6) Given the geometric sequence 2, 4, 8, 16,...

a) Determine the common ratio.

b) Write the explicit formula.

c) Find a10

d) Write the recursive formula.

The correct statement regarding the graph of the function f(x) = (x - 2)(x - 1)(x - 4) is given as follows:

The graph starts at the bottom left, continues up through the x axis at 1 to a maximum around y equals one half, goes back down through the x axis at 2 to a minimum at y equals negative 2, and goes back up through the x axis at 4.

The function is defined as follows:

f(x) = (x - 2)(x - 1)(x - 4).

Considering the linear factors of the function, the values of x through which the function intercepts the x-axis are given as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

As the function has three zeros with multiplicity one, it is a cube function, hence:

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Answer:1/30 is the correct answer

Step-by-step explanation:

first, calculate the total number of chips: 4+5+1=10

since we know that chips are not replaced.

probability of finding the first white chip: 4/10 (4 white chips,10 total)

after removing 1 white chip remaining white chips=3, total chips=9

probability of finding the second white chip:3/9 (3 white chips,9 total)

after removing 1 white chip remaining white chips=2, total chips=8

probability of finding the third white chip 2/8 (2 white chips,8 total)

after removing 1 white chip remaining white chips=1, total chips=7

Now the probability of finding 3 white chips is:

probability=(4/10) * (3/9) * (2/8)=1/30

After 10 years, the investment compounded periodically will be worth $ 132. 53 more than the investment compounded annually.

The worth of the investment compounded annually would be:

= investment principal x  ( 1 + Annual interest ) ^ number of years

= 9, 000 x ( 1 + 5 %) ¹⁰

= $ 14, 660.05

The worth of the periodically compounded interest investment would be:

= 9, 000 x ( 1 + 5 % / 4 ) ¹⁰ ˣ ⁴

= $ 14, 792. 58

The difference is :

= 14, 792. 58 - 14, 660. 05

= $ 132. 53

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Answer:

False

Step-by-step explanation:

False.  That is how a decimal is converted to a percent.  

A percent is converted to a decimal by  taking the percent and dividing by 100%

For example:

56% is converted to a decimal by dividing by 100%

56%/100%  The percents cancel out and when you divide by 100, you move the decimal two places to the left.  .65

The output when the input is 8 is 36 and the input when the output is 42 is 206

You should be aware that input involves materials used in producing a particular thing while the output is the yielding result of the production.

(The input)  n*5 - 4 = (The output)

When the input is 8,

8 * 5 -4

= 40 - 4

= 36

When the output is 42.

(The input)  n× 5 - 4

(The input) 42× 5 -4

(The input) = 206

The input was 206.

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Complete question:

Here is a number machine.

input

-5*3 output

a) Work out the output when the input is 8

b) Work out the input when the output is 42

Answer:

C) -24

Step-by-step explanation:

We have two functions here:

[tex]f(x) = x^{2} + 4[/tex]

and

[tex]g(x) = 2x + 1[/tex]

Now, both of these functions will be multiplied together after they are figured out (since they are next to each other), and they will have -2 replace x. For function f, we get:

[tex]-2^{2} + 4[/tex]

For function g, we get:

[tex]2 * -2 + 1[/tex]

Simplifying these two gives us:

[tex](4 + 4) * (1 - 4)[/tex]

Simplifying further gives us:

[tex]8 * -3 = -24[/tex]

So, the value of f(-2)g(-2) is C) -24.

Hope this helped!

Answer:

B)  -24

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2+4\\g(x)=2x+1\end{cases}[/tex]

To find f(-2)g(-2), substitute x = -2 into both functions and multiply them:

[tex]\begin{aligned}\implies f(-2)g(-2)&=\left((-2)^2+4\right)\left(2(-2)+1\right)\\&=\left(4+4\right)\left(-4+1\right)\\&=8 \cdot -3\\&=-24\end{aligned}[/tex]

Answer: Lena walks 63 miles in 10 days.

Step-by-step explanation:

To find out how many miles Lena walks in 10 days, you need to add up all the distances she walks each day.

From the information provided, it seems that the distances walked each day are:

23 miles, 11 miles, 10 miles, 19 miles and the remaining days is not given.

