If a1 =2 and an =-2an-1 then find the value of a6

The amount invested at 8% and 6% is 1000 and 1900 respectively.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, The person invested $2900 in two mutual funds and the total profit is $194.

Let the amount invested at 8% is x, then the amount invested at 6% is:

2900-x

Since the total profit is $194, it follows:
8% of x + 6% of (2900 - x) = 194

8x/100 + 6(2900 - x)/100 = 194

8x + 17400 - 6x = 19400

2x = 19400 - 17400

2x = 2000

x = 1000

The amount invested at 6% is:
2900 - 1000

= 1900

Hence, the amount invested at 8% and 6% is 1000 and 1900 respectively.

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Heather worked 5 hours every evening during each dinner shift.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

Let morning shift = m

evening shift = e

Representing the word problem in an equation;

4(m + e) = 28

Diving both sides by 4

m + e = 7

but she always works 2 hours in th morning shift

2 + e = 7

e = 7 - 2

e = 5

Therefore she worked 5 hours in the evening shift for 4 days.

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In a residual plot if the linearity assumption is the points are scattered and there is no obvious pattern.

Residual plot:

in statistics, residual value is a measure of how much a regression line vertically misses a data point.

Given,

Here we need to find what would you expect to see in a residual plot if the linearity assumption is correct.

As per the definition of residual plot, there is no obvious pattern for this plot and the positive and negative values are evenly spread across the whole range.

Therefore, in the regression line there are some points are misses the line on the vertical base.

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Answer: It is correct.

Step-by-step explanation:

The question is an illustration of equation of circles.

The equation of the dartboard circle is:  [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.

Given that,

h = 5 feet 8 inches ---- the height at which the dartboard was hung

d = 18 inches in diameter ---- the diameter of the dartboard

B = 12 feet --- the bull's eye

D = 11.5 feet , 5 feet --- Brian's dart

Equation of the circle

First, we convert all units to feet

This is done by dividing inches units by 12

h = 5 feet 8 inches

h = 5 ft + 8/12 ft

h = 5 ft + 2/3 ft

Take LCM

h = [tex]\frac{15+2}{3}[/tex] ft

h = [tex]\frac{17}{3}[/tex] ft

d = 18 inches

d = [tex]\frac{18}{12}[/tex] ft

d = [tex]\frac{3}{2}[/tex] ft

Divide by 2 to calculate radius

r = [tex]\frac{3}{2*2}[/tex] ft

r = [tex]\frac{3}{4}[/tex] ft

To find the equation of a circle when you know the radius and centre, use the formula as [tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex] , where represents the centre of the circle, and is the radius.

The equation of the circle is represented as:

[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]

In this case:

a = B = 12 feet -- the distance between the bull's eye and the wall

b = h = [tex]\frac{17}{3}[/tex] ft  ---- the height at which the dartboard was hung

So, we have:

[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]

[tex](x-12)^{2} +(y-\frac{17}{3}) ^{2} = (\frac{3}{4}) ^{2}[/tex]

Evaluate the exponents

[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Hence, the equation of the circle is:

[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Does Brian’s dart land on the dartboard?

Yes her dart lands on the dartboard because

D = 11.5 feet , 5 feet is within the circumference of the dartboard

Therefore,

The question is an illustration of equation of circles.

The equation of the dartboard circle is:  [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.

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Answer:  12

Step-by-step explanation:

hope this helps

Answer: 1452 units^3

The required volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The formula for the volume of a cylinder is given as:

V = πr²h

Where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the given values, we get:

V = π(11)²(12)

= π(121)(12)

= 1452π cubic units

Therefore, the volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.

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Answer: 11 / 20

Step-by-step explanation:

The values of x and w on the triangle are given as follows:

w = 14.4, x = 11.2.

The values of x and w are obtained applying the trigonometric ratios, as the triangle is a right triangle.

The three trigonometric ratios are given as follows:

For the angle of 48º, we have that:

Hence:

tan(48º) = 16/w

w = 16/tan(48º)

w = 14.4.

For the angle of 32º, we have that:

Hence:

tan(32º) = 16/(14.4 + x)

tan(32º)(14.4 + x) = 16

x = (16 - 14.4tan(32º))/tan(32º)

x = 11.2.

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Answer:

They would have sold 8.2 eggs

Step-by-step explanation:

^

Answer: $350 = t

Step-by-step explanation:

might help);   600-250 = t

t + 250 ≤ 600  INEQUALITY

Answer: $350.

Explanation: if you do  [tex]600 -250[/tex] you will end up with $350

The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.

As given in the question,

Let success be defined by health department inspection is passed by restaurant

Probability of success rate 'p' = 0.94

Value of ' 1 - p ' = 1 - 0.94

                        = 0.06

Number of owners of restaurant which are surveyed 'n' = 58

For the given binomial experiments calculation of the following distributions are:

Mean 'μ' = np

             = 58 × 0.94

             = 54.52

Standard deviation 'σ' = √ np (1 - p)

                                   = √ 58 × 0.94 × 0.06

                                   = √3.2712

                                   = 1.808

Variance 'σ²' =  np( 1 - p )

                    = 58 × 0.94 × 0.06

                   = 3.2712

Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.

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Answer:

√53 or 7.28

Step-by-step explanation:

To find the length of the line segment from the point (4, 2) to the point (-3, 4), you can use the distance formula, which is:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of the two points, you get:

distance = √((-3 - 4)^2 + (4 - 2)^2)

Simplifying this expression gives:

distance = √((-7)^2 + (2)^2)

Which simplifies to:

distance = √(49 + 4)

Which simplifies to:

distance = √53

So the length of the line segment from the point (4, 2) to the point (-3, 4) is approximately 7.28.

