PLEASE HELP!!!! what is the value of 6n - 2 when n = 3?

A: 7
B: 6
C: 16
D: 12
​

Answer:

We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).

Step-by-step explanation:

Answer: 3.00170455 miles

Step-by-step explanation:

Answer:

3 miles

Step-by-step explanation:

Answer:

2 brown

Step-by-step explanation:

The only time you can be so sure you've chosen 2 brown socks is when there are no more white socks and black socks. This means that to be 100% sure that you have chosen 2 brown socks you have to choose the 12 white socks and the 18 black socks and only then can you choose 2 brown socks without looking. Therefore, the total number of socks to choose from is:

Total number of socks = 12 white socks + 18 black socks + 2 brown socks

Total number of socks = 32 socks

A total picking of 32 socks is necessary to be sure without looking that 2 brown have already been chosen that way.

The least number of socks must choose, must choose without looking, to be certain that you have chosen two socks of the same color is 4.

The least number is "the smallest or lowest number or degree".

According to the question,

A drawer contains 12 identical white socks, 18 identical black socks, and 14 identical brown socks.

In order to find the least number of socks you must choose, without looking, to be certain that you have chosen two socks of the same color.

Since, we have only 3 different colors to get pair of one color we need to take 4 socks so that last one must matches color of socks what we have already have in our hand.

Hence, it clearly shows the least number of socks must choose, without looking, to be certain that you have chosen two socks of the same color is 4.  

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The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.

The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.

We are also told that Marama plans to fence the garden with 28 feet of wired fencing.

Now, let's break down the problem and find the appropriate values for the domain.

We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:

\(Perimeter = 2t + 2w\),

where t is the length of one side (the width) and w is the length of the other side (the width).

The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:

\(2t + 2w = 28\).

Simplifying this equation, we have:

\(t + w = 14\).

We can express w in terms of t as \(w = 14 - t\).

The area of a rectangle is given by the product of its length and width:

\(Area = t \times w\).

Substituting the expression for w from step 2, we have:

\(A(t) = t \times (14 - t)\).

Simplifying further:

\(A(t) = 14t - t^2\).

To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.

We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).

This shows that the value of t can range from 0 to 14, inclusive.

Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).

To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):

   ^

   |

A(t)|

   |

   |_______________________________

   0              t             14

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

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The linear function that models the situation is given as follows:

d = 0.85t.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The constant ratio for this problem is given as follows:

k = 0.83, as each division of d by t has a result of 0.83.

Hence the equation is given as follows:

d = 0.83t.

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Answer:

2=9/2

Step-by-step explanation:

Logarithmic form of \(4^{7} = 16384\)   is   \(log_{4}16384 = 7\) .

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. Logarithms, which were developed in the 17th century to expedite calculations, significantly decreased the amount of time needed to multiply integers with numerous digits. For more than 300 years, they served as the foundation for numerical work, but the development of mechanical adding machines in the late 19th century and computers in the 20th century made them obsolete for large-scale calculations.

If \(b^{x}\)  = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = \(log_{b}n\) .

Similarly,

\(4^{7} = 16384\)

Here, x = 7

         b = 4

         n = 16384

Therefore, by putting the values in the above expression, we will get

\(log_{4}16384 = 7\)

Hence, the logarithmic form is   \(log_{4}16384 = 7\)  .

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The exponential function that represents this situation is f(x) = 42 * (0.85)ˣ

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

Inital growth, a = 42

Rate of decrease, r = 15%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 - r)ˣ

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

f(x) = 42 * (1 - 15%)ˣ

So, we have

f(x) = 42 * (0.85)ˣ

Hence, the function is f(x) = 42 * (0.85)ˣ

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Question

Growth was worth $42 at tje beggining of the day. event every hour stock goes down by 15%. Write the exponential function that represents this situation.

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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If alpha specialize in growing apples beta specialize in growing oranges the both could gain profit by the trade is true for the statement

Comparative advantage describes a situation in which a person or a country involved in trade processes may not have an absolute advantage, but can still benefit from trade on a comparative basis.

The nations frequently trade goods based on their comparative advantages so that both parties can benefit from trade.

