Find the sum of the first six terms of the geometric sequence.

an = 8(3)n-1
2,952
8,774
2,910
2,912

Answer:

Percentage of cherries    = 60 %

Percentage of berries  = 40 %

Step-by-step explanation:

He orders  15 1/2 pounds every year.

He wants more=  1 1/4 pounds

So the total pounds = 15 1/2 + 1 1/4

                                 = 15 + 1 + 1/2 + 1/4

                                 = 16 + (2+1)/4

                                  =   16 + 3/4

                                  = 16 3/4 pounds

Out of 16  3/4 pounds they want 2/5 part to be of blue berries.

So blue berries = 16 3/4 * ( 2/5)

                          = 67/4 * ( 2/5)

                            = 67/10 = 6 7/10 pounds

Amount of cherries= 16  3/4- 6 7/10

                                 = 10 3/4- 7/10

                                  = 10 (15- 14)/20

                                   = 10 1/20 pounds

Percentage of cherries = Amount of cherries/ Total amount * 100

                                      = 201/20 / 67/4 *100

                                         = 201/20 * 4/67 *100

                                         = 201/335 *100

                                          = 60 %

Percentage of berries = 100- 60 = 40 %

The width of the rectangular garden is 6 meters. Hence, the correct answer is w = 6. Option B is correct answer.

The  rectangular garden has a perimeter of 42 meters. The length is 3 meters longer than twice the width.

We need to write and solve an equation using inverse operations to determine the value of w.

The perimeter of a rectangle is given by:

P = 2(l + w)

Where P is the perimeter, l is the length, and w is the width of the rectangle

.As per the question, the length is 3 meters longer than twice the width, so the length can be expressed as:

l = 2w + 3

The perimeter is given to be 42 meters, so we can write:

42 = 2(l + w)

Substituting the value of l from the above expression,

we get:

42 = 2(2w + 3 + w)

Simplifying, we get:

42 = 2(3w + 3)21 = 3w + 3

Subtracting 3 from both sides,

we get:

18 = 3w

Dividing both sides by 3,

we get:

w = 6

Therefore, the width of the rectangular garden is 6 meters.

Option B is correct.

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The relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."

Lοοking at the given pοints, we can see that the input x = -5 has an οutput y = 1, and the input x = 5 alsο has an οutput y = 1.

This means that there are twο different inputs (x-values) that cοrrespοnd tο the same οutput (y-value), viοlating the definitiοn οf a functiοn.

Tο determine if the relatiοn is a functiοn, we need tο check if fοr each input (x-value), there is exactly οne οutput (y-value).

Therefοre, the relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."

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Answer: a= 1

Step-by-step explanation:

a * b = b

Divide by “b” on both sides

a= b/b

“b/b” is equal to 1

a=1

Hope that helps

Lmk if you need a better explanation.

Answer:

10

Step-by-step explanation:

f(x) = 3x + 1

f^-1 = x-1/3 , it is known as inverse function.

f(3)= 3*3 +1

=9+1

=10

To find inverse,

x=3x + 1

y=3x+1

Exchanging the position or x and y

x=3y+1

x-1=3y

.•. y=x-1/3

Answer:

Step-by-step explanation: i think in my own word x+3<12 is A because it said julie only 3 notebook togerther it make itt less than 12notebook

The graph that best represents the Inequality given is; Graph A

We are given the Inequality as;

y ≤ -¹/₃x + 2

Now, the general formula for equation of a line in slope intercept form is written as;

y = mx + c

where;

m is slope

c is y-intercept

Thus, the y-intercept of our graph is y = 2

Now, less than or equal to symbol means we will shade below that line and the only one that has shading below the line is option A.

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The equation of the line that passes through the point (-8,6) is x + 4y = 16.

What is a slope?

A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given:

point = (-8,6)

equation : x+4y=20

x+4y=20

=> 4y = -x + 20

=> y = - x/4 + 5

Here the slope  m is -1/4.

Now  as the lines are parallel therefore the slope will be equal.

Therefore from the slope intercept form,

y - y1 = m (x - x1)

=> y - 6 = -1/4 ( x + 8 )

=> y - 6 = -x/4 - 2

=> x/4 + y = 4

=> x + 4y = 16

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Answer:

B) -2t^2+3t+5

and

C) 4t-7

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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The value x in the formula represents the value of each observation of the data-set.

