1. What is the median of the following set of numbers?
48.4, 47, 43, 47, 43.6, 41.6, 45, 51.4, 38.6

Hint: Order the numbers from least to greatest first!







A. 48.4 B. 43.6 C. 45
2. Each of the five math teachers are comparing the number of students in their homeroom classes. The number of boys and girls in each teachers’ classes are recorded in the table below.

Hint: Mean is the average.








Which statement best describes the means of the two sets of data?

A. The mean number of girls in 7 times greater than the mean numbers of boys in the homeroom classes.


B. The mean number of girls is the same as the mean number of bboys in the homeroom classes.

C. The mean number of girls is 7 more than the mean number of boys in the homeroom classes.

Answer:

For this case the amplitude is given by:

A = (l-1l + 3) / 2

A = 4/2

A = 2

The middle line is given by:

y = 1

The period of the function is given by:

T = l x2 - x1 l

T = l 0 - 2pi l

T = l - 2pi l

T = 2pi

Answer:

Amplitude: 2; period: 2π; midline: y = 1

Step-by-step explanation:

Answer:

It is D

Step-by-step explanation:

Answer:

Amplitude: 1; midline: y = 1

Step-by-step explanation:

From the graph we can conclude that it is a sine or cosine function. In their standard form, these functions are given by the following equations:

[tex]y(t)=Acos(\omega t +\phi)\\\\or\\\\y(t)=Asin(\omega t+ \phi)[/tex]

Where:

[tex]A=Amplitude=\frac{|A_m_i_n-A_m_a_x|}{2}\\\omega=Angular\hspace{3}frequency\\\phi=Initial \hspace{3}phase[/tex]

And:

[tex]A_m_a_x=Maximum\hspace{3}amplitude\\A_m_i_n=Minimum\hspace{3}amplitude[/tex]

On the other hand, we can define the midline of these kind of functions as the halfway between the maximum and minimum amplitude of the function, Therefore:

[tex]Midline=M_l=\frac{A_m_a_x+A_m_i_n}{2}[/tex]

From the graph you can see that the maximum value of the function(maximum amplitude) is 2 and the minimum value of the function (minimum amplitude) is 0, thus:

[tex]A=\frac{|A_m_i_n-A_m_a_x|}{2} =\frac{|0-2|}{2} =\frac{|-2|}{2} =\frac{2}{2} =1[/tex]

And:

[tex]M_l=\frac{A_m_a_x+A_m_i_n}{2}=\frac{2+0}{2} =\frac{2}{2} =1[/tex]

Answer:

a

Step-by-step explanation:

The statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.

A box plot shows how a data is distributed, as it displays the five-number summary.

here, we have,

The five-number summary of the box plot representing the average age of children is:

Min = 6 (youngest age)

Lower quartile (Q1) = 9 (25% of the children are below 9)

Median = 10

Upper quartile = 11 (50%, which is half of the children are between 9 years and 11 years old)

Max = 12 (oldest)

Therefore, the statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.

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The balance in the account after 7 years will be approximately $2,747.70.

To calculate the balance in the account after 7 years with a principal of $2,400 earning 2% interest compounded annually, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the principal amount ($2,400)

r = the annual interest rate (2% or 0.02 as a decimal)

n = the number of times the interest is compounded per year (annually, so n = 1)

t = the number of years (7 years)

Plug these values into the formula:

A = 2400(1 + 0.02/1)^(1*7)

A = 2400(1 + 0.02)⁷

A = 2400(1.02)⁷

A = 2400(1.144877)

A ≈ $2,747.70

So, the balance in the account after 7 years will be approximately $2,747.70.

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The correct answer is:

False.

Explanation:

Using the five number summary, we can estimate the standard deviation.

The quartiles are about 0.67 standard deviations from the mean; this could be used to estimate the standard deviation.

However, we cannot accurately calculate the standard deviation using only the fie number summary.

The formula for surface area of the sphere is -

Surface area of sphere = 4πr²

Now, the surface area of sphere is given to us as = 256π cm²

Thus,

4πr² = 256π cm²

While equating the equations, we will get

4r² = 256 cm²

r² = 64 cm²

64 is the square of 8, thus the radius of sphere will be = 8 cm.

