The data below represents the number of runners on each cross country team in the Northern Conference. 121212, 151515, 151515, 171717, 191919, 191919, 202020, 222222, 242424 Which box plot correctly summarizes the data?

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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well, let's read the Set Builder

the variable "x", where "x" is greater than or equals to 2

Oh by the way "x" is also less than or equals to 2

hmmm what the heck?  how can "x" be greater than 2 and at the same time be less than 2?  well, that's kinda like a logical collision, so we can conclude that "x" is neither less than or greater than 2, but another condition is that it could be equal to 2, since the other two collided, the only conclusion is that "x" must be equal to 2.

Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

The correct equation to find that can be used to find the width of the feed  trough is (b) 4620 = 8w×w×6, and the width of the "feed-trough"  is 9.8 inches wide.

The "Volume" of "rectangular-prism" can be found using formula V = l×w×h, where V is = volume, l is = length, w is = width, and h is = height.

We know that the volume of the "feed-trough" is 4,620 cubic inches, and

The height is = 6 inches. Let us denote the width as "w" and the length as "8w" (because trough's length is 8 times the width),

So, the equation for the volume of the feed trough is:

⇒ 4620 = (8w) × (w) × (6),

So, the correct equation to find the width is Option (b) 4620 = (8w) × (w) × (6).

Simplifying further,

We get,

⇒ w² = 96.25,

⇒ w ≈ 9.8 inches (rounded to the nearest tenth)

Therefore, the width of the feed trough will be approximately 9.8 inches.

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About 49.87% of buyers paid between $150,000 and $156,000 for the new homes.

According to the 68-95-99.7 rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean in a normal distribution.

In this case, the mean price of a certain model of new homes is $150,000, and the standard deviation is $2000. Thus, we can calculate the price range of one standard deviation above and below the mean as:

Lower Bound = Mean - 1 × Standard Deviation = $150,000 - $2,000 = $148,000

Upper Bound = Mean + 1 × Standard Deviation = $150,000 + $2,000 = $152,000

Therefore, approximately 68% of buyers paid between $148,000 and $152,000 for the new homes.

To find the percentage of buyers who paid between $150,000 and $156,000, we need to calculate the z-scores for these values using the formula:

z-score = (value - mean) / standard deviation

For $150,000:

z-score = ($150,000 - $150,000) / $2,000 = 0

For $156,000:

z-score = ($156,000 - $150,000) / $2,000 = 3

Looking at the z-score table, we can see that the area under the normal curve between z = 0 and z = 3 is approximately 49.87%.

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Answer:

The width of the garage is 22 feet

Step-by-step explanation:

64 = 20 + 2w

44 = 2w

22 = w

The width of the garage is 22 feet

The size of skis is 160 cm.

Given that, Tavon wants to buy new skis that are the same as his height he is 1.6 meters tall. skis are sold in cm. we need to find the height of skis,

Using the concept of unit conversion,

1 m = 100 cm

Therefore,

1.6 m = 100 × 1.6 = 160 cm

Since, the length of the skis and the height of Tavon are same so the skis are of 160 cm.

Hence, the size of skis is 160 cm.

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Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides, A, B, C are the corresponding opposite angles.

so,

16/sin(90) = x/sin(30)

16/1 = x/0.5

0.5 × 16 = x

x = 8 units

Pythagoras now gets us half the baseline (and therefore the full baseline) :

16² = x² + (baseline/2)² = 8² + (baseline/2)²

256 = 64 + baseline²/4

192 = baseline²/4

768 = baseline²

baseline = sqrt(768) = sqrt(256×3) = 16×sqrt(3) units

the area of a triangle is

baseline × height / 2

in our case

16×sqrt(3) × 8 / 2 = 16×sqrt(3) × 4 = 64×sqrt(3) units² =

= 110.8512517... units²

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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The area of the regular hexagon with apothem 3√3 mm is approximately 125 mm². (option d)

The area of a regular hexagon can be found using the formula:

Area = (3√3 × s²) ÷ 2

Where s is the length of one side of the hexagon, and 3√3 is the apothem.

To solve for the area, we need to find the value of s. We can do this by using the fact that a regular hexagon can be divided into six equilateral triangles, and each of these triangles has sides equal to s.

The height of each equilateral triangle is equal to the apothem, which is 3√3 mm in our case. Using the Pythagorean theorem, we can find the length of one side of the hexagon:

s = 2 × (3√3) ÷ √3

s = 6

Now that we know the value of s, we can substitute it into the formula for the area of a regular hexagon:

Area = (3√3 × 6²) ÷ 2 = 125

Hence the correct option is (d).

