A
Find the recursive definition
of this sequence.
3, 10, 17, 24
an = an-1 + 10
a1 = 3
B
an = 10an-1
a₁ = 3
C
an = an-1+7
a₁
a₁ = 3

For the given circle ,

three radii are BC, CD , and CF , diameter is BD , Chord is HD and BD , Secant is AD and Point of tangency is F.

From the figure of the circle,

Radius is line segment whose one end point is on circumference of circle and other is center.

Three radii of the circle are BC, CD , and CF.

Diameter is a line segment whose endpoints are on the circumference of circle and passing through center.

A diameter of the circle is BD.

Tangent of a circle is a line which touches the circle at one point only.

A tangent of the circle is GE.

A chord of  the circle is a line segment whose end points are on the circle.

A chord of a circle is HD and BD.

A secant of the circle is a line intersects at two points.

A secant of the circle is AD.

A  point of tangency is a point where tangent touches the circle.

A point of tangency is F.

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Step-by-step:

ANALYSIS:

From the question, we know that...

• 310m from his home to the meeting

• Average speed RETURNING: 7 mph LESS than the speed he went on

• Total time = 12 hours

• Rate of speed = ?

-Round off to the nearest TENTH-

EXPLANATION:

Speed = Distance / Time

• S = 310/12

• S = 25.83333... mph

• S = 25.83 (round off)

Then it says that speed returning is -7 from the speed he went on, so...

• 25.83 - 7 = 18.83 mph

Rounding off to the nearest TENTH:

18.83 = 18.8 mph

Final Answer : 18.8 mph

The volume of the smaller box is 900 cm³.

We have,

The dimensions of the smaller box are half the dimensions of the larger box.

Length = 24/2 = 12 cm

Width = 10/2 = 5 cm

Height = 30/2 = 15 cm.

The volume of the smaller box is the product of these dimensions:

Volume = length × width × height

= 12 cm × 5 cm × 15 cm

= 900 cm³

Therefore,

The volume of the smaller box is 900 cm³.

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The interval that is likely to contain the exact percent of all US adults who would support the policy is 0.7 ± 0.022.

Since the sample size is large (n = 2000) and the proportion of respondents who support the policy is 0.7, we can use the normal distribution to approximate the sampling distribution of the sample proportion.

The margin of error is ±2.2%, which means that we need to construct a 95% confidence interval. The critical value for a 95% confidence interval with a two-tailed test is approximately 1.96.

The formula for a confidence interval for a population proportion is:

sample proportion ± z* (standard error)

sqrt((sample proportion * (1 - sample proportion)) / n)

Substituting the values:

Therefore, the 95% confidence interval for the percentage of all U.S adults who would support a national policy requiring rooftop solar panels to be installed on all new homes is 0.678 - 0.722.

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The probability of winning the lottery on a single ticket is

P ( A ) = 1 / (12 * 30 * 24 * 60 * 60)

Given data ,

Let the probability of winning the lottery on a single ticket be P ( A )

Now , There are 12 months in a year.

There are 30 days in a month

There are 24 hours in a day.

There are 60 minutes in an hour.

There are 60 seconds in a minute.

And , the total number of possible outcomes for the date and time is:

12 (months) * 30 (days) * 24 (hours) * 60 (minutes) * 60 (seconds)

So, the probability of winning the lottery on a single ticket is:

1 (winning outcome) / (12 * 30 * 24 * 60 * 60) (total possible outcomes)

Simplifying this fraction, we get:

1 / (12 * 30 * 24 * 60 * 60)

Hence , the probability is P ( A ) = 1 / (12 * 30 * 24 * 60 * 60)

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The percent of saline solution in brand B  is 10.83%

Let's assume that brand B has x gallons of the 100% saline solution.

The amount of salt in brand A is 18% of 6 gallons = 0.18 * 6 = 1.08 gallons.

When the two brands are mixed, the total volume of the mixture is 6 + x gallons, and the total amount of salt is 1.08 + x gallons.

Since the resulting mixture is 18 gallons of 8% saline solution, we can set up the equation:

(1.08 + x) / (6 + x) = 0.08

Solving for x, we get:

1.08 + x = 0.48 + 0.08x

0.92x = 0.6

x = 0.65

So, brand B has 0.65 gallons of the 100% saline solution.

Therefore, the percent of saline solution in brand B is:

0.65 / 6) * 100% = 10.83%, which rounded to the nearest whole number is 11%.

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4.) The statement that is not true about the cube box is that the volume of the box is one square foot. That is option C.

5.) All the possible dimensions of the bottom layers include the following;

when length= 4 units; width = 3units

when length = 3 units; width = 4 units

when length = 2 units; width = 6 units

To calculate the volume of a cube box the formula that should be used = a³

where a = 1³

volume = (1×1×1) = 1ft³

The area of the cube = 6(a²)

But a = 1

area = 6(1²)

= 6ft²

Therefore the wrong statement is that the volume of the box is one square foot instead of 1ft³.