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The height of package is 34 inches.

According to the statement

we have given that the perimeter of cylinderical package is 123 inches.

and we have to find the volume of this package.

So,

According to the perimeter

2(Pi)r + h = 123

and then

h = 123 - 2(Pi)r

then the volume become

V = (Pi) r^2h

V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2  - 2(Pi)r^3

then differentiate it

dV/dr = 246(Pi) r - 6(Pi)r^2

Now take

r(246(Pi) - 6(Pi)r) = 0

then neglect r=0 and then find another value of r.

r = 246(Pi) / 6(pi)

here r=41 then

h = 123 - 2(Pi)r

h = 123 - 2(3.14)41

h = 123 - 2(Pi)r

Then put the value of r then h = 34 inches.

So, The height of package is 34 inches.

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Answer:

80 because that you need to work on

The correct answer is option (A). The answer is metes and bounds.

Given that,

Despite being antiquated, the most adaptable method of defining land, capable of characterizing even the most atypical of parcels, may be summed up as a very exact, compass-directed stroll around a parcel's boundaries.

To find : This approach is frequently known as ?

Metes and bounds are limits of  piece of a land that may be located on its natural features. Metes and bounds markers are frequently employed in a land's "legal description." Legal description, which is recorded with the land's deed, is the geographical description of a piece of land that pinpoints its exact location.

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The closest answer choice to this value is 4 seconds, which is the correct answer. Answer choice C, 4 seconds, is the correct answer.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

When the object hits the ground, its height, h(t), is equal to zero. So we can set h(t) = 0 and solve for the time, t:

h(t) = 0 = vot - 16t²

16t² = vot

t² = (vo/16)

Substituting the given value of vo = 240 ft/s:

t² = (240/16)

t² = 15

t = √(15)

Therefore, it will take the object √(15) seconds to hit the ground after takeoff, which is approximately 3.87 seconds.

Hence, the closest answer choice to this value is 4 seconds, which is the correct answer. Answer choice C, 4 seconds, is the correct answer.

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By speed fοrmula, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.

Mathematically, speed is calculated as fοllοws:

speed = distance/time

Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

We can use the fοrmula:

time = distance/speed

where distance is the distance frοm the star tο Earth, and speed is the speed οf light.

Putting the values, we get:

time = (3.9 x 10¹⁴ km) / (3.0 x 10⁵km/s)

Simplifying, we can divide the distances and divide the pοwers οf ten:

time = 1.3 x 10⁹ s

Therefοre, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

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Based on the information in the circle graph,  Brandi's total monthly allowance is equal to $50.

A circle graph is used to represent information in a circle. The circle is divided into different section to represent the magnitude of each grouping.

Total allowance = amount allocated to clothes / percentage of circle graph that is allocated to clothes

$20 / 0.40  = $50

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The following statement are true about the given function

Statements i,ii, and iv

Given Data

We have the following function to analyse

y = 3x

The following statement are true/false about the given function

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Answer:

I,II, and IV

Step-by-step explanation:

Social scientists gather data from samples instead of populations because c. populations are often too large to test.

Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.

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Answer:

6

Step-by-step explanation:

24/4=x

x=24/4

24 divided by 4 is 6 because 6 times 4 is 24

Answer:

\(4t^{2}+4t-35\)

Step-by-step explanation:

\((2t+7)(2t-5)\\4t^{2}-10t+14t-35\\4t^{2}+4t-35\)

Answer:

y= 3x

Step-by-step explanation:

Because between each point your going up by 3

Hope this helps you

Answer:

y = 3x

Step-by-step explanation:

This is dealing with slope so think of it as rise over run

\(\frac{Rise}{Run}\)

The y intercept is a 0 so you don't have to worry about adding a number after the plus symbol. You can if you want but that's not an option. You go up 3 over 1 and then you get to your next point.

Using missing length of each triangle are-

Part 6 (a) c = 4.25 m.

Part 6 (b) c = 1.65 m

The formula for the cosine rule:

cosФ = (a² + b² - c²)/2ab

Ф is the angle between sides a and b.

c is the side just opposite to the angle Ф.

The given values in question.

