A. Create two subsets of the state population data: one with 2018 population greater than or equal to 5 million and one with 2018 population less than 5 million. How many observations are in each subset?

The expression [tex]log(x^4)[/tex] can be expanded as a constant multiple of log(x).

What is the logarithms?

A logarithm is a mathematical function that measures the number of times a given value (called the base) must be multiplied by itself to produce a specified value.

We can use the following properties of logarithms to expand the expression:

The expression [tex]log(x^4[/tex]) can be expanded using the following property of logarithms:

[tex]log(a^n) = n * log(a)[/tex]

Using this property, we can write:

[tex]log(x^4) = 4 * log(x)[/tex]

Hence, the expression [tex]log(x^4)[/tex] can be expanded as a constant multiple of log(x).

To learn more about logarithms, Visit

https://brainly.com/question/25710806

#SPJ1

The amount we would have after 40 years will be $8183.27

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given that, an amount increasing exponentially every two years and with a rate of 15% and the amount is $500, we need to find the amount we would have after 40 years.

Since, the amount is increasing exponentially every two years, therefore,

T = 40 / 2 = 20 years

A = P(1+0.15)²⁰

A = 500(1+0.15)²⁰

A = 500(1.15)²⁰

A = 8183.27

Hence, the amount we would have after 40 years will be $8183.27

Learn more about exponential growth click;

https://brainly.com/question/12490064

#SPJ1

a) approximately 7.64% of all bags sold are underweight.

b)  the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

a) To find the fraction of all bags sold that are underweight, we need to find the area under the normal distribution curve to the left of 5 ounces. Using the standard normal distribution, we can calculate the z-score:

z = (5 - 5.1) / 0.07 = -1.43

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -1.43 is 0.0764. Therefore, approximately 7.64% of all bags sold are underweight.

b) To find the probability that none of the 5 bags in a bargain pack is underweight, we need to find the probability that each individual bag is not underweight. Using the result from part (a), the probability that one bag is underweight is approximately 0.0764. Therefore, the probability that none of the 5 bags is underweight is:

(1 - 0.0764)⁵ = 0.5595

Rounding to four decimal places, the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) To find the probability that the mean weight of the 5 bags is below the stated amount of 5 ounces, we need to use the sampling distribution of the mean. The mean of the sampling distribution is the same as the population mean, 5.1 ounces. The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size:

s = 0.07 / √(5) = 0.0313

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0313

= -3.19

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -3.19 is approximately 0.0007.

Therefore, the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) To find the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces, we need to use the sampling distribution of the mean again. The mean of the sampling distribution is still 5.1 ounces. The standard deviation of the sampling distribution is:

s = 0.07 / √(20)

= 0.0157

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0157
= -6.37

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -6.37 is essentially 0.

Therefore, the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

Learn more about mean weight  at:

https://brainly.com/question/15198706

#SPJ1

Answer:

When a car turns, the tire on the outside of the turn has to travel a greater distance than the tire on the inside of the turn. The difference in the distance traveled by the two tires is equal to the circumference of the circle that the car makes during the turn.

The radius of the circle is given as 16.1 ft, which means the diameter is 2 * 16.1 = 32.2 ft. The distance between the two front tires is given as 4.7 ft, which means that the radius of the circle traced by the inner tire is 16.1 - 2.35 = 13.75 ft, where 2.35 ft is half of the distance between the two front tires.

The circumference of the circle traced by the outer tire is 2 * π * 16.1 = 101.366 ft (rounded to three decimal places). The circumference of the circle traced by the inner tire is 2 * π * 13.75 = 86.415 ft (rounded to three decimal places).

The difference in the distance traveled by the two tires is:

101.366 - 86.415 = 14.951 ft (rounded to three decimal places)

Therefore, the tire on the outside of the turn travels about 14.951 ft further than the tire on the inside.

Step-by-step explanation:

3 - (1/4)×(8/3 × 9)

3 - (1/4)×(8×9/3)

3 - (1/4)×(8×3)

3 - (1/4)×24

3 - 24/4

3 - 6 = -3

The equation 4(x - 2) = 2(2x + 6) has no solution.

To solve the equation 4(x - 2) = 2(2x + 6), we must first use the distributive property to expand the equations. The distributive property states that a(b + c) = ab + ac.

Using the distributive property, we can expand the equation as follows:

4(x - 2) = 2(2x + 6)

4x - 8 = 4x + 12

Next, we must isolate the variable on one side of the equation. We can do this by subtracting 4x from both sides of the equation:

-8 = 12

This equation is not true, so there is no solution to the equation 4(x - 2) = 2(2x + 6).

In conclusion, the equation 4(x - 2) = 2(2x + 6) has no solution.

