Find the range of the data.

Answer:

a) z-distribution is used, as we have the standard deviation for the population.

b) Between [tex]\overline{x} - 1.86[/tex] and [tex]\overline{x} + 1.86[/tex], in which [tex]\overline{x}[/tex] is the sample mean of tics per hour.

Step-by-step explanation:

a. To compute the confidence interval use a, z or t distribution?

We have the standard deviation for the population, and thus, the z-distribution is used.

b. With 90% confidence the population mean number of tics per hour that children with Tourette syndrome exhibit is between ______ and _______ .

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{4.08}{\sqrt{13}} = 1.86[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is [tex]\overline{x} - 1.86[/tex]

The upper end of the interval is the sample mean added to M. So it is [tex]\overline{x} + 1.86[/tex]

Between [tex]\overline{x} - 1.86[/tex] and [tex]\overline{x} + 1.86[/tex], in which [tex]\overline{x}[/tex] is the sample mean of tics per hour.

Answer:

12 [tex]x[/tex]

Step-by-step explanation:

8 divided by two-thirds of x is

⇒ 8/2/3 × [tex]x[/tex]

⇒ 8 × (3/2) [tex]x[/tex]

⇒ 8×3 [tex]x[/tex] / 2

⇒ 24 [tex]x[/tex]/ 2

∴ 12 [tex]x[/tex]

Answer:

17.6369809748oz

Step-by-step explanation:

hope this helps

Answer:

17.637

Step-by-step explanation:

Answer: 128.5km

Step-by-step explanation:

Since we are given the information that the distance by road from town A to town B is 257 km. To get 50% of the distance, we simply have to multiply the distance given by 50%. This will be:

= 50% × 257km

= 50/100 × 257km

= 0.5 × 257km

= 128.5km

Therefore, 50% of the distance is 128.5km.

Answer:

The scale factor is k = 4.

Step-by-step explanation:

In the graph, we can see that g(x) is a dilation from f(x)

And a general vertical dilation of scale factor k is written as:

g(x) = k*f(x)

So here we want to find the value of k.

In the graph, we can see that:

f(1) = 1.5

f(3) = 0.5

Now, the values of g(x) in those x-values are:

g(1) = 6

g(3) = 2

And we must have:

g(1) = k*f(1)

g(3) = k*f(3)

we should get the same value of k in both equations, now let's replace the values of the functions:

For the ones evaluated in x = 1, we get:

6 = k*1.5

6/1.5 = k = 4

for the cases evaluated in x = 3, we get:

2 = k*0.5

2/0.5 = k = 4

In both cases we got the same value of k, so we can conclude that the scale factor from f(x) into g(x) is k = 4

Answer:

(3, -1)

Step-by-step explanation:

(3,-1)

I think this is the answer hope it helps!!

Answer:

23/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify and set up

4 + -2 ÷ -3 + 3

Step 2: Evaluate

Answer:

The maximum height the soccer ball reaches is 9.77 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

Reba kicks a soccer ball off the ground and in the air, with an initial velocity of 25 feet per second.

The formula for the height is:

[tex]h(t) = -16t^2 + v(0)t + h(0)[/tex]

In which v(0) is the initial velocity and s(0) is the initial height.

Initial velocity of 25 feet per second means that [tex]v(0) = 25[/tex]

Kicked off the ground means that [tex]h(0) = 0[/tex]. So

[tex]h(t) = -16t^2 + 25t[/tex]

Which is a quadratic equation with [tex]a = -16, b = 25, c = 0[/tex].

The maximum value is:

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

In which

[tex]\Delta = b^2-4ac = 25^2 - 4(-16)(0) = 625[/tex]

[tex]y_{v} = -\frac{\Delta}{4a} = \frac{625}{4(16)} = 9.77[/tex]

The maximum height the soccer ball reaches is 9.77 feet.

Answer:

110 and 100

Step-by-step explanation:

Angle 2 will have the same messurement as the one across, so 110

Angle 1 will be the difference between 180 and 80, so 100

Answer:

x = 43.4°

Step-by-step explanation:

when two straight line intersects, angles directly opposite of each other has the same value.

