Arrange in descending order: 101.121, 111.101, 101.112, 110.111

The 20th term of the expansion (c-d)³⁵ can be determined using the binomial theorem. The binomial theorem states that the coefficients of the terms in the expansion of (a+b)ⁿ can be found using the formula:

C(n, r) * a^(n-r) * b^r

where C(n, r) represents the binomial coefficient, given by n! / (r!(n-r)!). In the case of (c-d)³⁵, the exponent of c decreases by one in each term, while the exponent of d increases by one.

To find the 20th term, we need to find the value of r that satisfies the equation C(35, r) = 20. Solving this equation, we find that r = 15.

Substituting r = 15 into the formula, we have:

C(35, 15) * c^(35-15) * (-d)^15

Simplifying, we get:

C(35, 15) * c^20 * d^15

Therefore, the 20th term of the expansion is given by C(35, 15) * c^20 * d^15.

Learn more about binomial theorem here: brainly.com/question/30095070

#SPJ11

The length and width of a rectangle are 36cm and 4.5cm

Finding the Width:

The formula to find the perimeter of the rectangle is:

P=2(l+w),

where P is the perimeter, l be the length, and w be the width.

Now substitute the given values to solve for w, since we need to find the width.

The given information is:

the length of a rectangle is six inches more than eight times the width so the equation becomes:

L=8w+6

P=120

w=8w

now plug the values in the above formula:

P=2(l+w),

120=2(8w+6)+8w

120=16w+12+8w

120=24w+12

24w=108

w=4.5

To find the length just substitute in the L.

L=8(4.5)+6

L=30+6

L=36

To know more about the Perimeter of a rectangle:

https://brainly.com/question/24571594

#SPJ4

1. Point A on the number line is one interval mark to the right of -5, which means it is located at position 4 on the number line.

A number line is the visual representation of different numbers.

It is a straight line with numbers marked at equal intervals.

It can be used to represent both positive and negative numbers, with zero as the center point.

2. Point B on the number line is two interval marks to the left of 10, which means it is located at position -14 on the number line. Therefore, the opposite of Point B is 14.

3. The absolute value of a number represents its distance from zero on the number line, regardless of whether the number is positive or negative. The absolute value of 7 is simply 7.

4. The absolute value of -14 is the distance between -14 and 0 on the number line, which is 14 units. Therefore, │-14│ is equal to 14.

5. Two integers that have the same absolute value could either be the same integer or opposite integers. For example, 3 and -3 have the same absolute value of 3, while 4 and -4 have opposite values but the same absolute value of 4. Therefore, the answer is they could be the same or opposite integers.

To know more about straight line visit:

https://brainly.com/question/4889855

#SPJ1

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

for such more question on medium

https://brainly.com/question/14532771

#SPJ8

Answer:   \(x=10\) and \(y=10\sqrt{2}\)

Step-by-step explanation:

The percentage increase in the cost of oranges is 20%

A % is a quantity or ratio stated as a fraction of 100 in mathematics (from the Latin per centum, "by a hundred"). The abbreviation "pct.", "pct.", and occasionally "pc" are also used to indicate it, but the percent sign, "%," is more frequently employed. There is no unit of measurement for a %; it is a dimensionless number (pure number).

The symbol for "%" developed from the progressive reduction of the Italian term per cento, which means "for a hundred." It finally vanished totally. The word "per" was frequently shortened to "p." Two circles and a horizontal line made up the "cento," which is how the contemporary "%" symbol is now represented.

Given that the oranges at the grocery store went from $0.75/ib to $ 0.90/ib

=(0.90-0.75)/0.75

=0.15/0.75

=0.2

% increase= 0.2*100

=20%

Therefore, the percentage increase in the cost of oranges is 20%

To know more about percentage, visit:

https://brainly.com/question/16797504

#SPJ13

Answer:

both ansers are 2.7

Step-by-step explanation:

This is an 45˚, 45˚, 90˚ so the two smaller sides are equal so x=5.4.

the hypotenuse is always sqrt2 times bigger than the smaller sizes so y=\(5.4\sqrt{2}\)

Answer:

The equation is true when x = 4 because 6(4) = 24 that is x=4 satisfies the given equation.