Learn more about Distributive property

brainly.com/question/5637942

#SPJ11

Answer: EF, DF, DE

Step-by-step explanation:

The smaller the opposite angle, the smaller the side, and vice versa.

∠EDF = 85°

∠DEF = 60° (Because the total degrees in a triangle must be 180°)

∠DFE = 35°

EF, DF, DE

Hope this helps!

2 1/8 pints

2.125 pints

Answer: 11 1/4

Step-by-step explanation:

To multiply fractions, you must use the improper form so...

2 1/4 x 5 =

9/4 x 5 =

45/4 =

11 1/4

Hope this helps!

Answer:$18

Step-by-step explanation: Since 50% is half of a hundred and the item is half off, you multiply 36 by 0.5 and get $18. This is the price of the item with the sale and the the discount

Answer:

18$

Step-by-step explanation:

go to Safari and look it up is how I got the answer

A = |λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1= 4.79 λ 2= 4.79 λ3 = 4.79, as the highest value of lif it exists is 4.79. therefore X=4.79

To find the values of λ for which det(A) = 0, we need to solve the equation det(A) = 0. The matrix determinant of a 3x3 matrix A is given by:

[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]

In this case, the matrix A is:
A = |λ-6 0 0|
   |0 λ 4|
   |0 5 λ-1|

So, the determinant of A is:
[tex]det(A) = (λ-6)(λ(λ-1) - 4*5) - 0(0(λ-1) - 4*0) + 0(0*5 - λ*0)[/tex]
Simplifying the equation, we get:
[tex]det(A) = (λ-6)(λ^2 - λ - 20)[/tex]
Setting det(A) = 0, we can find the values of λ:
[tex](λ-6)(λ^2 - λ - 20) = 0[/tex]
This equation has three solutions:
[tex]λ 1 = 6λ 2 = (-1 + √81)/2 ≈ 4.79λ 3 = (-1 - √81)/2 ≈ -5.79[/tex]

So, the answer is:
λ 1 = 6
λ 2 = 4.79
λ 3 = -5.79
The greater value of λ is λ 2 = 4.79.

To know more about determinant here:

https://brainly.com/question/4470545

#SPJ11

The polynomial that 3x^(2)-22x+26 is divided by is x - 6.

To find the polynomial that 3x^(2)-22x+26 is divided by, we can use the formula:

Dividend = Quotient * Divisor + Remainder

In this case, the dividend is 3x^(2)-22x+26, the quotient is 3x-4, and the remainder is 2. We can plug these values into the formula and solve for the divisor:

3x^(2)-22x+26 = (3x-4) * Divisor + 2

Next, we can rearrange the equation to isolate the divisor:

Divisor = (3x^(2)-22x+26 - 2) / (3x-4)

Divisor = (3x^(2)-22x+24) / (3x-4)

Now, we can use polynomial long division to find the divisor:

```
3x - 4 | 3x^2 - 22x + 24
      - (3x^2 - 4x)
      -------------
           -18x + 24
          - (-18x + 24)
          -------------
                0
```

Therefore, the divisor is x - 6.

To know more about polynomial click on below link:

https://brainly.com/question/11536910#

#SPJ11

Answer: 55 miles per hour.

To find the unit rate, divide the miles traveled by the time taken:

275 miles ÷ 5 hours = 55 miles per hour

Step-by-step explanation:

Answer: 7/2 + 7b

Step-by-step explanation:

When applying the distributive property, you want to start by identifying which value you are distributing. That value in this case will be 7/8.

7/8 is going to be multiplied with 4, then multiplied with 8b, and you will then find the sum of those to products:

( (7/8) * 4 ) + ( (7/8) * (8b) )

The first product simplified will be 7/2.

The second product simplified will be 7b.

The sum of those two products is: 7/2 + 7b.

Hope this helps.

Answer: C

Step-by-step explanation:

The x-intercept is (-3,0) and the y-intercept is (0,9).

The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.

The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.

1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.

To find the x-intercept, set the function equal to 0 and solve for x:

0 = x^2 + 6x + 9

0 = (x+3)(x+3)

x = -3

To find the y-intercept, set x equal to 0 and solve for y:

y = 0^2 + 6(0) + 9

y = 9

Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).

To know more about y-intercept  click on below link:

https://brainly.com/question/14180189#

#SPJ11

Answer:

Step-by-step explanation:

Ok so we're just going to be doing a lot of supplementary work:

The angle adjacent to 85 degrees is equal to 180 - 85 = 95

We want to find the angle measures in the triangle where 95 degrees is. We can do this by using 40, finding the opposite angle, which is also 40 due to vertical angles theorem, finding the missing angle in the right-most triangle which is 180 - 105 - 40 = 35

Using vertical angles theorem again, we know the angle opposite 35 degrees is also 35. We found another angle for the middle triangle.

