30. The average of a list of 4 numbers is 92.0. A new list
of 4 numbers has the same first 3 numbers as the
original list, but the fourth number in the original list
is 40, and the fourth number in the new list is 48. What
is the average of this new list of numbers?
F. 81.0
G. 92.0
H. 94.0
J. 94.4
K. 96.6

Using the z-distribution, it is found that 1068 students have to be polled to be 95% confident of the outcome within +/- 3% of the vote.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate for the true proportion, hence we use [tex]\pi = 0.5[/tex], and solve for n when M = 0.03. Then:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{(0.5)(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96(0.5)[/tex]

[tex]\sqrt{n} = \frac{1.96(0.5)}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.03}\right)^2[/tex]

n = 1067.11.

Rounding up, 1068 students have to be polled to be 95% confident of the outcome within +/- 3% of the vote.

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Answer: 60° because 23 and 25 are alternate interior angles

Step-by-step explanation:

Answer:

42 ft²

Step-by-step explanation:

You need the total surface area of the box which is shaped like a rectangular prism.

surface area = area of bases + lateral area

Let length = 3 ft, width = 2 ft, height = 3 ft.

The base is a rectangle 3 ft by 2 ft.

The perimeter of the base is 2(3 ft + 2 ft) = 10 ft

The lateral area is (perimeter of the base) × height = 10 ft × 3 ft = 30 ft²

The area of the two bases is 2 × (3 ft × 2 ft) = 12 ft²

The total surface area is 30 ft² + 12 ft² = 42 ft²

Answer: (0, -6)

Step-by-step explanation:

The center is the midpoint of the diameter, meaning that the coordinates of Y must be (0, -6).

Answ.er:

x=146°

Step-by-step explanation:

the Exterior angle theorem states the exterior angle is equal to the sum of angle 1 and angle 2.

So add 107 and 39 to get 146.

Answer:

12 seconds

Step-by-step explanation:

we need to find the Lcm which is 12
they both flash after 12 seconds

Answer:

Every 12 seconds

Step-by-step explanation:

You must find the LCM (Least common denominator)

4 x 3 = 12

Because 3 goes into 6 and 4 is four so the LCM is 12

Answer:

See the attachment.

Answer:

C

Step-by-step explanation:

The fast way: Testing the options!

Teacher loving way:

An= d×n + A0

d= A4-A3=A5-A4=A6-A5...= 6

A3= 0 = 6×3 + A0

A0= -18

Then the equation is: An= 6n - 18

Step-by-step explanation:

Formula:

(c + d i)(e + f i) = (c e - d f) + (c f + d e) i

……………………………………………………………

if c, d, e, and f are positive real numbers

then

c f + d e  is a positive number.

then

The product of the two complex numbers

lies in Quadrant 1 or Quadrant 2.

Since , c, d, e, and f are positive real numbers

Then

The two complex numbers c + d i  and  e + f i  lie in Quadrant 1

We want to find an example of two complex numbers

That lie in Quadrant 1 ,such that ,their product lies in the other possible

Quadrant, which is Quadrant 2.

EXAMPLE:

Let c + d i = 1 + i

      e + f i = 2 + 3i

By applying the formula:

(c + d i)(e + f i) = (c e - d f) + (c f + d e) i

We get :

(1 + i)(2 + 3i) = -1 + 5i

Answer:

191

Step-by-step explanation:

the rule is +4 so 11+45*4=191 (45 is the number not including the first one)

191 is the answer

Answer:

191

Step-by-step explanation:

First, determine if the sequence is arithmetic or geometric.

If it is arithmetic, the difference between consecutive terms is constant.

If it is geometric, the ratio between consecutive terms is constant.

[tex]\sf 11 \underset{+4}{\longrightarrow} 15 \underset{+4}{\longrightarrow} 19[/tex]

As we add 4 to each term to get the next term, this is an arithmetic sequence with common difference of 4.

Arithmetic sequence

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

Given:

Substituting the given values into the formula to find an equation for the nth term:

[tex]\implies a_n=11+(n-1)4[/tex]

[tex]\implies a_n=4n+7[/tex]

Therefore, to find the 46th term, substitute n = 46 into the equation:

[tex]\implies a_{46}=4(46)+7=191[/tex]

Answer:

The answer is 54.

After the reflection and the translation of XYZ, the length of segment Y'Z'  is 6 units

The transformation is given as:

Both transformations are rigid transformations.

This means that the lengths YZ and Y'Z' would remain the same

The coordinates are given as:

Y = (8,3)

Z = (2,3)

Both points are on the same y coordinate.

So, the length YZ is

YZ = 8 - 2

Evaluate

YZ = 6

Hence, the length of segment Y'Z'  is 6 units

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Answer:

(-2.5, -2) (-2, -1.5) (1.5, 2) (2, 2.5)

Step-by-step explanation:

In these intervals, the y value is decreasing.

