Write a rule for the linear function whose graph has slope m and contains the given point.

scores on the act college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6. Wayne's standar

WITCHER [35]

Answer:

His actual score is 15

Step-by-step explanation:

Here, we are interested in calculating Wayne’s actual score on the ACT

when we say the scores have being standardized, it means the score was reported in terms of the z-score and not the initial raw scores.

Now, mathematically, for the scores to have a negative z-score, it means it is actually below the mean.

The formula for the z-score or standard score is given below;

z-score = (x - mean)/SD

where in this case, x = ? which is the score we are looking for , z-score = -0.5 , mean score = 18 and standard deviation of the scores = 6

So, substituting these values into the z-score equation, we have;

-0.5 = (x-18)/6

x-18 = 6(-0.5)

x -18 = -3

x = -3 + 18

x = 15

7 0

2 years ago

Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures xStartRoot 3 EndRoot

Brums [2.3K]

The area of the shaded region is $\rm (150\sqrt{3} \ - 75\pi ) \ feet^2$ option first is correct.

It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.

It is required to find the shaded area (missing data is attached shown in the picture).

<h3>What is a circle?</h3>

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a hexagon with a side length of 10 feet.

We know the area of the hexagon is given by:

$\rm A = \frac{3\sqrt{3} }{2} a^2$ where a is the side length.

$\rm A = \frac{3\sqrt{3} }{2} 10^2$ ⇒ $150\sqrt{3}$ $\rm feet^2$

We have the shortest length = x feet and from the figure:

2x = 10

x = 5 feet

The radius of the circle r = longer leg

$\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3}$ feet

The area of the circle a = $\pi r^2$ ⇒ $\pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2$

The area of the shaded region = A - a

$\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2$

Thus, the area of the shaded region is $\rm (150\sqrt{3} \ - 75\pi ) \ feet^2$

Learn more about circle here:

brainly.com/question/11833983

7 0

1 year ago

Complete the proof for the following conjecture.

Ray Of Light [21]

Answer:

Statements Reasons

AC+CD=AD and AB+BD=AD Segment Addition Postulate

AC+CD=AB+BD Transitive/Substitution Property

AC=BD Given

BD+CD=AB+BD Substitution Property

CD=AB Subtraction Property

AB=CD Symmetric Property

Step-by-step explanation:

By segment addition postulate, we can say the following two equations:

AC+CD=AD and AB+BD=AD.

By either substitution/transitive property, you can say AC+CD=AB+BD.

You are given AC=BD, so we use substitution and write AC+CD=AB+AC.

After using subtraction property (subtracting both sides by AC), you obtain CD=AB.

By symmetric property, you may say AB=CD.

So let's write it into the 2 column-proof you have there:

Statements Reasons

AC+CD=AD and AB+BD=AD Segment Addition Postulate

AC+CD=AB+BD Transitive/Substitution Property

AC=BD Given

BD+CD=AB+BD Substitution Property

CD=AB Subtraction Property

AB=CD Symmetric Property

Properties/Postulates used:

Transitive property which says:

If a=b and b=c, then a=c.

Substitution property which says:

If a=b, then b can be substituted(replaced with) for a.

Subtraction property which says:

a=b implies a-c=b-c.

Segment Addition Postulate says:

If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.

3 0

2 years ago

Give one combination of two factors whose product is 0.24, if one of the factors is a whole number greater than 1.

Nutka1998 [239]

0.24 is an even number....so 2 will be a factor

2x = 0.24
x = 0.24 / 2
x = 0.12

so 2 factors would be 2 and 0.12.....because 2 * 0.12 = 0.24

6 0

3 years ago

Read 2 more answers

jayce runs 2 1/2 miles on monday. Each day after that, he runs the same 1 1/3 mile route every morning. His goal is to run at le

PtichkaEL [24]

Answer:

Step-by-step explanation:

6 < 2 1/2 + 1 1/3R

3 0

1 year ago