So, to find the total miles Lena walks in 10 days, you would add up the distances walked each day:

23 + 11 + 10 + 19 = 63 miles

So, Lena walks 63 miles in 10 days.

The total miles in 10 days will bed 14 miles. The closest option is OD, which is 19 miles.

To find the total distance Lena walks in 10 days, we need to add up all the distances on the line plot:

Starting from day 1, we can count the distances and add them up:

On day 1, Lena walks 1 mile

On day 2, Lena walks 2 miles

On day 3, Lena walks 1 mile

On day 4, Lena walks 1 mile

On day 5, Lena walks 2 miles

On day 6, Lena walks 1 mile

On day 7, Lena walks 2 miles

On day 8, Lena walks 1 mile

On day 9, Lena walks 1 mile

On day 10, Lena walks 2 miles

Adding up all these distances, we get:

1 + 2 + 1 + 1 + 2 + 1 + 2 + 1 + 1 + 2 = 14

Therefore, Lena walks a total of 14 miles in 10 days.

Thus, the closest option is OD, which is 19 miles.

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Measure of ∠CEA = 91°

The arc of a circle is defined as the part or segment of the circumference of a circle.  A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle.

Given,

In figure

chord AB and chord CD intersect at E

m(arc CA) = 140°

m(arc DB) = 42°

∠CEA intercepts arc CA and has it vertex inside the circle

Thus,

∠CEA = (m(arc CA) + m(arc DB))/2

∠CEA = (140° + 42°)/2

∠CEA = 182°/2

∠CEA = 91°

∠CEA measures 91°

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Answer: To find the perimeter of a triangle, we need to add the length of all three sides of the triangle.

To find the length of each side, we can use the distance formula which is the square root of (x2-x1)^2 + (y2-y1)^2.

The distance between point A (9,-2) and point B (5,1) is: √((9-5)^2 + (-2-1)^2) = √16 + 9 = √25 = 5.

The distance between point B (5,1) and point C (9,-3) is: √((9-5)^2 + (-3-1)^2) = √16 + 16 = √32 = 5.66.

The distance between point C (9,-3) and point A (9,-2) is: √((9-9)^2 + (-3- -2)^2) = √1 + 1 = √2 = 1.41

The perimeter is the sum of the length of all three sides:

Perimeter = 5 + 5.66 + 1.41 = 12.07

Round the answer to two decimal places, the perimeter of the triangle is 12.07.

Step-by-step explanation:

Answer:

Rs. 7.50

or a gain of 10%

Step-by-step explanation:

Let x be the price of the stool

10% = 10/100 = 0.10

Loss = 0.1x

Selling price at 10% loss = x - 0.1x = 0.x

We are given this sale price is 67.50

So

0.9x = 67.50

x = 67.50/0.9 = 75

If he sells it at 82.50, the profit would be 82.50 - 75 = 7.5

This would represent a gain of 7.5/75 x 100 percent

= 10%

Answer:

The carpenter would gain 10% profit.

Step-by-step explanation:

67.5 is 90% of 75.

82.50 is 110% of 75.

Answer: Let's call the number of hours Deborah drives "d" and the number of hours Cornell drives "c".

We know that:

c = 3d (because Cornell drives 3 times the hours that Deborah does)

and

c + d = 8 (because they drive for a total of 8 hours)

We can use the first equation to substitute the value of c in the second equation:

3d + d = 8

4d = 8

d = 2

So Deborah drives 2 hours.

Now we can use the first equation to find the number of hours Cornell drives:

c = 3d

c = 3(2) = 6

So Cornell drives 6 hours.

Step-by-step explanation:

The number of tiles in figure 70 and figure 93 are 142 and 188.

Figure 2 = 6

Figure 3 = 8

The common difference = 8 - 6

= 2

figure 2 = a + (n - 1)d

Where,

a = first term

figure 2 = a + (n - 1)d

6 = a + (2 - 1)2

6 = a + (1)2

6 = a + 2

6 - 2 = a

a = 4

Figure 70 = a + (n -1)d

= 4 + (70-1)2

= 4 + (69)2

= 4 + 138

Figure 70 = 142

Figure 93 = a + (n -1)d

= 4 + (93 - 1)2

= 4 + (92)2

= 4 + 184

Figure 93 = 188

Therefore, figure 70 and 93 have 142 and 188 tiles respectively.