According to the stated information,

Alpha can produce either 18 oranges or 9 apples per hour, while beta can only produce 16 oranges or 4 apples per hour, it is stated.

so ,If alpha specialize in growing apples and beta specialize in growing oranges the both could gain profit by the trade

Hence, option C is true

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Answer:

x1 = √(509) /100 + 3/10

x2  = -√(509) /100 + 3/10

Step-by-step explanation:

We do completing the square as follows:

1. Put all terms with variable on one side and the constants on the other side.

5x^2 - 3x = 25

2. Factor out the coefficient of the x^2 term.

5(x^2 - 3x/5) = 25

3. Inside the parentheses, we add a number that would complete the square and also add this to the other side of the equation. In this case we add 9/100 and on the other  side we add 9/20.

5(x^2 - 3x/5 + 9/100) = 25 + 9/20

4. We simplify as follows:

5(x^2 - 3x/5 + 9/100) = 25 + 9/20

5(x - 3/10)^2 = 509/20

(x - 3/10)^2 = 509/100

x1 = √(509) /100 + 3/10

x2  = -√(509) /100 + 3/10

Answer:

60

Step-by-step explanation:

12(1^1+2^2)

1*1=1

2*2=4

12*1=12

12*4=48

12+48=60

Emily will have $45.26 more money in her account

Answer:

A would be correct

Step-by-step explanation:

the answer is A.

.......................

Answer:

$971

Step-by-step explanation:

To find the median value, place the numbers in value order (from lowest to highest) then find the middle:

So putting the weekly earnings for 2010 in value order:

501, 900, 971,  977, 1071

So the middle value is 971.  Therefore, the median = $971

The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)

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

2ˣ⁺⁴

The above expression is an exponential expression with the following properties

When the above expression is expanded, we have

2ˣ⁺⁴ = 2ˣ * 2⁴

Evaluate the expression 2 exponent 4

So, we have the following representation

2ˣ⁺⁴ = 2ˣ * 16

Rewrite as follows

2ˣ⁺⁴ = 16 * 2ˣ

This gives

2ˣ⁺⁴ = 16(2ˣ)

Hence, the expression that is equivalent to the expression is 16(2ˣ)

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The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.

What is increasing function?

⇒ The function is said to be increasing if the y value increases as the x value increase over a given range

What is average rate of change?

⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another

As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)

And it is true for the interval [0,2]

The faster the growth rate higher the average rate of change

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Answer:

C.

Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Complete question :

Assume that both populations are normally distributed. ​a) Test whether mu 1 not equals mu 2 at the alpha equals 0.05 level of significance for the given sample data. ​b) Construct a 95​% confidence interval about mu 1 minus mu 2. Sample 1 Sample 2 n 19 19 x overbar 16.2 14.1 s 4.5 3.1

Answer:

(-0.445 ; 4.645)

Null:

H0: mu1 - mu2 = 0

H1 : mu1 - mu2 ≠ 0

Step-by-step explanation:

__________Sample 1 ____ Sample 2

n ___________19 _________19

x overbar ____16.2 ________14.1

s __________ 4.5 _________3.1

The confidence interval : (2 independent means)

(x1 - x2) ± Tcritical * √(s1²/n1) + (s2²/n2)

T(1 - α/2), 36 = 2.03

(16.2 - 14.1) ± 2.03 * √(4.5²/19) + (3.1²/19)

2.1 ± 2.545

Lower boundary = (2.1 - 2.545) = - 0.445

Upper boundary = (2.1 + 2.545) = 4.645

(-0.445 ; 4.645)

Answer:

Point estimate = 76.4

Margin of Error = 2.680

Step-by-step explanation:

Given that distribution is approximately normal;

The point estimate = sample mean, xbar = 76.4

The margin of error = Zcritical * s/√n

Tcritical at 95%, df = 42 - 1 = 41

Tcritical(0.05, 41) = 2.0195

Margin of Error = 2.0195 * (8.6/√42)

Margin of Error = 2.0195 * 1.327

Margin of Error = 2.67989

Margin of Error = 2.680

Answer: D

Step-by-step explanation:

A) 3*0^2+2(0-5)>8

-10>8 -> not true

B) 3*(-1)^2+2(-1-5)>8

3*1+2*(-6)>8

3- 12>8

-9> 8 -> not true

C) 3*(-2)^2+2(-2-5)>8

3*4+2*(-7)>8

12-14>8

-2> 8 -> not true

D) ) 3*(-3)^2+2(-3-5)>8

3*9+2*(-8)>8

27-16>8

11> 8 -> true

The required total cost of all the purchases is $7,930.00. Option C is correct.