The missing angle for the middle triangle is 180 - 35 - 95 = 50

The angle opposite 50 is 50 because of the vertical- you already know.

Now the left triangle has angles Z, 60 and 50.

m<Z = 180 - 60 - 50

m<Z = 70

Hope this helps!

The answer of equation for the function is y=(x-2)^(2)-1.

The equation for a function that has the shape of y=x^(2), but shifted right 2 units and down 1 unit is y=(x-2)^(2)-1.

To shift a function to the right, we subtract the amount of the shift from the x variable.

In this case, we want to shift the function 2 units to the right, so we subtract 2 from x: (x-2).

To shift a function down, we subtract the amount of the shift from the entire function.

In this case, we want to shift the function down 1 unit, so we subtract 1 from the entire function: (x-2)^(2)-1.

Therefore, the equation for the function is y=(x-2)^(2)-1.

To know more about equation for a function refer here:

https://brainly.com/question/22964920#

#SPJ11

The solutions to the given polynomial equation are x = 1/3 and x = 1.

According to the given polynomial equation f(x)=-3x^(2)+4x-1, we can find the values of x by using the quadratic formula, which is x = (-b ± √(b^(2)-4ac))/(2a).

In this equation, a = -3, b = 4, and c = -1.

Plugging these values into the quadratic formula, we get:

x = (-(4) ± √((4)^(2)-4(-3)(-1)))/(2(-3))

Simplifying this equation, we get:

x = (-4 ± √(16-12))/(-6)

x = (-4 ± √4)/(-6)

x = (-4 ± 2)/(-6)

Therefore, the two possible values of x are:

x = (-4 + 2)/(-6) = -2/(-6) = 1/3

x = (-4 - 2)/(-6) = -6/(-6) = 1

To know more about polynomial equation click on below link:

https://brainly.com/question/30127172#

#SPJ11

Answer:

Step-by-step explanation:

You want linear equations in standard form that describe the relations in the given tables.

A useful two-point formula for creating an equation in general form is ...

  (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

This will simplify to an equation of the form ...

  ax +by +c = 0 . . . . . . general form equation for a line

The corresponding standard form equation is ...

  ax +by = -c . . . . . . . . standard form equation for a line

The standard form has mutually prime coefficients and a positive leading coefficient. That may require removal of any common factors.

  (2 -(-2))(x -(-5) -(-1 -(-5))(y -(-2)) = 0

  4x +20 -4y -8 = 0 . . . . . . . . coefficients have a common factor of 4

  x -y +3 = 0 . . . . . . . . . general form

  x -y = -3 . . . . . . . . . standard form

  (12 -20)(x -(-2)) -(0 -(-2))(y -20) = 0

  -8x -16 -2y +40 = 0 . . . . . . coefficients have a common factor of -2

  4x +y -12 = 0 . . . . . . . . simplified to general form

  4x +y = 12 . . . . . . standard form

__

Additional comment

Another useful form of the equation of a line is "intercept form":

  x/a +y/b = 1 . . . . . . . where 'a' is the x-intercept and 'b' is the y-intercept

The table for line k shows the x-intercept is (3, 0) and the y-intercept is (0, 12). Then the line can be written as ...

  x/3 +y/12 = 1

Multiplying by 12 gives ...

  4x +y = 12 . . . . the required standard form

When [tex]3x^{4}-x^{2}[/tex] is divided by [tex]x^{3}-x^{2}+2[/tex], the quotient is 3x and the remainder is [tex]5x^2-2x[/tex].

To see why, we perform long division as follows:    

    [tex]3x[/tex]

[tex]x^3 - x^2 + 2 | 3x^4 + 0x^3 - x^2 + 0x + 0[/tex]

                [tex]- 3x^4 + 3x^3 - 6x^2[/tex]

               -----------------------

                            [tex]3x^3 - 7x^2[/tex]

                         [tex]- 3x^3 + 3x^2 - 6x[/tex]

                          -------------------

                                    [tex]5x^2 - 2x[/tex]

The divisor is [tex]x^3 - x^2 + 2[/tex] and the dividend is [tex]3x^4 - x^2[/tex]. We start by dividing the highest degree term of the dividend by the highest degree term of the divisor, which gives 3x. We then multiply the divisor by this quotient and subtract the result from the dividend. We repeat this process with the resulting polynomial until the degree of the remainder is less than the degree of the divisor.

In this case, the remainder is [tex]5x^2-2x[/tex], which has a degree of 2 (less than the degree of the divisor). Therefore, we have found the quotient and remainder of the division.

For more questions like Division visit the link below:

https://brainly.com/question/12011210

#SPJ11

Answer:

Step-by-step explanation: First you do 5*5 and get 25. Then you do 25/8 and get 3 1/8.

