Use the sum of cubes identity to find the factors of the expression 8x^6 + 27y^3. Write your answer in the form of the expression on the right of the sum of cubes identity.

since 4000 ---> 210

then x -----> 336

(4000 * 336) / 210 = x

x = 6,400

10) The factor of the expression (x³ + 7x² + 6x) is,

⇒ x (x + 1) (x + 6)

11) The value of a in factor of (x² - 16x + 63) is, - 9

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

10) The expression is,

⇒ x³ + 7x² + 6x

11) The expression is,

⇒ x² - 16x + 63

Now, We can factor as;

10) The expression is,

⇒ x³ + 7x² + 6x

⇒ x (x² + 7x + 6)

⇒ x (x² + 6x + x + 6)

⇒ x (x (x + 6) + 1 (x + 6))

⇒ x (x + 1) (x + 6)

11) The expression is,

⇒ x² - 16x + 63

⇒ x² - 9x - 7x + 63

⇒ x (x - 9) - 7 (x - 9)

⇒ (x - 7) (x - 9)

Hence, By compare the factors (x - 7) (x + a), we get;

⇒ a = - 9

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The domain of the function is {-2, -1, 0, 1, 2}

The domain

This is the elements in the set A

So, we have

Domain =  {-2, -1, 0, 1, 2}

The range

To do this we calculate the value of the function at each x value

So, we have

y = -(-2)³ + 2 = 10

y = -(-1)³ + 2 = 3

y = -(0)³ + 2 = 2

y = -(1)³ + 2 = 1

y = -(2)³ + 2 = -6

So, the range is

Range = {10, 3, 2, 1, -6}

If it is a function

The relation is a function

Because each x value have unique y values

So, the notation is

f(x) = -x³ + 2

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The number of hours for both the motorcycles to meet is given by the equation T = 4 hours

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of the motorcycle 1 = 55 mph

Let the speed of the motorcycle 2 = 70 mph

Let the total distance between them be D = 500 miles

Now , the number of hours for them to meet be T

So , the distance traveled by motorcycle 1 d = 55T

The distance traveled by motorcycle 2 = ( 500 - d ) = 70T

Substituting the values in the equation , we get

( 500 - d ) = 70T

500 - 55T = 70T

Adding 55T on both sides of the equation , we get

500 = 125T

Divide by 125 on both sides of the equation , we get

T = 500/125

T = 4 hours

Hence , the number of hours is 4 hours

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There are 10 numbers of form ab554433221100 is divisible by 11.

To decide if a fraction has to be decreased, divisibility rules can be applied. The patterns that appear when we list the multiples of any number serve as the foundation for the rules.

Given:

Form: ab554433221100

If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.

Let us take value of a, b= 0, 1, 2, 3, ....9

So, the possible number divisible by 11.

00554433221100

11554433221100

22554433221100

33554433221100

44554433221100

55554433221100

66554433221100

77554433221100

88554433221100

99554433221100

Thus, we have 10 numbers.

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As per the equation, we are able to calculate the total cost of sundae being $17.

To calculate,

Per person cost × number of people = cost of sundaes

4.25 × 4 = 17

One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction. Divide a rational expression by multiplying the first fraction by its reciprocal. We factor everything and search for common factors after rewriting the division as multiplication of the first expression by the reciprocal of the second. rational arguments are divided. A division problem has three main components: the dividend, the divisor, and the quotient. That which will be divided is the dividend. The number of "people" into which the number is divided is referred to as the divisor. The ratio is the response.

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The value of the correlation coefficient for the number of baggage handlers and the number of arriving passengers is 0.842.

Therefore the answer is D. 0.842

The correlation coefficient is a measure of the strength of the linear relationship between two variables. It is a value between -1 and 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

In this case, the output from the regression equation analysis states that the correlation coefficient is √0.709 = 0.842, which means that there is a strong positive linear relationship between the number of baggage handlers and the number of arriving passengers. A correlation coefficient of 0.842 is considered a strong positive relationship.

In this case, an increase in the number of arriving passengers is associated with an increase in the number of baggage handlers needed, as reflected by the positive correlation coefficient.

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Insertion Sort with Binary Search is still a linear time-complexity algorithm in the average and worst case, but it is not the best option for sorting large arrays of elements, as the time complexity remains quadratic.

