Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.

The formula for determine the slope is given by

m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y2) are points on the line

m = ( 4 - -1)/(4 - -4)

Rewriting

m = ( 4+1)/( 4+4)

= 5/8

The slope is 5/8

The volume formula of a cylinder is :

From the problem, we have :

r = 3 in and h = 2 in

Using the formula above, the volume will be :

The answer rounded to the nearest tenth is V = 56.5 in^3

The probability that the oldest child is a girl is given by the quotient between two numbers:

- The number of combinations where a girl is the oldest child i.e. the number of elements in the sample space that start with a G.

- The total number of elements in the sample space.

The first number is 4 since we have 4 elements starting with G: GBB, GBG, GGB, GGG. The second number is 8. Therefore the probability that we are looking for is given by:

Then the answer is 1/2.

The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).

In the question ,

it is given that ,

the equation is y = x² - 6x + 5

we need to write the equation in the vertex form ,

we know that the vertex form of the equation is

y = m(x − a)² + b  , where (a,b) is the vertex .

On using the completing the square method for the equation,

y = x² - 6x + 5

Adding and subtracting 9 , in the equation

y = x² - 6x + 9 + 5 - 9

y = x² - 6x + 3² + 5 - 3²

y = (x - 3)² - 4                       ....because (x - 3)² = x² - 6x + 3²

Therefore , The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).

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√72

Express 72 as 6^2 x 2

√(6^2 * 2 )

Pull terms out from under the radical

6 √2

a = 6

b= 2

Statement Reason

angle P = angle S Given

angle P + angle Q = 180 Given

angle R + angle S = 180 Given

If we substitute angle P = angle S into angle R + angle S = 180, then

angle R + angle P = 180

The figure shows a cube with a cone shape extracted from it.

Thus, to get the volume of the composite solid, we need to subtract the volume of the cone from the volume of the cube.

i.e. Volume of Solid = Volume of Cube - Volume of Cone

Therefore the volume of the cube is:

Now we need to get the volume of the cone:

The formula of the volume of a cone is:

The radius of the cone is the same as half the length of one edge of the cube

While the height of the cone is the same as the height of the cube.

A sketch is shown below:

Thus, height (h) of cone = 5.1m

radius (r) of cone = 2.55m

Thus, we can now find the volume of the composite solid as:

The volume is: 97.92 cubic meters

The measure of the angle ∠CEB is 65°.

We are given a circle. The center of the circle is denoted by R. There are two chords, AB and CD. The point of intersection of the chords is E. The angles subtended by the arcs CB and AD are 73° and 57°, respectively. We have to find the measure of the angle ∠CEB. We can see that there is no direct relationship between the angles, but it is certain that the angle ∠CEB lies between the measures of angles subtended by the two arcs. So, we can write it in the form of an inequality. The measure of the angle ∠CEB is more than 57° but less than 73°. We can take the average value of these angles as an approximation. The average is (57° + 73°)/2 = 65°.

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Answer:

The percentage increase in his petrol bill is 16 2/3%

The percentage increase in his petrol bill would be equal to 16 2/3%

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Given that When the price of petrol increases by 20%, a motorist decreases his volume of petrol consumption by 10%.

Let the inital price be 100 and consumption be 100t.

Now increased price

= 120 % of 100

= 120

New consumption

= 100 x 100 / 120

= 83.33

Hence, percentage reduction in the consumption will be;

(100 - 83.33)/ 100 x 100

16 and 2/3 %

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We have to find which of the graph options is best to track the number of books that the students read each week and encourage them to increase them.

Option 1 (scatter plot): in this case, it is not useful in the sense that we can not compare the evolution in time of each student. We can only see the number of books per student for specific weeks.

Option 2 (time series): in this case, the attendance is not a variable of interest, so it is not suitable.

Option 3: A pie chart is only useful to compare proportions and percentages, and not track an evolution of a variable in time.

Option 4: This aggregation of the data in a Pareto only allows to compare the total number of books per week, but the evolution is not clear, as we sort the columns by the number of books instead of time.

Option 5: A time series with weeks in the x-axis and number of books in the y-axis let the teacher clearly see the evolution of books read in time. So this option is the most suitable.

