The first six terms in a geometric sequence are shown, where a1=-4
-4 -16 -64 -256 -1024 -4096

Based on this information, which equation can be used to find the nth term in the sequence, an?

The value of x which could replace the missing value in the table so that y is not a function of x is; 7.

It follows from the task content that the value of x which could make y not a function of is required to be determined.

Recall that a function is a special kind of relation in which case each value of x is assigned one value of y.

On this note, if we assign 7 as the missing value of x, then y is not a function of x as u has now been assigned more than 1 output, y values.

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Answer: 0

Step-by-step explanation:8th Place 100*10 1000th Place is 0

The angle formed by the two hands have a measure less than 1/4 turn

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

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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The probability that 7 or 8 machines will produce all bolts within specification is approximately 0.9841.

Using the binomial distribution formula, we get:

P(X = 7) = (8 choose 7) * (0.002)⁷ * (0.998)¹ ≈ 0.0081

P(X = 8) = (8 choose 8) * (0.002)⁸ * (0.998)⁰ ≈ 0.000003

Therefore, P(X = 7) + P(X = 8) ≈ 0.0081 + 0.000003 ≈ 0.9841.

Probability is a branch of mathematics that deals with the study of the likelihood of occurrence of events or outcomes in situations where there is uncertainty or randomness. It is a measure of the degree of uncertainty of an event, typically expressed as a number between 0 and 1. Probability is used to make predictions and decisions in various fields, including science, engineering, economics, finance, and social sciences.

It is based on the analysis of past events or observations, and it enables us to estimate the likelihood of future events or outcomes. Probability theory provides a mathematical framework for modeling and analyzing random phenomena and helps us understand the laws of chance that govern various natural and artificial systems.

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If the coordinates of the intersection of the diagonals of ABCD

with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4). The coordinates of the intersection of the diagonals are (4/3, 0).

Using the two point form of the equation of a line to determine the The equation of the line that contains AC

y₋y₁ = (y₂-y₁)/(x₂-x₁) * (x₋x₁)

where:

(x₁, y₁) and (x₂, y₂)= two points on the line

y - 2 = (-4 - 2)/(4 - 0) * (x - 0)

Simplify

y - 2 = -3/2 * x

2y - 4 = -3x

3x + 2y = 4

Equation of the line that has BD

y - 2 = (-4 - 2)/(8 - (-4)) * (x - 8)

Simplify

y - 2 = -3/4 * x + 9/2

4y - 8 = -3x + 36

3x + 4y = 44

Now let find the point of intersection:

3x + 2y = 4

3x + 4y = 44

Multiplying the first equation by -2

-6x - 4y = -8

Eliminate x

0x + 0y = 36

So,

y = 0

3x + 2(0) = 4

3x = 4

x = 4/3

Therefore the coordinates  is (4/3, 0).

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The probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).

To calculate the probability that a female student chose strawberry ice cream, we need to consider the total number of female students who made an ice cream choice and the number of female students who chose strawberry ice cream.

From the given information, we have the following breakdown:

         Male    Female   Total

Vanilla 6 4 10

Strawberry 9 14 23

Chocolate 13 4 17

Total 28 22 50

To find the probability, we divide the number of female students who chose strawberry ice cream by the total number of female students:

Probability = (Number of female students who chose strawberry ice cream) / (Total number of female students)

Therefore, the probability of a female student choosing strawberry ice cream is:

Probability = 14 / 22

Simplifying the fraction, we have:

Probability = 7 / 11

Therefore, the probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).

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Step-by-step explanation:

Using the roots given in order given:

y=  ( x+4)(x+2)(x-4)(x-2)     would  fit the bill.....

A. Since the remainder is zero, (x+2) is indeed a factor of f(x).

B. So, f(x) is completely factored as (x+2)(x-1)(x-3).

C. The zeros of F(x) are: -2, 1, and 3.

To determine if (x+2) is a factor of f(x) = x³-3x²-7x+6 can use synthetic division or long division.

Using synthetic division:

-2 | 1  -3  -7  6

   -2   10  -6

    1  -5   3  0

Using the result from part A we can write:

f(x) = (x+2)(x²-5x+3)

The quadratic factor can be factored further using the quadratic formula or factoring by grouping:

f(x) = (x+2)(x-1)(x-3)

So, f(x) is completely factored as (x+2)(x-1)(x-3).

The zeros of f(x) are the values of x that make f(x) equal to zero.

From the factored form of f(x) we can see that the zeros are -2, 1 and 3. So:

The zeros of F(x) are: -2, 1, and 3.

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The monthly payments on the 20 yrs mortgage would be $946.69.

