A sequence can be generated by using gn = 2(gn-1), where g1 = 1/3 and n is a whole number greater than 1.
What are the first 5 terms of the sequence?

The poster has an area equal to 192.423 square inches.

In this problem we must determine the area of a heart shaped poster, that is, the combination of the areas of a square and two semicircles, whose resulting formula is introduced below:

A = D² + (π / 4) · D²

Where:

If we know that π = 3.14 and D = 7 in, then the area of the poster is:

A = 7² + (π / 4) · 7²

A = (5π / 4) · 7²

A = 192.423 in²

The area of the poster is equal to 192.423 square inches.

The image is missing and the statement is not well explained. A correct statement is shown below:

Sarah uses a square with side length of 7 inches and two semicircles with diameter of 7 inches to design a heart shaped poster. Find the area of the heart. Then, find the approximate area by using 3.14.

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Answer:

----------------------

See attached graph to help with answer choices.

Given function:

Answer choices:

Answer:

Anything greater than or equal to 46,500, and less than or equal to 47,499 could be the answer.

For example, a number, let's say 46,589 falls within that range and may have been the number that was rounded.

The interest rate if Ted made $56 in interest for 1 year on a principle of $700 will be 8%.

Given, the interest amount is $56.

The principal amount is $700.

The time period of investment is 1 year.

Now, we have to find the interest rate.

The formula to find the simple interest is,

  S.I = PTR/100.

Now, we need to substitute the values in the above formula.

S.I = PTR/100

56 = 700×1×R / 100

56 = 700R/100

5600 = 700R

R = 5600/700

R = 8

Therefore, the interest rate is 8%.

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Answer: Therefore, the first person gets $476,190.48 and the second person gets $323,809.52.

Step-by-step explanation: To divide $800,000 into a 25:17 ratio, we first need to add the ratio terms (25 + 17 = 42) to determine the total number of parts. Then, we divide the total amount by the total number of parts to determine the value of each part. Finally, we multiply the value of each part by the respective ratio term to determine the amount that each person gets.

The calculation steps are as follows:

Determine the total number of parts: 25 + 17 = 42

Determine the value of each part:

Value of each part = Total amount / Total number of parts

= $800,000 / 42

= $19,047.62 (rounded to two decimal places)

Determine the amount that each person gets by multiplying the value of each part by the respective ratio term:

First person gets: 25 parts * $19,047.62 per part = $476,190.48

Second person gets: 17 parts * $19,047.62 per part = $323,809.52

For the given right-angled triangle the measure of the angle is 11.30°.

Given adjacent base of the triangle =  10

given opposite side of the triangle = 2

To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.

So, we can use the above tan ∠ relation to find the angle.

Tan ∠ = opposite side / adjacent side

Tan ∠ = 2/10

Tan ∠ = 1/5

∠ = Tan⁻¹(1/5)

∠ = 11.30°.

From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.

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The number of games that the team did play in the last season is 23.

The frequency is the number of times an event happens. Therefore, frequency is the number of repetitions of a digit or an event.

The given frequency table represents the frequency of different runs scored by the team in the entire season.

The frequency is written in tally form, which means that each of the vertical lines represents the count of 1, while a group of fours lines such that the four lines are vertical while the fifth line cuts the other four represents a count of 5 as shown in the second column of the second row.

Therefore, the frequency table can be made as:

Number of runs     Frequency

            0                         8

            1                          5

            2                         3

            3                         6

            4                         1

Total:                              23

Hence, the team played 23 games.

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Answer:

  a)  |x -8| = 6

  b)  |x -15| = 0

Step-by-step explanation:

You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...

The solutions to |x -b| = c are the solutions to ...

  x -b = c   ⇒   x = b +c

  x -b = -c   ⇒   x = b -c

Given the two solutions P and Q, the values of 'b' and 'c' can be found from ...

  P = b +c

  Q = b -c

Adding these two equations gives ...

  P +Q = 2b   ⇒   b = (P +Q)/2

Subtracting the second equation from the first gives ...

  P -Q = 2c   ⇒   c = (P -Q)/2

  b = (2 +14)/2 = 8

  c = (14 -2)/2 = 6

The equation is ...

  |x -8| = 6

  b = (15 +15)/2 = 15

  c = (15 -15)/2 = 0

The equation is ...

  |x -15| = 0

The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.