Insertion Sort is a simple sorting algorithm that works by inserting each element in its correct position in a sorted list.

a. It uses Θ(n²) comparisons in the worst case: This statement is true. In the worst-case scenario, Insertion Sort with Binary Search still takes Θ(n²) comparisons to sort an array of n elements. This happens when the array is sorted in descending order, and the elements need to be inserted one by one at the beginning of the list.

b. It uses Θ(n log n) comparisons in the average case: This statement is false. Insertion Sort with Binary Search still uses Θ(n²) comparisons in the average case, even though the use of Binary Search reduces the number of comparisons compared to Linear Search.

c. It uses Θ(n) comparisons in the best case: This statement is false. In the best-case scenario, Insertion Sort with Binary Search still takes Θ(n²) comparisons, as every element needs to be compared and inserted in its correct position

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Answer:

Step-by-step explanation:

18+4(m-3)+4m

18+4m-12+4m

=8m+6

Answer:  options a and c

Answer:

c=42

Step-by-step explanation:

have a good day!

Answer:

AB = 10ft

Step-by-step explanation:

First, we need to know that ED and AD share the same proportions as CB and AB. Since we know ED:AD is 9:6 and CB:AB is 15:x, we can now solve the problem.

ED:AD  =  9:6

CB:AB  =  15:x

Since we have to multiply the length of ED by 5/3 to get the length of CB, if we multiply the length of AD by 5/3, we can find the length of AB. Since 6*(5/3)=10, the length of AB must be 10.

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Answer: 70, 11, 91

Step-by-step explanation:
g - gumball
/ - fraction line
=> - results

The current total of gumballs = 200 - 25 = 175 gumballs

There are ? red gumballs in the machine:
red g/175 gumballs = 10/25 (the probability of a red gumball to fall in a sample)
red g/175 = 0.4 => 175 x 0.4 = 70 red gumballs

There are ? more green gumballs than white gumballs in the machine:
First, we need to find both green and white gumballs.

green g/175 gumballs = 5/25
green g/175 = 0.2 => 175 x 0.2 = 35 green gumballs

white g/175 gumballs = 2/25
white g/175 = 0.08 => 175 x 0.08 = 14 white gumballs

35 - 14 = 11 more green gumballs than white gumballs

There are ? gumballs that are either blue or green in the machine.

blue g/175 gumballs = 8/25
blue g/175 = 0.32 => 175 x 0.32 = 56 blue gumballs
or
175 - (70 red g + 35 green g + 14 white g) = 175 - 119 = 56 blue gumballs

35 green g + 56 blue g = 91 gumballs that are either blue or green


How do you find the probability?

It's simple, pretend like you have a dice. A dice has 6 faces and you need a six to (example) get out of Jail. You have 6 faces but you only need one, so the probability you get a 6 is 1/6 = 0.1(6)
But let's say you have 2 dices and you need both to be 6 to get out of jail. well thats 1/6 x 1/6 which is equal to 1/36  = 0.02(7)

In the problem, we have the sample of 25 gumballs in which 10 are red.
The probability a red gumball to fall is 10/25 = 0.4 (as calculated above)


I hope it was helpful! :]

The numerical value of x and y in the right triangle are 8√5 and 8 respectively.

The figure in the diagram is a right angle triangle.

Using the trigonometric ratios;

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Next, we determine the value of x.

sin( θ ) = Opposite / Hypotenuse

sin( 60 ) = x / 16

x = sin( 60 ) × 16

x = 8√5

For y;

cos( θ ) = Adjacent / Hypotenuse

cos( 60 ) = y / 16

y = cos( 60 ) × 16

y = 8.

Therefore, the value of x is 8√5 and y is 8.

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Answer:

total number of cherries=780

number of cherries on the plate=145

number of cherries on the bowl is 4 times the number of cherry in the plate=145×4=580

number of cherry in the cup =580+145-780=45

Consequently, point N's ordered pair is (2,6).  A pair that has two values stated in a specific order between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate

N's coordinates are: (-2,-6)

To create point N', point N is reflected over the y-axis.

Point N is then created by reflecting point N' over the x-axis ".

To locate: The ordered pair describing N's location ".

Solution:

Point N's coordinates are (-2,-6). To create point N', point N is reflected over the y-axis.

[tex]& (x, y) \rightarrow(-x, y) \\[/tex]

[tex]& N(-2,-6) \rightarrow N^{\prime}(2,-6)[/tex]

Point N is then created by reflecting point N' over the x-axis.

