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Alex73 [517]
4 years ago
6

a set of data items is normally distributed with a mean of 210 and a standard deviation of 28. Convert 294 to a z-score

Mathematics
1 answer:
anastassius [24]4 years ago
3 0

The z-score is 3, because 294-210=84; 84/28=3

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According to the distributive property, 6 (a + b) =
lilavasa [31]
<span>6 (a + b) = 6a +  6b

answer is </span><span>B) 6a + 6b </span>
7 0
3 years ago
How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y
son4ous [18]

Solution:

Given:

x^2=6y

Part A:

The vertex of an up-down facing parabola of the form;

\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}

Rewriting the equation given;

\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\  \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\  \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\  \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\  \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}

Therefore, the focus is;

(0,\frac{3}{2})

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}

Therefore, the directrix is;

y=-\frac{3}{2}

3 0
1 year ago
A 20 foot ladder leaning against a wall is used to reach a window that is 17 feet above the ground. How far from the wall is the
GarryVolchara [31]

The bottom of the ladder is 10.5 feet away from the wall

Step-by-step explanation:

The given scenario forms a right triangle.

Where

The length of ladder will be the hypotenuse

The wall on which the window is situated will ebt he perpendicular and

The distance between the foot of ladder and the wall will be the base

So,

Hypotenuse = H = 20 foot

Perpendicular = P = 17 feet

Base = B = ?

Using the Pythagoras theorem

H^2=P^2+B^2\\(20)^2=(17)^2+B^2\\400=289+B^2\\400-289=B^2\\B^2=111\\Taking\ square\ root\ on\ both\ sides\\\sqrt{B^2}=\sqrt{111}\\B=10.53\\Rounding\ off\ to\ the\ nearest\ tenth\\B=10.5

The bottom of the ladder is 10.5 feet away from the wall

Keywords: Triangle, Pythagoras Theorem

Learn more about Pythagoras theorem at:

  • brainly.com/question/9532142
  • brainly.com/question/9590016

#LearnwithBrainly

8 0
3 years ago
In a young woman's study group, 7 percent of the students are from the town where the young woman's school is located, 80 percen
Umnica [9.8K]

Answer: the percent of study group students from outside the state is 13%

Step-by-step explanation:

The total number of students in the young woman's study group that are from the town where the young woman's school is located is 7%

The total number of students in the young woman's study group that are from in-state (but not from the school's town) is 80%.

Since the rest are from outside the state, the percent of study group students from outside the state would be

100 - (80 + 7) = 100 - 87 = 13%

5 0
3 years ago
Complete 6,7 for 5 points.
seraphim [82]

Answer:

idk the answer

Step-by-step explanation:

4 0
3 years ago
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