Heights of female students at ohs follows a normal distribution that has a mean of 65.2 inches with a standard deviation of 2.1 inches. Random samples of size 15 are taken from the population of students.

The central angle is approximately 2.357 radians.

To find the central angle, we can use the formula:

Central angle (θ) = arc length ÷ radius

Given:

Arc length (mXY) = 18 in

Radius (ZY) = 7.64 in

Plugging in the values:

Central angle (θ) = 18 in ÷ 7.64 in

Calculating the division:

θ ≈ 2.357 radians

Therefore, the central angle is approximately 2.357 radians.

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We currently have two fractions: y / 1 and (y - 3) / 3.

In both cases, we are only concerned with the denominator. Yes, the numerator will change when we change the denominator, but that will not affect the answer to this question.

As such, we need to find the least common multiple of 1 and 3. That is 3. Therefore, the common denominator is 3.

Hope this helps!

The points on a parabola with the focal axis parallel to the abscissa axis, of parameter p and A, B is -12.

Since A and B are points on the parabola, write two equations using the general form of the parabolic equation:

(x - h)² = 4p(y - 1)

The focal axis is parallel to the x-axis, so the distance from the vertex to the focus is equal to p. Therefore, use the distance formula to write an equation for the distance between the vertex and point A:

√((13 - h)² + (a - 1)²) = p

Similarly, write an equation for the distance between the vertex and point B:

√((4 - h)² + (b - 1)²) = p

A and B lie on the line 2x - y - 13 = 0, so substitute the x and y coordinates of A and B into this equation and solve for a and b:

2(13) - a - 13 = 0

2(4) - b - 13 = 0

Solving these equations gives us a = 3 and b = -5.

Now three equations and three unknowns (a, b, and h):

√((13 - h)² + 4) = p + 1

√((4 - h)² + 36) = p + 1

2h - 3 - 13 = 0

The third equation simplifies to 2h = 16, or h = 8.

Substituting this value of h into the first two equations and squaring both sides:

(13 - 8)² + 4 = (p + 1)²

(4 - 8)² + 36 = (p + 1)²

Simplifying these equations and solving for p gives us p = 3.

Finally, find a" + bP by substituting the values found for a, b, and p:

a" + bP = 3 + (-5)(3) = -12

Therefore, the solution is a" + bP = -12.

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Using L'hopital we can see that the limit is equal to 1/22

Here we want to take the limit of x tending to zero for x/sin(22x)

Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:

y = x

y' = 1

And for:

y = sin(22x)

y' = 22*cos(22x)

Now taking the limit we will get:

\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)

That is the value of the limit.

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To know if the triangle is congruent we need to follow the below three steps :

Step 1: Verify the triangle's measurements for its legs, hypotenuse, and included angle between its two legs.

Step 2 is to compare the triangles' dimensions.

Step 3: Use HL congruency to determine that the two right triangles are congruent if the included angle is 90 degrees, one leg and hypotenuse of one triangle are the same length as the corresponding leg and hypotenuse of the other triangle, and the included angle is equal to both legs of the other triangle.

Thus, the triangle is found whether it is congruent or not by using above steps :

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Answer:

5/6 is the probability

Step-by-step explanation:

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and rolling a 6-sided die you can get 1, 2, 3, 4, 5, 6 so 5 is the only thing you can roll that isn't a factor of 24 so

7 ( 1 + 3 )

Solve the sum inside the parentheses ( 1 + 3 = 4 )

7 ( 4 )

multiply

7*4 = 28

Since the sum must equal 28

7 + 21 = 28

Correct option = 7+21

Answer:

Radius= 11

Circumference= 69.12

Area= 380.133

Step-by-step explanation:

Radius is half of the diameter.

Circumference is 2\(\pi\)r.

Area is \(\pi r^2\).

Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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Answer:

1674

Step-by-step explanation:

Answer:

7.615773105864

Step-by-step explanation:

\(\text{let A and B be the points of coordinates} \ A\left( 3,-9\right) \text{and} \ B\left( 6,-2\right)\)

\(AB=\sqrt{\left( 6-3\right)^{2} +\left( -2-(-9)\right)^{2} }\)

     \(=\sqrt{\left( 3\right)^{2} +\left( 7\right)^{2} }\)

     \(=\sqrt{58} =7.615773105864\)

An expression for given sequence of operations is: j + 3^9

In this question, we need to write an expression for the sequence of operations described below.

raise 3 to the 9th power, then add the result to j

Consider the part of given statement,

raise 3 to the 9th power

We write this as: 3^9

then we add this result to j.