Answer: Option 5 (time series)

We need to calculated first the 50% of $60

60*0.5=30

then we calculated the final bill

original bill + tip = money leave by mr Brown

60+30=90

he leave $90

Given

The function is defined as:

x-intercepts

The x-intercepts of the function y are the values of x when y = 0

Substituting 0 for y and solving for x

Hence, the x-intercepts are:

y-intercepts

The y-intercepts are the values of y when x = 0

Hence, the y-intercept is (0, 17)

Maximum or minimum of the function

The given equation is in vertex form.

Hence, the minimum value of the function is (3,-1)

To solve this problem, it is necessary to use the fundamental counting principle, which is the multiplication counting rule.

It says that if we have two events, a and b. The total number of possible outcomes will be a times b (a*b).

In this case, a are the destinations she can choose and b are the departure dates. To find how many cruises can she plan, multiply the number of options of a and b, this is 4*5:

In this case, she can plan 20 different cruises.

Step 1. We have two equations represented in the graph. One is the red line and the other is the blue graph.

The red line represents a linear equation,

and the blue segments represent a rational equation.

Step 2. For the linear equations, we have only two options given:

Graphing both lines to pick which one is the line shown in the problem:

The green line is y=x+4,

and the purple line is y=x-4.

Compared with our graph, we have the one that crosses the y-axis at -4, Thus it is the equation y=x-4.

Step 3. For the rational equation, we are given two options to choose from:

We graph the two equations to check which one is correct:

In the graph, we show in green

and in purple, we have the equation

As you can see, the second one, (the purple one) is the one shown in the graph from this problem, thus, the second equation is:

Answer: D

We are required to find the inverse of the function

The first step is to interchange the variable x for y

The next step is to make y the subject of the formula

The answer is y = 2x + 3

we have the next information

24 dinner tables

each has 8 chairs

First we need to calculate 3/4 of the tables

24 mesas ----- 4/4=1

x ----- 3/4

x = the number of tabl

For the provided two-column proof, the following factors are accordingly absent:

Reason 2: Supplementary Angles' Definition

Reason 3: Equality's Substitution Property

Reason 4: Equality's Subtraction Property

Let we should finish the two-column proof step by step.

We learn that from the two column proof;

m∠2 = m∠3

Now that m∠1 + m∠2 = 180° has been established, we can see that m∠1 and m∠2 are on a straight line and that the sum of the angles on a straight line is 180°. They are hence supplementary angles, which is the explanation.

Similarly, since m∠3 and m∠4 are in a straight line;

So,

m∠3 + m∠4 = 180°

Therefore,

m∠1 + m∠2 = m∠3 + m∠4. The substitution property of equality makes this true.

Last but not least, because m∠2 = m∠3, they will cancel out in statement 3, and as a result, we now have;

m∠1 = m∠4. The equality's subtraction attribute is the cause.

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Given the coordinates of recatangle ABCD:

A(-3, 1), B(2, 1), C(2, -2), D(-3, -2)

Let's find the new coordinates after the rectangle is translated 4 units horizontally and -2 units vertically.

Let's apply rules of translation.

A translation 4 units horizontally means a shift 4 units to the right.

It is written as: (x + 4)

A translation -2 units vertically means a shift 2 units downwards.

It is written as: (y - 2)

Thus, to find the new coordinates, add 4 to the x-coordinates and subtract 2 from the y-cooridnates.

We have the translation rule: (x + 4, y - 2)

We have:

A(-3, 1) ==> (-3 + 4, 1 - 2) ==> A'(1, -1)

B(2, 1) ==> (2 + 4, 1 - 2) ==> B'(6, -1)

C(2, -2) ==> (2 + 4, -2 - 2) ==> C'(6, -4)

D(-3, -2) ==> (-3 + 4, -2 - 2) ==> (1, -4)

Therefore, the new coordintes of the figure are:

A'(1, -1), B'(6, -1), C'(6, -4), D(1, -4)

ANSWER:

A'(1, -1), B'(6, -1), C'(6, -4), D'(1, -4)

Answer:

  1.9532×10⁻¹¹

Step-by-step explanation:

You want the product (3.8 × 10^-2)(5.14 × 10^-10) in scientific notation.

The product is computed in the usual way, making use of the rules of exponents.

  (3.8 × 10^-2)(5.14 × 10^-10) = (3.8×5.14) × (10^-2)(10^-10)

  = 19.532 × 10^(-2-10) = 19.532 × 10^-12

Moving a factor of 10 from the coefficient to the exponent gives ...