Step-by-step explanation:

Given: \(6x=24\)

To find: x

Solution:

A equation is a statement that defines the equality of two expressions or numbers.

\(6x=24\)

Divides both sides by 6

\(\frac{6x}{6}=\frac{24}{6}\\x=4\)

Therefore,

The equation is true when x = 4 because 6(4) = 24 that is x=4 satisfies the given equation.

Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.

a) The value of x is 155.56 mm (rounded to two decimal places).

b) The value of R is 4.44 mm (rounded to two decimal places).

c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:

UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)

The Lower Control Limit (LCL) for the diameter is calculated as:

LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)

d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:

UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)

The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.

e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:

UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)

LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)

Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.

Learn more about diameter here:

https://brainly.com/question/32968193

#SPJ11

The complete question is:

What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5

The percent of the purchase price would be 20% of the sale price.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

First we need to calculate the difference between the purchase and sale price.

$72.00 - $60.00 = $12.00

Since $12 is the increase in dollars.

To increase as a percentage we need to divide the increase by the original purchase price.

12.00 ÷ 60.00 = 0.2

This simply means moving the decimal place two columns to the right;

0.2 x 100 = 20

Therefore, the percent of the purchase price would be 20% of the sale price.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ5

Answer:

556

Step-by-step explanation:

So, 378/189=2. So it will double two times. x2x2=x4. 139x4=556.

Answer:

556

Step-by-step explanation:

There's an initial population of 139 bacteria in a colony. If it doubles every 189 minutes, then the population would be 556 in 378 minutes from now.

189th minute= 139+139=278

Since 189+189= 378, Just double 278 again, which gives you 556.

Answer:

70 pounds

Step-by-step explanation:

12/4=3

40/4=10

3x7=21

10x7=70

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

Step-by-step explanation:

9c+63

You multiply the nine to every number in the parentheses

Answer:

Step-by-step explanation:

here we have the expression 9(3+c+4) which is the same as 9(c+7) using the Distributive Property we get 9c+63 becasue a(b+c) is the same as ab+ac.

Therefore, the equation representing the total area of the pool and pool deck is y = 25 * 9 + (x+25) (x+9).

Length is a measure of the size of an object, typically referring to the distance from one end to the other end in one dimension. It is commonly used to describe the size of objects such as lines, segments, curves, and shapes. Length is often measured in units such as meters, feet, inches, or centimeters, depending on the context and the system of measurement being used. In mathematics, length can also refer to the total number of elements in a sequence or the number of digits in a number.

The length of the pool deck is (x+25) yards and the width is (x+9) yards. The area of the pool deck can be found by multiplying the length and width:

Area of pool deck = (x+25) (x+9)

The area of the pool itself is 25 yards by 9 yards, or:

Area of pool = 25 * 9

To find the total area of the pool and pool deck, we need to add the area of the pool to the area of the pool deck:

Total area = Area of pool + Area of pool deck

y = 25 * 9 + (x+25) (x+9)

Therefore, the equation representing the total area of the pool and pool deck is y = 25 * 9 + (x+25) (x+9).

To know more about dimension, visit:

brainly.com/question/29306119

#SPJ1

No, f(x) does not have a limit as x approaches infinity, as seen from its graph and the fact that the function evaluates to 1 for odd x.

No, f(x) does not have a limit as x approaches infinity. To prove this, we first note that the function is undefined for x = 0 and any negative number. For positive x, as x approaches infinity, the denominator in 1 - 1/x will approach infinity, and the entire expression will approach 0. On the other hand, for odd positive x, the expression will always evaluate to 1, so the limit does not exist. Therefore, f(x) does not have a limit as x approaches infinity. To show this more clearly, we can look at a graph of the function. As x increases, the graph will initially follow the y = 1 line. As x approaches infinity, the graph will approach the y = 0 line. Since the value of the limit is different at the two ends, the limit does not exist.  Therefore, f(x) does not have a limit as x approaches infinity.