Part 6 (a)

a = 4.4m, b = 3.2m, Ф = 66°.

cos 66 = (4.4² + 3.2² - c²)/2(3.2)(4.4)

On simplification;

c² = 18.24

c = 4.25 m

(b) a = 1.8m, b = 2.2m, Ф = 46°.

cos 46 = (1.8² + 2.2² - c²)/2(1.8)(2.2)

On simplification;

c² = 2.72

c = 1.65 m

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The correct question is  question 6. (a) and (b).

The result of 3.95 x 10² ÷ 1.5 x 10⁶ is 0.00263 which when converted in proper decimal notation is written as 2.63 x \(10^{-3\)

To solve the given equation, we convert the given decimal notation into normal numerals:

To do this we multiply the number by 10 the times the power of 10 or shift the decimal to the right by the power of 10 if the sign of exponent is positive or to the left if the sign of exponent is negative

and we get the equation as 395 ÷ 150000

By solving the above equation, we get:

= 0.00263

In proper decimal notation, we get 2.63 x \(10^{-3\)

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Answer:

The value of \(f(2) - g(7)=-58\)

Step-by-step explanation:

We have

\(f(x) = 3 ^ x - 7\\\\f(2) = 3 ^ 2 - 7\\\\=9-7\\\\=2\\\\g(x) = x ^ 2 + 11\\\\g(7) = 7 ^ 2 + 11\\\\=49+11\\\\=60\\\\f(2) - g(7)=2-60\\\\=-58\)

Based on the given information, Toby's faucet ripped a total of 1.92 liters of water over a period of 24 hours. We can calculate the amount of water that was ripped each hour by dividing the total amount by the number of hours and  each hour is 0.08 liters.

1.92 liters / 24 hours = 0.08 liters per hour

Therefore, Toby's faucet ripped 0.08 liters of water each hour.

It's worth noting that "ripped" may not be the most appropriate word to describe the water flow from the faucet. Typically, we use words like "flowed" or "dispensed" to describe the water coming out of a faucet. However, assuming "ripped" is used here to mean the same as "flowed" or "dispensed," the amount of water ripped each hour is 0.08 liters.

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An open circle is used to represent x > 4 as we do not want to include 4 in our solution set.

Treat the <, ≤, >, or ≥  as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.

Using the open instructions when we plot the inequality we see that x > 4 has an open circle at 4.

This indicates that we do not want to include 4 in our solution set.

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The function f(x) = 4x + 3 has a greater rate of change from x = 0 to x = 1 compared to the function g(x) = (1/2)x² + 2.

The rate of change of a function represents how much the function's output values change for a given change in the input values. To compare the rate of change between the two functions, we need to calculate the difference in their outputs when the inputs change from x = 0 to x = 1.

For f(x) = 4x + 3, when x changes from 0 to 1, the output changes from f(0) = 3 to f(1) = 7. The difference in output is 7 - 3 = 4.

On the other hand, for g(x) = (1/2)x² + 2, when x changes from 0 to 1, the output changes from g(0) = 2 to g(1) = (1/2)(1²) + 2 = 2.5. The difference in output is 2.5 - 2 = 0.5.

Comparing the differences, we can see that the function f(x) has a greater rate of change. In the given interval, the output of f(x) changes by 4 units, while the output of g(x) changes by only 0.5 units. Therefore, f(x) has a greater rate of change from x = 0 to x = 1 compared to g(x).

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There is no solution in this case. Finally, we write the solution set as:1 < x < 6

Given quadratic inequality is x² - 7x + 6 ≤ 0To find: solution set for this inequality.

The quadratic expression can be factorized as follows:x² - 7x + 6 = (x - 1)(x - 6)Now, the quadratic inequality can be written as:

(x - 1)(x - 6) ≤ 0

The product of two factors is less than or equal to zero only when one factor is positive and the other factor is negative.  

So, we consider two cases:

Case 1: (x - 1) > 0 and (x - 6) < 0

In this case, x > 1 and x < 6. But the inequality (x - 1) > 0 is redundant because it is already implied in (x - 6) < 0.

So, the solution is 1 < x < 6.Case 2: (x - 1) < 0 and (x - 6) > 0In this case, x < 1 and x > 6. But the inequality (x - 6) > 0 is redundant because it is already implied in (x - 1) < 0.

Therefore, there is no solution in this case. Finally, we write the solution set as:1 < x < 6

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