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3 years ago

Use the probability distribution graph to answer the question. P(X≤a)=0.6 What is the value of a?

2 answers:

8 0

Answer: If P(x<a) = 0.6, then the value of a will be 0.25.

In this type of problem, it is safe to assume the normal distribution unless you are told something different.

In this probability, we have to find the z-score for a that gives a probability of 0.6. You will need a normal distribution chart to do this problem. Just find the probability that is closest to 0.6 and use that z-score.

quester [9]3 years ago

7 0

the answer will be 5

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Maths functions <br> please help!

Vlad [161]

Answer:

$\textsf{1)} \quad f(x)=-x+3$

2) A = (3, 0) and C = (-3, 0)

$\textsf{3)} \quad g(x)=x^2-9$

4) AC = 6 units and OB = 9 units

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=mx+c\\g(x)=ax^2+b \end{cases}$

Given points:

H = (-1, 4)
T = (4, -1)

As points H and T lie on f(x), substitute the two points into the function to create two equations:

$\textsf{Equation 1}: \quad f(-1)=m(-1)+c=4 \implies -m+c=4$

$\textsf{Equation 2}: \quad f(4)=m(4)+c=-1 \implies 4m+c=-1$

Subtract the first equation from the second to eliminate c:

$\begin{array}{r l} 4m+c & = -1\\- \quad -m+c & = \phantom{))}4\\\cline{1-2}5m \phantom{))))}}& = -5}\end{aligned}$

Therefore m = -1.

Substitute the found value of m and one of the points into the function and solve for c:

$\implies f(4)=-1(4)+c=-1$

$\implies c=-1-(-4)=3$

Therefore the equation for function f(x) is:

$f(x)=-x+3$

Function f(x) crosses the x-axis at point A. Therefore, f(x) = 0 at point A.

To find the x-value of point A, set f(x) to zero and solve for x:

$\implies f(x)=0$

$\implies -x+3=0$

$\implies x=3$

Therefore, A = (3, 0).

As g(x) = ax² + b, its axis of symmetry is x = 0.

A parabola's axis of symmetry is the midpoint of its x-intercepts.

Therefore, if A = (3, 0) then C = (-3, 0).

Points on function g(x):

A = (3, 0)
G = (1, -8)

Substitute the points into the given function g(x) to create two equations:

$\textsf{Equation 1}: \quad g(3)=a(3)^2+b=0 \implies 9a+b=0$

$\textsf{Equation 2}: \quad g(1)=a(1)^2+b=-8 \implies a+b=-8$

Subtract the second equation from the first to eliminate b:

$\begin{array}{r l} 9a+b & = \phantom{))}0\\- \quad a+b & =-8\\\cline{1-2}8a \phantom{))))}}& = \phantom{))}8}\end{aligned}$

Therefore a = 1.

Substitute the found value of a and one of the points into the function and solve for b:

$\implies g(3)=1(3^2)+b=0$

$\implies 9+b=0\implies b=-9$

Therefore the equation for function g(x) is:

$g(x)=x^2-9$

The length AC is the difference between the x-values of points A and C.

$\implies x_A-x_C=3-(-3)=6$

Point B is the y-intercept of g(x), so when x = 0:

$\implies g(0)=(0)^2-9=-9$

Therefore, B = (0, -9).

The length OB is the difference between the y-values of the origin and point B.

$\implies y_O-y_B=0-(-9)=9$

Therefore, AC = 6 units and OB = 9 units

3 0

2 years ago

Read 2 more answers

Can somebody solve these 2 probelms for me with work?

mel-nik [20]

Answer:

Sorry I am in class latet

Step-by-step explanation:

LIVE AND LET me know if you want me to send you

3 0

3 years ago

Find an equation in point slope form that passes through the points -1,3 and 1,7 show all your work

liberstina [14]

Answer:

Step-by-step explanation:

1. Find the slope:

7 -3/ 1 + 1 = 4/2 = 2 = m

2. Find b by plugging in the m and one of the points given into y = mx + b

7 = 2 ( 1 ) + b

7 = 2 + b

5 = b

3. Write the equation using the m and the b you just found

y =2 x + 5

4 0

3 years ago

What is the slope of the line?<br> $<br> 2<br> 45<br> 6>x<br> -3

Nikitich [7]

Step-by-step explanation: i am pretty sure it is 1

4 0

4 years ago

Given a quadratic function that is reflected across the

deff fn [24]

Answer:

y=1/3 x2

Step-by-step explanation:

7 0

3 years ago