The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?

Rational exponents are beneficial in removing the root over or radicals

Let's check the rule

Take an example

We know that cos2x=cos²x-sin²x

=cos²x-(1-cos²x)         [since, cos²x+sin²x=1]

=cos²x-1+cos²x

=2cos²x-1

So, cos2x=2cos²x-1

Hence, cos²x= (1+cos2x)/2

Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables occurring on both sides of an equation. Geometrically, these identities involve certain trigonometric functions (such as sine, cosine, tangent) of one or more angles.

Most common trigonometric identities are:

- cos²x + sin²x = 1

- sec²x - tan²x = 1

- cosec²x - cot²x = 1

- cos2x = cos²x - sin²x

Therefore we get that the statement cos² x = (1 - cos 2x)/2 is false.

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Answer:

[tex] \boxed{ \rm(6x)²-(5)²}[/tex]

Step-by-step explanation:

Given expression/polynomial :

[tex]3 6{x}^{2} - 25[/tex]

Let's evaluate.

We can re-write the polynomial as

Further

Hence, the expression is equivalent to last Choice, (6x)²-(5)².

-Regards, Hannah :)

Answer:

Since we want to find radius and the diameter is 28 we will divide by two = ²⁸/2 which gives a radius of 14

since the radius is 14cm. we move on to the volume .

WE SUBSTITUTE

⁴/3× ²²/7× 14 equals 58.2cm²

therefore radius; 14cm

volume; 58.2cm

The height of the tree is 249.5 feet

The given parameters are:

Let the height of the tree be x.

So, we have:

tan(80) = x/44

Multiply both sides by 44

x = 44 * tan(80)

Evaluate

x = 249.5

Hence, the height of the tree is 249.5 feet

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The average rate of change of the function will be 63.

The average rate of change of the function is used to find the slope of the graphed function which can be calculated by the change in y value divided by the change in x value.

The average rate of change of function f(x) in the interval [a,b] can be calculated as avearge rate of change= (f(b)- f(a))/(b-a)

Here given function is g(x) = 7x³-4

which is defined in the interval [-3,3].

So using the defination of the average rate of change, The average rate of change= (g(3)-g(-3))/(3-(-3))

= {(7(3³)-4)-(7*(-3)³-4)}/(3-(-3))

= {(189-4)-(-189-4)}/(3+3)

= (185-(-193))/6

= (185+193)/6

= 378/6

= 63

Therefore the average rate of change of the function will be 63.

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Considerando la definición de mínimo común múltiplo, el mínimo común múltiplo entre 10, 18 y 36 es 180.

Un número es múltiplo de otro cuando lo contiene n veces de forma exacta. Es decir, los múltiplos de un número son aquellos que obtienes cuando multiplicas un número por otros.

El mínimo común múltiplo (mcm) es la cifra más pequeña que satisface la condición de ser múltiplo de todos los elementos de un conjunto de números. En otras palabras, el mínimo común múltiplo (mcm) es el número positivo más pequeño que es múltiplo de dos o más números.

Una forma de calcular el mcm es descomponiendo los números en sus divisores (número que está contenido en otro de forma exacta una cantidad n de veces) y que estos sean números primos (que solo pueden dividirse entre ellos mismos y el 1 para obtener un número entero). Es decir, se debe descomponer en factores primos cada número.

Luego, se debe seleccionar los factores primos comunes y no comunes con mayor exponente para finalmente multiplicar los factores primos seleccionados.

En primer lugar, se descomponen los números:

Los factores primos comunes y no comunes con mayor exponente:

Entonces, el mínimo común múltiplo entre 10, 18 y 36 es calculada como:

M.C.M(10,18,36)= 2²×3²×5= 2×2×3×3×5= 180

Finalmente, el mínimo común múltiplo entre 10, 18 y 36 es 180.

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Answer:

600

Step-by-step explanation:

Let's consider this question using algebra.

Imagine the number of bricks in the original pile is [tex]x[/tex].

We are told that [tex]\frac{3}{4}[/tex] of the bricks are used for a project, meaning that [tex]\frac{3}{4} x[/tex] has been used, leaving us with [tex]\frac{1}{4}x[/tex] as our remainder.

Then, we are told that [tex]\frac{2}{3}[/tex] of the remainder are used to leave us with 50 bricks. This means that [tex]\frac{1}{3}[/tex] of the remainder is left, and this is equal to 50 bricks. This means that the remainder's original amount is equal to 150, because we are told that [tex]\frac{1}{3}[/tex] of the remainder is equal to 50.

