In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit. The zip line extends from the top of a tower to a point on the ground 46 feet away from the base of the tower. The angle of elevation of the zip line is 26°. Estimate the length of the zip line to the nearest tenth of a foot.

Answer:

Geometric sequences and exponential functions are alike in that they both involve repeated multiplication by a constant factor. In a geometric sequence, each term is found by multiplying the previous term by the same constant factor. In an exponential function, the value of the function is found by raising a constant base to an exponent that increases by a constant amount.

However, they differ in the way they are expressed. In a geometric sequence, each term is written as a discrete value in the sequence, while in an exponential function, the value of the function is written as a continuous function of the input variable. Additionally, geometric sequences are often used to model discrete phenomena, while exponential functions are often used to model continuous phenomena.

Step-by-step explanation:

The length of the whole movie was 130 minutes.

Let's call the length of the whole movie "x". According to the problem, Newton and his friends watch 50% of the movie before taking a break. This means they watched 0.5x minutes of the movie.

After the break, they watch the remaining 65 minutes of the movie. So the total time they watched the movie is:

0.5x + 65

But we know that the total time they watched the movie is the same as the length of the whole movie "x". So we can set these two expressions equal to each other and solve for "x":

0.5x + 65 = x

Subtracting 0.5x from both sides, we get:

65 = 0.5x

Dividing both sides by 0.5, we get:

x = 130

Therefore, the length of the whole movie was 130 minutes.

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It will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.

First, we need to calculate the amount of money that we need to save in order to cover the cost of the trip. This can be done by subtracting the amount we have already saved from the total cost of the trip:

Total cost of trip = 2500

Amount already saved = 2200

Amount to save = 2500 - 2200 = 300

Next, we can use the compound interest formula to calculate how long it will take to earn 300 with an interest rate of 1.55% compounded annually. We can set up the formula as follows:

A = P(1 + i)n

where:

A = accumulated amount = 300 + 2200 = 2500 (the total cost of the trip)

P = principal = 2200

i = interest rate per year = 1.55%

n = number of years we need to save for

We can now solve for n:

2500 = 2200(1 + 0.0155)n

Divide both sides by 2200:

1.13636 = 1.0155n

Take the natural logarithm of both sides:

ln(1.13636) = n ln(1.0155)

Divide both sides by ln(1.0155):

n = ln(1.13636)/ln(1.0155) ≈ 4.4 years

Therefore, it will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.that we rounded our final answer to the nearest tenth as instructed.

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The equation to calculate the probability that this coin is gold is (X / (X + Y)) x (R / (R + S)) x (T / (T + U))

Let's assume that after the first transfer, there are M gold coins and N silver coins in pot A, and R gold coins and S silver coins in pot B. The probability of selecting a gold coin from pot B after the first transfer is R / (R + S).

After the second transfer, the number of gold and silver coins in each pot changes again. Let's assume that there are T gold coins and U silver coins in pot A, and V gold coins and W silver coins in pot B. The probability of selecting a gold coin from pot A after the second transfer is T / (T + U).

To find the probability that a gold coin is selected from pot A after all transfers are complete, we need to multiply the individual probabilities together. That is:

Probability of selecting a gold coin from pot A after all transfers = (X / (X + Y)) x (R / (R + S)) x (T / (T + U))

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The journal entry to close the Income Summary will include a C) credit to Emile, Capital for $26,667.

To close the Income Summary account, the net income of $40,000 needs to be allocated to the partners' capital accounts based on their profit and loss sharing ratio.

Dana is allocated 2/3 of the net income, which is $26,667 (2/3 x $40,000). Emile is allocated 1/3 of the net income, which is $13,333 (1/3 x $40,000).

Therefore, the journal entry to close the Income Summary account would be:

Credit Income Summary for $26,667 (to close the account)

Debit Dana, Capital for $26,667 (to allocate Dana's share of net income)

Debit Emile, Capital for $13,333 (to allocate Emile's share of net income)

This is calculated by multiplying the net income of $40,000 by the ratio of Emile's share (1/3), which equals $26,667.

