Simplify 3√-1000 and 3√g6h30

Answer:

Second option.

Step-by-step explanation:

In a mathematical sense, all real values of x are possible, as no real values of x will make it undefined.

However, in a reasonable sense, the length and width of a rectangle should be positive, so 0.5x -2 > 0.

Therefore, in a reasonable sense, x > 4.

Answer:

a.  [tex]P(Both) = \frac{1}{60}[/tex]

b.   [tex]P(None) = \frac{3}{4}[/tex]

c.  [tex]P(At least 1) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

A fair 6-sided die

A fair 10-sided die

Both have an ace side

For the 6-sided die;

Probability of landing on Ace: P(A)

[tex]P(A) = \frac{1}{6}[/tex]

Probability of not landing on Ace: P(A')

[tex]P(A') = \frac{5}{6}[/tex]

For the 10-sided die;

Probability of landing on Ace: P(B)

[tex]P(B) = \frac{1}{10}[/tex]

Probability of not landing on Ace: P(B')

[tex]P(B') = \frac{9}{10}[/tex]

Solving (a): Both landing on Ace

This is calculated as thus;

[tex]P(Both) = P(A) * P(B)[/tex]

[tex]P(Both) = \frac{1}{6} * \frac{1}{10}[/tex]

[tex]P(Both) = \frac{1}{60}[/tex]

Solving (b): None landing on Ace

This is calculated as thus;

[tex]P(None) = P(A') * P(B')[/tex]

[tex]P(None) = \frac{5}{6} * \frac{9}{10}[/tex]

[tex]P(None) = \frac{1}{6} * \frac{9}{2}[/tex]

[tex]P(None) = \frac{1}{2} * \frac{3}{2}[/tex]

[tex]P(None) = \frac{3}{4}[/tex]

Solving (c): At least one landing on Ace

This is calculated as thus;

[tex]P(At least 1) = 1 - P(None)[/tex]

[tex]P(At least 1) = 1 - \frac{3}{4}[/tex]

[tex]P(At least 1) = \frac{4 - 3}{4}[/tex]

[tex]P(At least 1) = \frac{1}{4}[/tex]

The required probabilities are,

(a):[tex]P(A)=\frac{1}{60}[/tex]

(b):[tex]P(B)=\frac{3}{4}[/tex]

(c):[tex]P(C)=\frac{59}{60}[/tex]

Given that the die having the 6 sides.

The formula for finding the expected probability is,

[tex]P(A)=\frac{m}{n}[/tex]

Where m= Number of expected observation

n= Number of total observation

Part(a):

P(Both landed on ace) is,

[tex]P(A)=\frac{1}{6} \times\frac{1}{10} \\=\frac{1}{60}[/tex]

Part(b):

P(Neither landed on ace) is,

[tex]P(B)=[1-\frac{1}{6} ][1-\frac{1}{10} ]\\=\frac{3}{4}[/tex]

Part(c):

P(At least one not land on ace) = 1 - P(Both landed on ace)

[tex]1-\frac{1}{60} =\frac{59}{60}[/tex]

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Answer:

65

Step-by-step explanation:

5(6 + 7)

5 • 6 = 30

5 • 7 = 35

30 + 35 = 65

Answer:

yes because

Step-by-step explanation:

this point, we pause to see if it makes sense that we actually have two viable cases to consider. As we have discussed, both candidates for are ‘compatible’ with the given angle-side pair ( ;a) = (30 ;3) in that both choices for can t in a triangle with and both have a sine of 2 3. The only other given piece of information is that c= 4 units.

Answer:

[tex]\Huge \boxed{\mathrm{16 \ marbles}}[/tex]

Step-by-step explanation:

Let the number of marbles that Charlotte has be x.

Let the number of marbles that Vinny has be y.

[tex]x+y=20[/tex]

[tex]x=4y[/tex]

Substitute for x.

[tex]4y+y=20[/tex]

Combine like terms.

[tex]5y=20[/tex]

Divide both sides by 5.

[tex]y=4[/tex]

Vinny has 4 marbles.

Let y = 4.

[tex]x=4(4) \\ \\ \\ x=16[/tex]

Charlotte has 16 marbles.