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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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Answer:

Put your calculator in degree mode.

a = 2, b = 1. So y = 2sin(x)

sin(k) = 12/25, so k = 180° - 28.69° = 151.31°

The figure is omitted--please sketch it to confirm my answer.

√(25^2 - 12^2) = √481

So tan(k) = -(12√481)/481

Answer:Need answer choices to answer

Step-by-step explanation:

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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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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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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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:

In order to find the height of 2 different 3-D shapes, we must identify which dimension represents the height for each individual shape and then add them together.

The first thing is that we must identify which dimension represents the height for each individual shape, for instance, if one shape is a rectangular prism, its height would be the length of one of its sides.

After we identified the height for each shape, you can add them together to get the total height of the composite figure, but, we must understand that this method assumes that the two shapes are stacked vertically on top of each other with their bases aligned.

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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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Answer:

Find the mean and variance of 2,2,3,3,3,4,4,4, and 4

O 4.21, 0.58

O 6.53, 0.74

O 7.69, 0,69

Step-by-step explanation:

You're welcome.

Answer: The first one

Average x = 3.2222222222222

Count n = 9

Sum Sum = 29

Step-by-step explanation: Mean means the usual set of numbers found by adding all the numbers together and then dividing that by the number of the numbers.

Hope it helped

Note that the probability - P(X ≤25 or X ≥ 45) = 0.0784

P(X ≤25 or X ≥ 45)  = 1- P(X ≤25.5 or X ≥ 44.5)

= 1 - p [ (25.5 - 10(3.5)/ √(35/12) √10)   ≤ (X-10(3.5)/√(35/12) √10) ≤ (44.5 - 10(3.5)/√(35/12) √10)]

≈ 1 - (2Ф (1.76) - 1)

≈ 2(1-0.9608)

≈ 0.0784

Thus, P(X ≤25 or X ≥ 45) = 0.0784

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Full Question:

You roll a 6-sided die 10 times. Let X be the total value of all 10 dice = X1 + X2 + ...... + X10.
You win the game if  X ≤ 25 or X ≥ 45. Use the central limit theorem to calculate the probablity that you win.

Note that E[Xi] = 3.5 and Var (Xi) = 35/12

Asked equations are written below with the explanation.

Here are three equations that involve adding negative numbers:

-5 + (-3) = -8

This equation involves adding the negative numbers -5 and -3.

-10 + (-2) + (-3) = -15

This equation involves adding the negative numbers -10, -2, and -3.

-7 + (-1) + (-4) + (-2) = -14

This equation involves adding the negative numbers -7, -1, -4, and -2.

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Triangle A and Triangle C are congruent to each other because a series of rigid transformations, a translation and a reflection, were applied to A to form C. Therefore, the correct answer is "A Is congruent to B and B Is congruent to C". So, the correct answer is A).

Identify the coordinates of the vertices of Triangle A and Triangle C

Triangle A: (1, -2), (3, -2), (3, -5)

Triangle C: (4, 0), (6, 0), (6, 3)

Apply the first transformation that was used to transform Triangle A to Triangle C, which is a translation of 3 units right and 2 units up. To do this, add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of Triangle A to get

Triangle A': (4, 0), (6, 0), (6, -3)

Triangle A' is not congruent to Triangle A because the translation changes the position of the vertices, but it does not change the size or shape of the triangle.

Apply the second transformation that was used to transform Triangle A' to Triangle C, which is a reflection over the x-axis. To do this, negate the y-coordinates of each vertex of Triangle A' to get

Triangle C': (4, 0), (6, 0), (6, 3)

Triangle C' is congruent to Triangle C because the reflection over the x-axis preserves the size and shape of the triangle, and negating the y-coordinates of the vertices only changes their position, not their size or shape.

Compare Triangle A with Triangle C'

Triangle A: (1, -2), (3, -2), (3, -5)

Triangle C': (4, 0), (6, 0), (6, 3)

We can see that Triangle A is congruent to Triangle C' because they have the same shape and size, and the corresponding angles and sides are equal.

Therefore, since Triangle A is congruent to Triangle C', and Triangle C' is congruent to Triangle C, we can conclude that Triangle A is congruent to Triangle C.

Therefore, the correct answer is "A Is congruent to B and B Is congruent to C" and option is A).

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--The given question is incomplete, the complete question is given

" Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3). Which best explains why figure A is congruent to figure C?A Is congruent to B and B Is congruent to C A Is congruent to A, B Is congruent to B, C Is congruent to C Each triangle is a right triangle. Each triangle is an isosceles triangle."--