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Answer: 7

Step-by-step explanation:

To find the median, we need to first put the data points in order from least to greatest:

2, 3, 5, 9, 12, 21

There are six data points, so the median is the middle value. In this case, the middle two values are 5 and 9. To find the median, we take the average of these two numbers:

(5 + 9) / 2 = 7

Therefore, the median number of songs written by the members of Python Sunboat is 7.

Using the law of sines, the length of the other side of the sail, which is the third side of the isosceles formed, is calculated as about 32.5 feet.

An isosceles triangle is a triangle with at least two sides of equal length.

Let's call the length of the other side of the sail "x". Since the sail is an isosceles triangle, the other two angles opposite the two equal sides are also equal, each measuring (180 - 54)/2 = 63 degrees.

We can use the law of cosines to find x:

x² = 23² + 23² - 2(23)(23)cos(63)

x² = 1054.75

x ≈ 32.5

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Answer:

(1, 2 )

Step-by-step explanation:

y = - 2x + 4 → (1)

y = 3x - 1 → (2)

substitute y = 3x - 1 into (1)

3x - 1 = - 2x + 4 ( add 2x to both sides )

5x - 1 = 4 ( add 1 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (2)

y = 3(1) - 1 = 3 - 1 = 2

solution is (1, 2 )

Differential equation of the total quantity Q of dead leaves at time t= dt/dQ = -0.65Q + 5. and 7.69 grams per square centimeter is the equilibrium level.

The differential equation for the total quantity Q of dead leaves (per square centimeter) at time t is given by:dt/dQ = -0.65Q + 5.B.

Assuming that there are no leaves on the ground initially, t = 0.  

Q(0) = 0.

Qeq = 7.69 grams per square centimeter.

The solution to the differential equation is given by: Q(t) = (20/13) + Ce^(-0.65t) where C is an arbitrary constant. At equilibrium, dQ/dt = 0, or -0.65Q + 5 = 0.Qeq = 7.69 grams per square centimeter is the equilibrium level.

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Answer:

Step-by-step explanation:

If a square has a perimeter of 100 feet, then each side of the square must be 25 feet long, since all four sides of a square are equal.

The area of a square is given by the formula A = s^2, where s is the length of one side of the square. Substituting s = 25 feet, we get:

A = (25 feet)^2

A = 625 square feet

Therefore, the area of the playground is 625 square feet.

Answer:

625 ft^2

Step-by-step explanation:

A square will have all 4 sides equal to each other.  Let x be the length of 1 side.  The perimeter, P, of such a square would be:

  P = 4x

We are told that p = 100 feet

 100 feet = 4x

 x = 25 feet

Each side has a length of 25 feet.

The area of this square wuld be (25')*(25') = 625 ft^2

Twο pοints (8,8) and (-2,6) are the set οf the equatiοn  [tex]y < \frac{3}{4} x+6\\[/tex] οf the graph [tex]y = \frac{3}{4} x+6[/tex].

Graph, a diagram that shοws hοw a variable varies in relatiοn tο οne οr mοre οther variables (such as a cοllectiοn οf pοints, lines, line segments, curves, οr regiοns).

Nοw we have tο find the value οf the equatiοn i.e. [tex]y < \frac{3}{4} x+6\\[/tex],

(x, y) = (8,8) , we get 8 < 12 , First pοint

(x, y) = (-4,3) , we get 3 = 3 , Nο match

(x, y) = (6,-2) , we get -2 < 10.5 , Secοnd Pοint

(x, y) = (0, 8) , we get 8 > 6 , Nο Match

(x, y) = (-9,2) , we get 2>-0.75 , Nο Match

Sο, we get οur pοints, which are pοints (8,8) and (-2,6) fοr the equatiοn [tex]y < \frac{3}{4} x+6\\[/tex].