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The equation of the line in slope intercept form is  y = - 1 / 2 x - 8.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Let's find the slope of the line before we can find the equation of the line.

The slope is the change in the dependent variable with respect to the change in the independent variable.

Hence,

m = y₂ - y₁ / x₂ - x₁

Therefore,

(0, -8)(-2, -7)

Hence,

slope = m = -7  + 8 / -2 - 0

m = 1  / -2

m = - 1 / 2

The y-intercept is -8.

Therefore, the equation of the line is y = - 1 / 2 x - 8.

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Answer:

in 3 days Tom made $149.25

Step-by-step explanation:

If Tom made 298.50 in 6 days, you can find the amount made in 3 days by dividing that number in half.

298.5 / 2 = 149.25

The area of the Triangle is 24.11 inch².

The area of any triangle can be calculated using the lengths of two of its sides and the sine of their included angle.

The trigonometric formula for the area of triangles is

area sin C= 1/2  , where and are the lengths of two sides and is the measure of the included angle.

Given:

a= 14 inch

b= 6.5 inch

and, angle = 32 degree

Now, The area of Triangle

= ab sin [tex]\theta[/tex] /2

= 14 x 6.5 x sin 32 /2

= 7x 6.5 x sin 32

= 7 x 6.5 x 0.5299

= 24.11 inch²

hence, the area is 24.11 inch²

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Dalton's Atomic Theory (1804)

From his experiments and observations, as well as the work of peers of his time, Dalton proposed a new theory of the atom. This later became known as Dalton's atomic theory. The general tenets of this theory were as follows:

According to Dalton’s atomic theory, all matter, whether an element, a compound, or a mixture is composed of small particles called atoms.

Dalton based his theory on two laws: the law of conservation of mass and the law of constant composition.

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The statement that is true is D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25

To convert between pounds and kilograms, we use the conversion factor of 1 pound = 2.2 kilograms. This means that 1 pound is equal to 2.2 kilograms, and 2 pounds is equal to 4.4 kilograms, and so on.

In this case, we are given that there is 25 pounds of dog food in a bag, and we want to convert this to kilograms. To do this, we can multiply 25 pounds by the conversion factor of 1 pound = 2.2 kilograms.

25 pounds * (1 kilogram / 2.2 pounds) = 25/2.2 = 11.3636363636 kg.

So, there is approximately 11.36 kilograms of dog food in the bag.

The other options are incorrect. In option A, 1/2.2= 55/22 which is not equal to 25 pounds and the same case in option C. In option B the calculation is not correct as well because 1/2.2 = 25/11.36 doesn't make sense.

Therefore, the only true statement is D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25

The second function 100(.1593)^t decays faster than the first function 100(.2661)^t.

To find which function decays the fastest, we need to compare the decay rates of the two functions.

The decay rate of a function is determined by the exponent in the function. In this case, the exponent is t.

The smaller the exponent, the faster the decay rate.

So, in the first function 100(.2661)^t, the exponent is t.

In the second function 100(.1593)^t, the exponent is also t.

We can compare the decay rates of the two functions by comparing the values of the bases, .2661 and .1593.

The base of a function represents the rate of decay, the smaller the base the faster the decay rate.

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The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

Since the region is the one for  then the intersection we are interested on is x=1 as it can also be seen in the graph.

Where h(x) is the height of the shell which here is the distance between the parabola and the line, so  (since the line is on the top we subtract from it the parabola

Notice the limits of the integral are the x-axis (x=0) and the intersection of the parabola and the line that we found before (x=1)

We want the volume generated when the area bounded by the curves :

v = x2 v = 8 —7x , and

x = 0 for x > 0 is revolved about the y axis using the cylindrical shell method .

The intersection of y = x2 and y = 8 —7x is :

y= x2 = 8 — 7x x2 + 7x —8 = 0

(x + 8)(x — 1) = 0 x = —8 or

x = 1 .

