Drag each number to a box on the right to match each expression on the left with its product.
0.832 added to
Expression Product
83.2 × 0.1
832
8.32 × 102
8.32
83.2 × 102
8,320
832 × 0.001
0.832

An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

An inequality is comparison of  two values, showing if one is less than, greater than, or simply not equal to another value.

Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.

Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

Induction hypothesis:

Suppose 100n ≤ k³ for some positive integer k ≥ 10.

We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.

Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100

                                                 ≤ k³ + 3k²    (∵ k ≥ 10 )

                                                 ≤ k³ + 3k² + 3k

                                                 ≤ k³ + 3k²+3k + 1

So 100( k + 1 ) ≤ ( k + 1 )³, which is true.

Hence by the principle of mathematical induction, 100n ≤ k³ for every integer  k ≥ 10.

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Answer:

8

Step-by-step explanation:

Due to lines r & s being parallel to each other, we can apply the rule of alternate interior angles to solve for y in this problem.

Applying this, we'll be obtaining the equation that of:

[tex]116=15y-4[/tex]

We now simply solve for y.

[tex]120=15y\\y=8[/tex]

Therefore, y is equal to 8.

This can be checked by plugging it into the equation:

[tex]15(8)-4[/tex]

[tex]120-4[/tex]

[tex]116[/tex]

And look at that, we got 116 for our answer, exactly the same as the other angle.

Any questions feel free to ask :)

x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).

Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.

The given expression is x² + 12.

We have the identity (a + b) (a - b) = a² - b²

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²

                                = x² - (2² × √3² × i²)

We know that i² = -1, where i is the imaginary number in complex numbers

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)

                                = x² + 12

Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.

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Answer:

u should add 118/9

Step-by-step explanation:

please mark me as brainlest

Answer:

C. 4x²√(3x)

Step-by-step explanation:

if x > 0

[tex]\sqrt{48x^{5}} =\sqrt{48} \times \sqrt{x^{5}}[/tex]

          [tex]=\sqrt{16\times 3} \times \sqrt{x^{4}\times x}[/tex]

          [tex]=\sqrt{16} \times \sqrt{3} \times \sqrt{x^{4}} \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times \sqrt{\left( x^{2}\right)^{2} } \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times x^{2}\times \sqrt{x}[/tex]

          [tex]=4\times x^{2} \times \sqrt{3} \times \sqrt{x}[/tex]

          [tex]=4\times x^{2}\times \sqrt{3x}[/tex]

Answer:

212520 different committees

Step-by-step explanation:

Candidates

For a President: 23

For a Vice President: 22

For a Secretary: 21

For a Treasurer: 20

Number of ways: (23)(22)(21)(20) = 212520

Hope this helps

Answer:

To whom it may concern the answer to this problem would be 212,520.

Step-by-step explanation:

Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...

[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]

Remember that the 19! cancel each other out. Hope this helps!

It is not okay to conduct the simulation because people generally favor some numbers.

From the information given, the student wants to simulate 37 birthdays, but she does not have a calculator or software program available.

In this case, it's not okay to conduct the simulation because people generally favor some numbers.

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Answer:

x² + 4x + 3

---------------

       2

---- => fraction line

Answer: 2 3/4 > 2.68 is correct (only)

Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68

The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.

Sqrt(63) = 7.93, and 7.93 > 8.11 is false.

Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

Answer:

[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]

Step-by-step explanation:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

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

Answer:

y = 1, 9.

Step-by-step explanation:

They are the y values of the points of intersection of the 2 parabolas.

y = 1, 9.

The equation for the red graph is f(x) = -x².

From the information given, g(x) = 4 - x².

The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:

(x, y) = (x, y -4).

The equation of the function will be:

f(x) = g(x) - 4

f(x) = (4 - x²) - 4

f(x) = -x²

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2x + 9 = 5x - 12

2x - 5x = - 1- 9

- 3x = - 21

x = 21/3

x = 7

Y = 60°

y=2x+3

to find inverse swap x and y

x=2y+3

x-3=2y

y=(x-3)/2

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

The inverse is f^-1(x)=(x/2)-(3/2)

Hope it helps!

Answer:

BC is 22.5 mi

Step-by-step explanation:

Using the pythagorean theorem formula. c² = a² + b²

BC² = AB² + AC²

BC² = 19² + 12²

BC² = 361 + 144

BC² = 505

√BC² = √505

BC = 22.5

Therefore BC is 22.5 mi

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]

The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.

