What is the common difference in the following arithmetic sequence?

2.8, 4.4, 6, 7.6, ...
–4.8
–1.6
1.6
4.8

Answer:

[tex]\frac{5pi}{6}[/tex]

Step-by-step explanation:

Answer:

[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]

Therefore, the value of x in the interval [0, 2π) is:

[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]

Answer:

Step-by-step explanation:

1 ft/s = 0.681818 mph

355.7 * 0.681818 = 242.5226626

355.7 ft/s = 242.5226626 mph

If we want the slope to be -6/7, then the value of x must be -5.

Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:

[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]

Where on the second line we multiplied and divided the right fraction by 2.

Comparing the fractions, we see that we must have:

9 -x = 14

9 - 14 = x

-5 = x

So the value of x must be -5.

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[tex](10^4)^4[/tex]

[tex]10^8[/tex]

Therefore in simplified form [tex](10^4)^4[/tex] is [tex]10^8[/tex]

Answer: 925

Step-by-step explanation:

This is an arithmetic series with first term 1 and last term 3(25)-2=73, with a total of 25 terms.

Using the sum of an arithmetic series formula, we get the sum is:

[tex]\frac{25}{2}(1+73)=\boxed{925}[/tex]

The Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

A function is a type of relation, or rule, that maps one input to a specific single output.

Given

Base salary = $2500 per month

Commision = 3% on Sales over 48000

Determine the function s(x) for sales over $48000

Let's Represent the total sales in a month with s.

So, the function s(x) is:

s(x)  = Base Amount + Commission x Sales over $48000

s(x) = 2500  + 3% (s - 48000)

s(x) = 2500  + 0.03(s - 48000)

s(x) = 2500  + 0.03s - 1440

s(x) = 0.03s - 1060

Hence, the Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

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Answer:

Damien is 74 years old now

Step-by-step explanation:

Define the variables:

Given information:

From the given information, create 2 equations:

Equation 1:  d + k = 100

Equation 2:  d - 10 = 4(k - 10)

Rewrite Equation 1 to make k the subject:

⇒ k = 100 - d

Substitute this into Equation 2 and solve for d:

⇒ d - 10 = 4(100 - d - 10)

⇒ d - 10 = 400 - 4d - 40

⇒ d - 10 = 360 - 4d

⇒ d - 10 + 10 = 360 - 4d + 10

⇒ d = 370 - 4d

⇒ d + 4d = 370 - 4d + 4d

⇒ 5d = 370

⇒ 5d ÷ 5 = 370 ÷ 5

⇒ d = 74

Therefore, Damien is 74 years old now.

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

In this case we have a cubic equation, that is, a third order polynomial. There are two strategies to determine the roots of cubic equations: (i) Cardano's formula, (ii) Numerical methods.

The quickest though most effective way consists in determining the roots by numerical methods (i.e. Newton-Raphson method). By using numerical methods we conclude that the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7

x₁ = - 1, x₂ = (- 5 + i √3)/2, x₃ = (- 5 - i √3)/2

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

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The expression which is the simplest form of; - (4x³ + x²) + 2 (x³ − 3x²) is; -2x³ -7x².

The expression given in the task content whose simplest form is to be determined is;

- (4x³ + x²) + 2 (x³ − 3x²)

Hence, upon opening up the parentheses, it follows that;

-4x³ - x² +2x³ -6x²

Upon collection and summing up of like terms; -2x³ -7x².

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Considering the given equations for the revenue and the cost, it is found that 36 tickets have to be sold each night to break even.

The break-even point is when the revenue and the costs are equal.

In this problem, the equations are given as follows:

At the break-even point:

R(x) = C(x)

15x = 1.25x + 495

13.75x = 495

x = 495/13.75

x = 36.

36 tickets have to be sold each night to break even.

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Part 1

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

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is [tex]\boxed{[0, \infty)}[/tex]

Part 2

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

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,

[tex]4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}[/tex]

Thus, the domain in interval notation is [tex]\boxed{\left[-\frac{1}{4}, \infty)}[/tex]

The multiplicity of the function is 1 for each term after factorization.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial function:

[tex]\rm F(x)= 4x^3+19x^2-41x+9[/tex]

After factorization:

[tex]\rm F(x) = \left(4x-1\right)\left(x^2+5x-9\right)=0[/tex]

[tex]\rm F(x) =(4x-1)^1(\:x-\frac{-5+\sqrt{61}}{2})^1(\:x+\frac{-5-\sqrt{61}}{2})^1[/tex]

The multiplicity of the function is 1 for each term.

Thus, the multiplicity of the function is 1 for each term after factorization.

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Answer:

120

Step-by-step explanation:

10%=12

20%=12x2

100%=12x10

        =120

Answer:

Let the number be x.

