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A group of tourists are on a three-day hiking trip. They hike ⅛ of the trail on the first day. On the second day, they hike 4/7 of the remaining distance. On the third day, they hike 1/3 of the remaining distance, plus the final 8 km. How many kilometers long is the trail?

The sum of the given geometric sequence to 2 dp is 936.00

To get the sum of a geometric sequence, we will use the formula for calculating the sum to infinity of the sequence as shown:

[tex]S_\infty=\frac{1}{1-r}[/tex]

a is the first term

r is the common ratio

Given the sequence  S = 0.936 + 0.935 + ... + 0.92 + 0.9 + 1

a = 0.936

r = 0.935/0.936 = 0.998

Substitute into the formula

[tex]S_\infty=\frac{0.936}{1-0.999}\\S_\infty=\frac{0.936}{0.001}\\S_\infty=936[/tex]

Hence the sum of the given geometric sequence to 2 dp is 936.00

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Answer: 8/3

You first do 4x2 than you would have to divide by 3. 4x2*3

The number of cups of warm water need for 2/3 cup of soap to make solution is [tex]5\frac{1}{3}[/tex]. Therefore, option C is the correct answer.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, a bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap.

Let the number of cups of warm water need for 2/3 cup of soap be x.

Now, the proportion is

4:1/2 :: x:2/3

1/2 x=4×2/3

x/2=8/3

x=16/3

x= [tex]5\frac{1}{3}[/tex]

Therefore, option C is the correct answer.

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Answer:

The triangles are similar.

Step-by-step explanation:

They share a common angle (∠S) and the ratio of the two sides is the same, i.e. SP/SQ = SR/ST

Answer:

6.7 in bcoz 4-3.2=0.8 and 7.5-0.8=6.7

Answer:

x = 6

Step-by-step explanation:

This problem can be solved by setting up ratios. The ratio of lengths is 4: 3.2, so we can say that the same ratio should apply to the widths. Thus we get the equation, [tex]\frac{4}{7.5} = \frac{3.2}{x}[/tex], and we get x = 6.

The weight of the boy in the robot costume is 351/8 lb or 43 7/8 lb.

To find the weight of the boy, we need to subtract the weight of the costume from the total weight of the boy in the costume.

Total weight of boy and costume = 50 7/8 lb

Weight of costume = 3 1/2 lb

To find the weight of the boy, we can subtract the weight of the costume from the total weight:

Weight of boy = Total weight - Weight of costume

Convert both the total weight and the weight of the costume to improper fractions:

Total weight = 50 + 7/8 = 400/8 + 7/8 = 407/8 lb

Weight of costume = 3 + 1/2 = 6/2 + 1/2 = 7/2 lb

Now, subtract:

Weight of boy = (407/8) lb - (7/2) lb

To perform subtraction, we need to have a common denominator, which is 8 in this case:

Weight of boy = (407/8) lb - (56/8) lb

Now, subtract the fractions:

Weight of boy = (407 - 56)/8 lb

Weight of boy = 351/8 lb

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Answer:

The minimum is 1

Step-by-step explanation:

1 is the lowest point of the function so that's your answer (:

The minimum of the sinusoidal function is 1.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

y = 2sin(x + ∅) + 3 is a function

The minimum of the sinusoidal function.

y = 2sin(x + ∅) + 3 is a function is given

For the minimum value of sin(x + ∅) = -1, then

y = 2(-1) + 3

y = -2 + 3

y = 1

Thus the minimum of the sinusoidal function is 1.

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Answer:

10 1/8 or 81/8

Step-by-step explanation:

Profit, revenue and cost are related, and can be calculated from one another.

The cost function is given as:

[tex]\mathbf{C(x) =30x + 150}[/tex]

The revenue function is given as:

[tex]\mathbf{R(x) =-0.5(x -90)^2 + 4050}[/tex]

(a) Calculate the profit function

This is calculated using:

[tex]\mathbf{P(x) = R(x) - C(x)}[/tex]

So, we have:

[tex]\mathbf{P(x) =-0.5(x -90)^2 + 4050 - 30x - 150}[/tex]

Evaluate like terms

[tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]

(b) The domain of the profit function

When profit is 0 or less, then it becomes no profit.

Hence, the domain of the profit function is x > 0

(c) The profit for 60 and 70 items

Substitute 60 and 70 for x in P(x)

[tex]\mathbf{P(60) =-0.5(60 -90)^2 - 30 \times 60 + 3900}[/tex]

[tex]\mathbf{P(60) =1650}[/tex]

The profit when producing 60 items is 1650

[tex]\mathbf{P(70) =-0.5(70 -90)^2 - 30 \times 70 + 3900}[/tex]

[tex]\mathbf{P(70) = 1500}[/tex]

The profit when producing 70 items is 1600

(d) Why producing 10 more units less profit

When a function reaches the optimal value, the value of the function begins to reduce.

This means that, producing 10 more units takes the profit function beyond its maximum point.