Answer:

Tangent

Step-by-step explanation:

Tangent - A line that intersects the circle at exactly one place

Answer:

perimeter for rectangle: (x-2+x+2)×2=4x

perimeter for triangle : 2x-8+2x-8+x+6

=5x-10

The question said both geometry has same perimeter,so we have equation :

4x=5x-10

=>x= 10

put x in triangle's perimeter: 2×10-8+2×10-8+10+6

= 40

Step-by-step explanation:

the answer is C, hope you understand it

Answer:

A. The three angle bisectors of the angles of a triangle meet in a single point, called the incenter .

B. All triangles have three medians, which, when drawn, will intersect at one point in the interior of the triangle called the centroid

C. A point where three or more lines intersect is called a point of concurrency.

D. The three altitudes of a triangle intersect at the orthocenter,

Answer:

A. Weather conditions

Step-by-step explanation:

Answer: d

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

check below :)

Step-by-step explanation:

first, make a table of values

then graph each value and see where do they connect. if they dont connect there is no solution

the point where they connect is the solution to the system

for number 3 the solution is (3,2)

for number 4 its (-6.5, -2.5)

Answer:

Above is correct

Step-by-step explanation:

Answer:

We will begin with the graph of the tangent function, plotting points as we did for the sine and cosine functions. Recall that

tan

x

=

sin

x

cos

x

The period of the tangent function is π because the graph repeats itself on intervals of kπ where k is a constant. If we graph the tangent function on

−

π

2

to

π

2

, we can see the behavior of the graph on one complete cycle. If we look at any larger interval, we will see that the characteristics of the graph repeat.

We can determine whether tangent is an odd or even function by using the definition of tangent.

tan

(

−

x

)

=

sin

(

−

x

)

Step-by-step explanation:

Answer:

it is y=sin x

Step-by-step explanation:

i got it right on the test

Answer:

A

Step-by-step explanation:

-8 + (-10) = -8 -10

Answer:

Step-by-step explanation:

angle 3 and angle 4 are co interior angles.so,

angle 3+angle 4=180 degree

sum of co interior angle is always 180 degree.

Answer: Angle 3 and 5 = 180° because consecutive angles formed by parallel lines are supplementary

Step-by-step explanation:

It should be noted that Angle 3 and 5 = 180° because consecutive angles formed by parallel lines are supplementary.

For example, if angle 3 is 60°, the value of angle 5 will be:

= 180° - 60°

= 120°

Step-by-step explanation:

draw the net

there are 3 squares, each with a L = 5m and W = 1.5 +1.5m

2 triangles with a base of 1.5 + 1.5 and a height of 2.6m

Area of a rectangle = L x W

" " Triangle = 0.5 x b x h

so youd write and solve 3 rectangles x ( 5 m x 1.5 + 1.5) + 2 triangles x (0.5 x (1.5 +1.5) x 2.6m)

also look up the equation for surface area for this shape. Should give you the same thing. This method makes it more intuitive

Answer:

326.56 in².

Step-by-step explanation:

Mathematics: Define/explain.

SURFACE AREA: The measure of the total area that an object occupies.

The formula for finding the surface area for a cylinder is:

[tex]SA=2\pi r^2+2\pi rh[/tex]

[tex]r-radius[/tex]

[tex]h-height[/tex]

Mathematics: Solve.

According to the image, the cylinder has a height of 9 inches and a base radius of 4 inches.

Now, we can plug the numbers into the formula.

[tex]SA=2\pi 4^2+2\pi4*9- (2*3.14*4*4)+(2*3.14*4*9)=326.56.[/tex]

Mathematics: Conclude.

Therefore, the surface area of this cylinder is 356.56 in².

Answer:

The zeroes are at (-2, 0), (0, 0) and (2, 0).

The (0, 0) is a double root as the graph just touches the x axis at (0, 0).

The zero at (0, 0) is sometimes referred as  x = 0 (multiplicity 2).

I think the duplicate roots are counted as 2 distinct roots but im not sure.

So the answer is either a or c.

Step-by-step explanation:

The zeroes are the points where the graph cuts the x axis.

Answer:

a

Step-by-step explanation:

Answer:

B. 1 6/10

Step-by-step explanation:

”How many more” means find the difference.
So first you convert the fractions:

5 7/10= 57/10

7 3/10=73/10

Subtract the two converted fractions and you get a difference of 16/10 then you will simply 16/10, which becomes 1 6/10.

the answer is I don't know