The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.

There are 4 tickets purchased so the equation would be:

4 x Cost of tickets - Parking cost = Total spent

4 x - 25 = 175

The cost of each admission ticket is:

4 x - 25 = 175

x = 150 / 4

x = $ 37.50

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You have to invest $15,506.08

PV = FV / (1 + r)^n

where:

PV = present value (amount of money you need to invest today)

FV = future value (amount of money you want to have in 5 years, which is $25,000)

r = interest rate (10% or 0.1)

n = number of periods (5 years)

Plugging in the values into the formula:

PV = $25,000 / (1 + 0.1)^5

PV = $25,000 / 1.61051

PV = $15,506.08

Therefore, you need to invest approximately $15,506.08 today at a 10% interest rate in order to have $25,000 in 5 years to purchase a car in cash.

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Answer:

x=28

Step-by-step explanation:

solve for x by simplifying both sides of the equation, then isolating the variable.

have a good day :)

Answer

x=3 1/9

Step-by-step explanation:

Here is the truth table for the statement (~ p V q) → q:

```

p     q     ~p    ~p V q   (~p V q) → q

---------------------------------------

T     T     F      T           T

T     F     F      F           T

F     T     T      T           T

F     F     T      F           T

```

In the table, `p` and `q` represent the truth values of the propositions `p` and `q`, respectively. The symbol `~` represents negation (i.e., "not"). The symbol `V` represents the logical connective "or" (i.e., "inclusive or"). The symbol `→` represents the conditional connective "implies" (i.e., "if...then").

To fill in the truth table, we first evaluate `~p` and `~p V q` for each combination of truth values for `p` and `q`. Then, we evaluate `(~p V q) → q` for each combination of truth values.

We can see that the statement is always true, regardless of the truth values of `p` and `q`, except for the case where `p` is true and `q` is false.

a. The perimeter of the paddock is 120 meters

b. The cost of the wire will be $600

a. To find the missing sides and calculate the perimeter of the paddock, let's analyze the given sketch.

The length of the missing side on the left can be determined by subtracting the known length of 10m from the total height of 20m. Therefore, the left side has a length:

20m - 10m = 10m.

The missing side on the right is equal in length to the known side of 40m.

Now we can calculate the perimeter by adding up all the side lengths:

Perimeter = 10m + 40m + 20m + 10m + 40m

= 120m.

b. To calculate the cost of the wire, we need to multiply the perimeter of the paddock by the cost per meter of fencing wire, which is $5/m.

Wire Cost = Perimeter × Cost per meter

= 120m × $5/m

= $600.

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The amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:

T = 2π/ω.

Let's assume that a straightforward harmonic motion can be used to simulate the horse's movements. The simple harmonic motion equation is:

y = A sin(ωt + φ)

where:

The deviation from equilibrium is represented by the number y.

The maximum displacement's amplitude is A.

The angular frequency is equal to two times the frequency ω.

It's time t

The phase angle is φ

The equation can be written as follows, assuming that the horse is moving vertically and that its highest point corresponds to y = 0.

y = A sin(ωt)

where is the angular frequency and A is the motion's amplitude.

On a graph, where the horizontal axis denotes time and the vertical axis denotes displacement, we can draw this function as a sine wave. The

amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:

T = 2π/ω

We need to know the duration of the horse's motion in order to predict when Ivan will have another chance to make a flawless shot. It's challenging to determine the period precisely in the absence of more details.

You can name the graph of the carousel equation θ = A cos(ωt) as follows:

The time, t, is displayed on the x-axis as seconds.

The angular position from the midline, θ, expressed in degrees, is shown on the y-axis.

The horizontal axis at θ = 0 degrees is the midline.

The largest angle of departure from the midline, or the distance between the wave's crest (highest point) or trough (lowest point), is known as the amplitude, or A.

The interval between two consecutive wave crests or troughs is known as the period, or T, which is the length of time it takes for one full cycle of motion.