So, we get an expression: 3^9 + j

Therefore, an expression for given sequence of operations is: j + 3^9

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Answer:

im horrible at this kinda stuff-but is it 18......? ive always been bad-so if im wrong-dont get mad-

Step-by-step explanation:

happy new year!

Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways

The right answer is C. It is a technique applied when creating an object.

When an object is generated from a class in object-oriented programming, a constructor, a particular method, is called. It is in charge of initializing the object and establishing its starting state. Typically, constructors are specified in the class specification and called when an object is created with the new keyword. They are used to create and initialize objects of that class and share the same name as the class.

In the event that a constructor's arguments include default values, it is possible to call it without any arguments. Additionally, a class may have many constructors with various amounts or kinds of parameters due to overloading, which allows for this.

Option A is erroneous since a constructor does not figure out the class's return values. Because a constructor does not call each of the class methods sequentially, option B is incorrect. Option D is erroneous since the class definition, not the client code, contains the definition of a constructor. Because a constructor gives access to methods and instance variables, Option E is valid, but it's not the only one.

The complete question is:-

Which statement is true about a constructor?

A. It calculates the return values for the class

B. It invokes all the class methods in order

C. It is a method used when instantiating an object

D. It is defined in the client code for the class

E. It provides access to methods and instance variables

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Answer:

The car will depreciate at a rate of 21.14% per year.

Step-by-step explanation:

Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:

13,500 x (1 + X) ^ 1x3 = 24,000

13,500 x (1 + 0.2114) ^ 3 = 24,000

X = 21.14%

Therefore, the car will depreciate at a rate of 21.14% per year.

Answer:

The answer is B) x = 8x² + 34; 45.52 centemiters

Step-by-step explanation:

The probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

Let's calculate the probability that the teacher chooses a student with glasses.
a) A girl with glasses: There are 6 girls in the class, and 3 of them wear glasses. There are a total of 16 students (6 girls + 10 boys).
Probability = (Number of girls with glasses) / (Total number of students)
Probability = 3 girls with glasses / 16 total students
Probability = 3/16
b) A boy with glasses: There are 10 boys in the class, and 4 of them wear glasses.
Probability = (Number of boys with glasses) / (Total number of students)
Probability = 4 boys with glasses / 16 total students
Probability = 1/4
So, the probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

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Answer:

As = 256\(\pi\) or 804.25cm

Step-by-step explanation:

By formula As = \(4\pi r^{2}\)

As = 256\(\pi\) or 804.25cm

Answer:

B) 4,700

Step-by-step explanation:

6000 - 4000 = 2000

2000 in 15 year, find how much for each year

2000/ 15 = 133.3333333

133.3333333 estimated = 133

133 approximately for each year

1975 to 1980 is five years

133 x 5 = 665

4000 + 665 = 4665

4665 rounded the the nearest hundred

4700

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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We have different options to solve this problem.

In this case we will use the fact that the volume of a prism is the product of the base and the height, being the height constant and perpendicular to the base.

In this case, the base is a composite figure:

Then, we can calculate the area of the base as the sum of the area of this two rectangles:

Now, as the height is 10, we can calculate the volume as:

Answer: the volume is 960 cubic units (option H)

Answer:

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

Find the difference of the initial and used amounts:

The equation parallel to the given equation and passing through the point (8, 3) is:

The equation perpendicular to the given equation and passing through the point (8, 3) is:

The equation of the line parallel to the line y = mx + c and passing through the point (x₁, y₁) is given as:

The equation of the line perpendicular to the line y = mx + c and passing through the point (x₁, y₁) is given as:

Now, for the equation:

The line parallel to the equation and passing through the point (8, 3) will be:

The line perpendicular to the given equation and passing through the point (8, 3) will be:

Answer:

x = 33 degrees.

Step-by-step explanation:

You can see that there is triangle ABC. There are 180 degrees in a triangle. One angle of the triangle is 42 degrees, and the other is 105 degrees. 105 + 42 = 147. The angle at point C would then be 180 - 147 = 33 degrees.

Because lines BC and DE are parallel, you can say that the 33 degree angle and the x-degree angle are the same, since they are alternate angles. Hence, the x is 33 degrees.

I think the answer is C :)

Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.