We thus have for x > 0 the two curves intersect at x = 1 and y = 12 = 1 .

The limits for integration are --- 0 <x < 1 .

The upper curve is --- y2 = 8 —7x ,

and the lower curve is --- yi = x2 .

The height of the shell is --- h = y2 -yi = 8 —7x — x2 •

The radius of the shell is --- R = x •

[tex]$$The surface area of the shell is :$$A=2 \pi \mathrm{Rh}=2 \pi x\left(8-7 x-x^2\right)=2 \pi\left(8 x-7 x^2-x^3\right) .$$The differential of volume which is the cylindrical shell is :$$\mathrm{dv}=\mathrm{Adx}=2 \pi\left(8 x-7 x^2-x^3\right) \mathrm{dx}$$[/tex]

[tex]$$We then have the volume of revolution is :$$\begin{aligned}v & =2 \pi \int_0^1\left(8 x-7 x^2-x^3\right) \mathrm{d} x \\& =2 \pi\left(4 x^2-\frac{7}{3} x^3-\frac{1}{4} x^4\right)_0^1 \\& =2 \pi\left[4\left(1^2-0^2\right)-\frac{7}{3}\left(1^3-0^3\right)-\frac{1}{4}\left(1^4-0^4\right)\right] \\& =2 \pi\left(4-\frac{7}{3}-\frac{1}{4}\right) \\& =2 \pi\left(\frac{48-28-3}{12}\right) \\& =2 \pi\left(\frac{17}{12}\right) ; \text { or, we have : } \\v & =\frac{17 \pi}{6} .\end{aligned}$$[/tex]

17π/6 = 8.90 unit³

Thus, The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

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Answer:

You could convert 21/2 to a whole number by multiplying it by 2 and then dividing by 2, so 21/2 = 21/2 = 10.5, then dividing the total by the number of people that is 10.5 / 7 = 1.5 glasses/person.

Answer: 8.8 hours

Step-by-step explanation:

To start off, we’ll make an equation that “connects” both companies:

10 + 4.75h = 21 + 3.5h (we put h to represent the number of hours)

Move all similar terms to one side:

4.75h - 3.5h = 21 - 10

Simplify:

1.25h = 11

h = 8.8

I hope this helps!

The oil and coolant will be changed together after 15000 miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a car manual recommends changing the oil every 5000 miles and inspecting the engine coolant system every 15,000 miles.

The change for both together for the first time will be after 15000 miles.

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9.6 KB kilobytes is equal to 0.0096 MB

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

1kB=1000 bytes

1MB=1000 KB

1kB=1/1000MB=0.001 MB

9.6 KB is nothing but 9600 bytes

9.6 KB in MB we have to convert

Now multiply 9.6 with 0.001

9.6×0.001

0.0096 MB

Hence,  9.6 KB kilobytes is equal to 0.0096 MB

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Answer:

Step-by-step explanation:

.

The best way for Anthony to plan his garden is to create a rectangular plot. He can use the side of the barn as one side of the rectangle, and then measure out the other three sides. The total length of the three sides will be 176 feet. He can divide this into two sides that are 88 feet long and two sides that are 44 feet long. This will give him a rectangular plot that is 176 square feet.

Once Anthony has the dimensions of the plot, he can build a fence around it to protect it from rabbits. He can use a variety of materials such as wood, wire, or plastic mesh to build the fence. The fence should be at least four feet tall and buried at least six inches deep to be effective. If he chooses to use wire, he should use thick, galvanized wire to make sure that the rabbits cannot chew through it.

Once the fence is in place, Anthony can begin planting his garden. He should also consider adding a layer of mulch or straw around the outside of the fence to discourage the rabbits from digging underneath it. With the right planning and protection, Anthony should be able to enjoy a successful garden.

The area of this circle is 12.5 yd²

The incircle is defined as the largest circle that can be made in a triangle and is tangent to each side of the triangle.

The area of the circle is the product of the pie and the square of the radius.