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A graph is a visual representation or diagram that shows facts or values in an ordered way. The only graph that satisfies the above shape is the third one.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between multiple items are frequently represented by the points on a graph. The term "pictograph" refers to the visual depiction of information. Each graphic represents a specified number of objects. The only graph that satisfies the above shape is the third one.

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,    

The area of the face of a clock with a circumference of 14 inches is approximately 15.6 square inches. This is calculated using the formula for the area of a circle, which is πr², where r is the radius of the circle.

To find the area of the face of the clock, we need to use the formula for the area of a circle, which is

A = πr²

where A is the area of the circle, π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle.

Since the circumference of the clock is 14 inches, we can use the formula for the circumference of a circle to find the radius

C = 2πr

14 = 2πr

r = 14 / (2π)

r = 2.227 in (approx)

Now that we know the radius, we can use the formula for the area of a circle

A = πr²

A = 3.14 x (2.227)²

A = 15.6 sq in (approx)

Therefore, the area of the face of the clock is approximately 15.6 square inches.

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The coordinates of the vertices for the image if the preimage is translated 3 units up is A′(−3, 6), B′(0, 10), C′(−3, 3) (option b).

In this particular question, we are given a triangle ABC with vertices at A(−3, 3), B(0, 7), and C(−3, 0). Our task is to determine the coordinates of the vertices for the image if the preimage is translated 3 units up.

When a figure is translated, it is moved to a new location without changing its shape or size.

Let's start by looking at vertex A(−3, 3). If we translate this vertex 3 units up along the y-axis, its new coordinates will be A′(−3, 6).

Similarly, if we translate vertex B(0, 7) 3 units up, its new coordinates will be B′(0, 10). Finally, if we translate vertex C(−3, 0) 3 units up, its new coordinates will be C′(−3, 3).

Therefore, the vertices of the image triangle are A′(−3, 6), B′(0, 10), and C′(−3, 3). This is option (B) from the given answer choices.

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The statements that are true about diagonal of parallelogram;

A. AP is equal to CP

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal and the sum of the adjascent angles is 180°.

The diagonal of a parallelogram is a line that touches the vertex of opposite angles. Here are some of the properties of diagonal of a parallelogram.

1. The diagonal divides the parallelogram into congruent triangles

2. The diagonal of parallelogram bisects each other but they are not equal.

3. The diagonal of parallelogram bisect each other at 90°.

Therefore, the statement that is true is AP is equal to CP since AC is a diagonal.

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Answer:

2 students play both

Step-by-step explanation:n(u)=28

n(b)=7,n(b)=5,n(who play neither sport)=18

HERE,

n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)

28=7+5-n(BnB)+18

28=30-n(BnB)

n(BnB)=30-28

 =2 answer

The rate of the second car (r) is 52 miles/ hour.

There are many ways in which we can solve word problems leading to algebraic equations depending on the form, variables, and constants given in the equation.

Here, we are given two cars in which the first car travels 10 miles faster than the second car.

Let's assume that:

In three miles, they are 342 miles apart, Thus, we can express this mathematically as:

3(r + 10) + 3r = 342

3r + 30 + 3r = 342

6r + 30 = 342

Collect like terms

6r = 342 - 30

6r = 312

r = 312/6

r = 52

Therefore, we can conclude that the rate of the second car (r) is 52 miles/ hour.

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The equation of the axis of symmetry of the parabola is x = 7.

We have,

The axis of symmetry of a parabola is a vertical line that passes through the vertex.

Now,

The equation of the axis of symmetry is the vertical line passing through the x-coordinate of the vertex.

And,

The x-coordinate of the vertex is 7.

Now,

So the equation of the axis of symmetry is x = 7.

Thus,

The equation of the axis of symmetry of the parabola is x = 7.

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The new mixture contains 34% peanuts. The correct option is A

The idea of weighted averages can be applied.

First, let's determine the mixture's entire weight:

Total weight = 4 kg + 12 kg = 16 kg

We can now calculate how many peanuts there are overall in the mixture:

Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Finally, we can find the percentage of peanuts in the mixture:

Percent of peanuts = (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

   = 34%

Therefore, the new mixture contains 34% peanuts, which is option A.

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Answer:

To find the probability of getting no heads, we need to add the frequencies for the outcomes where tails appears twice and divide by the total number of trials:

No heads = Tails, Tails = 50

P(No Heads) = 50/200 = 0.25 = 25%

Therefore, the answer is 25%.

Answer:

The probability of getting no heads when flipping a coin twice is 25%.

The probability of getting heads on a single flip of a coin is 50%.

The probability of getting no heads when flipping a coin twice is:

```

(1 - 0.5)^2 = 0.25

```

Therefore, the probability of getting no heads when flipping a coin twice is 25%.