So, we know that the remainder is 150, and we also know that the remainder is [tex]\frac{1}{4} x[/tex]. Let's now use these to form an equation.

[tex]\frac{1}{4} x = 150[/tex]

Because we know that a quarter of the original amount of bricks is equal to 150, we can multiply both sides of the equation by 4 to get the original amount of bricks in the pile.

[tex]x = 150 * 4 = 600[/tex]

So, there were 600 bricks in the original pile.

Answer:

(6,2)

Step-by-step explanation:

When solving a system of simultaneous equations, we want to see where the graphs intersect.

2x+5y =22 is the red line

x+y = 8 is the green line

They intersect at a point

The point is x=6   y=2

(6,2)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: slope = not \:\: defined [/tex]

with closest value = [tex] \sf{\infin} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: slope = \cfrac{rise}{run}[/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{ - 8 - ( - 9)}{1 - 1} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{ - 8 + 9}{0} [/tex]

[tex]\qquad \tt \rightarrow \: m \: \: is \: \: not \: \: defined[/tex]

[ Any real number divided by 0 is not defined ]

You can also assume it's closest value if possible, that is infinity ([tex]\sf{\infin}[/tex])

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

true

Step-by-step explanation:

this is absolutely true

No. of pounds of seed it takes to plant an 8-acre field = 70 pounds.

No. of acres can be planted per pound of seed = 70/8

= 8.75.

thus, 8.75 acres can be planted per pound of seed.

Answer:

70 (100-30)

Rambling (Unrelated):

Although if you take 30 apples from your own stockpile of 100 apples, you still have 100 apples

100 apples

Answer:

  (a)  9, 8, 7, 6, 5, ...

Step-by-step explanation:

The solution to the inequality can be done a couple of ways. The solution is similar to that for a one-step linear equation.

__

We know that multiplying numbers by a negative value reverses their order. For example, 1 < 2, but -1 > -2. That is, multiplying by -1 requires a change in the comparison operator if it is to remain true.

For our inequality, we want to solve it by multiplying both sides by -1/4:

  -4y > -40

  (-1/4)(-4y) < (-1/4)(-40) . . . . . multiply both sides by -1/4 (reverses order)

  y < 10 . . . . . . . . . . . simplify

The first few decreasing integer values that are part of this solution are ...

  {9, 8, 7, 6, 5, ...}

__

We can add 4y+40 to both sides of the inequality. The result will be an inequality with positive coefficients. This can be solved in one step.

  -4y > -40 . . . . . given

  (-4y) +(4y +40) > (-40) +(4y +40) . . . . . . add 4y+40 to both sides

  40 > 4y . . . . . . . . . . . . . . . simplify

  10 > y . . . . . . . . . . . . divide by 10 (order is unchanged)

  y < 10 . . . . . . . . . rearrange to put y on the left

Integer solutions to this inequality are ...

  {9, 8, 7, 6, 5, ...}

Answer: [tex]y-3=-4(x+3)[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{-1-3}{-2-(-3)}=\frac{-4}{1}=-4[/tex]

So, using the point (-3, 3) to substitute into point-slope form, the equation is [tex]\boxed{y-3=-4(x+3)}[/tex]

The length of the infinite zigzag path is 1

Note that the infinite zigzag path is embedded in an isosceles triangle

Using angle π/4, we have that

Tan π/4 = opposite/ adjacent

[tex]tan \frac{3. 412}{4} = \frac{x}{1}[/tex]

[tex]tan 0. 7855 = x[/tex]

[tex]x = 0. 014[/tex]

To find the longer part 'y',  use the Pythagorean theorem

[tex]y^{2} = (0.014)^2 + (1)^2[/tex]

[tex]y^2 = 1.879 * 10^-4 + 1[/tex]
[tex]y^2 = 1. 00[/tex]

[tex]y = \sqrt{1. 000}[/tex]

[tex]y = 1. 000[/tex]

The length of the infinite zigzag path is the same as the length of the longer part of the triangle which equals 1.

Thus, the length of the infinite zigzag path is 1

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Answer:

Step-by-step explanation: 1. 5040 because 10x9x8x7

3. 10000 because 10^4=1000

1)There are 5040 possible codes are there if the digits cannot be repeated.

2)The probability that you will guess the correct code on your first try will be (1/5040).

3) Possible code = 10000 .