[tex]& (x, y) \rightarrow(x,-y) \\[/tex]

[tex]& N^{\prime}(2,-6) \rightarrow N^{\prime \prime}(2,6)[/tex]

Consequently, point N's ordered pair is (2,6)

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In rapidminer, correlation matrix is used to create correlation coefficients.

Correlation matrix Operator determines correlation between all attributes and it can produce a weights vector based on these correlations. Correlation is a statistical technique that can show whether and how strongly pairs of attributes are related.

Suppose we have two Attributes X and Y, with means X' and Y' respectively and standard deviations S(X) and S(Y) respectively. The correlation is computed as summation from 1 to n of the product (X(i)-X').(Y(i)-Y') and then dividing this summation by the product (n-1).S(X).S(Y) where n is total number of Examples and i is the increment variable of summation.

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Answer:

20

Step-by-step explanation:

Given that the triangles are similar, we know that the corresponding side lengths should all have similar ratios.

This means that ab/ef = bc/fg = ca/ge as they're corresponding.

We know that ge = 8, ca = 4, ab = 10 and we want to find ef

Remember ab/ef = ca/ge so 10/ef = 4/8

4/8 = 10/ef

==> cross multiply

80 = 4ef

==> divide both sides by 4

20 = ef

We can test our answer by seeing if the ratios are the same

ab/ef = 4/8 = 1/2

ca/ge = 10/20 = 1/2

The ratios are the same, therefore our answer is correct.

The expression of the composite function is (d) 192 - 24t

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

B(t) = 2(8 - t)

M(n) = 12n

To calculate the required function, we make use of

M(B(t))

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

M(t) = 12 * 2(8 - t)

So, we have

B(t) = 192 - 24t

Hence, the expression is (d) 192 - 24t

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Answer: Alan would have to sell less than 540 boxes.

Step-by-step explanation:

Part A: The point (2, 80) represents that when the number of hours is 2, the number of miles of water in the tank is 80.

Part B: y = 40x

The theory used in this question is the concept of proportional relationships.

A proportional relationship between two variables is one in which one variable is a constant multiple of the other.

In this case, the number of miles of water in the tank is a constant multiple of the number of hours.

The equation y = mx is used to describe a proportional relation, where m is the constant of proportionality.

The equation for the proportional relationship between hours, x, and number of miles, y, of water in a tank can be written in the form of y = mx. To find the value of m, we can use the point (2, 80) from the graph. We know that when x = 2, y = 80. We can use this information to solve for m.

m = y/x

m = 80/2

m = 40

Therefore, the equation for the proportional relationship is y = 40x.

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As per the given random number, the expected value of Y which counts how many of the Xi's are ≤ 1 is tₐ.

The term called random number in math is defined as a number chosen by chance that is randomly from a set of numbers.

Here we know that let us consider that n random number generators, where the a th one draws a number uniformly at random from the interval [0, tₐ].

Here we have also know that tₐ's are arbitrary positive integers.

Let us consider that Xₐ be the number drawn by the ₐ th random number generator.

Then the the expected value of the sum is written as,

=>  S = X1 + X2 + ... + Xₐ

Where it can be simply written as,

=> S = ∑Xₐ

Here we have also know that  the expected value of Y, which counts how many of the Xi's are ≤ 1 is calculated as,

=> Y = ∑Xₐ where {0 < tₐ < a}.

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The required thickness of member BC to the nearest 1/16​ in. and the diameter of the pins at A and B is dA​= [tex]1\frac{1}{8}[/tex] in

To solve thsi It is necessary to determine the thickness of BC. The allowed normal stress is σ[tex]_{allow[/tex]=29 ksi and the permissible shear stress is τ[tex]_{allow[/tex]=10 ksi.

In the first we will determine the reactions of the system.

We apply the conditions of equilibrium:

→+∑Fₓ=0

+↑∑F[tex]_y[/tex]=0

+↺∑M=0

From picture b

∑M[tex]_B[/tex]=0

⇒−2⋅8⋅4+Ay⋅8=0

⇒Ay​=8 kip

∑Fy=0

⇒−2⋅8+Ay​+By​=0

⇒−2⋅8+8+By​=0

⇒By=8 kip

From picture c)

∑M[tex]_C[/tex]=0

⇒+By​⋅cos60∘−Bx​⋅sin60∘=0

⇒+8⋅cos⁡60∘−Bx⋅sin⁡60∘=0

⇒Bx=4.6188 kip

In the next step we will determine the dimensions of the BC rod:

[tex]\sigma BC= \frac {F_{BC}}{A_{BC}}\leq \sigma _{allow}[/tex] =29 ksi

The cross-sectional area has a value:

[tex]A_{BC}=1.5.t[/tex]

The force acting in the BC stick is calculated as follows:

[tex]F_{BC}=\sqrt{4.6188^2+8^2}=9.258 \ kip \\\\=\frac{9.258}{1.5.t}=29 \\\\=t=0.2128 \ in=1/4in[/tex]

Now we can switch to determining the diameter of the pins.