Answer:

x+y=20

x=4yx=4y

Substitute the given equation for x.

4y+y=20

4y+y=20

Collect all like terms.

5y=20

Divide both sides by 5.

y=4y=4

Vinny has 4 marbles.

Let y = 4.

x=4(4)

x=16

Answer:

y = 6/5x -2

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b

y = 6/5 x +b

We have a point on a line

4 = 6/5( 5) +b

4 = 6+b

Subtract 6 from each side

4-6 = 6+b-6

-2 = b

The equation is y = 6/5x -2

Answer:

Its either 1.98 percentage or 51.

Step-by-step explanation:

Divison?

Answer:2%

Step-by-step explanation: 38.76-0.76=38

38(1+r)=38.76

__________

38

1+r=1.02

R=0.02 (2%)

Answer: f = x^2-7yx+4y^2-6y

Step-by-step explanation:

A vector field is conservative if the work done by that vector field around any loop is 0 or the end points only matter when calculating the work done, not the path in between (think of gravity). The curl(F) must equal 0.

curl(F) = ∇ x F =0

= det( [tex]\left[\begin{array}{ccc}\frac{d}{dx} &\frac{d}{dy} \\(2x-2y)&(-7x+8y-6)\end{array}\right][/tex] ) (***partial derv)

-7 - (-7) = 0

Yes, it is conservative, which means we can find the potentional energy function by turning the vector field into the gradient of scalar function.

[tex]f_x=2x-7y\\f_1=x^2-7yx+C(y)\\f_1y=-7x +C'(y)\\\\C'(y)=8y-6\\C(y)=4y^2-6y\\\\f=x^2-7yx+4y^2-6y\\[/tex]

Answer:

The correct option is;

b. Simpsons Rule

Step-by-step explanation:

The midpoint rule involves the estimation of the area under the curve with the aid of rectangular shaped approximations

The trapezoidal rule, involved the approximation of the curve by linear approximations by using piece by piece linear functions

In the Simpson's rule the curve is approximated using piece by piece quadratic functions. The intervals are partitioned into even numbered smaller intervals having the same width and we approximate the resulting integrals of the intervals.

Answer:

Natural numbers < Whole Numbers < Rational numbers < Integers

Step-by-step explanation:

Natural numbers are the numbers that are called counting numbers.They are numbers you can count. But Zero is not among them. Basically, Natural numbers are numbers you can count with the exception of Zero.

Whole numbers are a bit more than natural numbers. Unlike Natural numbers, whole numbers contain Zero. As a result, we can say they're counting numbers Zero inclusive.

Rational numbers are numbers that are written as ratio. They can be written as a fraction, but then, both the denominator and the numerator would have to be whole numbers.

Integers are whole numbers including negative numbers. Remember, whole numbers are an extension of natural numbers? Well then, Integers are an extension of Whole numbers.

Answer: B

Step-by-step explanation:

To find the inverse function, you switch x with y and y with x. Then, you solve for y.

[tex]y=(x-1)^{2} -4[/tex]                                  [switch x with y, and y with x]                        

[tex]x=(y-1)^2-4[/tex]                                  [add both sides by 4]

[tex]x+4=(y-1)^2[/tex]                                  [square root both sides]

[tex]\sqrt{x+4} =y-1[/tex]                                    [add both sides by 1]

[tex]\sqrt{x+4} +1=y[/tex]

[tex]f^-^1(x)=1+\sqrt{x+4}[/tex]

Now that we know the inverse function, we can actually tell that the answer is B. We know this because of the restriction that f(x) is x≤1. This makes it positive, and B the answer.

Answer:

2x + 6 = 30

hope this helps

Answer:

x >3

Step-by-step explanation:

2(2x - 3) > 6

Divide each side by 2

2/2(2x - 3) > 6/2

2x-3 > 3

Add 3 to each side

2x-3+3 > 3+3

2x>6

Divide by 2

2x/2 > 6/2

x >3

Answer:

x > 3

Step-by-step explanation:

First, you're going to divide both sides by two

2( 2x - 3) / 2 and 6/2

After that, you will simplify that into....

