stem-and-leaf displays can be used to multiple select question. observe individual data points. analyze qualitative data. determine central tendency and dispersion. analyze the shape of the data.

The freezing point is normally distributed with mean of 0 degrees celsius and a standard deviation of 1 degree celsius. The probability of getting a score between -1.5 and 2.5 is 0.9332.

To find the probability of getting a score between -1.5 and 2.5, we need to find the area under the normal distribution curve for this range using a z-score table.

First, we need to convert the range into standard units, which is done by subtracting the mean and dividing by the standard deviation:

z1 = ( -1.5 - 0 ) / 1 = -1.5

z2 = ( 2.5 - 0 ) / 1 = 2.5

Next, we look up the z-scores in a z-score table to find the area under the normal curve:

P(-1.5 < Z < 2.5) = 0.9332

This means that the probability of getting a score between -1.5 and 2.5 is 0.9332 or 93.32%.

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Therefore, the distance covered by a passenger vehicle during one turn of the wheel is roughly 471.2 feet (rounded to the nearest tenth).

The ratio of a circle's circumference to width serves as the basis for the traditional meaning of Pi (). The diameter or extent of a circular is its circumference. A straight line connecting a spot on one point of the circular to a point at the other end, going through the middle, is the diameter.

The following algorithm determines a circle's circumference:

C = πd

where d is the diameter of the circle. In this case, the diameter of the Ferris wheel is 150 ft, so its circumference is:

C = π(150) ≈ 471.2 ft

This indicates that a full rotation of the Ferris wheel is equal to a passenger vehicle moving about 471.2 feet.

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The value of VT is 13 units and the value of ST is 23.56 units

Consider the following diagram of rectangle RSTU

We know that the diagonals of rectangle bisect each other, intersect at right angles.

For rectangle RSTU,

2RV = RT

But RT = US

So, 2RV = US

2(x + 6) = 5x - 9

2x + 12 = 5x - 9

12 + 9 = 5x - 2x

3x = 21

x = 7

So, RV = 7 + 6

RV = 13 units

But RV = VT

So, VT = 13

Now we find the value of ST using Pythagoras theorem.

RT² = ST² + RS²

ST = [tex]\sqrt{RT^2 - RS^2}[/tex]

ST = 23.56 units

Thus, VT = 13 and ST = 23.56

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For a quadratic equation:

a*x^2 + b*x + c = 0

The quadratic formula is just:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

For a general quadratic equation:

a*x^2 + b*x + c = 0

The quadratic formula is:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

So for example, let's assume that we have the quadratic equation:

3x^2 + 7x - 12 = 0

Here we have the values:

a = 3

b = 7

c = -12

Now you could just replace them in the quadratic formula and you will get:

[tex]x = \frac{-7 \pm \sqrt{7^2 - 4*3*-12} }{2*3}[/tex]

And if you simplify that you will get the two solutions.

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Answer:20x^8+28

Step-by-step explanation:multiply both terms by 4

Answer: ez question, the answer is F = 200, and V = 8

Step-by-step explanation:

After answering the provided question, we can conclude that Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).

In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of side lengths. A parallelogram is a type of quadrilateral in which both sets of opposite corners are similar and equal. Parallelograms are classified into four types, three of which are unique. The four different shapes are parallelograms, squares, geometric shapes, and rhombuses. A quadrilateral is a parallelogram when it has two sets of equal spacing. The opposing sides and angles of a parallelogram are both the same length. The interior angles on each side of the solid line are also angles. The total number of interior angles is 360.

Option C: The fact that V is the midpoint of PR suffices to demonstrate that PORS is a parallelogram.

We know that PV = VR because V is the midpoint of PR. Furthermore, because QR = SP (as shown in the drawing), we can conclude that triangles QRP.

We can deduce from this congruence that angle QRP is congruent to angle SPR, which means that angle POR is congruent to angle PSR (because they are corresponding angles). Angle OPS is also congruent with angle ORP (because they are corresponding angles).

Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).