  = 1.9532×10^-11 . . . . . . final answer in scientific notation

__

Additional comment

Scientific notation has 1 digit to the left of the decimal point in the coefficient.

Here, we had to divide by 10 to put the coefficient decimal point in the right place. To keep the number at the same value, we had to increase the exponent of 10 by 1 from -12 to -11.

Your calculator can display the product in scientific notation for you, as can any spreadsheet.

Sometimes it is convenient to adjust the exponents before the multiplication. Here, you can see the product of the coefficients will be greater than 10, so will ultimately need to be divided by 10. One way to get there is rewriting the problem as (0.38×10^-1)(5.14×10^-10). This will give a product coefficient between 1 and 10 with an exponent of -11.

<95141404393>

Answer:

B

Step-by-step explanation:

x + y = 180

co-interior

co-interior starts with C and x + y make a C shape (easier to remember)

Answer

The length of the garden = 84 m

Explanation

Part (a)

The given parameters are:

Perimeter of the rectangular garden = 306 m

The width of the garden = 69 m

The length of the garden = ?

Solution:

Using the formula for the perimeter of a rectangle:

The length of the garden = 84 m

Part (b):

The given parameters are:

The area of the rectangular window = 6364 cm²

The length of the window = 86 cm

The width of the window = ?

Solution:

The width of the rectangular window can be calculated using the formula for the area of a rectangle.

The width of the window = 74 cm

The first figure is a shape of four squares including a shaded square at the bottom left column.

The second figure has 6 squares including a shaded square at the bottom left column.

The third figure has 8 squares including a shaded square at the bottom left column.

The fourth figure has 10 squares including a shaded square at the bottom left column.

Thus, the general pattern is that the number of squares are increasing constantly by 2 but the shaded square remains unchanged.

Thus, the next figure is;

The next figure in the pattern shows a shaded square at the bottom left column with one unshaded square at the top left column. It has 12 squares in total.

In order to solve this exercise you need to remember the following:

In this case, based on the information given in the exercise, a school day is 8 hours. Then, you need to make the conversion from hours to minutes.

You can set up the following:

Therefore, evaluating you get:

Hence, the answer is:

We have a system of 2 equation (Eq):

y = 3x + 7 (Eq 1)

y = 2x + 8 (Eq 2)

To solve the system, we can match both equations.

3x + 7 = 2x + 8

3x - 2x = 8 - 7

x = 1

This is an example of a quadratic function

The real roots are where it crosses the x axis

Where it crosses the x axis are also called the zeros of the function or the x intercepts. They can also be called the roots of the quadratic.

Without the choices, I am unsure of the words to fill in the blank.

The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.

Given data -

Perimeter of circular plate = 10[tex]\pi[/tex] cm

We know that perimeter of a circle is 2[tex]\pi[/tex]r

Therefore   10[tex]\pi[/tex] = 2[tex]\pi[/tex]r

r = 5 cm

The given error Alan can make is +-1 cm.

Minimum radius is given by

2[tex]\pi[/tex]r = 10[tex]\pi[/tex] - 1

r = [tex]\frac{10\pi - 1 }{2\pi }[/tex]

r = 5 - [tex]\frac{1}{2\pi }[/tex]

Maximum radius is given by

2[tex]\pi[/tex]r = 10[tex]\pi[/tex] + 1

r = [tex]\frac{10\pi + 1 }{2\pi }[/tex]

r = 5 + [tex]\frac{1}{2\pi }[/tex]

The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.

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The rate of change of the perimeter of this rectangle is equal to 2 feet per second.

The rate of change of the area of this rectangle is equal to 20 feet per second.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2L + 2W

Where:

The rate of change for the perimeter of this rectangle is given by:

P = 2L + 2W

Differentiating with respect to t, we have:

dP/dt = 2dl/dt + 2dw/dt

Substituting the given parameters into the formula, we have;

dP/dt = 2(3) + 2(-2)

dP/dt = 6 - 4

dP/dt = 2 feet per second.

For the rate of change of the area of this rectangle, we have:

dA/dt = ldw/dt + wdl/dt

dA/dt = 8(-2) + 12(3)

dA/dt = -16 + 36

dA/dt = 20 feet per second.

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The sum of -6 ,12 and -4 is,

Express it on number line implies,