Learn more about graph here

https://brainly.com/question/10712002

#SPJ4

Answer:. 400%

Step-by-step explanation:

Divide 160 by 40.

The result is 4.

To Change to a percentage, multiply by 100.

4 × 100 = 400%

The integer number 40 will be 25 percent of the integer number 160.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The percentage of 40 out of 160 will be given as,

P = (40 / 160) x 100

P = 0.25 x 100

P = 25%

The integer number 40 will be 25% of the integer number 160.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ2

Answer:

3.25 inches

Step-by-step explanation:

5/8 = .625

5 1/5 = 5.2

5.2 x .625 = 3.25, or 3 1/4 in

There are 969 methods for the quality control inspector to randomly check 5 smartphones, of which 2 are defective, from the shipment of 21 smartphones.

We can solve this problem using combinations formula, that is a way of counting the number of ways to select k objects from a fixed of n items without regard to order. The range of combinations of k items from a fixed of n objects is given via:

\(C(n, k) = n! / (k! * (n-k)!)\)

in which:

In this situation, we want to pick out 2 defective smartphones out of 2 defective smartphones and 19 non-defective smartphones, and we need to pick out out three non-defective smartphones out of the ultimate 19 non-defective smartphones.

Consequently, the number of approaches to choose 2 defective smartphones and 3 non-Defective smartphones from the set of 21 smartphones is:

\(C(2, 2) * C(19, 3) = 1 * (19! / (3! * 16!)) = 191817 / (321) = 969\)

Therefore, there are 969 methods for quality control.

Learn more about Combination formula:-

https://brainly.com/question/28065038

#SPJ4

The general form of such a model that predicts the volume of sales (Y) as a function of advertising (X) in which sales increase as advertising increases, but at a decreasing rate is given by  Y^ = b0 + b1X + b2X². Option C.

The general form of the model that fits the description of the sales model that is given in the problem is C. Y^ = b0 + b1X + b2X². Where Y^ represents the predicted or estimated value of Y. b0, b1, and b2 are the coefficients of the model, and they represent the intercept, the slope, and the curvature of the relationship between X and Y, respectively.

In this model, the variable X has a quadratic relationship with the variable Y because of the presence of the squared term X². This indicates that the effect of X on Y is not linear but curvilinear, which means that the effect of X on Y changes as X increases. Specifically, the effect of X on Y increases initially but then levels off or diminishes as X becomes larger. Answer option C.

More on models: https://brainly.com/question/848129

#SPJ11

The equation of the graph after it is reflected is g(x) = 3|x|

The equation of the graph is given as

f(x) = -3|x|

The transformation rule is given as

Reflection over the x-axis

The mathematical representation of this transformation rule is

(x, y) = (x, -y)

The above transformation rule means that

g(x) = -f(x)

So, we have

f(x) = -3|x|

Substitute f(x) = -3|x| in g(x) = -f(x)

g(x) = -1 * -3|x|

Evaluate

g(x) = 3|x|

Hence, the equation of the reflected graph is g(x) = 3|x|

Read more about reflection at

brainly.com/question/27224272

#SPJ1

The equation that represents the regrouping needed for the problem 52,134 - 36,091 is: "0 hundred + 10 tends". (Option D).  This is because you need to move a ten from a hundred so you can subtract 9 from 13.

In arithmetic, regrouping is when you construct groups of 10 when doing operations like addition or subtraction. This is most common when working with double digits. However, technically, it occurs whenever you have an answer that is more than 10.

Often, when working with Regrouping, you can either be solving addition or subtraction and the Place Value Table often becomes very useful.

Learn more about Regrouping:
https://brainly.com/question/20490807
#SPJ1

The distance between skew lines with the given parametric equations can be found using the formula for the shortest distance between two skew lines. The main answer is that the distance between the skew lines is 4 units.

