What is the period of f(x) = sin(x)?

The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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Answer:

its 60, need proof?

Step-by-step explanation:

Answer: 60

Step-by-step explanation: I took the test and got it right. Goodluck with the rest!

Answer:

It's all in the picture. good luck :)

Step-by-step explanation:

Domain : R

Range :   ( - ∞, 0)

(Refer the image attached for complete question)

We have the following function -

k(x) = \(-2^{x}\)

We have to determine its domain and range.

For any function y = f(x), Domain is the set of all possible values of y that exists for different values of x. Range is the set of all values of x for which y exists.

According to question, we have -

k(x) = \(-2^{x}\)

for x = 0, the function k(0) = 1

The function k(x) has the exponential function (\(e^{x}\)) as its parent function.

If we plot the graph of the function k(x), it will look like as shown in the figure attached.

The graph of the function k(x) =  \(-2^{x}\) is the reflection of the graph \(2^{x}\) along x - axis.

The Domain of the function k(x) : R

The Range of the function k(x) : ( - ∞, 0)

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Answer:

$9 per week

Step-by-step explanation:

36/4 = 9

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

$ 7770.81

Step-by-step explanation:

2.5 % each year means the car retains  97.5 % ( or .975 in decimal)  of its value per year

    8599 ( .975) ^4  = $ 7770.81

We have the following:

solving by substitution

The answer is x is equal -1

Answer:

600

Step-by-step explanation:

.7x = 420

x = 420/0.7

x = 600

Answers:

Length = 13 inches

Width = 11 inches

=====================================================

Work Shown:

w = width, some positive number

w+2 = length, since it is 2 inches more than the width

P = perimeter of the rectangle

P = 2(width + length)

P = 2(w + w+2)

P = 2(2w+2)

P = 4w+4

We're told that the perimeter is 48 inches. So we'll set the previous result equal to 48 and solve for w.

P = 48

4w+4 = 48

4w = 48-4

4w = 44

w = 44/4

w = 11

The width is 11 inches.

w+2 = 11+2 = 13

The length is 13 inches.

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

Checking the answers:

P = 2(L+W)

P = 2(13+11)

P = 2(24)

P = 48

The answers are confirmed.

Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

Note that: Area of a circle is expressed as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that;

A = πr²

A = 3.14 × ( 35cm )²

A = 3.14 × 1225cm²

A = 3846.5cm²

Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

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The solutions for the equation (3x + 12)(x + 4) = (4x² + 8x + 18x²)/2 are given by, x = -3/2, 4.

Given that the equation is,

(3x + 12)(x + 4) = (4x² + 8x + 18x²)/2

we have to find the solution that is the value(s) of the x for which this relation is true.

Solving the the equation we get,

3x*x + 12x + 3x*4 + 12*4 = (22x² + 8x)/2

3x² + 12x + 12x + 48 = 2 (11x² + 4x)/2

3x² + 24x + 48 = 11x² + 4x

11x² - 3x² + 4x - 24x - 48 = 0

8x² - 20x - 48 = 0

4(2x² - 5x - 12) = 0

2x² - 5x - 12 = 0

2x² - 8x + 3x - 12 = 0

2x(x - 4) + 3(x - 4) = 0

(2x + 3)(x - 4) = 0

Either 2x + 3 =0

x = -3/2

Or, x - 4 = 0

x = 4

Hence the solutions are, x = -3/2, 4.

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Answer:i am not sure

Step-by-step explanation:

This question is very hard to answer

Answer: I think your brain needs cheese but..............................................

Step-by-step explanation:

Don't know

ii. Now consider the second number 8888

Here the last digit of 8888 is 8.

The cube of 8 is 512.

⇒83=512

Here the last digit of 83 is 2.

Hence the one’s digit of the cube of 8888 is 2.

The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.

Alice always takes the first turn. Bob can either take the leftmost card or the rightmost card. If Alice takes the leftmost card and Bob takes the rightmost card, then Alice will have the advantage of being able to make the last move. If Bob takes the leftmost card and Alice takes the rightmost card, then Bob will have the advantage of being able to make the last move.

The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.

Alice should also be aware of Bob's strategy and try to anticipate what card he will take. If Alice can guess correctly, she can adjust her strategy to ensure she takes the card with the highest point value. If she guesses incorrectly, she should still attempt to take the card with the highest point value.