According to the question, the down payment on the house is 20% of $165000, which is:

0.2 * $165,000 = $33,000

The amount that is needed to be financed is:

$165,000 - $33,000 = $132,000

This rate of interest on the payment is 7.5% per year, which is equal to 0.075 as a decimal. We know that the mortgage is for 20 yrs or 240 months:

To calculate the monthly payment, we can use the formula:

monthly payment = [tex][P * r * (1 + r)^n] / [(1 + r)^n - 1][/tex]

where P is the principal amount i.e. the amount being borrowed, r is the monthly interest rate, whereas n is the number of payments.

we need to find the monthly interest rate, for which we can use divide the yearly interest by the number of months in a year, we get:

r = 0.075 / 12 = 0.00625

Now substituting the values into the formula above we get:

monthly payment = [tex][$132,000 * 0.00625 * (1 + 0.00625)^240] / [(1 + 0.00625)^240 - 1][/tex]

monthly payment = $946.69 which is rounded to the nearest cent.

Therefore, the monthly payments on the 20 yrs mortgage would be $946.69.

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The area of the given rectangle is 121/16 square inches.

As know that the area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

To find the area of the rectangle, we need to multiply the length by the width. We have:

Length = 2 3/4 inches = 11/4 inches

Width = 2 3/4 inches = 11/4 inches

Area = Length x Width

Area = (11/4) inches x (11/4) inches

Area = 121/16 square inches

Therefore, the area of the rectangle is 121/16 square inches.

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From matrix property it can be showed that A=B.

Given,

If A,B and x are matrices with x≠0 and AX=BX

Now.

X must be non-singular matrix because

A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]

[tex]XX^{-1}[/tex]  = I( identity matrix )

AI = BI

A = B

Hence Proved, A = B .

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The resolution of the given force applied to the shovel is: A vertical force of 592 NA horizontal force of 215.47 N

The components of a force represent the combined vertical and horizontal forces that combine to make the resultant force. Components are two vectors that add up to the given vector which are perpendicular to each other.

Now, when we apply a force F to an object at an angle θ, it can be said that the resolution of the forces is:

In the horizontal direction: F_x = F * cos θIn the vertical direction: F_y = F * sin θTyri pushes a shovel into the ground with a force of 630 newtons at an angle of 70° with the ground.

Thus, the diagram that shows the resolution of the forces is:

A vertical line showing a force of 630 * sin 70 = 592 N

A horizontal line showing a force of 630 * cos 70 = 215.47 N

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The arc lengths and the angle measures are arc length = 0.67 meters, AC = 45 degrees and TV = 23 degrees

Arc length

Given that

Central angle = 6 degrees

Circumference = 40 meters

The arc length is calculated as

arc length = Central angle/360 * Circumference

So, we have

arc length = 6/360 * 40

Evaluate

arc length = 0.67 meters

The measurement of AC

Here, the arc AC subtends the angle 45 degrees at the center of the circle

This means that

AC = 45 degrees

The measurement of TV

Here, the arc TV subtends the angle 23 degrees at the center of the circle

This means that

TV = 23 degrees

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Answer:

Option : A

Step-by-step explanation:

To find the x-coordinate of the solution to the system of equations, we need to solve the system by eliminating either x or y. Let's eliminate y by multiplying the first equation by 3 and the second equation by 1:

Equation 1: 2x + y = -4 (multiply by 3)

Equation 2: 5x + 3y = -6 (multiply by 1)

Multiplying equation 1 by 3 gives us:

6x + 3y = -12

Multiplying equation 2 by 1 gives us:

5x + 3y = -6

Now we can subtract equation 2 from equation 1 to eliminate y:

(6x + 3y) - (5x + 3y) = -12 - (-6)

6x + 3y - 5x - 3y = -12 + 6

x = -6

Therefore, the x-coordinate of the solution to the system of equations is x = -6.

The correct option is: Ox=-6.[tex][/tex]

Answer:

3:55

Step-by-step explanation:

3:55

Answer:

1/9

Step-by-step explanation:

P =

[tex](no \: of \: favorable \: outcomes) \div (total \: numeber \: of \: outcomes \: )[/tex]

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Answer: There are 32,760 color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options.

Step-by-step explanation: To determine the number of color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options, we need to calculate the number of permutations.

Since each room is assigned a different color, we can arrange the colors in a specific order. The number of ways to arrange 15 colors in 4 distinct positions is given by the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of options (15 colors) and r is the number of positions (4 rooms).

Using the formula, the number of color arrangements possible is:

P(15, 4) = 15! / (15 - 4)!

= 15! / 11!

= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)

= 32,760

The number of green t-shirts sold are 45.

Given that a bar graph showing the sell of t-shirts of 4 different colour,

It is saying that the sell has increased by 50% next week, we need to find the number of green t-shirts to be sold in next week,

So, the number of green t-shirts sold in previous week = 30

So this week the sell should have been increased by 50%

Therefore, the number of green t-shirts sold this week = 150/100 × 30

= 1.5 × 30 = 45

Hence the number of green t-shirts sold are 45.

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Based on the application of the complementary angles, the measures of the angles are: m<DEG = 54 degrees;   mm<GEF = 36 degrees

When two angles make up a right angle, they are referred to as complementary angles because they add up to 90 degrees when summed.