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Answer:

Step-by-step explanation:

The standard form equation for an ellipse with center at the origin is:

x^2/a^2 + y^2/b^2 = 1

where 'a' is the distance from the center to the vertices along the x-axis and 'b' is the distance from the center to the vertices along the y-axis.

In this case, the center is at the origin, and a vertex is at (3, 0). So, we know that 'a' = 3.

We also know that the distance from the center to the focus is 'c', and that:

c^2 = a^2 - b^2

Since the center is at the origin, 'c' is the distance from the focus (1, 0) to the origin, which is 1. So, we can solve for 'b' as:

c^2 = a^2 - b^2

1^2 = 3^2 - b^2

b^2 = 3^2 - 1^2

b^2 = 8

b = sqrt(8) = 2sqrt(2)

Substituting these values into the standard form equation, we get:

x^2/3^2 + y^2/(2sqrt(2))^2 = 1

Simplifying:

x^2/9 + y^2/8 = 1

So, the equation in standard form for the given ellipse is:

9x^2 + 8y^2 = 72

Answer:

Does this shape have at least 1 pair of parallel lines? 40

Has at least 1 pair of parallel lines

Does not have at least 1 pair of parallel

lines

More

Answer:

93 + 7 = 100

Step-by-step explanation:

I would assume positive because 100 is above the x-axis not below it.

Answer:

w≤9

Step-by-step explanation:

8w ≤ 72

Divide by 8 on both sides

w ≤ 9

For graph, draw a number line and label a point as 9. Draw a solid line facing to the left and having a closed point at 9. The line should not extend past 9.

The limit of the function will be:

lim f(x) = ∞ as x → ∞

lim f(x) = 0 as x → -∞

The limit of f(x) as x goes towards infinity is infinite while the limit of f(x) approaches 0 when x tends to a negative value. Mathematically speaking,

lim f(x) = ∞ as x → ∞

lim f(x) = 0 as x → -∞

We can comprehend such behavior because the function's base is greater than 1 which explains how its growth accelerates as x increases and diminishes quickly as x declines towards zero.

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A measure of variability which the charity should use to accurately represent the data include the following: D. The range of 45 is the most accurate to use to show that they have plenty of money.

In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Minimum (Min) = 10.

First quartile (Q₁) = 13.75.

Median (Med) = 20.

Third quartile (Q₃) = 26.25.

Maximum (Max) = 55.

For the IQR, we have:

IQR = Third quartile (Q₃) - First quartile (Q₁)

IQR = 26.25 - 13.75

IQR = 12.50

For the range, we have;

Range = maximum - minimum

Range = 55 - 10

Range = 45.

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The missing probability is P(A or B) = 131/200

It should be noted that in order to find the probability of the union of two events A and B, i.e., P(A or B), we can use the following formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = P(A) + P(B) - P(A and B) = (9/20) + (1/4) - (9/200)

Simplifying the expression, we get:

P(A or B) = 45/100 + 25/100 - 9/200 = (90+50-9)/200 = 131/200

The probability is 131 / 200.

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Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.

Given data:

From the figure:

m∠RST  = m∠QST + m∠QSR

Put the values

70 = 2x + 3x - 10

5x = 80

x = 16

Thus,

m∠QSR = 3x - 10  = 3(16) - 10

m∠QSR = 38

Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

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Complete question:

If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.

The figure is attached:

16

48

32

38

The total cost equation is 200,000 + 40n and the break-even revenue is 20,000.

Given that a company is starting a new production, it cost the company $200,000 to construct the factory building.

The cost per unit of production is estimated to be Birr 20.

The company will incur a 20% commission expense.

The price per unit of products is decided to be Birr 50.

We need to find the total cost equation in terms of quantity and determine the break-even quantity.

a) The fixed cost of the company is $200,000, and 40 per unit sell,

Therefore for n units the total cost =

200,000 + 40n

b) BEQ = FC / P−VC

= 200,000 / 50-40

= 20,000

Hence the total cost equation is 200,000 + 40n and the break-even revenue is 20,000.

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If a, b, c are in Harmonic Progression, b+ca+ca+b ac' ab bc are in Arithmetic Progression.