Given,

Numbers : 0 to 9

Here,

Total number of digit = 0,1,2,3,4,5,6,7,8,9

Given condition;

a)

Four digit card must be drawn;

The total possible ways there if the digits cannot be repeated will be;

⇒10×9×8×7

⇒5040

b)

The probability that you will guess the correct code on your first try is;

P(A) = n(A)/n(S)

Where,

n(A) is the event has the right code

n(S) is the total possible ways;

P(A) =1/5040

Hence the total possible ways there if the digits cannot be repeated and the probability that you will guess the correct code on your first try will be 5040 and (1/5040) respectively.

c)

If the gits can be repeated then we have 10 digits for each place :

Possible code = 10 * 10 * 10 *10

Possible code = 10000

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Answer:

[tex]1.3\cdot 10^3\text{ J}[/tex]

Step-by-step explanation:

Power is defined by work over time. In physics, work can be defined as the energy transferred over from an applied force over some distance. As a formula:

[tex]W=Fd[/tex], where F = force applied and d = distance that force is applied over.

*It is worth noting that F must be parallel to the distance travelled. If it is perpendicular, no work is done, and if it is at an angle, find the parallel component and use that for F.

In this case, the force applied must counter the force of gravity on Martha, which is given by [tex]F_g=mg[/tex], where m = Martha's mass and g = gravitational constant 9.8 m/s/s. Therefore, [tex]F_g=75\cdot 9.8=735\text{ N}[/tex]. Since she raises her body 4.0 meters, the work done must be [tex]W=Fd=735\cdot 4=2940\text{ J}[/tex].

Since power is equal to work over time and t = 2.3 seconds, we have:

[tex]\displaystyle P=\frac{W}{t}=\frac{2940}{2.3}=\boxed{1278\text{ J}}\approx \boxed{1.3\cdot 10^3\text{ J}}[/tex] (to two significant figures)

Using a linear function, we have that:

a) The percentage will be 47% during the year of 2001.

b) The predicted percentage in 2005 is of 44.97%.

A linear function is modeled by:

y = mx + b

In which:

The percentage in 1980 is considered as the initial amount, hence b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by:

m = (50.5 - 58.8)/15 = 0.5533.

Hence the percentage in t years after 1980 is given by:

P(t) = 58.8 - 0.5533t.

Item a:

This is t + 1980, for which P(t) = 47, hence:

P(t) = 58.8 - 0.5533t

47 = 58.8 - 0.5533t.

0.5533t = 11.8.

t = 11.8/0.5533

t = 21.3.

1980 + 21 = 2001, hence the percentage will be 47% during the year of 2001.

Item b:

2005 is 25 years after 1980, hence the percentage is P(25), given as follows:

P(25) = 58.8 - 0.5533x25 = 44.97%.

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Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Given equation:

[tex]2 \ln 4+\ln x=3 \ln 2+\ln(x+1)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x = \ln x^n[/tex]

[tex]\implies \ln 4^2+\ln x=\ln 2^3+\ln(x+1)[/tex]

Simplify:

[tex]\implies \ln 16+\ln x=\ln 8+\ln(x+1)[/tex]

Subtract ln 8 from both sides:

[tex]\implies \ln 16+\ln x- \ln 8=\ln(x+1)[/tex]

Subtract ln x from both sides:

[tex]\implies \ln 16-\ln 8=\ln(x+1)-\ln x[/tex]

[tex]\textsf{Apply the quotient law}: \quad \ln x - \ln y = \ln \frac{x}{y}[/tex]

[tex]\implies \ln \left\dfrac{16}{8}\right = \ln \left(\dfrac{x+1}{x}\right)[/tex]

Simplify:

[tex]\implies \ln 2 = \ln \left(\dfrac{x+1}{x}\right)[/tex]

[tex]\textsf{Apply the equality law}: \quad \textsf{if }\: \ln x= \ln y\:\textsf{ then }\:x=y[/tex]

[tex]\implies 2=\dfrac{x+1}{x}[/tex]

Multiply both sides by x:

[tex]\implies 2x=x+1[/tex]

Subtract x from both sides:

[tex]\implies x=1[/tex]

Answer:

w= 2v/3 plus 5

2v+15=3w.forw

Swap sides so that all variable terms are on the left hand side.

3w=2v+15

Divide both sides by 3.

3

3w

​

=

3

2v+15

​

Dividing by 3 undoes the multiplication by 3.

w=

3

2v+15

​

Divide 2v+15 by 3.

w=

3

2v

​

+5

Step-by-step explanation:

2v+15=3w.forw

Swap sides so that all variable terms are on the left hand side.

3w=2v+15

Divide both sides by 3.

3

3w

​

=

3

2v+15

​

Dividing by 3 undoes the multiplication by 3.

w=

3

2v+15

​

Divide 2v+15 by 3.

w=

3

2v

​

+5

Step-by-step explanation:

2v+15=3w.forw

Swap sides so that all variable terms are on the left hand side.