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To measure length ABAC=3.5 cm, open the compass,=3.5cm is a positive value because. Hence, BD will be higher than BC. Cut an arc on ray BX using point B as the center. Let D be where the arc crosses BX.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

According to our question-

draw perpendicular bisector of CD

A where perpendicular bisector intersects BD

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The values of a, b and c are given as follows:

a = 9, b = 15, c = 25.

The law of cosines states that we can find the side c opposite to an Angle C of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which the parameters are listed as follows:

The parameters for this problem are given as follows:

a = 3x, b = x + 5, c = y, C = θ.

Hence the expression is given as follows:

y² = (3x)² + (x + 5)² - 2(x + 5)(3x)(1/6)

y² = 9x² + x² + 10x + 25 - x² + 5x

y² = 9x² + 15x + 25.

Hence the values of a, b and c are given as follows:

a = 9, b = 15, c = 25.

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Answer:

y = 2x - 6

Step-by-step explanation:

Using the 'y=mx+c' form,

Since m = 2,

y = 2x + c

Substituting (1, -4) into the above equation:

-4 = 2 + c

c = -6

Hence,

y = 2x - 6

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The probability of having an older son is 1/2 in families with two children and The proportion of all sons who are eldest sons = 1/3, when each family has three children.

If each family has two children, then the two possible situations are that the family has two sons or a son and a daughter. So the chance of having an older son is 1/2 in families with two children. Thus, the proportion of all sons who are older sons is 1/2.

If each family has three children, then the possible situations are having three sons, two sons and one daughter, or two daughters and one son. If two sons and one daughter are there in the family, then the older one will be the eldest son. If two daughters and one son are there in the family, then the only son will be the eldest son.

Therefore, there is only one eldest son among three children in the second case. If the family has three sons, then the probability that the eldest son is responsible for taking care of their parents is 1. Hence, if each family has three children, the proportion of all sons who are eldest sons is 1/3.The following is the step-by-step answer to this question:

Probability of having an older son = 1/2 in families with two children. Probability of having an eldest son = 1/3 in families with three children. The proportion of all sons who are older sons = 1/2, when each family has two children. The proportion of all sons who are eldest sons = 1/3, when each family has three children.

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Answer: $4496

Step-by-step explanation:

Since we know that one pack of croissanwich costs $562, multiply $562 by 8 to get $4496.

There are now 29 business majors enrolled in both business calculus and elementary statistics based on Venn Diagram.

To find the number of students who are currently enrolled in both Elementary Statistics and Business Calculus, we need to use the information given in the problem and draw a Venn diagram. Let's assume that the set of students who are enrolled in Elementary Statistics is E, and the set of students who are enrolled in Business Calculus is C. We want to find the size of the intersection of these two sets, denoted by E ∩ C.

From the problem, we know that the total number of Business majors who are currently enrolled in at least one of the two courses is 100. This means that the size of the union of the sets E and C is 100. We also know that 77 students are enrolled in Elementary Statistics and 52 students are enrolled in Business Calculus.

Using this information, we can set up an equation that relates the sizes of the sets E, C, and E ∩ C:

E + C - E ∩ C = 100

77 + 52 - E ∩ C = 100

E ∩ C = 29

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By secant line formula, the slopes corresponding to the lines are listed below:

In this problem we have nine representations of lines, whose slopes must be determined. A line is represented by equations of the form:

y = m · x + b

Where:

According to analytic geometry, slope can be found by knowning the location of two points (initial, final) set on Cartesian plane and secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where:

Case 1: (x₁, y₁) = (0, - 3), (x₂, y₂) = (2, 1)

m = (2 - 0) / [1 - (- 3)]

m = 2 / 4

m = 1 / 2

Case 2: (x₁, y₁) = (- 3, 2), (x₂, y₂) = (1, - 3)

m = (- 3 - 2) / [1 - (- 3)]

m = - 5 / 4

Case 3: (x₁, y₁) = (- 3, - 4), (x₂, y₂) = (2, 3)

m = [3 - (- 4)] / [2 - (- 3)]

m = 7 / 5

Case 4: (x₁, y₁) = (0, 3), (x₂, y₂) = (3, - 3)

m = (- 3 - 3) / (3 - 0)

m = - 6 / 3

m = - 2

Case 5: (x₁, y₁) = (- 2, 1), (x₂, y₂) = (3, 2)

m = (2 - 1) / [3 - (- 2)]

m = 1 / 5

Case 6: (x₁, y₁) = (- 4, 3), (x₂, y₂) = (4, 1)

m = (1 - 3) / [4 - (- 4)]

m = - 2 / 8

m = - 1 / 4

Case 7: (x₁, y₁) = (2, - 4), (x₂, y₂) = (4, 2)

m = [2 - (- 4)] / (4 - 2)

m = 6 / 2

m = 3

Case 8: (x₁, y₁) = (- 4, - 1), (x₂, y₂) = (0, - 3)

m = [- 3 - (- 1)] / [0 - (- 4)]

m = - 2 / 4

m = - 1 / 2

Case 9: (x₁, y₁) = (- 2, 0), (x₂, y₂) = (4, 1)

m = (1 - 0) / [4 - (- 2)]

m = 1 / 6

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Answer:

? = 7.2

Step-by-step explanation:

The given equation is comprised of two ratios.

Using the given ratio 5.4 : 3, we can reduce it and see the ratio is 1.8 : 1

Now, using the same idea for the unknown value, we must multiply 1.8 by 4, giving 7.2.

The statement that correctly explains the association in the scatter plot is; A. Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.

When interpreting scatterplots, it is possible to claim that two variables have a negative connection when the values of one variable tend to fall as the values of the other variable rise.

Similarly to this, we can say that two variables have a positive connection when one variable's values tend to rise along with those of the other.

In the scatterplot shown, we can see that there is a negative correlation between the two variables because the y-value is falling while the x-axis is rising.

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Answer:

x=3
y=4

Step-by-step explanation:

y=3x-9
5x+4y=32

You substitute what y is into the equation:
5x + 4(3x - 9) = 32
5x + 12x - 36 = 32
17x - 36 = 32
17x = 68
x = 4
Now you substitute x into y:
y = 3x - 9
12 - 9 = 3
y = 3

Answer:

We can use the expression 2x = y , where 'x' is the amount she saves yesterday and y being the amount she saves this day.

Table = if x = 0 , y = 0
            if x = 1 , y = 2
            if x = 2 , y =4
            if x = 4 , y= 8

Answer:

Since the number of bacteria doubles every 3 hours, after 3 hours there will be 400 x 2 = 800 bacteria. After 6 hours, there will be 800 x 2 = 1600 bacteria. After 9 hours, there will be 1600 x 2 = 3200 bacteria. After 12 hours, there will be 3200 x 2 = 6400 bacteria. Finally, after 15 hours, there will be 6400 x 2 = 12800 bacteria. Therefore, there will be 12800 bacteria at the end of 15 hours.

Step-by-step explanation:

Answer:

(5, -1) or x = 5, y = -1

Step-by-step explanation:

[tex]\mathrm{Substitute\:}y=2x-11[/tex]

[tex]\begin{bmatrix}2x+3\left(2x-11\right)=7\end{bmatrix}[/tex]

[tex]8x-33=7[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:8x-33=7[/tex]

[tex]8x=40[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}8[/tex]

[tex]\frac{8x}{8}=\frac{40}{8}[/tex]

[tex]x=5[/tex]

[tex]y= 2x-11 \\ \mathrm{Substitute\:}x=5[/tex]

[tex]y=2\cdot \:5-11[/tex]

[tex]y=-1[/tex]