So the answer is 25%

Step-by-step explanation:

It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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Polynomial M is 2(x - [tex](\frac{1}{12}a)^{2}[/tex] - (1/72)[tex]a^{2}[/tex] + by

To find the polynomial M, we need to rearrange the equation given to us. We can start by adding M to both sides of the equation to isolate the constant term. This gives us:

2[tex]x^{2}[/tex] - (1/3)ax + by = M

Now, we have the polynomial M in terms of x, a, b, and y. However, this is not in its simplest form yet. We can simplify this further by factoring out the coefficient of x. This gives us:

2([tex]x^{2}[/tex] - (1/6)ax) + by = M

Now, we can complete the square inside the brackets to get a perfect square trinomial. This means taking half of the coefficient of x, squaring it, and adding it and subtracting it inside the brackets. This gives us:

2((x - [tex](\frac{1}{12}a)^{2}[/tex]  - (1/144)[tex]a^{2}[/tex]) + by = M

Simplifying this further, we get:

2(x - [tex](\frac{1}{12}a)^{2}[/tex]  - (1/72[tex]a^{2}[/tex] + by = M

Therefore, the polynomial M is given by:

M = 2(x - [tex](\frac{1}{12}a)^{2}[/tex]  - (1/72)[tex]a^{2}[/tex] + by

This is the final answer for the polynomial M.

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Answer:

B. (x - 5)^2 = 21

Step-by-step explanation:

The y-values are 5, 2, 1, 2, 5, 10 and 17.

Given that an equation of a curve, y = x²+1, we need to find the values of the y-intercept corresponding to the given x-intercept,

So,

y = x²+1

Putting the values of x,

x = -2,

y = (-2)²+1

y = 5

(-2, 5)

x = -1

y = (-1)²+1

y = 2
x = 0,

y = (0)²+1

y = 1

x = 1

y = 2

x = 2,

y = 2²+1

y = 5

x = 3,

y = 3²+1

y = 10

when x = 4,

y = 4²+1

y = 17

Hence, the y-values are 5, 2, 1, 2, 5, 10 and 17.

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Find the limit...

[tex]\lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )[/tex]

Factor the top and bottom of the expression.

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{(x+2)(x-2)}{3x(x-2)} )[/tex]

Cancel the common factor "(x-2)."

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{x+2}{3x} )[/tex]

Now plug in the limit.

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{2+2}{3(2)} ) \Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{4}{6} )=\boxed{tan^{-1}(\frac{2}{3} )}[/tex]

[tex]\lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )=\boxed{\boxed{tan^{-1}(\frac{2}{3} )}} \therefore Sol.[/tex]

Thus, the limit is solved.

The translation is of 5 units to the right and 3 units down, it can also be written as:

(x, y) ---> (x + 5, y - 3)

To study the translation, just look at some vertex in both figures.

The top left vertex of F is at (2, 7)

And the top left vertex at G is (7, 4)

Taking the difference between these, we will get:

(7, 4) - (2, 7) = (5,, - 3)

Then the translation from F to G can be defined as:

(x, y) ---> (x + 5, y - 3)

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Answer:

  8 cm³

Step-by-step explanation:

You want the volume of Prism B similar to Prism A, where the volume of Prism A is 216 cm³, its height is 9 cm, and the height of Prism B is 3 cm.

The ratio of volumes is the cube of the ratio of heights:

  (Prism B volume)/(Prism A volume) = ((Prism B height)/(Prism A height))³

  (Prism B volume)/(216 cm³) = ((3 cm/(9 cm))³ = 1/27

  Prism B volume = (216 cm³)·(1/27) = 8 cm³

The volume is 8 cubic centimeters.

The information given in the table is the number of bullseyes hit by each team in a dart competition.

The organizer wants the display to show the performance of each team in hitting the bullseye in the competition.

The team with the highest number of bullseyes will be considered the best performer, while the team with the lowest number of bullseyes will be considered the worst performer

We have,

The information given in the table is the number of bullseyes hit by each team in a dart competition.

The organizer wants the display to show the performance of each team in hitting the bullseye in the competition.

The display will allow the audience to compare the performance of different teams and draw conclusions about which team performed better in hitting the bullseye.

The display will be analyzed by comparing the number of bullseyes hit by each team.

The team with the highest number of bullseyes will be considered the best performer, while the team with the lowest number of bullseyes will be considered the worst performer.

The audience may also analyze the performance of each team in relation to their expectations or previous performance in similar competitions.

Thus,

The information on the data displayed and its analysis is given above.

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Blueland's nominal exchange rate with Redland decreased by 25% from last year to this year.

Blueland's real exchange rate with Redland decreased by 13.3% from last year to this year.

The nominal exchange rate is ratio at which one currency can be exchanged for another. The real exchange rate account for changes in the inflation rate between two countries and provides accurate picture of the purchasing power of the currencies.

Here, Blueland's nominal exchange rate with Redland decreased by 25% from last year to this year, as the blue decreased in value relative to the red.

But Blueland's real exchange rate with Redland decreased by only 13.3%, as Blueland's inflation rate was higher than Redland's inflation rate which means Blueland's goods became relatively more expensive compared to Redland's goods.

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