Pin B:

τB=VB/AB⩽τallow=10 ksi

The cross-sectional area has a value:

AB=π/4⋅d²B

The force acting in the BB pin is calculated as follows:

VB=[tex]\sqrt{4.618^2+82^2[/tex]=4.629 kip

[tex]\frac{4.629}{\pi/4 . d^2_B} =10[/tex]

⇒dB​=0.767in=13/16in

Now we can switch to determining the diameter of the pins.

Pin A

τA=VA/AA⩽τallow=10 ksi

The cross-sectional area has a value:

[tex]A_A​=\pi/4 . d^2B[/tex]

The force acting in the AA pin is calculated as follows:

[tex]V_A=4.618^2+8^2[/tex]=9.258 ki

9.258 ÷ π/4⋅d²A=10

⇒dA​=1.0859in=[tex]1\frac{1}{8}[/tex]in

The solution is:

{σs=208 MPa​}

{dB=13/16in}

{dA=[tex]1\frac{1}{8}[/tex]in​}

Complete Question:

Determine the required thickness of member BC to the nearest 1/16in. and the diameter of the pins at A and B if the allowable normal stress for member BC is σ allow =29 ksi and the allowable shear stress for the pins is τ allow =10τ allow ​=10 ksi.

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The derivatives of tan^2(x) and sec^2(x) are the same because they are related by the identity tan^2(x) = sec^2(x) - 1.

By using the chain rule, the derivative of tan^2(x) can be found by first finding the derivative of tan(x), then squaring it. The derivative of sec^2(x) can also be found using the chain rule, by first finding the derivative of sec(x), then squaring it.

Since tan^2(x) and sec^2(x) are related by a constant difference, their derivatives will be the same. This means that the rate of change of tan^2(x) with respect to x will be equal to the rate of change of sec^2(x) with respect to x. This is a useful relationship because it allows us to relate the derivatives of two important trigonometric functions, making it easier to integrate or differentiate expressions involving them.

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Answer:

The probability that two random numbers, x and y, both of which are uniformly distributed on the interval [0,1] and independent, will have a product greater than 1/2 is 1/8.

Probability is a field of mathematics that deals with the study of random events.

In this question, we're looking at the probability of two random numbers having a product greater than 1/2.

Let's take two random numbers, x and y, both of which are uniformly distributed on the interval [0,1].

And since x and y are independent, the occurrence of one event does not affect the occurrence of the other event.

To find the probability that x * y is greater than 1/2, we need to find the area of the region in the x-y plane where x * y is greater than 1/2.

This region is a triangle whose vertices are (0,1), (1,0), and (1/2, 1/2).

The area of this triangle is 1/8, so the probability that

=> x * y  > 1/2 = 1/8.

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Answer: 16cm

Step-by-step explanation:

1 metre = 100cm

16% of 100 = 16

Therefore your answer will be 16cm !

0.079 liters is 79.1 ml with correct significant numbers.

We know that 1 liters = 1000 ml

Hence, 1 ml = 0.001 liters

In the given question we need to convert 79.1 ml to liters. So, we multiply 79.1 ml by 0.001 l to convert ml to liters.

79.1 x 0.001 = 0.0791 l

The given question 79.1 ml has 3 significant figures. Hence, we can write 0.0791 as 0.079 l as 3 significant figures, counting the digits on the right of decimal point.

Therefore, 0.0791 liters is 79.1 ml. On rounding it to correct significant numbers, we get 0.079 l.

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Answer:

9 m , 23 m , 23 m

Step-by-step explanation:

let the third side be represented by x , then the 2 equal sides are

3x - 4 and 3x - 4

the perimeter (P) is the sum of the 3 sides

P = x + 3x - 4 + 3x - 4 = 7x - 8

given P = 55 m , then equating

7x - 8 = 55 ( add 8 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

3x - 4 = 3(9) - 4 = 27 - 4 = 23

sides of triangle are 9 m , 23 m and 23 m