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Answer: H = -1

Step-by-step explanation:

12 + 7h = 5

7h = -7

H = -1

There are 39 nickel coins in the jar.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given a coin jar contains a combination of nickels and quarters,

let the number of nickels be x,

number of quarters be y,

total coins = 60

x + y = 60

y = 60 - x.........(1)

and total coins in the jar worth = $7.20

we know the value of a nickel coin = $0.05

value of quarters coin = $0.25

so, 0.05x + 0.25y = 7.20

substitute the value from equation 1

0.05x + 0.25(60 - x) = 7.20

0.05x + 15 - 0.25x = 7.20

-0.2x = 7.20 - 15

x = 7.8/0.2

x = 39

Hence there are 39 nickel coins.

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The table with the correct values for A, B and C are,

Black 9 36 63 90

White 13 52 91 130

A proportional relationship is defined as follows:

⇒ y = kx.

In which k is the constant of proportionality.

Here, The input and output variables for this problem are given as follows:

Input:     number of black keys.

Output:  number of white keys.

Hence, The constant k is obtained as follows:

91 = 63k

k = 91/63

k = 13/9.

So, The equation is,

⇒ y = 13x/9.

Hence, the values are given as follows;

For A:

when x = 9,

y = 13 × 9 / 9

y = 13

For B:

when x = 36,

y = 13 x 36/9

y = 52.

For C:

when x = 90,

y = 13 x 90/9 = 130.

Thus, First table is correct.

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The inverse function of p(x) = 50x - 400 is p⁻¹(x) = x/50 + 8.

Given the function in the question;

p(x) = 50x - 400

To determine the inverse, replace p(x) with y.

p(x) = 50x - 400

y = 50x - 400

Now, interchange the variables y and x.

x = 50y - 400

Solve for y

Add 400 to both sides

x + 400 = 50y - 400 + 400

x + 400 = 50y

Reorder the equation

50y = x + 400

Divide both sides by 50

50y/50 = x/50 + 400/50

y = x/50 + 400/50

y = x/50 + 8

Replace y with p⁻¹(x)

p⁻¹(x) = x/50 + 8.

Therefore, the inverse is  x/50 + 8.

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The value of y is 45.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given that, water level rises 15 centimeters every 7 minutes.

Water level in 7 minutes = 15 cm

Water level in 1 minute = 15/7 cm

So the rate of change of the water rising is 15/7 cm per minute.

That is the point is (1, 15/7).

Let x represent the time and y represent the rise of water.

You have to calculate y of the point (21, y).

Water level rise in 21 minutes = 21 × (15/7) = 45 cm

Value of y is 45.

Slope of a line with two points (x, y) and (x', y') is,

Slope = (y' - y) / (x' - x)

We have slope = 15/7 since it is a proportional relationship.

Take the points (1, 15/7) and (21, y).

(y - 15/7) / (21 - 1) = 15/7

(y - 15/7) / 20 = 15/7

(7y - 15) / (20 × 7) = 15/7

7y - 15 = 15/7 × (20 × 7)

7y - 15 = 300

7y = 315

y = 45

Using slope, it is justified.

Hence the value of y is 45.

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Answer:

30

Step-by-step explanation:

5 + 5 + 10 + 4 + 6 = 30

The length of the tunnel is approximately 205.6 meters to the nearest tenth.

What is Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

       a²+b²=c²

Here's one way to find the length of the tunnel:

1) Draw a diagram to represent the situation

2) Draw the perpendiculars from the surveyor to each entrance, and label the height of the triangle formed by each entrance and the surveyor as h1 and h2, respectively

3) Use trigonometry to find h1 and h2:

h1 = 243 * sin(47) = 160.1

h2 = 186 * sin(27) = 105.8

4) Find the horizontal distance between the two entrances, which is the length of the tunnel, by using the Pythagorean theorem:

[tex]d = \sqrt{(h1^2 + h2^2) }\\\\ d = \sqrt{(160.1^2 + 105.8^2)}\\\\ d = 205.6[/tex]

So, The length of the tunnel is approximately 205.6 meters to the nearest tenth.

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The answer is :

a. If each car has space for four passengers, then the equation states how many passengers (p) may be transported by n cars:

p = 4n

where n is the number of automobiles and p is the total number of passengers.

b. By using n = 78 instead of n, we can solve for the number of passengers that could fit in 78 cars as follows:

p = 4n

p = 4(78)\sp = 312

Hence, 78 automobiles could accommodate 312 passengers.

c. By rearranging the equation, we can determine how many cars would be required to fit 78 passengers:

p = 4n\sn = p/4

When we enter p = 78 into this equation, we obtain:

n = 78/4\sn = 19.5

We would need to round up to the nearest whole number of cars, which is 20, as the number of cars must be a whole number. Hence, 20 automobiles would be required to accommodate 78 individuals.