Sine and cosine are the fundamental trigonometric functions associated to the sides of a right triangle and tangent is a derivate trigonometric function.

Let be a right triangle, whose features are introduced in the figure attached below. The side with measure y is the side opposite to the angle θ, whereas the side with measure x is the side adjacent to the angle θ. The side with measure r represents the hypotenuse of the right triangle, which can be found by means of Pythagorean theorem:

r = √(x² + y²)

Trigonometric functions are trascendent functions that relates two sides of the right triangle. There are two fundamental trigonometric functions and four derivate trigonometric functions:

Fundamental

sin θ = y / r = (Opposite side) / (Hypotenuse)

cos θ = x / r = (Adjacent side) / (Hypotenuse)

Derivate

tan θ = sin θ / cos θ = y / x = (Opposite side) / (Adjacent side)

cot θ = 1 / tan θ = cos θ / sin θ = x / y = (Adjacent side) / (Opposite side)

sec θ = 1 / cos θ = r / x = (Hypotenuse) / (Adjacent side)

csc θ = 1 / sin θ = r / y = (Hypotenuse) / (Opposite side)

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Answer:

There are 9 small $5 bags and 6 large $8 bags

Step-by-step explanation:

9 x 5 = 45

6 x 8 = 48

45 + 48 = 93

Answer:

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

Given sum of cubes, use identity a³ + b³ = (a + b)(a² - ab + b²):

The matching choice is B.

Answer:

B)  (2x + 3)(4x² - 6x + 9)

Step-by-step explanation:

Given expression:

[tex]8x^3+27[/tex]

Rewrite  8 as 2³  and  27 as 3³:

[tex]\implies 2^3x^3+3^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^nc^n=(ac)^n:[/tex]

[tex]\implies (2x)^3+3^3[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Sum of Cubes Formula}\\\\$a^3+b^3=(a+b)(a^2-ab+b^2)\\\end{minipage}}[/tex]

Therefore:

Using the Sum of Cubes formula:

[tex]\begin{aligned}\implies (2x)^2+3^3&=(2x+3)((2x)^2-2x(3)+3^2)\\&=(2x+3)(4x^2-6x+9)\end{aligned}[/tex]

Answer:

Hi again, use the sine rule for length. answer: 82.42

Step-by-step explanation:

For the given number line the inequality equation would be -10 < x ≤ 20.

What is inequality?

In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

In the given number line, a hollow circle represents that the number is excluded and solid circle represents that the number is included in the range

and the range lies between -10 to 2.

Let's take a variable to describe the relationship,

By using inequality we can prepare the inequality equation as

                -10 < x ≤ 20

Hence, for the given number line the inequality equation would be -10 < x ≤ 20.

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The reaction described by 2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of oxidation - reduction reaction

Any chemical process in which a participating chemical species' oxidation number changes is known as an oxidation-reduction reaction, often known as a redox reaction. The phrase refers to a broad range of procedures.

The equation of the reaction is written as

2H₂O + 2K → 2KOH + 2H₂

The reducing agent here is Potassium which is K it transformed from Potassium to Potassium Hydroxide. Potassium is electron donor

The oxidizing agent is water which ended up as Hydrogen molecule

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Answer: 166

Step-by-step explanation:

The sum of two odd numbers is an even number.

85 is odd, and so is the sum of an odd number and an even number.

2×83=166

The system of equations is  y = 50 + 3x; y = 34 + 4x. The number of cups that Aunt Emily orders is 16. The cost of either shop for 16 cupcakes is $98.

What is substitution method?

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

Assume that x number of cups that ordered by Aunt Emily.

Given that, Clarksville Bakery charges $3 for each cupcake, plus $50 for the large cake.

Therefore, the cost of x cupcake is 50 + 3x.

y = 50 + 3x

Also, Sebastian's Sweet Shoppe charges $34 for the large cake and $4 for each cupcake.

Therefore, the cost of x cupcake is 34 + 4x.

y = 34 + 4x

The system of equations is

y = 50 + 3x  ....(i)

y = 34 + 4x  ...(ii)

To find the number of cupcakes that Aunt Emily orders, use substitution method to solve the system of equation.

Substitute y = 50 + 3x in equation (ii)

50 + 3x = 34 + 4x

Subtract 3x from both sides:

50 = 34 + x

x = 16

Putting x = 16 in equation (i)

y = 50 + (3 × 16) = 98

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Answer:

Step-by-step explanation:

17-8=9 but if 18-7=11 then 19-8=7

Two more adults can board the elevator if there are 17 children present inside.

The number of adults who can still enter will be determined by the linear equation solution.

let

20c = 15a ; 5 divided by both sides

4c = 3a

Another 3 kids can enter the elevator if there are already 17 in it.

The fact that;

3c =  9/4 a

3c =  9/4 a

3c = 2.25 a

3c = 2 a (no fraction)

Thus, two more adults can board the elevator if there are 17 children present inside.

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There are 2 hours of television must you watch in the eighth week to meet your goal.

What is television?

The transmission of audio and video data electronically between a source and a recipient.

The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.

Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.

Suppose x is the hours of watching television in the 8th week.

Let the average of watching television per week is 1.5.

⇒

[tex]\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2[/tex]

Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.

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