3w=2v+15

Divide both sides by 3.

3

3w

​

=

3

2v+15

​

Dividing by 3 undoes the multiplication by 3.

w=

3

2v+15

​

Divide 2v+15 by 3.

w=

3

2v

​

+5

Step-by-step explanation:

2v+15=3w.forw

Swap sides so that all variable terms are on the left hand side.

3w=2v+15

Divide both sides by 3.

3

3w

​

=

3

2v+15

​

Dividing by 3 undoes the multiplication by 3.

w=

3

2v+15

​

Divide 2v+15 by 3.

w=

3

2v

​

+5

Step-by-step explanation:

Between Steps 1 and 2, the student added 6x to the left hand side, but subtracted 6x from the right hand side.

Answer:

b

Step-by-step explanation:

just took it

Answer:

B. m∠JXY = m∠NXY

Step-by-step explanation:

I got the answer correct

Answer : C. 512

step-by-step explanation :

[tex]\qquad\qquad\qquad\boxed{\bf\:\: \: (c) \: 512}[/tex]

[tex] \purple{\bold{\underline{\underline{ Cube \: of \: 8 \: is = 512:}}}}[/tex]

[tex]\red{\bold{\underline{\underline{so \: option \:( c ) \: is \: correct \: \: :}}}}[/tex]

[tex]\orange{\bold{\underline{\underline{ more \: additional \: information \: :}}}}[/tex]

To find Cubes -:

To find Cube Root -:

60 percent of 92 is 55.2

The statement is given as:

60 percent of 92

This means:

60% of 92

Express of as *

60% * 92

Evaluate the product

55.2

Hence, 60 percent of 92 is 55.2

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Answer:

[tex]\left[\begin{array}{cccc}-1\\1\\1\\0\end{array}\right][/tex], [tex]\left[\begin{array}{cccc}0\\2\\0\\1\end{array}\right][/tex] Are two vectors which are basis of null space of A

Step-by-step explanation:

Basis of a null space is a vector matrix which when multiplied by the reduced echelon form of the matrix gives null matrix or 0 matrix

So, to find the reduced echelon form we apply the row operations :

R₁ = R₁/2

[tex]\left[\begin{array}{cccc}1&-2&3&4\\2&-1&3&2\\4&-5&9&10\\0&-1&1&2\end{array}\right][/tex]

R₂ = R₂ - 2R₁

[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&3&-3&-6\\4&-5&9&10\\0&-1&1&2\end{array}\right][/tex]

R₃ = R₃ - 4R₁

[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&3&-3&-6\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]

R₂ = R₂/3

[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&1&-1&-2\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]

R₁ = R₁ + 2R₂

[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]

R₃ = R₃ - 3R₂

[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&-1&1&2\end{array}\right][/tex]

R₄ = R₄  + R₂

[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&0&0&0\end{array}\right][/tex]

which is a reduced echelon form of the matrix A

now ,

[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&0&0&0\end{array}\right][/tex]    [tex]\left[\begin{array}{cccc}x1\\x2\\x3\\x4\end{array}\right][/tex]  [tex]=\left[\begin{array}{cccc}0\\0\\0\\0\end{array}\right][/tex]

therefore,

x₁ + x₃ = 0

x₁  = -x₃

x₂ - x₃ - 2x₄ = 0

x₂ = x₃ + 2x₄

so now replacing values of x₁ , x₂ in the vector matrix

[tex]\left[\begin{array}{cccc}-x3\\x3 + 2x4\\x3\\x4\end{array}\right][/tex]

we can write the above matrix as,

[tex]x3\left[\begin{array}{cccc}-1\\1\\1\\0\end{array}\right][/tex] [tex]+ x4\left[\begin{array}{cccc}0\\2\\0\\1\end{array}\right][/tex]

therefore we can say that above mentioned vector matrices are the basis of the null space of matrix A

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Answer:

2

Step-by-step explanation:

The subpopulations of mechanical and civil engineers are not earning different salaries.

If a study determines the difference in average salary for subpopulations of mechanical engineers and civil engineers is NOT significant.

This assertion simply means that average salaries of the  mechanical and civil engineers are not different.

Thus, the subpopulations of mechanical and civil engineers are not earning different salaries.

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The margin of error will be 20 and 10 respectively.

The margin of error for Robert will be:

= 1.96 × 50/✓25

= 1.96 × (50/5)

= 1.96 × 10

= 20 approximately

The margin of error for Val will be:

= 1.96 × 50/✓100

= 1.96 × 50/10

= 1.96 × 5

= 10 approximately

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