Given that,
Al Roy bought five bonds of Jort Co. 11 3/4 at 93.25% and four bonds of Inst. System 12x08 for 81.125%, the commission on the bonds is $2.50 per bond.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Total bond = 4 + 5 = 9

Face value of a bond = $1000
Total cost = $1000 × 0.9325 × 5 + $1000 × 0.81125 × 4 + 2.50 × 9

Total cost = $7,930.00

Thus, The required total cost of all the purchases is $7,930.00. Option C is correct.

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The given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

What is Euclid's algorithm?

The Euclidean algorithm, also known as Euclid's algorithm, is an effective way to determine the greatest common divisor of two integers, or the biggest number that divides them both evenly without leaving a remainder. It is named after the Greek mathematician Euclid, who first discussed it in his Elements and gave it that name.

A common fraction can be reduced to its simplest terms using the Euclidean algorithm. For instance, the algorithm will demonstrate that the GCD of 765 and 714 is 51, and that 765/714 = 15/14 as a result. Additionally, it has several applications in more complex mathematics.

Hence, the given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

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Leasing and buying are two popular options for acquiring a car or other assets. Both options have their own advantages and disadvantages, and the decision between leasing and buying will depend on individual needs and preferences. Below are some pros and cons of leasing and buying.

Initial and Monthly Payments: When it comes to initial and monthly payments, leasing typically requires lower upfront costs and lower monthly payments compared to buying. This is because leasing only covers the cost of the car's depreciation during the lease term, while buying involves financing the full cost of the vehicle.

Total Cost: When considering the total cost of leasing and buying, it's important to look beyond just the initial and monthly payments. While leasing may have lower monthly payments, the total cost of the lease over the long term may be higher than buying. This is because at the end of the lease term, the lessee has no equity in the car and must either lease a new car or purchase a new car.

Ownership and Customization: One of the main advantages of buying is that the car is owned outright, giving the owner the freedom to customize the vehicle as desired. With leasing, the lessee is limited to the terms of the lease agreement and cannot make any major modifications to the car.

Flexibility: Leasing provides greater flexibility in terms of upgrading to a newer car at the end of the lease term, while buying requires selling or trading in the old car to acquire a new one.

In summary, leasing and buying both have their own advantages and disadvantages, and the decision between the two will depend on individual needs and preferences.

Leasing may be a good option for those who prioritize lower monthly payments and want the flexibility to upgrade to a newer car every few years, while buying may be a good option for those who prioritize ownership, customization, and long-term cost savings.

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Answer:

8 units

Step-by-step explanation:

Given:

Formula:

\(\text{Area of triangle:} \ \dfrac{1}{2} \times \text{Base} \times \text{Height}\)

Substitute the base, height and the area of the triangle to determine the measure of the height (x).

\(\implies 16 \ \text{units}^{2} = \ \dfrac{1}{2} \times 4\times x\)

Simplify the right hand side of the equation.

\(\implies 16 \ \text{units}^{2} = \ 2\times x\)

Divide both sides by 2 to isolate "x".

\(\implies \dfrac{16 \ \text{units} }{2} = \dfrac{2\times x}{2}\)

\(\implies 8 \ \text{units} = x\)

The measure of the height (x) is 8 units.

Answer:  8

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

I hope this is what you where asking for?

The measure of the length of x is equal to 12 + 8√3 using the trigonometric ratios of sine and cosine

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangle with hypotenuse = 8√3 and adjacent = 12, the angle between them is derived and used to solve for the opposite side as follows:

cos⁻¹(3/2√3) = 30°

sin30° = opposite/8√3

opposite side = 8√3 × sin30°

opposite side = 4√3

the whole right triangle have its interior angles as 30°, 60°, and 90° {sum of interior angles of a triangle

Let y be the remaining length of the base so that;

x = 12 + y

we shall evaluate for y as follows:

cos60° = 4√3/y {adjacent/hypotenuse}

y = 4√3/cos60°

y = 8√3

so; x = 12 + 8√3.

Therefore, the measure of the length of x is equal to 12 + 8√3 using the trigonometric ratios of sine and cosine

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