of parallel sides, are always equal.

Also, the sum of angles on a straight line is 180 degree.

The angles 5 and 7 constitute a pair of corresponding angles, formed by the transversal 'r' on the pair of parallel sides 'p' and 'q'. So they must be equal,

The angles 4 and 5 constitute a straight line, so they must add up to be 180 degrees,

Thus, the angle 4 measures 49 degrees.

The expression that represents the perimeter of the figure is  6x - 2

The figure above is a rectangle. A rectangle is a quadrilateral that has opposite sides equal to each other. Opposite sides are also parallel to each other.

Therefore, the perimeter of a rectangle is the sum of the sides of the rectangle.

Hence,

perimeter of the rectangle = 2(l + w)

where

Therefore,

l = 2x - 3

w = x + 2

Hence,

perimeter of the rectangle = 2(2x - 3 + x + 2)

perimeter of the rectangle = 2(2x + x - 3 + 2)

perimeter of the rectangle = 2(3x - 1)

Therefore,

perimeter of the rectangle = 6x - 2

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Answer:

Step-by-step explanation:

4 - 3 x = 6 - 5 xx

[tex]-3x+4=6-5xx^{2}[/tex]

x = 1

x = - [tex]\frac {2}{5}[/tex]

Answer:

x=1

Step-by-step explanation:

sense x's are on both sides you need to bring one of them over, add 3x to both sides to get 4=6-2x , then subtract 6 from each side to get -2=-2x , then to get x by itself divide both sides by -2 to get 1=x

The error occurs in the second line, the correct solution is x > -5/2.

The relation between two unequal expressions is defined as inequality.

Given inequality is -5x/4 - 7/2 < -3/8.

The solution of the inequality is:

-5x/4 - 7/2 < -3/8

10x + 28 > 3

10x > -25

x > -25/10

x > -5/2

Hence, the error occurs in the second line, the correct solution is x > -5/2.

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Answer:

(4, 1 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = C (1, 9 ) and (x₂, y₂ ) = D (7, - 7 ) , then

midpoint = ( [tex]\frac{1+7}{2}[/tex] , [tex]\frac{9-7}{2}[/tex] ) = ( [tex]\frac{8}{2}[/tex] , [tex]\frac{2}{2}[/tex] ) = (4, 1 )

The position of N on the line segment is at the -14 mark

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

The complete question is added as an attachment

From the attachment, we have

The ratio is given as:

MN : NP = 7 : 2

Also, we have

Location of M = -27

Location of P = -9

The location of N is then calculated as

N = MN/(MN + NP) * (M - P)

Substitute the known values

N = 7/(7 + 2) * (-27 + 9)

Evaluate the sum

N = 7/9 * -18

Evaluate the product

N = -14

Hence, the location of point N is -14

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Tom will need to pay $93.60 for 36 cans of Coca-Cola.

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=3x+2.

The question gives:

Tom bought 10 cans of Coca-cola drink at a cost of USD26.00. Here you can convert this text into an algebraic expression, see:

10x = 26, where x represents the unit cost.

You can find x, solving the previous algebraic expression. Thus,

10x=26

x=26/10

x=2.6

So, 1 can of Coca-Cola costs $2.60.

For knowing the cost total for 36 cans of Coca-Cola, you need to multiply 36 units by the unit cost ($2.6). See below:

36*2.6= $93.60

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If function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31

The function is

f(x) = [tex]x^2[/tex] + 4x -1

The function is the expression that represents the relationship between one variable and another variable. If one variable is dependent variable then the another variable is independent variable.

The value of g(x) = f(x+4)

First we have to find the value of f(x+4)

Substitute the values in the function

f(x) = [tex]x^2[/tex] + 4x -1

f(x+4) = [tex](x+4)^2[/tex] + 4(x+4) - 1

= [tex]x^2[/tex] + 8x +16 + 4x+16 - 1

Rearrange the terms and combine the like terms

= [tex]x^2[/tex] + 8x+4x + 16+16-1

= [tex]x^2[/tex] + 12x +31

Hence, if function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31

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Answer:

Inconsistent: parallel lines.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=4x+4\\-12x+3y=3\end{cases}[/tex]

Use arithmetic operations to isolate y in the second equation:

[tex]\implies -12x+3y+12x=3+12x[/tex]

[tex]\implies 3y=12x+3[/tex]

[tex]\implies\dfrac{3y}{3}=\dfrac{12x}{3}+\dfrac{3}{3}[/tex]

[tex]\implies y=4x+1[/tex]

Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.

The solution to a system of linear equations is the point of intersection.

As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.

7 + 7 + 7 + 7 + 7​ means 7 is added 5 times

It could be written as

5(7)

7 x 5 and

7 . 5

But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7

Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7​

This makes the correct option to be the third option. That is 7^5

Answer:

top: y=f(x)=-2x+5

middle: y=4x

last: y=(9/2)x-3

The truck can haul 1102 pounds.

According to the question,

We have the following information:

A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.

(More to know: ton, pounds and kilograms are the most commonly used units for measuring weight.)

Now, we already have the knowledge that 1 ton is equal to 1000 kilograms.

So, half ton will make 500 kg.

Now, in order to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg makes 2.205 pounds.

1 kg = 2.205 pounds

500 kg = (500*2.205) pounds

500 kg = 1102.5 pounds

Hence, the truck can haul 1102.5 pounds.

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A forest is decreasing in size by 60 hectares every 3 years. In 7 years, the forest will have decreased by 140 hectares.

Using the Unitary Method:

∵ In '3' years, a forest decreased in size by '60' hectares

∴ In '1' year, a forest will be decreased in size by '20' hectares

Every year 20 hectares is decreased. Considering a regular trend in the decrement of forest area, the time span of '7' years will diminish 'to 140' hectares.

The 'Unitary Method' is also known as the 'Mango Method'. It establishes a relation between given data. The relation is used to predict results in different conditions. The Unitary Method is always used for regular trends.

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The measurement is closest to the length of the rectangle is √119 ft.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Where c is the diagonal that divides the rectangle into two equal triangle, a and b are the other legs of the triangle.

Given the data in the question;

Plug the values into the formula and solve for b.

12ft = √( (5ft)² + b² )

Take the square of both sides

( 12ft )²  = (5ft)² + b²

144ft²  = 25ft² + b²

b² = 144ft² - 25ft²

b² = 119ft²

b = √( 119ft² )

b = √119 ft

Therefore, the measure of the length is √119 ft.

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A fifth-degree polynomial function can have five turning points in its graph.

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Answer:

The correct is answer is option C: "four or less"

The answers to the next  part of the question on Edge are options A and C :)

Step-by-step explanation:

Hope this helped!

Brainliest would be greatly appreciated - Have a great day :3

Solution

Given, ABCD is a rectangle AC is diagonal

Then AD=BC and AB=CD

And ∠ABC=∠BCA=∠CDA=∠DAB=90

0

In ΔABC and ΔADC

∠ABC=∠ADC (Angle of rectangle)

AB=DC (Opposite side of rectangle )

AC=AC (Common side)

∴ΔABC≅ΔADC

∴∠ACD=∠ACB

∵∠ACD+∠ACB=90

0

..........[Angle ACB is the angle of rectangle]

∴2∠ACD=90

0

⇒∠ACD=45

0