Given a, b, c are in H.P.:

1/a + 1/b = 2/c

Multiplying both sides by abc:

bc + ac = 2ab

Adding c to both sides:

bc + ac + c = 2ab + c

Rearranging the terms:

c + ab = ac + bc

Adding the terms b + ca and ca + b to both sides:

b + ca + ca + b + ac' + ab + bc = ac + bc + b + ca + ca + b

Simplifying:

b + ca + ca + b + ac' + ab + bc = 2ac + 2b

Dividing both sides by 2:

(b + ca + ca + b + ac' + ab + bc)/2 = ac + b

Hence, b+ca+ca+b ac' ab bc are in A.P.

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Answer:

Step-by-step explanation:

If the hypotenuse of a right triangle is twice the length of the shorter leg and the shorter leg is 4 cm, then the hypotenuse is 2 * 4 cm = 8 cm.

Using the Pythagorean theorem, we can find the length of the longer leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Letting c represent the length of the hypotenuse and a and b represent the lengths of the other two sides, we can write this as c^2 = a^2 + b^2.

Substituting in the known values for c and one of the other sides (let’s say a), we have:

8^2 = 4^2 + b^2 64 = 16 + b^2 b^2 = 48 b = sqrt(48)

So, the length of the longer leg is sqrt(48) cm, or approximately 6.93 cm.

The exact value of sin 2θ is 12/37

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have:

cot θ = 6

Thus, tan θ = 1/6

Using the given information, we can sketch the location of the angle θ in the quadrant (See the attached image).

Thus, we can calculate the value of the hypotenuse using the Pythagoras theorem. That is:

hypotenuse = √((-6)² + (-1)²) = √37

sin θ = -1/√37

cos θ = -6/√37

Using trig. identity:

sin 2θ = 2sinθ·cosθ

sin 2θ = 2 * (-1/√37) * (-6/√37)

sin 2θ = 12/37

Therefore, the exact value of sin 2θ is 12/37

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Complete Question

If cot θ = 6,and θ lies in quadrant 3, find the exact value of sin 2θ

Answer:

C

Step-by-step explanation:

Positive numbers represent a positive situation. And negative numbers coincide with a negative situation.

 Ex: An increase in temperature corresponds to a positive number, and a decrease in temperature with a negative number.

Answer:

[tex]\large\boxed{\tt No.}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to determine if the equation has a solution given a value.}[/tex]

[tex]\textsf{Since x is given to us, we can use the \underline{Substitution Property of Equality} to evaluate}[/tex]

[tex]\textsf{the equation.}[/tex]

[tex]\large\underline{\textsf{What is the Substitution Property of Equality?}}[/tex]

[tex]\textsf{The Substitution Property of Equality is a Property that allows us to substitute}[/tex]

[tex]\textsf{a known term, or expression for an unknown variable, or some kind of placeholder.}[/tex]

[tex]\textsf{After Substitution, we can prove that the expressions are still equal with this}[/tex]

[tex]\textsf{property.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\tt \frac{1}{4} x + 3 = " 3 = " 4x+1[/tex]

[tex]\textsf{There's likely a typo in your equation given, hence I will fix it.}[/tex]

[tex]\tt \frac{1}{4} x + 3 = 4x+1[/tex]

[tex]\textsf{Substitute 8 for x in both sides of the equation using our property.}[/tex]

[tex]\underline{\textsf{Use the Substitution Property of Equality;}}[/tex]

[tex]\tt \frac{1}{4} (8) + 3 = 4(8)+1[/tex]

[tex]\underline{\textsf{Follow PEMDAS, multiply first;}}[/tex]

[tex]\tt 2 + 3 = 32+1[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\tt 5 \neq 33[/tex]

[tex]\textsf{If the "typo" was the actual equation;}[/tex]

[tex]\tt 5 \neq 3 \neq 33[/tex]

[tex]\large\boxed{\tt No.}[/tex]

(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.

(a) For loan 1, $3200 at 6.7% for 4 years and 7 months (4 years in college + 3 months deferment), the simple interest = 3200 * 0.067 * (55/12) ≈ $1023.33.

(b) For loan 2, $12,000 at 7.3% for 2 years and 7 months (2 years in college + 3 months deferment), simple interest = 12000 * 0.073 * (31/12) ≈ $2362.33.

(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.

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