6x and 4x make up a right angle, this means their sum will give us 90 degrees when we add them up. Therefore:

6x + 4x = 90

10x = 90

Divide both sides by 10

10x/10= 90/10

x = 9

measure of angle DEG = 6x = 6(9) = 54 degrees.

Measure of angle GEF = 4x = 4(9) = 36 degrees

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Answer:

Step-by-step explanation:

General formula

(x-h)^2 + (y-k)^2 = r^2

where (h,k) center of circle whose radius r

applying the formula to our Q

(x – 5)² + y² = 81

(x – 5)² + (y-0)² = 9^2

---> center of circle (5,0)

---> radius is 9

The expression O cos(k0 + 0) + i sin(k0 + 0) is commonly used in proofs involving complex numbers and trigonometric functions, representing the complex exponential function [tex]e^(ik0)[/tex].

The expression that will complete the proof depends on the given context and what exactly needs to be proved. However, in general, the expression O cos(k0 + 0) + i sin(k0 + 0) is often used in proofs involving complex numbers and trigonometric functions.

This expression represents the complex exponential function [tex]e^(ik0)[/tex], where k0 is a constant. The cosine term represents the real part of the complex number, while the sine term represents the imaginary part.

The addition of 0 in the arguments of both cosine and sine indicates that the complex number is in polar form, with a magnitude of 1 ([tex]since cos^2 +[/tex] [tex]sin^2 = 1[/tex] for all angles).

Using this expression, we can perform various operations and manipulations to prove different results, such as De Moivre's theorem or Euler's formula.

Ultimately, the choice of expression will depend on the specific problem and what needs to be proved.

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Answer:

Step-by-step explanation:

To calculate the values of the given function, substitute the given values of x into the function f(x) = 7x^2 - 8x + 8:

f(-2) = 7(-2)^2 - 8(-2) + 8

= 7(4) + 16 + 8

= 28 + 16 + 8

= 52

f(-1) = 7(-1)^2 - 8(-1) + 8

= 7(1) + 8 + 8

= 7 + 8 + 8

= 23

f(0) = 7(0)^2 - 8(0) + 8

= 0 - 0 + 8

= 8

f(1) = 7(1)^2 - 8(1) + 8

= 7(1) - 8 + 8

= 7 - 8 + 8

= 7

f(2) = 7(2)^2 - 8(2) + 8

= 7(4) - 16 + 8

= 28 - 16 + 8

= 20

Therefore, the values of the function for the given inputs are:

f(-2) = 52

f(-1) = 23

f(0) = 8

f(1) = 7

f(2) = 20

Answer: D: 1/5

Step-by-step explanation:

sinx = 5/13

this ratio is special; it is a 5-12-13 right triangle, (pythagorean triple).

there is also a formula to find tan(x/2); It is tan(x/2) = ±[tex]\sqrt{\frac{1-cosx}{1+cosx} }[/tex]

the + or - sign is decided by the quadrant the half angle is in;

since x is in quad one, it is somewhere between 0 and pi/2. To find the half angles position, simply divide it; x/2 is somewhere between 0/2 and pi/4.

so its also in the first quadrant. Since tangent is positive in the first quadrant, we will take the positive answer:

One more thing. we need the cosx in our formula. cosx will be 12/13, since this is a special right triangle as we said before.

tan(x/2) = [tex]\sqrt{\frac{1-12/13}{1+12/13} }[/tex]

tan(x/2) = [tex]\sqrt{\frac{1/13}{25/13} }[/tex]

tan(x/2)= [tex]\sqrt{1/25}[/tex]

tan(x/2) = 1/5

Option D is the answer :)

Answer:

In mathematics, a function is a rule that assigns one unique output value for each input value. A linear function is a function that has a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will form a straight line.

For example, the function f(x) = 2x + 1 is a linear function because its graph is a straight line. As x increases by 1, the output of the function increases by 2.

On the other hand, a nonlinear function is a function that does not have a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will not form a straight line.

For example, the function f(x) = x^2 is a nonlinear function because its graph is a curve. As x increases, the output of the function increases at an increasing rate.

In general, nonlinear functions can take many different forms and can have complex behaviors, whereas linear functions have a simple, predictable behavior.

The data is best described by an increasing function. The regression equation is y =0.0965x - 0.61.

Here is a table of the data:

Temperature (K) Gas Volume (cm³)

173     16

223     21

273     26

323     30

373     36

423     40

The data is best described by an increasing function, and it is likely to be linear since the volume of the gas increases uniformly with the temperature.

Let x be the temperature and y be the volume of the gas.

The slope is given by (nΣxy - ΣxΣy) / (nΣx² - (Σx)²),

where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, and Σx² is the sum of the squares of x.

The y-intercept is given by (Σy - bΣx) / n, where b is the slope.

Using the data, we have n = 6, Σx = 17788, Σy = 169, Σxy = 4225, and Σx² = 43750.

Substituting these values into the formulas gives the slope b = 0.09657 and the y-intercept a = -0.61.

Therefore, the regression equation is y =0.0965x - 0.61.

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