To find the first term in the series, substitute n = 1 into the expression:

[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]

The common ratio of the geometric series can be found by dividing one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]

As | r | <  1  the series is convergent.

When a series is convergent, we can find its sum to infinity (the limit of the series).

Sum to infinity formula:

[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]

where:

Substitute the found values of a and r into the formula:

[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]

Therefore:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]

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Answer:

Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.

So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.

Step-by-step explanation:

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } [/tex]

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } [/tex]

[tex] = \frac{ 2( \sqrt{2} - \sqrt{3} )( \sqrt{2} - \sqrt{3} )}{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} }[/tex]

[tex] = \frac{2(2 - \sqrt{6} - \sqrt{6} - 3) }{2 - 3} [/tex]

[tex] = \frac{2( - 1 - 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = \frac{ - 2(1 + 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = 2(1 + 2 \sqrt{6} )[/tex]

[tex] = 2 + 4 \sqrt{6} [/tex]

[tex]3x+6-2 = 6x-( \frac{7}{2} \times \frac{9}{0} ) \\ \\ 3x + 4 = 6x - \frac{63}{0} \\ \\ 3x + 4 = 6x - 0 \\ \\ 4 + 0 = 6x - 3x \\ \\ 3x = 4 \\ \\ x = \frac{4}{3} .[/tex]

The value of x is 4/3 .

Answer: No Solution

Why?

Any number divided by 0 is not defined, but we are given 9/0 in the question. Hence we cannot solve the equation for the value of ‘x’.

If the factors of quadratic function f are (x – 7) and (x + 3). The solution of the quadratic function f will be the negative 3 and 7.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

If the factors of quadratic function f are (x – 7) and (x + 3).

Then the zeroes of function f will be

(x – 7)(x + 3) = 0

                x = 7, -3

Then the solution of the quadratic function f will be the negative 3 and 7.

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Rewriting the equation of the given line in slope-intercept form,

[tex]8x-7y=87\\\\-7y=-8x+87\\\\7y=8x-87\\\\y=\frac{8}{7}x-\frac{87}{7}[/tex]

The slope of the given line is thus 8/7, and since parallel lines have the same slope, the slope of the line we want to find is also 8/7.

Substituting into point-slope form,

[tex]y+17=\frac{8}{7}(x-3)\\\\y+17=\frac{8}{7}x-\frac{24}[7}\\\\\boxed{y=\frac{8}{7}x-\frac{143}{7}}[/tex]

Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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The answer for each of the differentiation are; f'(-6) = 432;  f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432

1) f(x) = 4x³ - 5

We will differentiate it to get;

f'(x) = df/dx = 12x²

f'(-6) = 12(-6)²

f'(-6) = 432

2) We are given the formula;

x = f⁻¹(y)

Thus;

y = 4x³ - 5

4x³ = y + 5

x³ = (y + 5)/4

x = ∛((y + 5)/4)

f⁻¹(y) = ∛((y + 5)/4)

c)  f⁻¹(y) = ∛((y + 5)/4)

df⁻¹/dy = -1/12y²

At f(-6), we have;

df⁻¹/dy = 1/432

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Using subtraction of perfect squares, it is found that the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

It is given as follows:

a^2 - b^2 = (a - b)(a + b)

In this problem, the binomial is given as follows:

9t² - 4.

Hence:

Hence the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

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A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.

We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is

y = mx + c...(1), where m is the gradient of the straight line and c is a constant.

Given that the gradient of the given straight line = m = -3.

Putting this value in (1), we get

y = -3x + c ...(2)

Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.

So, 1 = (-3)(-2) + c

i.e. 6 + c = 1

i.e. c = 1 - 6 = -5

(2) can be written as

y = -3x - 5

Therefore the equation of the given straight line is

y = -3x - 5

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Smaller angle = 50
Larger angle = 130

Let smaller angle be x degree

=> larger angle= [tex]3x - 20[/tex]

Since these angles are supplementary , So

[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]

So smaller angle would be 50 deg & larger angle would be  130 deg.

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Answer:

1 1/2

Step-by-step explanation:

Convert both fractions into decimals

⇒ 3/4 (0.75) and 1/2 (0.50)

Divide the decimals:

⇒0.75 ÷ 0.50

Find the quotient

⇒ 1.5

Convert the quotient to a fraction

⇒ 1 1/2

Terms:

Operations with fractions