Compute 10% of x and equate it to 12 to compute the value of x as follows:

[tex]x[/tex] x [tex]\frac{10}{100} = 12[/tex]

[tex]x[/tex] = 12 x [tex]\frac{100}{10}[/tex]

[tex]x[/tex] = 120

Thus, the number is 120.

Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]

Step-by-step explanation:

This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.

To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.

Answer:

C = 2√(πA) units

Step-by-step explanation:

Answer:

• f(g(x)) =  [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = 16[tex]\sqrt{x}[/tex] + x + 65

Step-by-step explanation:

• f(g(x)) = f(x² + 1)

         = [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = g([tex]\sqrt{x + 8}[/tex] )

            = [tex](\sqrt{x } + 8)^{2}[/tex] + 1

            =  x + 16[tex]\sqrt{x}[/tex] + 64 + 1

            = 16[tex]\sqrt{x}[/tex] + x + 65

Answer:

1. santina drove 14 more miles than carole

2. the owner will need to buy 8 bags this week

Step-by-step explanation:

1. 203-189= 14

2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds

1. 14

2. 8

3. 48

4. 318

5. 23

6. 4

7. a) 10 b) 60 c) 8 d) 107

8. $1,532

9. 1

10. $15.50

11. .95

Step-by-step explanation:

The critical probability, assuming a confindence level of 58% is 0.79.

From the information given, the confidence level is 58%. The alpha will be:

= 1 - (58/100)

= 1 - 0.58

= 0.42

The critical probability will be:

= 1 - (0.42/2)

= 1 - 0.21

= 0.79

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Answer:

option c (19.2, -6.7) is correct

Step-by-step explanation:

Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.

if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is

given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]

according to question :

given : end point T(-16.8, 31.7)  and mid point M(1.2, 12.5)

let coordinates of another end point S (a, b)

therefore, using mid point formula

1.2 = (-16.8 + a)/2

2.4= (-16.8 + a)

19.2 = a

and,

12.5 = (31.7 + b)/2

25 = 31.7 + b

-6.7 = b

so the option c (19.2, -6.7) is the correct answer

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Answer:

Step-by-step explanation:-49 - + 65= ?, 65-49 = 16 , so we take 65-49 as normal which is = 16 but it's -16,cuz we were given negative45

Answer:

1

Step-by-step explanation:

It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.

Answer: 1

The Medication A mixed this week should be 10 milligrams.

We have,

Medications to be mixed in the proper proportions.

Last week's proportions as the doctor indicated ;

Medication A = 90 milligrams

Medication B = 72 milligrams

This week's proportions as doctor indicated;

Medication B = 8 milligrams

Let, Medication A = x milligrams

As we are instructed to mix the Medication in the proper proportions,

So,

According to the question,

90/72 = x/8

10/8 = x/8

⇒ x = 10 milligrams

Here,  the Medication A mixed is 10 milligrams.

Therefore, the Medication A mixed this week should be 10 milligrams.

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Answer:

a) quantitative - continuous

b) qualitative

c) quantitative - discrete

d) quantitative - discrete

Explanation:

A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.

A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.

The recursive formula would be: 100 - XN = B.

When a function calls itself and uses its own previous terms to define its subsequent terms, it is called a recursive function. It is the technical recursive function’s definition, i.e., a recursive function builds on itself.

X: represents how many weeks

N: represents books per week

B: represents books she has at anytime

So the recursive formula would be: 100 - XN = B

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The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c

An equation is an expression that shows the relationship between two or more numbers and variables.

The associative property states that when adding or multiplying it can be represented by:

(a + b) + c = a + (b + c)

For multiplication:

a * (b * c) = (a * b) * c

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Answer:

slope: 3

y-intercept: (0, -1)

Find slope:

[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given points are: (0, -1), (3, 8)

[tex]\rightarrow \sf slope : \dfrac{8-(-1)}{3-0} = \dfrac{9}{3} = 3[/tex]

When finding y-intercept, the value of x is 0. Here given y is -1 when x is 0.

y-intercept: -1  or  (0, -1)

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

If a linear function contains these points: (0,-1) and (3,8), what is its slope and y-int.?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Formula utilised, here [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

Put in the values,

[tex]\bf{\dfrac{8-(-1)}{3-0}}[/tex]  | subtract on top and bottom

[tex]\bf{\dfrac{9}{3}}[/tex] | divide on top and bottom

[tex]\bf{3}[/tex]

The y-intercept is the second co-ordinate of the point (0,-1)

[tex]\bf{Which\;is\;-1}[/tex].

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                      [tex]\bf{\begin{cases} \bf{Slope=3} \\ \bf{Y-int. -1} \end{cases}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1 \theta l}}[/tex]

Answer:

log12=log(2.2.3)

=log2+log2+log3

=0.30103+0.30103+0.47712

=0.60206+0.47712

=1.07918