The area of the circle = πr²

We are given that floor of a round hut has a diameter of 4 yards.

r = 2 d

Then we know that

Area = πr²

Substitute the values r = 2

π = 3.14

Area = 3.14(2)²

Area = 3.14 × 4

Area = 12.5663706 yd²

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So, The line is a horizontal one, and the equation is y = -2 of a line in slope-intercept form if the slope is 0 and the point is (-3, -2).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

Positive slope lines lean to the right, and they become steeper as the slope increases. A line with a negative slope slopes left, and the slope's magnitude determines how steep the line is. Since there is no slope on a horizontal line, it has a slope of zero.

The slope of the line is 0, which means the line is horizontal.

The point-slope form of the equation of a line is: y - y1 = m(x - x1)

With the point (-3, -2) and the slope of 0, we have:

y - (-2) = 0(x - (-3))

y = -2

The slope-intercept form of the equation of a line is: y = mx + b

The y-intercept of the line is -2, so the equation of the line in slope-intercept form is: y = 0x + (-2)

The line is a horizontal one and it's equation is y = -2

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The survey methods that would result in a valid random sample of the community include:

Option E. All of the above is correct.

Simple random sampling involves selecting a random sample of participants from a larger population using a random number generator or a random sampling software. This method ensures that every member of the population has an equal chance of being selected.

Stratified random sampling involves dividing the population into smaller groups or strata based on certain characteristics, such as age, gender, income, etc. A random sample is then selected from each stratum. This method is useful when the population is heterogeneous and you want to ensure that the sample is representative of the entire population.

Systematic sampling involves selecting participants at regular intervals from a list of the population. This method is useful when the population is ordered, such as a list of customers.

Cluster sampling involves selecting a random sample of clusters or groups from the population, and then sampling individuals within those clusters. This method is useful when the population is geographically dispersed or it's difficult to obtain a complete list of the population. So Lily can use any of these survey methods to come up with a sample of the community.

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Options for this question include:

Part (a)

Line p can be named as "line RV" or "line AV" since these points are on line p. The order of the lettering doesn't matter.

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

Part (b)

Pick any three non-collinear points in plane W. In other words, we pick three points in the plane that do not fall on the same line.  

The following points are located in this plane: S, R, Q, T, Z

Here are some possible names:

Something like "Plane SRQ" isn't valid since those three points are on the same line. Infinitely many planes pass through these three points.

The ordering of the letters doesn't matter. For instance, "plane STR" is the same as "plane RTS".

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

Part (c)

As mentioned in part (b) earlier, these points fall on the same straight line. Hence they are considered collinear.

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

Part (d)

Pick any four points that reside in plane W.

You have this list to choose from: S, R, Q, T, Z

Let's say we pick the first four to write S, R, Q, T as the answer

These points are coplanar because they reside in the same plane. The non-coplanar points are A and V since they are outside the plane W.

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

Part (e)

Technically there aren't any line segments shown. Instead the diagram shows lines. But we can focus on a subset of a particular line to form a segment.

For instance, line p has points A and V on it. Therefore we can form segment AV

The symbolic notation for this would be to write [tex]\overline{\text{AV}}[/tex]

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

Part (f)

Reason:

A line is composed of opposite rays. For instance, a vertical line consists of a ray pointing north and a ray pointing south. The two rays are glued together at the endpoints.

For line p, we can glue together ray RA and ray RV to form this line. Unlike the other naming conventions, the order does matter. Something like "ray RV" is not the same as "ray VR". The first letter tells us the endpoint that doesn't go on forever.

Answer:

[tex]\frac{y-7}{y+8}[/tex]

y cannot equal -8

Step-by-step explanation:

[tex]\frac{(y-7)(y-5)}{(y+8)(y-5)}[/tex]           y-5 cancel out

[tex]\frac{y-7}{y+8}[/tex]

Answer:

The probability that a given household has lost electricity is 10%, or 0.1. So the probability that a given household has not lost electricity is 1 - 0.1 = 0.9.

Since the loss of electricity is independent among the households of the management team, we can find the probability that none of them has lost electricity by multiplying the probability of no loss in any one household (0.9) by itself 6 times, since there are 6 members of the team:

0.9 * 0.9 * 0.9 * 0.9 * 0.9 * 0.9 = 0.54

So the probability that none of the management team members has lost electricity in his or her household is  54%.