To explain further, let's consider the parametric equations of the two skew lines:

Line 1: x = 1 + t, y = 1 + 6t, z = 2t

Line 2: x = 3 + 3s, y = 4 + 15s, z = -1 + 4s

To find the distance between these two lines, we need to find the shortest distance between any two points on the two lines. This can be done by considering a point on each line and finding the vector connecting them. The vector connecting the two points will be perpendicular to both lines.

Let's choose a point on each line: A(1, 1, 0) on Line 1 and B(3, 4, -1) on Line 2.

The vector connecting A and B is AB = <3 - 1, 4 - 1, -1 - 0> = <2, 3, -1>.

The shortest distance between the skew lines is equal to the length of the projection of AB onto a vector perpendicular to both lines. The direction vector of Line 1 is <1, 6, 2>, and the direction vector of Line 2 is <3, 15, 4>. To find a vector perpendicular to both lines, we can take their cross product:

N = <1, 6, 2> x <3, 15, 4> = <-12, -2, 3>.

Now, we can use the formula for the distance between a point and a line in three dimensions, which is given by:

d = |AB · N| / |N|,

where AB · N is the dot product of AB and N, and |N| is the magnitude of N.

Plugging in the values, we get:

d = |<2, 3, -1> · <-12, -2, 3>| / |<-12, -2, 3>|.

  = |-24 - 6 - 3| / sqrt((-12)^2 + (-2)^2 + 3^2).

  = |-33| / sqrt(153).

  = 33 / sqrt(153).

Therefore, the distance between the skew lines is approximately 4 units.

Learn more about distance here:

brainly.com/question/26711747

#SPJ11

Classroom objects can be categorized as vertical or horizontal. Examples of vertical objects include doors, bookshelves, and clocks, while horizontal objects include desks, tables, and chairs.

In a classroom, there are many objects that are vertical and horizontal. Here are ten examples of each:

Vertical objects in a classroom:

1. Door                     6. Clock

2. Cabinet               7. Electrical outlets

3. Bookshelf            8. Light switches

4. Whiteboard         9. Window blinds

5. Flagpole             10. Bulletin board

Horizontal objects in a classroom:

1. Desks                  6. Keyboard trays

2. Chairs                 7. Carpet tiles

3. Tables                 8. Ceiling tiles

4. Countertops       9. Whiteboard markers

5. Shelves              10. Paper trays

These are just a few examples of vertical and horizontal objects that can be found in a classroom.

It is important to recognize the different shapes and orientations of objects in our environment, as they can affect the way we perceive and interact with them.

For more questions on Bulletin board

https://brainly.com/question/30369348

#SPJ8

Let's break down the expression for Tony's combined total earnings step by step.

First, we consider Tony's earnings as a tutor. He earns $11 per hour as a tutor, so the amount he earns from tutoring is given by the product of his hourly rate ($11) and the number of hours he worked as a tutor (t). This can be represented as $11t.

Next, we consider Tony's earnings as a waiter. He earns $13 per hour as a waiter, so the amount he earns from waiting tables is given by the product of his hourly rate ($13) and the number of hours he worked as a waiter. Since Tony worked a total of 106 hours this month and spent t hours as a tutor, he must have worked (106 - t) hours as a waiter. This can be represented as $13(106 - t).

To calculate Tony's combined total earnings for the month, we add the amount he earned as a tutor ($11t) to the amount he earned as a waiter ($13(106 - t)). This yields the expression:

Earnings = $11t + $13(106 - t)

This expression represents the total dollar amount Tony earned this month, considering the number of hours he worked as a tutor (t) and waiter (106 - t).

Answer:  See the image below.

The x-intercepts of the graph of the function defined by (x - 2)(2x + 1) will be at (2,0) and (0.5,0).

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at x-axis.

Here we are having an equation:-

(x-2)(2x+1)=0

2x²+x-4x-2=0

2x²-3x-2=0

2x²-4x+x-2=0

2x(-1)(x-2)=0

x=2    x=0.5

Hence the x-intercepts of the graph of the function defined by (x - 2)(2x + 1) will be at (2,0) and (0.5,0).

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ1