If 24000 bricks of the same shape and size are required to build a wall of dimension 15m*6m*20m find the volume of each brick
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The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²

An expression is combination of variables, numbers and operators.

(4c − 3d)(3c + d) is the given expression.

Four times c minus three times d into three times f c plus d.

In the given expression c and d are variables.

Plus and minus are operators.

We need to find the equivalent expression of (4c − 3d)(3c + d).

(4c − 3d)(3c + d)

4c(3c+d)-3d(3c + d)

Apply the distributive property.

12c² + 4cd - 9cd - 3d²

Add the like terms

12c² - 5cd - 3d²

Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).

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The correct matching regarding the linear functions are given as follows:

i. A set of points where the coordinates of each point has a sum of 2: Line n.

ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.

b - i) Two numbers with a sum of 2: A and C.

b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.

b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.

The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function

x + y = 2.

In slope-intercept form, it is of:

y = 2 - x.

Which is the decreasing line n, with an intercept of 2.

A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function

y = x - 10.

Which is the increasing line m, which an intercept of m.

The coordinates of each point are given as follows:

These points are then used to match the sentences in item b.

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Answer: She needs to ride 13.9 more kilometers on her bike to finish the race.

Step-by-step explanation:

==> 30 = 3.75 + 12.35 + x

Take 16.1 from both sides:

==> 30 = 16.1 + x

==> 30 = 13.9km

Answer:

Step-by-step explanation:

The answer would be 13.9, if you add 12.35 to 3.75 you get 16.1, then 16.1 added to 13.9 equals 30

The total income from the machines over the first 5 years is $185.89

From the question, we have the following parameters that can be used in our computation:

f(t) = 160e0.03t

Where

Rewrite the function properly

so, we have the following representation

f(t) = 160e⁰.⁰³ⁿ

The above function is an exponential function

So: In the first 5 years, we have the value of t to be 5

This is represented as follows

t = 5

Substitute the known values in the above equation, so, we have the following representation

f(5) = 160e⁰.⁰³ ˣ ⁵

Evaluate the product of the exponents

f(5) = 160e⁰.¹⁵

The products above give

f(5) = 185.89

Hence, the total income is $185.89

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Answer: 160 inches

Step-by-step explanation:

To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.

Answer:

[tex] \sqrt{176} [/tex]

[tex] \sqrt{16 + 11} [/tex]

[tex]4 \sqrt{11} [/tex]

Step-by-step explanation:

The answer is

[tex]4 \sqrt{11} [/tex]

We

need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.

i hope this helped

The population standard deviation [tex]\sigma[/tex] is 6.697.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

The given data set can be arranged as 4, 7, 8, 10, 12, 12, 15, 18, 23, 26.

Mean[tex](\overline{x})[/tex] = (4 + 7 + 8 + 10 + 12 + 12 + 15 + 18 + 23 + 26)/10.

Mean[tex](\overline{x})[/tex] = 135/10 = 13.5.

We know variance[tex](\sigma)[/tex] = [tex](\[ \sum_{i=1}^{n}x_i^2 \]/n) - \overline{x}^2[/tex].

= (4² + 7² + 8² + 10² + 12² + 12² + 15² + 18² + 23² + 26²)/10 - (13.5)².

= (16 + 49 + 64 + 100 + 144 + 144 + 225 + 324 + 529 + 676)/10 - 182.25.

= 44.85

And we also know the standard deviation is [tex]\sqrt{\sigma}[/tex] = [tex]\sqrt{44.85}[/tex] = 6.697

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The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.

A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.

The expression for the volume of a regular pentagon is given as V =  5/2 × abh

Where h is the height and a and b are the length of the sides.

Now, the value of a, b and h as per the question is given as,

a = b = h = 1.

Then, the volume can be calculated as,

V = 5/2 × 1 ×1 × 1
   = 2.5

Hence, the volume of the regular pentagonal prism  is given as 2.5 cm³.

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The values for the given data set is as follows 120 , 720 , 8 ,40320 , 6720 ,3628800 respectively.

The formula to calculate the permutation is , P = n! / (  n - r )!. Using this formula we get the result as,

P(6,3) = 6! / (6−3)!

​= 6! /  3!

​ = 120

P(8,1) = 8! / (8 - 1)!

​= 8! /  7!

​ = 8

P(6,5) = 6! / (6-5)!

6! / 1!

720

Similarly ,

P(8,8)= 40320

P(8,5) = 6720

P(10,9) = 3628800

A permutation is a specific arrangement of items. Set members or elements are arranged in a sequence or linear order here.

For example, the permutation of set A=1,6 is 2, as in 1,6,1.

There are no alternative ways to arrange the items in set A, as you can see.

In permutation, the elements must be organised in a specific sequence, whereas in combination, the order of the elements is irrelevant. Read also: Permutation And Combination

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The option b "The index for any quarter must be between 0 and 2" is correct.

In the given question, we have to find the incorrect statement about a company has computed a seasonal index for its quarterly sales.

For its quarterly sales, the corporation has created a seasonal indicator.

Consequently, it is correct that the four quarterly seasonal index figures add up to 4.

True, the average index is 1.

In this situation, an index of 0.75 for the first quarter's sales implies that they were 25% below average, while an index of 1.10 shows that they were 10% over average.

Hence, the incorrect statement of the option b "The index for any quarter must be between 0 and 2" is correct.

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The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.

The price of a bond is its present value.

The present value can be computed by setting the following parameters:

This can be done using an online finance calculator with the results as follows:

N (# of periods) = 20 semiannual periods (10 years x 2)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)

FV (Future Value) = $105

Results:

Present Value (PV) = $115.87

Sum of all periodic payments = $100 ($5 x 20)

Total Interest = $89.13

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Answer: 115.87 (If you don't get this answer then the solution is incorrect.)

By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)

The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.

To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.

Given the system of equations,

y = 5x + 2

y = x - 2

The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.

The point of intersection is at (-1, -3). Therefore, the solution is:

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The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given

A line passes through the point (-6,3)

and has a slope of 3/2

Slope intercept form

y = mx + b

Equation,

y - 3 = 3/2(x - (-6))

y - 3 = 3/2(x+6)

2y - 6 = 3x + 18

2y = 3x + 24

y = 3/2x + 12

The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.

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The scientific terms for peaks and valleys is B. Crests and troughs.

The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.

The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.

The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.

Therefore, based on the information given, the correct option is B.

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The procedure is correct is  1 + tan²(theta) = sec²(theta)

What is  Fraction?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

And

cos²(theta) = 1 - sin²(theta)

Are both valid identities

Keisha and the David.

As per the question Kisha and the David found the same value of the cosine theta as given by the  Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).

Thus the answer is both procedures are correct.

As they both wanted to find the solutions to the numerical problems they made two different methods.

Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).

Hence both options are the same and true.

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Answer:

x is 44 Hope that helps.

Answer:

x = - 3

Step-by-step explanation:

2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify

2x - 12 + 2 = 4x - 4

2x - 10 = 4x - 4 ( subtract 4x from both sides )

- 2x - 10 = 4x - 4 ( add 10 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer:

SOLUTION

2(X-6)+2=4X-4

open the blanket by multiplication

2x-12+2=4x-4

2x-10=4x-4

collect like term

2x+4x=-4+10

6x=6

divide both side by 6

x=1

We had written an algorithm, using pseudo code.

//Define the required variables.

total_number_of_steps = 0

number_of_steps = 0

//robot stands up to walk.

stand

//the robot moves forward till the wall is not reached.

while (wall is not reached)

//the robot senses the wall with the help of arms.

raise arms

sense_the_wall

if (wall is not there)

//if the wall is not found, the robot lowers the arms

lower arms

//if wall is not detected, the robot moves forward.

step_forward

//increment the number of steps forward.

number_of_steps=number_of_steps+1

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

else

exit

end if

end while

//else if the wall is found, lower the arms

lower arms

//the robot turns 90 degrees right once.

turn_right_90

//the robot turns 90 degrees right again.

turn_right_90

//till the number of steps does not reach 0, move

for (number_of_steps! = 0)

step

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

//the robot moves backwards on detecting the wall, so

//decrement the number of steps.

number_of_steps = number_of_steps-1

//end the for loop.

end for

//the robot turns 90 degrees left once.

turn

//the robot turns 90 degrees left again.

turn

//the robot sits down.

sit

//display the total number of steps taken by robot

display total_number_of_steps

The last line ends the pseudocode

Stop

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A solid figure is a three-dimensional object. That is, it has length, width, and height. Because they are three-dimensional, they have depth and occupy space in our universe. Body types are identified according to characteristics specific to each body type. In particular, we can observe the number of faces, edges, vertices, and the shape of the base.

A flat face of a solid is its face or side, as it is commonly called. The base is the surface on which the figure rests. A solid edge is a line segment where two faces meet. A vertex  is an angle formed where the endpoints of two or more face segments meet.

A sphere is a solid figure that has no faces, edges, or vertices. This is because it is perfectly round. No flat sides or corners.

A cone has faces but no edges or vertices. His face is circular. A circle is a plane because it is a flat planar shape. However, since it is rounded on the outside, it does not form edges or corners.

Cylinder that has two circular faces but no edges or corners:

A pyramid has a base and at least three triangular faces. There are edges where faces meet each other or meet the bottom, vertices where two faces meet the bottom, and top vertices where all the triangle faces meet. Pyramids are named for the shape of their base.

A triangular pyramid has a triangular base and his other three triangular faces, or four triangles in total.

A pyramid has a rectangular base and a pyramid has a square base. Both have four triangular faces, for a total of five faces.

Prism:

A prism is a solid with two congruent parallel faces and any number of sides. That is, it can have any number of faces, but at least two faces must be parallel. The shape of the two parallel faces can be triangles, squares, rectangles, pentagons, hexagons, or other types of polygons. Prisms are named after the shape of the base.

Sphere:

A sphere is a geometric object that is the three-dimensional analogue of the two-dimensional circle. A sphere is a set of points that are all the same distance r from a given point in 3D space. This given point is the center of the sphere and r is the radius of the sphere. Spheres are fundamental objects in many areas of mathematics. Spherical and near-spherical shapes also occur in nature and industry. Bubbles, like soap bubbles, are spherical in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy.

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(a) Using y the manufacture can find the required diameter of the hole.

(b) The mean of the random variable y is 0.003.

(c) The standard deviation of the y is 0.0063.

(d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

(e)  We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

Given that x1 be the peg diameter with mean 0.25 in. and standard deviation 0.0006 in.and x2 be the hole diameter with mean 0.253in. and deviation 0.002 in.

a) y=x2-x1 denote the difference between hole and peg diameter

if y<0 , the peg won’t go inside the hole and

if y>0 ,the peg be loose to the hole

So using y the manufacture can find the required diameter of the hole.

b)Now, we have to find the mean of the random variable y

μ(y) = μ(x2) - μ(x1)

μ(y) = 0.253-0.25

μ(y) = 0.003

c) Now we have to find the standard deviation of the y

σ(y) = √{var(x1)+ var(x2)}(x1 and x2 are independent)

σ(y) = √0.000036+0.000004

σ(y) = √0.00004

σ(y) = 0.0063

d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

e) With a standard deviation larger than the mean , it would be fairly likely to observe a negative value of y, so it would be a relatively common occurrence to find a peg that was too big to fit in the predrilled hole. We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

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The if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

What is the Converse Statement?

That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.

We have given the statement:

Vertical angles are equal in measure.

A). Rewrite the statement as an if-then statement.

If angles are vertical angles then their measure is equal.