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Answer:

pink and green same shape, but pink 7 units lower than green

Step-by-step explanation:

Both f(x) and f'(x) equations are the same except that f'(x) has the term "-7" at the end, denoting that the whole graph has been shifted down by 7 units. In other words, there is a vertical translation by -7. And since f'(x) is the pink graph, choose the option in which green and pink have the exact same shape but pink is located 7 units lower than the green.

Answer:

f(-8) = 169

Step-by-step explanation:

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Answer:

Step-by-step explanation:

If mike burns 392 calories when he walks 4 miles then we just need to divide

/ =

Mike burns 98 calories when he walks 1 mile.

"It is a method of finding the value of a single unit and based on that value, we can find the required value."

For given example,

Mike burns 392 calories when he walks 4 miles.

This means, 4 miles = 392 calories

By using unitary method we find the number of calories he burns when he walks 1 mile.

4 miles = 392 calories

So, 1 mile = 392/4 calories

1 mile = 98 calories

Therefore, Mike burns 98 calories when he walks 1 mile.

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Answer:

4          /           6                   or 2/3

pecan           total tree

Answer:

2/3

Step-by-step explanation:

So, Bill planted -

Pecan trees = 4

Apple trees = 2

Total trees = 6

We want the fraction of Pecan trees. Thus,

4/6

Where 4 is Pecan trees, (What we want)

And 6 is the total.

4/6 in its simplest form is 2/3.

I hope it helps.

Answer:

3,280/38650 x 100% = 8%

Answer:

There's 2 red jacks in a deck and 2 black queens in a deck so you have a total of 4 possible cards out of a 52 total in a deck so that would be 4/52 or 1/13 of the time. Statistically 7.6% of the time you will get a red jack or a black queen.

Step-by-step explanation:

Answer:

45 5+[5(4+2)]?

Step-by-step explanation:

i hope is helped:)

Answer:

1. -64

2.-27

Step-by-step explanation:

Hopes this helps

:)

Answer:

2

Step-by-step explanation:

the formula is y^2-y^1 over x^2-x^1

so the y coordinates here are 5 and -5

5--5=10

the x coordinates are -2 and 3

3--2=5

so we are left with 10/5

the answer is 2

hope this helped

Answer:

60 kilometers per hour.

420 kilometers will be covered

Step-by-step explanation:

speed = distance ÷ time.

so 60kmh = 240km divided by 4 Hours

60km = 1 Hour of distance

240km = 4 Hours of distance

Therefore 60 x 3 hour is 180km added to 240 is 420km. So in 7 hours traveling 60 kilometers per hour the will cover 420kms.

Answer: 28

Step-by-step explanation:

well the answer is 107.8823529411764705 (repeating decimal)

Answer:

-1, -24

Step-by-step explanation:

-9-(-8)

double negative = positive

-9+8=-1

21-45=-24

Answer:

-5/6 or 5/6

Step-by-step explanation:

Im assuming you want this equation equal to 0, so (6x-5)(6x+5) would reduce to 36x²-25=0. I would then add 25 to the other since and get

36x²=25, divide the whole thing by 36 to single out x

x²=25/36, which would reduce to x²=5/6.

thus x could be either -5/6 or 5/6

If the given equation is

[tex]27^{\frac13} = 9^{14} + 3^{x + 1}[/tex]

first simplify the left side using the fact that 27 = 3³:

[tex]27^{\frac13} = (3^3)^{\frac13} = 3^{\frac33} = 3^1 = 3[/tex]

and on the right side, 9 = 3²:

[tex]9^{14} = (3^2)^{14} = 3^{2\times14} = 3^{28}[/tex]

So we have

[tex]3 = 3^{28} + 3^{x + 1}[/tex]

Next,

[tex]3^{x+1} = 3^x \times 3^1 = 3 \times 3^x[/tex]

so that

[tex]3 = 3^{28} + 3 \cdot 3^x[/tex]

and dividing both side by 3 gives

[tex]1 = 3^{27} + 3^x[/tex]

Isolate 3ˣ :

[tex]3^x = 1 - 3^{27}[/tex]

Solve for x by taking the base-3 logarithm of both sides:

[tex]\log_3(3^x) = \log_3(1-3^{27})[/tex]

[tex]x \log_3(3) = \log_3(1-3^{27})[/tex]

[tex]\boxed{x = \log_3(1-3^{27})}[/tex]

Answer:

She is incorrect; Paloma's ratio of seconds travelled to feet travelled is 1:10.

Step-by-step explanation:

Her ratio is 1:10 because the first number is the number of seconds, and the second number is the number of feet. So for every 1 second, she travels 10 feet, as indicated in the original problem.

Hope this helps.

Answer:

$0.46

Step-by-step explanation:

6 apples = $2.82

1 apple = 2.82 / 6

= $0.46

Answer:

The answer would be 780 miles

Step-by-step explanation:

The reason that that's the answer because since it says that they will average about 65 miles per hour on a 12 hour trip, you have to multiply 65 time 12, which is 780 miles, so

65 miles x 12 hours = 780 miles   :)

Hope this helped!