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Answer:

28, 36, 40

Step-by-step explanation:

Add up the numbers in the ratio, giving us 26. Perimeter divided by 26 equals 4. Then, four times each of the numbers in the ratio gives you the lengths

Answer:

there is no question. but these are two of the same lines with different Y-intercepts.

The probability of rolling 5 distinct values in 5 rolls is equal to the value:

5/162.

Every one of the 5! = 120 distinct occurrences represents a different combination of the digits 1,...,5. Each of these events has a

[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{3}[/tex] percent probability of occurring.

So let's begin. the sides 1, 2, 3, 4, 5, 5A, and 5B. There are 6^5 potential side combinations that might occur in five rolls. You must see either 5A or 5B precisely once in addition to each of the numbers 1, 2, 3, and 4 exactly once in order to have five unique sides in five rolls. That is, you must see each of the following numbers precisely once: 1, 2, 3, 4, and 5A. You must also see each of the following numbers exactly once: 1, 2, 3, 4, and 5B. Each of these two types of sequences has five distinct variations.

P(1)=P(2)=P(3)=P(4)=16, P(5)=1/3, and for each of the 120 distinct occurrences given above and P(1)=P(2)=P(3)=P(4)=1, P(2)=P(3)=P(4)=1,

P In light of this, the chance of the event you describe is

120×1/6×1/6×1/6×1/6×1/3=120/6^4*(3)=5/162 is the probability.

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The kind of sampling that is being used by the snack food company, which is developing a new flavor for crackers and which asks customers to text their preference between two possibilities, is known as non-probability sampling.

Non-probability sampling refers to a sampling technique where a researcher selects samples that are based on the subjective judgment of the researcher rather than random selection. This kind of sampling is a less stringent method, and the method depends heavily on the expertise of the researchers.

Non-probability sampling is carried out by observation, and it is used widely for qualitative research.

Since the food company selects only samples that the company would like (the samples being the company's own customers), the company uses non-probability sampling.

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The exact value of the given trigonometry expression is 16/65

Given the following trigonometry expressions

Cos (x + y)

sin x = 5/13 and:

sin y = 4/5

We need to find the exact value of cos(x+y)

According to the trigonometry identity

cos(x+y) = cosxcosy - sinxsiny

If sinx = 5/13, then cosx = 12/13. Also, if siny = 4/5, then cosy = 3/5

Substitute to have:

cos(x+y) = 12/13(3/5) - 5/13(4/5)

cos(x+y) = 36/65 - 20/65

cos(x+y) = 16/65

Hence the exact value of cos(x+y) is 16/65

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According to square root and multiplication, the simplified answer is 126.54.

Rewriting the equation first to perform multiplication and simplify the equation -

Equation = (5✓3 + ✓15) × (3✓5 + ✓15)

Firstly multiplying the possibile entities in the equation

Equation = 15✓15 + 5✓3×✓15 + 3✓5×✓15 + 15

Keep the value of ✓3 and ✓15 in the equation

✓15 = 3.9

✓3 = 1.7

Equation = 15×3.9 + 5×1.7×3.9 + 3×1.7×3.9 + 15

Performing multiplication on Right Hand Side of the equation

Equation = 58.5 + 33.15 + 19.89 + 15

Performing addition on Right Hand Side of the equation

Equation = 126.54

Thus, the simplified form of equation is 126.54.

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Answer:

Step-by-step explanation:

Let's start by calculating the distance traveled in the first scenario:

Distance = Average speed x time

First, we need to convert 2 hours and 45 minutes to hours. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours. Therefore, the total time is:

2 hours and 45 minutes = 2 + 0.75 = 2.75 hours

Now we can calculate the distance:

Distance = 106 km/h x 2.75 hours = 291.5 km

So the car travels 291.5 km in 2 hours and 45 minutes.

To find the constant speed the car must drive to travel the same distance in 2 hours and 35 minutes, we can use the same formula:

Distance = Speed x time

We know the distance is 291.5 km, and the time is 2 hours and 35 minutes. Again, we need to convert the minutes to hours:

2 hours and 35 minutes = 2 + 35/60 = 2.583 hours

Now we can solve for the speed:

Speed = Distance / time = 291.5 km / 2.583 hours ≈ 113 km/h

Therefore, the car must drive at a constant speed of approximately 113 km/h to travel the same distance in 2 hours and 35 minutes.