B). Write the converse of the implication

If the measure of angles is equal then they are vertical angles.

Hence, the if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

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The degree to turn before walking 673 paces is 59 degrees

From the question, we have the following parameters that can be used in our computation:

Lengths = 989 paces, 673 paces and 861 paces

These paces can be represented as

x = 989

y = 673

z = 861

The measure of the required angle (angle Z) i.e.  the degree to walk can be calculated using the following cosine rule

z² = x² + y² - 2xy * cos(Z)

Substitute the known values in the above equation, so, we have the following representation

861² = 989² + 673² - 2 * 989 * 673 * cos(Z)

Evaluate the exponents, the products and the summation

So, we have the following representation

741321 = 1431050 - 1331194 * cos(Z)

Evaluate the like terms

- 1331194 * cos(Z) = -689729

Divide both sides by  - 1331194

cos(Z) = 0.51812808651

Take the arc-cos of both sides

Z = 58.7

Approximate

Z= 59 degrees

Hence, the measure of the angle is 59 degrees

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The value of down payment will be;

⇒ $705

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Now,

Since, Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Hence, The value of down payment = 15% of $4700

                                                        = 15/100 × 4700

                                                        = 15 × 47

                                                        = 705

Thus, The value of down payment = $705

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For an independent-measures t test, the option that describes the estimated standard error of the difference in sample means is D. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.

A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment actually affects the population of interest or whether two groups differ from one another.

The Independent Samples t Test compares the means of two separate groups to see if there is statistical support that the population mean values are statistically significantly different. A parametric test is called the Independent Samples t Test. For instance, you could determine whether first-year graduate salaries varied by gender using an independent t-test.

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Complete question

for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is

a. a weighted average of the two sample

b. the difference between the standard deviationa

c. The variance

d. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.

Step-by-step explanation:

similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).

so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.

some correct answer options are not listed, so we need to adjust to the existing ones.

remember, the sum of all angles in a triangle is always 180°.

so,

angle A + angle B + angle C = 180

40 + angle B + 60 = 180

angle B = 80°

so, angle E = 80° for the triangles to be similar.

AC × c = DF

12 × c = 16

3 × c = 4

c = 4/3

so,

AB × c = DE

9 × 4/3 = DE

36/3 = DE

DE = 12

so, either angle E = 80° or DE = 12.

A set-to-set function f is a relation that assigns one element of the set A to each element of the other set B. The set A is the domain of the function (also called the set of inputs) and the set B contains the range (also called the set of outputs).

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

1. Not an exponential function:

We have the following equation:

[tex]y = 100 (1 - 12)^{t}[/tex]

We can write the equation as:

[tex]y = 100 (-11)^{t}[/tex]

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

Therefore: a must be more than 01.

In this problem, a = -11, therefore this is not an exponential function.

2. Growth.:

The function:

[tex]y= 0.1(1.25)^{t}[/tex]

The above equation is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

Therefore, k = 0.1 and  a = 1.25 . So, a is greater than 1.

3. Growth:

The function:

[tex]y = {(1 - 0.03)12}^2t[/tex]

The above equation can be written as:

[tex]y = 11.64^{2t}[/tex]

which  is an exponential function because is a function of the form

[tex]f(t) = a^{bt}[/tex]

where, a > 0 and b is constant.

So, a = 11.64 and b = 4 . Since a is greater than 1.

4. Decay:

The function:

[tex]y = 426(0.98)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

So, k = 426 and a = 0.98. Since, a is less than 1.  

5. Growth:

The function:

[tex]y = 2050(12)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant.

So, k = 2050 and a = 12  . Since, a is greater than 01.  

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The graph that shows the linear relationship of the table is attached below.

To determine the graph of a linear relationship, do the following:

Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:

Slope = change in y / change in x = (1 - 0) / (2 - 0)

Slope = 1/2.

The y-intercept (b) = 0.

Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.

Thus, the graph is shown below.

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