2x - 3 > 3

Then you want to add three to both sides like so

2x - 3 + 3 > 3 + 3

Once you're done with that, go ahead and simplify the problem

2x > 6

Then, divide by two on each side

2x/2 > 6/2

Lastly, simplify your answer and that's the solution

x > 3

I hope this helped! :)

Step-by-step explanation:

Hey, there!!

It's so simple, you just use the formula as given and put the values in it.

Radius of a circle (r) = 13 cm.

pi= 3.14

Now,

Circumference = 2× pi × r

= (2× 3.14 × 13) cm

= 81.64 cm

Therefore, the answer is 82 cm.

Hope it helps..

Answer:

The answer = 82 cm.

Step-by-step explanation:

By using the formula,

C=2×3.14×13

C= 81.64

then,

The nearest hundredth = 82 cm.

Answer:

y = 1/3x + 4

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find slope m

m = (2 - 3)/(-6 - -3)

m = -1/(-6 + 3)

m = -1/-3

m = 1/3

y = 1/3x + b

Step 2: Find y-intercept b (plug in coordinates)

3 = 1/3(-3) + b

3 = -1 + b

b = 4

Step 3: Rewrite linear equation

y = 1/3x + 4

Here is the correct question

Gin Rummy and are holding 10 cards in your hand from a standard deck of 52 cards.

a) How many ways can you select three kings and four 6's from the deck, the remaining cards not kings or 6's

b) Find the probability that three kings and four 6's are being held by you from the deck.

Answer:

a) 52976

b) [tex]\mathbf{3.34866744 \times 10^{-6}}[/tex]

Step-by-step explanation:

So from the information above,

no of ways three kings can be selected and four 6's from the deck without the remaining cards being kings or 6's can be expressed as:

no of ways to select 3 kings from 4 kings is [tex](^4_3)[/tex]

no of ways to select 4 6's from (4 6's) is [tex](^4_4)[/tex]

no of ways to select the remaining 3 cards from (52 - 4 - 4) = 44 cards is [tex](^{44}_3)[/tex]

Mathematically, multiplying the three together we have:

[tex]= (^4_3) (^4_4) (^{44}_3)[/tex]

[tex]= \dfrac{4!}{3!(4-3)!} \times \dfrac{4!}{4!(4-4)!} \times \dfrac{44!}{3!(44-3)!}[/tex]

[tex]= 4 \times 1 \times 13244[/tex]

= 52976

To find the probability that you are holding three kings and four 6's from the deck, the remaining cards not kings or 6's can be calculated as follows;

To do this, we need to first know the no of ways we can  select 10 cards out of the pack of 52 cards

i.e

[tex](^{52}_{10})[/tex]

= [tex]\dfrac{52!}{10!(52-10)!}[/tex]

= [tex]\dfrac{52!}{10!(42)!}[/tex]

= 1.58200242 × 10¹⁰

Now, to find the  probability that you are holding three kings and four 6's from the deck, the remaining cards not kings or 6's :

we will need to divide the number of ways we can select three kings and four 6's from the deck by the no of ways we can select 10 cards out of the pack of 52 cards.

Mathematically; we have,

[tex]=\dfrac{52976}{1.58200242 \times 10^{10}}[/tex]

= [tex]\mathbf{3.34866744 \times 10^{-6}}[/tex]

Answer:

Step-by-step explanation:

f 35 = 100 % as a whole number then 50% = 17.5

50 % more than 35 must be 35 + 17.5 = 52.5

Answer:

Hey!

Your answer is 52.5

Step-by-step explanation:

50% x 35=

(50/100) x 35=

(50 x 35) / 100=

1750 / 100 = 17.50

NOW...

35+17.5=52.5

ANSWER: 52.5

Answer:

x<6/5, x>14/5

Step-by-step explanation:

Steps

$5\left|x-2\right|+4>8$

$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

$5\left|x-2\right|+4-4>8-4$

$\mathrm{Simplify}$

$5\left|x-2\right|>4$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\frac{5\left|x-2\right|}{5}>\frac{4}{5}$

$\mathrm{Simplify}$

$\left|x-2\right|>\frac{4}{5}$

$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$

$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$

Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$

Answer:

  1000

Step-by-step explanation:

1000/1 = 1000

Multiplying or dividing any number by 1 does not change its value.