The value of x in triangle HJK is 5 √2, So correct option is (A). The value of x in triangle ABC is 25√3, So correct option is (H).

The Pythagorean Theorem is a fundamental theorem in mathematics that relates the lengths of the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, the Pythagorean Theorem can be expressed as:

a² + b² = c²

where "a" and "b" are the lengths of the two sides of the right triangle and "c" is the length of the hypotenuse.

The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It is a widely used theorem in mathematics and has numerous applications in many fields, including geometry, trigonometry, engineering, physics, and computer graphics.

For example, in geometry, the Pythagorean Theorem can be used to find the distance between two points in two-dimensional space. In trigonometry, it can be used to find the sine, cosine, and tangent of an angle. In physics, it can be used to calculate the force required to accelerate an object, or to determine the velocity of an object at a given time.

Overall, the Pythagorean Theorem is an important theorem that provides a simple and elegant solution to many problems involving right triangles and is widely used in mathematics and science.

9. To find the value of x in triangle HJK, we can use the Pythagorean theorem. Let's call JK = x.

HK² + JK² = KH²

Since Angle HKJ is 60 degrees and Angle KHJ is 90 degrees, we can use the trigonometric ratios to find the length of HK:

HK = JK × tan 60 = JK / √3

Substituting this into the equation above, we get:

JK² / 3 + JK² = 5²

Expanding and solving for JK, we find that:

JK = 5 √2

So, the answer is (a) 5√2.

10. To find x in triangle ABC, we can use similar methods as in question 9. Let's call BC = x. Then, by the Pythagorean theorem, we have:

AC² + BC² = AB²

Since Angle BAC is 60 degrees and Angle ABC is 90 degrees, we can use the trigonometric ratios to find the length of AB:

AB = AC / √3

Substituting this into the equation above, we get:

AC² + BC² = (AC / √3)²

Expanding and solving for BC, we find that:

BC = AC * √3 / 2 = 50 × √3 / 2 = 25√3

So, the answer is (H) 25√3

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The merchant uses Selling Price = Cost + $3.00 to determine the selling price.

Addition is a process of combining two or more numbers.

A merchant adds $3.00 to his cost to determine his selling price.

The cost is denoted by c.

The selling price is given by f(c).

As there is given add in the sentence, it means we have to use the addition rule.

Selling price is the sum of cost plus three

Selling Price = Cost + $3.00

So the table becomes as below

c 1, 2, 3, 4, 5,

f(c) 4, 5, 6, 7, 8,

Hence, the merchant uses Selling Price = Cost + $3.00 to determine the selling price.

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The cardinality of a set refers to the number of elements in the set. If the set X has cardinality 16 and the set Y has cardinality 24, then the number of elements in set X is 16 and the number of elements in set Y is 2.

If their intersection has cardinality 21, then the number of elements that both sets have in common is 21.To determine the number of elements contained in the union of X and Y, we need to subtract the number of elements in their intersection from the sum of the cardinalities of X and Y. That is,

|X U Y| = |X| + |Y| - |X ∩ Y| = 16 + 24 - 21 = 19

Therefore, the union of X and Y contains 19 elements.

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Answer:

Step-by-step explanation:

$300

Answer:

A=50 B=50 too C=180

The  Probability of (3 or even) = 3/4

Probability is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

From the question;

The p(3) = 1/4

The P(even) = 2/4 =1/2

P(3 or even) = 1/4 + 1/2

P(3 or even) = 6/8

Reducing to the lowest terms

P(3 or even) = 3/4

Hence, 3/4 is the Probability of (3 or even) of picking a card at random

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Answer:

The answer is C). 4 ÷ one third.

The solution of the system of equations include the following:

(0, 2)

(-4, 0).

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the above, we can logically deduce the following system of equations:

y = 1/2(x) + 2     .......equation 1.

2y = x + 4           .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

2(1/2(x) + 2) = x + 4

x + 4 = x + 4

x - x = 4 - 4 (no solution).

However, we would solve the system of equations graphically in order to determine the solutions as shown in the image attached below.

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