1x1=1

1x2=2

2x3=6

6x4=24

24x5=120

120x6=720

720x7=5040

the answer is 720 and 5040

Answer:

1/2 split into 1/3 = 1/6

Answer:

8x-9

Step-by-step explanation:

You have to combine like terms in order to simplify this problem.

The like terms you have are 5x, and 3x. If you add 5x+3x, you get 8x.

Now, you do nothing with the 9 because there is nothing to combine it with. For example, if your problem was 5x+3x-9+10, you combine 5x and 3x to get 8x, but now with the 9, you keep the subtraction symbol so it is 10-9, (think of it as -9), and when you finish that, you get 1. Now there are no more symbols so you add, 8x+1.

Answer:

8×-9

Step-by-step explanation:

You have to combine like terms in order to simplify this problem.

The like terms you have are 5x, and 3x. If you add 5x+3x, you get 8x.

Now, you do nothing with the 9 because there is nothing to combine it with. For example, if your problem was 5x+3x-9+10, you combine 5x and 3x to get 8x, but now with the 9, you keep the subtraction symbol so it is 10-9, (think of it as -9), and when you finish that, you get 1. Now there are no more symbols so you add, 8x+1.

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That which is equivalent to tanθ is A sinθ/cosθ

To answer the question, we need to know what tanθ is

Tanθ is a trigonometric identity which is the tangent of the angle .

Now, from the unit circle, with radius, r = 1, we have that tanθ = y/x.

Also, the sine of the angle θ is sinθ = x/1 = x

And also, the cosine of the angle θ is cosθ = y/1 = y

Since we have that

Substituting the values of the variables y and x into tanθ, we have

tanθ = y/x

tanθ = sinθ/cosθ

So, that which is equivalent to tanθ is A sinθ/cosθ

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Answer:

2x + 4 = 20 + x

Step-by-step explanation:

X = 16

X+4 = 20

2x + 4 = 20 + x

Answer:

well the odds would be 2:3 because 1 3 5 and 7 are prime numbers so the pin might just land on one of them

Step-by-step explanation:

Answer:

( [tex]\frac{1}{4}[/tex], 8 )

Step-by-step explanation:

y = 8x + 6 → (1)

y = 32x → (2)

substitute y = 32x into (1)

32x = 8x + 6 ( subtract 8x from both sides )

24x = 6 ( divide both sides by 24 )

x = [tex]\frac{6}{24}[/tex] = [tex]\frac{1}{4}[/tex]

substitute this value into either of the 2 equations and solve for y

substituting into (2)

y = 32 × [tex]\frac{1}{4}[/tex] = 8

solution is ( [tex]\frac{1}{4}[/tex], 8 )

The value of C=1/3 for the probability density function f(x)=cx , 0<x<2.

The probability density function is a function of a continuous random variable, whose integral across an interval gives the probability that the value of the variable lies within the same interval.

Given that:

[tex]f(x)=cx\ \ at\ 0 < x < 2[/tex]

Here we can see that the value of x is varies as 0,1,2

So at 0,1,2 the value of the function is

[tex]f(1)=c\times 1=c\\\\\\f(2)=c\times 2=2c\\\\[/tex]

So the probability density function is given as:

[tex]\sum f(x)=f(1)+F(2)=1\\\\\sum f(x)=c+2c=1[/tex]

[tex]3c=1\\\\c=\dfrac{1}{3}[/tex]

Hence the value of C=1/3 for the probability density function f(x)=cx , 0<x<2.

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Answer:

Step-by-step explanation:

Area of shaded region= area of rectangle- area of triangle

Area of rectangle= l×b

                            =9×3

                            = 27m²

Area of triangle= [tex]\frac{1}{2}[/tex] b×h

                        =[tex]\frac{1}{2}[/tex] ×3×3

                        =[tex]\frac{9}{2}[/tex] ⇒4.5

Area of shaded region= area of rectangle- area of triangle

                                     =27-4.5

                                     =22.5m²

Answer:

37.68 ft

Step-by-step explanation:

Formula

Diameter = 2r  (where r is the radius)

Circumference of a circle = πd  (where d is the diameter)

Given:

⇒ Diameter = 2 × 6 = 12 ft

Substituting the given values into the formula:

⇒ C = πd

⇒ C = 3.14 × 12

⇒ C = 37.68 ft

Answer:

22.25

Step-by-step explanation:

Pythagorean theorem is a^2+b^2=c^2

a---leg                          a=17

b---leg                          b=?

c----hypotenuse          c=28

[tex]17^2+b^2=28^2\\289+b^2=784\\b^2=495\\\sqrt{b^2}=\sqrt{495}\\b = 22.25[/tex]