__

In the US, "standard form" is the number written in the usual way: digits to the left and/or right of a decimal point, with zeros as placeholders where required. (If there is no fractional part, the decimal point is optional.*)

In the UK, "standard form" is what is called "scientific notation" in the US. There is one digit to the left of the decimal point, and the remaining significant digits are to the right of the decimal point. The number is multiplied by ten to the power corresponding to the place value of the most significant digit. In this "standard form", 1000 = 1.×10³.

_____

* When you're concerned about significant digits, the presence of a decimal point will indicate any zeros immediately to its left are significant. That is, 20 has 1 significant digit; 20. has 2 significant digits. The zero is indicated as being significant by the presence of the decimal point.

Answer:

see attachement

Step-by-step explanation:

Solve for x:

8 x + 26 - 3/x + 6/x^2 = 0

Hint: | Write the left hand side as a single fraction.

Bring 8 x + 26 - 3/x + 6/x^2 together using the common denominator x^2:

(8 x^3 + 26 x^2 - 3 x + 6)/x^2 = 0

Hint: | Multiply both sides by a polynomial to clear fractions.

Multiply both sides by x^2:

8 x^3 + 26 x^2 - 3 x + 6 = 0

Hint: | Look for a simple substitution that eliminates the quadratic term of 8 x^3 + 26 x^2 - 3 x + 6.

Eliminate the quadratic term by substituting y = x + 13/12:

6 - 3 (y - 13/12) + 26 (y - 13/12)^2 + 8 (y - 13/12)^3 = 0

Hint: | Write the cubic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

8 y^3 - (187 y)/6 + 799/27 = 0

Hint: | Write the cubic equation in standard form.

Divide both sides by 8:

y^3 - (187 y)/48 + 799/216 = 0

Hint: | Perform the substitution y = z + λ/z.

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

799/216 - 187/48 (z + λ/z) + (z + λ/z)^3 = 0

Hint: | Transform the rational equation into a polynomial equation.

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 187/48) + (799 z^3)/216 + z^2 (3 λ^2 - (187 λ)/48) + λ^3 = 0

Hint: | Find an appropriate value for λ in order to make the coefficients of z^2 and z^4 both zero.

Substitute λ = 187/144 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 + (799 u)/216 + 6539203/2985984 = 0

Hint: | Solve for u.

Find the positive solution to the quadratic equation:

u = (17 (9 sqrt(157) - 188))/1728

Hint: | Perform back substitution on u = (17 (9 sqrt(157) - 188))/1728.

Substitute back for u = z^3:

z^3 = (17 (9 sqrt(157) - 188))/1728

Hint: | Take the cube root of both sides.

Taking cube roots gives 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) times the third roots of unity:

z = 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) or z = -1/12 (-1)^(2/3) 17^(1/3) (188 - 9 sqrt(157))^(1/3) or z = -1/12 17^(1/3) (188 - 9 sqrt(157))^(1/3)

Hint: | Perform back substitution with y = z + 187/(144 z).

Substitute each value of z into y = z + 187/(144 z):

y = 1/12 (-17 (188 - 9 sqrt(157)))^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 11/12 17^(2/3) ((-1)/(188 - 9 sqrt(157)))^(1/3) - 1/12 (-1)^(2/3) (17 (188 - 9 sqrt(157)))^(1/3) or y = -(11 17^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) - 1/12 (17 (188 - 9 sqrt(157)))^(1/3)

Hint: | Simplify each solution.

Bring each solution to a common denominator and simplify:

y = 1/12 (153 sqrt(157) - 3196)^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 1/12 17^(1/3) (11 ((-17)/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) or y = -1/12 17^(1/3) (1/(188 - 9 sqrt(157)))^(1/3) ((188 - 9 sqrt(157))^(2/3) + 11 17^(1/3))

Hint: | Perform back substitution on the three roots.