Alice should take the card with the highest point value and Bob should take the card with the lowest point value. Alice should also anticipate Bob's strategy and adjust accordingly to ensure she takes the card with the highest point value.

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The answers are a) the fraction of the state that can claim that they have a 4-star hotel is 4/5, b) 10 4-states which do not have a 4-star hotel and c) the fraction of states without a 4-star hotel is 10/50 = 1/5

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, forty states have 4-stars hotels and there are 50 states.

Assuming that each of the forty states has 1 4-star hotel,

(A) The fraction of states with a 4-star hotel :-

(number of states with a 4-star hotel)/(total number of states)

= 40/50 = 4/5

Therefore, the fraction of the state that can claim that they have a 4-star hotel is 4/5

(B) The number of states without a 4-star hotel is the number remaining after states with a 4-star hotel are removed from the list of all states.

States without 4-star hotel = (total number of states) - (number of states with a 4-star hotel)

= 50-40 = 10

Therefore, there are 10 4-states which do not have a 4-star hotel.

(C) The fraction of states without a 4-star hotel :

10 / 50 = 1/5

Hence, the answers are a) the fraction of the state that can claim that they have a 4-star hotel is 4/5, b) 10 4-states which do not have a 4-star hotel and c) the fraction of states without a 4-star hotel is 10/50 = 1/5

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When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.

Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.

We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:

Using the formula V = \(Pe^rt\)

Principal (P) = $48,800.00

Annual Rate (R) = 3.1%

Compound (n) = Compounding Continuously

Time (t in years) = 13 years

Result:

V = $73,019.78

V = P + I where

P (principal) = $48,800.00

I (interest) = $24,219.78

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.1/100

r = 0.031 rate per year,

Solving the equation for V:

V = \(Pe^rt\)

V = \(48,800.00(2.71828)^(0.031)(13)\)

V = $73,019.78

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Answer: 7.364%...............

Answer:

Step-by-step explanation:

small amount = 10

Large amount = 135.8

% = (small amount / large amount ) * 100

% = (10 / 135.8) * 100

% = 0.0736* 100

% = 7.36%

Answer:

no solution

Step-by-step explanation:

Answer:

47%

Step-by-step explanation:

26+27=53

100-53=47

47/100=.47

Answer:

a. Using the empirical rule, approximately 68% of healthy adults have body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F.

b. Using the empirical rule, approximately 99.7% of healthy adults have body temperatures between 96.34°F and 99.88°F, which is within 3 standard deviations of the mean.

Answer:  ΔABC ≅ ΔADB

Step-by-step explanation:

In order to be similar, they must have the same angles.

    ΔABC                                  ΔADB                              ΔDBC

∠A = 180 - (2a + b)             ∠A = 180 - (2a + b)         ∠D = 180 - (a + b)

∠B = a + b                           ∠D = a + b                      ∠B = b

∠C = a                                 ∠B = a                            ∠C = a

ΔABC and ΔADB have the same angles so they are similar.

Answer:

396 in²

Step-by-step explanation:

The area of a rectangular prism is given by the formula:

\(A = 2(wl+hl+hw)\)

A = 2((6×7)+(12×7)+(12×6))

A = 2(42+84+72)

A = 2(198)

A = 396

Units will be in² since it is area. It will not be in³ as it is not volume!

an equation to model this situation is 200 = x+ 2 *t and 220 pounds is  his total weight after 30 weeks

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

x  initial weight of John

weight gained 1 week = 2 pounds

no. of weeks = 20=t

Final weight of John = 200 pounds

200 = x+ 2 *t ---------(1)

no. of weeks = 20=t

From eq(1)

x = 160 pounds= intial weight

So,

\(y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds\)

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The statements that are true regarding the expression with the exponents -1, -3, and 1 are;

An exponent is a quantity or power to which a value, expression or number is to be raised.

The specified expression can be presented as follows;

8⁻¹ × 8⁻³ × 8

Therefore; 8⁻¹ × 8⁻³ × 8 = 8⁽⁻¹ ⁺ ⁻³ ⁺ ¹⁾ = 8⁻³ = 1/8³

1/8³ = 1/512

Similarly, we get; 8⁷ × 8⁻¹⁰ = 8⁽⁷ ⁻ ¹⁰⁾ = 8⁻³ = 1/8³

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Answer:

21,42,63,84,105 126,147,168,189, and 210.

I hope this helps.

Answer:

2x+30=x+80 (corresponding angles)

2x-x=80-30

x=50

Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

Check the picture below.

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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