Answer:

(5, - 1 )

Step-by-step explanation:

2x + 3y = 7 → (1)

y = 2x - 11 → (2)

substitute y = 2x - 11 into (1)

2x + 3(2x - 11) = 7

2x + 6x - 33 = 7

8x - 33 = 7 ( add 33 to both sides )

8x = 40 ( divide both sides by 8 )

x = 5

substitute x = 5 into (2)

y = 2(5) - 11 = 10 - 11 = - 1

solution is (5, - 1 )

Answer:

x=50

Step-by-step explanation:

2x=100

divided both sides by 2

x=50

answer: x=50

Answer:

50

Step-by-step explanation:

2x = 100, divide 2 from 2x and also 100, you will be left with x = 50

After 45 blue counters are removed, the remaining number of blue counters is 63 more than yellow counters. Setting up an equation, we find that there were 162 blue counters to start with.

Let's start by assigning variables to the unknowns:

Let x be the number of yellow counters.

Then, the number of blue counters is 3x.

After 45 blue counters are removed, the number of blue counters is 3x - 45.

Finally, there are 63 more blue counters than yellow, so we can set up the equation:

3x - 45 = x + 63

Solving for x, we get:

2x = 108

x = 54

Therefore, there were 3x = 3(54) = 162 blue counters to start with.

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Answer:

x = 15/4

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 4x - 10 = 5

Then the value of x will be,

→ 4x - 10 = 5

→ 4x = 5 + 10

→ 4x = 15

→ [ x = 15/4 ]

Hence, the value of x is 15/4.

Answer: [tex]x=24[/tex]

Step-by-step explanation: Since the ratio of 6:3 is a 2:1 ratio simplified, you know that x will need to double the value on the other side. Therefore, you can just multiply 12 by 2 to get the x-value which is 24. Another method is to see that the 3 on the other side of the ratio is 1/4 the value of 12. This means that the 6 is 1/4 the value of x. if you multiply 4 on both sides x=24. Those are the two methods I recommend you use to solve these ratio problems.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{Equation:}\\\\\large\boxed{\mathsf{6:3}}\\\\\large\textsf{Simplifying for:}\\\\\large\boxed{\rightarrow \mathsf{x:12}}\\\\\large\textsf{Simplifying:}\\\\\large\boxed{\mathsf{\rightarrow 6\times 4: 3\times4}}\\\\\large\boxed{\mathsf{\rightarrow{24:12}}}\\\\\\\huge\text{Therefore your answer should be: }\\\huge\boxed{\mathsf{\bold{24}:12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex]9.9[/tex]

Step-by-step explanation:

Interpreted:

[tex]3^2-(4\div5\div8)+1[/tex]

1) Simplify 4 ÷ 5 to 0.8.

[tex]3^2-0.8\div8+1[/tex]

2) Simplify 3² to 9.

[tex]9-0.8\div8+1[/tex]

3) Simplify 0.8 ÷ 8 to 0.1.

[tex]9-0.1+1[/tex]

4) Simplify 9 - 0.1 to 8.9.

[tex]8.9+1[/tex]

5) Simplify.

[tex]9.9[/tex]

The given sequence is a recursive sequence. Hence -2, 9, -24, 75 is the first four terms of the sequence.

The given sequence is a recursive sequence, where each term is defined in terms of the previous term. Here, each term is obtained by multiplying the previous term by -3 and adding 3. The first term, a1, is given. Using this, we can find the second term, a2, and then using a2, we can find a3, and so on.

Given: an = -3an-1 + 3 and a1 = -2

To find: the first four terms of the sequence

a1 = -2

a2 = -3a1 + 3 = -3(-2) + 3 = 9

a3 = -3a2 + 3 = -3(9) + 3 = -24

a4 = -3a3 + 3 = -3(-24) + 3 = 75

Therefore, the first four terms of the sequence are: -2, 9, -24, 75.

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