The correct answer will be = 8 cm radius

Answer:

The number is 3 and the another number is 9

Step-by-step explanation:

Let

x-------> the number

y-----> another number

we know that

[tex]y=x+6[/tex] ----> equation A

[tex]\sqrt{y}=x[/tex] ----> equation B

Substitute equation A in equation B

[tex]\sqrt{x+6}=x[/tex]

squared both sides

[tex]x+6=x^{2} \\x^{2}-x-6=0[/tex]

Using a graphing tool

solve the quadratic equation

see the attached figure

The solution is  x=3

Find the value of y

[tex]y=x+6[/tex] -------> [tex]y=3+6=9[/tex]

In the parallelogram QRST then measure of  ∠Q is 62 degrees.

A quadrilateral is a four-sided polygon, having four edges and four corners.

Given that  QRST is a parallelogram.

We have to find the measure of ∠Q.

Both pairs of opposite sides are parallel, quadrilateral QRST is a parallelogram.

∠Q= ∠S

4x+10=5x-3

We have to find the value of to find ∠Q measure.

10+3=5x-4x

13=x

Now let us plug in the value of x in ∠Q measure.

∠Q = 4x+10

Now plug in x value in ∠Q

∠Q = 4(13)+10

=52+10

=62 degrees

Hence, in the parallelogram QRST then measure of  ∠Q is 62 degrees.

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Explaining how to determine the symmetry of a polar graph based on the given equation r = 5 + 4 cos θ.

To determine the symmetry of the graph r = 5 + 4 cos θ, we can substitute (-θ) for θ in the equation and check if the resulting polar equation remains the same, indicating symmetry about the origin.

If replacing (-θ) gives us the same equation, the graph is symmetric about the y-axis. If replacing (π - θ) gives the same equation, then the graph is symmetric about the x-axis.

In this case, replacing (-θ) in r = 5 + 4 cos θ gives r = 5 + 4 cos(-θ), which simplifies to r = 5 + 4 cos θ, indicating symmetry about the y-axis.

Answer:

B. (x+4)(x+i)(x-i)

Step-by-step explanation:

Let [tex]P(x)=x^3-4x^2+x-4[/tex]

We can factor this polynomial by grouping:

[tex]P(x)=x^2(x-4)+1(x-4)[/tex]

We factor further to obtain:

[tex]P(x)=(x^2+1)(x-4)[/tex]

[tex]P(x)=(x^2-\sqrt{-1}^2)(x-4)[/tex]

We apply difference of two squares to get:

[tex]P(x)=(x-i)(x+i)(x-4)[/tex]

Answer:

(x+1)(x-1)(x+4)

Step-by-step explanation:

Distance walked = 85.088 feet

The distance Sina walked would be equal to the length of the diagonal of rectangle.

As every angle in a rectangle is 90 degree. So, we can apply Pythagoras theorem in right triangle formed by sides,

Base- 74 feet, Altitude-  42 feet and Hypotenuse- Diagonal

Base^2 + Altitude ^ 2 = Hypotenuse ^2

74^2 + 42 ^ 2 = Diagonal ^2

On solving,

Diagonal = 85.088 feet

To calculate the distance Sina walked diagonally across the basketball court, we utilize the Pythagorean theorem using the court's length and width. The calculation gives us a diagonal distance of approximately 85 feet.

To calculate the distance Sina walked across the rectangular basketball court diagonally, we can use the Pythagorean theorem. This theorem states that in a 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. Since the court is 74 feet long and 42 feet wide, these dimensions can be considered the two shorter sides of a right triangle, with the diagonal Sina walked being the hypotenuse.

The Pythagorean theorem formula is:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Substituting the known values:

[tex]c^2 = 742 + 422\\c^2 = 5476 + 1764\\c^2 = 7240[/tex]

To find c, we take the square root of 7240:

c ≈ 85.09 feet

Therefore, Sina walked approximately 85 feet diagonally across the basketball court.