Substitute back for x = y - 13/12:

Answer: x = -13/12 - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) + 1/12 (153 sqrt(157) - 3196)^(1/3) or x = 1/12 17^(1/3) (11 (-17/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) - 13/12 or x = -1/12 (17/(188 - 9 sqrt(157)))^(1/3) (11 17^(1/3) + (188 - 9 sqrt(157))^(2/3)) - 13/12

Answer:

The correct answer is, "8x + 2x^2 + 21 / (x + 5)(x - 3)"

Step-by-step explanation:

This is 100% correct! :)

14

(a + b)² = a² + 2ab + b²

x² + _x + 49

a = x

b = 7

2ab = 2×x×7 = 14x => 2b = 14

Answer:

[tex]\Huge \boxed{\mathrm{14}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

Square of a sum formula:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

x² + ___ x + 49

The value of a is x.

The value of b is 7, since 7² = 49.

[tex]x^2 +2(x)(7)+7^2[/tex]

[tex]x^2 +14x+49[/tex]

The missing coefficient is 14.

[tex]\rule[225]{225}{2}[/tex]

Answer:

Strong Negative

Step-by-step explanation:

Took the test and know this is the right answer.

The direction and strength of the association between the variables is  strong negative.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The relationship between the variable X and Y plotted on the graph depicts a strong negative association between the two variables.

The direction of the trend on a linear plot gives an information about the direction of the slope of the graph, the graph slopes downwards as variable X increases, hence we have a negative relationship between X and Y

The trend produced by the graph is straight forward with points close to one another, hence forming a well - defined pattern. These depicts a Strong association between the variables.

When the trend isn't clearly defined and obvious, the relationship is weak.

Hence, the direction and strength of the association between the variables is strong negative.

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Answer:

( 9w - 2z)^2

Step-by-step explanation:

81w^2 - 36wz + 4z^2

Rewriting as

(9w)^2 - 2 * 9 w 2z + (2z)^2

We  recognize that this is a perfect square binomial

a^2 -2ab + b^2 is a perfect square binomial because it factors to (a - b)^2

let a = 9w  b = 2z

81w^2 - 36wz + 4z^2 = ( 9w - 2z)^2

Multiplying M by any matrix A would return new matrix, B, in which

• the 1st row of B is equal to the 4th row of A,

• the 2nd row of B is equal to the 3rd row of A,

• the 3rd row of B is equal to the 2nd row of A,

• the 4th row of B is equal to the 5th row of A, and

• the 5th row of B is equal to the 1st row of A.

The pattern here is

1 => 4 => 5 => 1

2 => 3 => 2

Let {4, 3, 2, 5, 1} denote the matrix M, where each number refers to the row of the identity matrix, I.

Using this notation, the pattern above gives

M² = {5, 2, 3, 1, 4}

M³ = {1, 3, 2, 4, 5}

M⁴ = {4, 2, 3, 5, 1}

M⁵ = {5, 3, 2, 1, 4}

M⁶ = {1, 2, 3, 4, 5}

so that n = 6.

(Notice that the first cycle has length 3 and the second one has length 2; the minimum n needed here is then LCM(2, 3) = 6.)

Answer:

the value of M angle 3 is 70° and M angle 1 is (90-70)=20° and angle 3 - angle 1 is 70° - 20° is 50°

The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first point be A ( x₁ )

The value of A ( x₁ ) = A ( -12 )

Let the second point be B ( x₂ )

The value of B ( x₂ ) = B ( -7 )

Let the distance between the two points on the number line be = D

Now , the equation will be

The distance between the points A and B is calculated by

The distance D = B - A

Substituting the values in the equation , we get

The distance D = -12 - ( -7 )

Distance D = -12 + 7

Distance D = -5

Therefore , the value of D is -5

Hence , The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

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Answer:

5 cases

Step-by-step explanation:

you'll need at least five cases to fulfill the requirement of 60

Answer:

5 cases are needed

Step-by-step explanation:

Answer:

  3z^2

Step-by-step explanation:

Factors of the different terms are ...

  12z^3 = 2·2·3·z·z·z

  45z^2 = 3·3·5·z·z

  18z^5 = 2·3·3·z·z·z·z·z

The common factors are 3 and z·z.

The greatest common factor is 3z^2.