The expression to represent the length of the rectangular space is 2x - 3.

The product of the length and breadth makes up the area of a rectangular space. Area is defined mathematically as Length x Width. So, using the equation Length = Area / Width, we can determine the length of a rectangular space if we know its area and breadth. Instead, using the formula Width = Area / Length, we may determine the width of a rectangular region if we know its area and length.

Given that the width of the rectangle is 4x.

The Area of the rectangle is given as:

A = lw

Substituting the values we have:

8x² - 12x = 4x (Length)

l = 2x - 3

Hence, the expression to represent the length of the rectangular space is 2x - 3.

Learn more about area here:

https://brainly.com/question/27444262

#SPJ1

The whole number that is a solution for the inequality x ≥ 4 but is not a solution for the inequality x > 4 is 4.

Option B is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

here,

We have,

x ≥ 4 and x > 4

Now,

x ≥ 4 means that x can be 4 and greater than 4.

x > 4 mean x is greater than 4.

So,

4 is a solution to x ≥ 4 but not a solution to x > 4.

Thus,

4 is the whole number.

Learn more about inequalities here:

brainly.com/question/20383699

#SPJ1

Given trigonometric equation is equal to 2 so the it has been proved.

what is trigonometric identity?

A trigonometric identity is a mathematical equation that expresses a relationship between trigonometric functions of an angle. These identities are true for all values of the angle, and they allow us to simplify expressions involving trigonometric functions, manipulate them algebraically, or evaluate them more easily.

Trigonometric identities include basic relationships such as [tex]sin^2(x) + cos^2(x) = 1,[/tex] as well as more complex identities involving multiple functions such as the Pythagorean identity.

According to the question:
Let us begin by applying the trigonometric identity[tex]cos^2(x) + sin^2(x) = 1,[/tex]which is true for any angle x. Solving for[tex]cos^2(x)[/tex], we get [tex]cos^2(x) = 1 - sin^2(x).[/tex]

Using this identity, we can rewrite the given equation as

[tex]1 - sin^2((1/8)^2) + 1 - sin^2(3n/8) + 1 - sin^2(5n/8) + 1 - sin^2(7n/8) = 2[/tex]

Simplifying, we get:

[tex]4 - (sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8)) = 2[/tex]

Rearranging, we get:

[tex]sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8) = 2[/tex]
Now, let us apply the trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex], which is true for any angle x. Solving for [tex]sin^2(x),[/tex] we get [tex]sin^2(x) = 1 - cos^2(x)[/tex].
2=2
Therefore, the equation is true

To know more about trigonometric identities visit:
https://brainly.com/question/30396301
#SPJ1

Answer: $139.00

Step-by-step explanation: 5x11 = 55
12x7 = 84

55+84=139

Answer:

3) The commercial costs $900 to produce and $110 each times it is aired.

Step-by-step explanation:

We can determine how expensive it is to produce a commercial by looking at the function C(n)'s output when n = 0 (when the commercial hasn't been aired yet).

C(0) = 110(0) + 900

C(0) = $900

So, the cost of producing a commercial is $900.

We can see that $110 is added to the cost each time n is incremented by 1. Therefore, it costs $110 each time the commercial is aired.

We can put these two statements together to deduce that answer option 3 is correct:

The commercial costs $900 to produce and $110 each times it is aired.

Answer:

Option 3

Step-by-step explanation:

900 is a constant number that never changes. However, the value of "110n" changes every time it is aired, because 110 is multiplied by a different number. This means that $110 represents the cost of airing it each time, because if it was hypothetically aired three times, you would multiply 110 by 3, proving that it is the cost to air it, and $900 is the production cost. It also makes no sense to produce the same commercial over and over again, so the cost that is multiplied has to be the amount of times that it is aired.

The formula for the polynomial P(x) with degree 3, real coefficients, zeros at x=3-3i and x=1, and y-intercept at (0,-36) is P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

To find the formula for the polynomial, we first need to find the conjugate of the complex zero, which is 3+3i. This is because a polynomial with real coefficients must have complex zeros in conjugate pairs.

Next, we can use the factored form of a polynomial, P(x) = a(x-r1)(x-r2)(x-r3), where r1, r2, and r3 are the zeros of the polynomial and a is a constant. In this case, r1 = 1, r2 = 3-3i, and r3 = 3+3i.

Finally, we can use the y-intercept to find the value of a. When x = 0, P(x) = -36, so we can plug in the values and solve for a:
-36 = a(0-1)(0-(3-3i))(0-(3+3i))
-36 = a(-1)(-3+3i)(-3-3i)
-36 = a(9+9i-9i-9)
-36 = a(-36)
a = 4

So the formula for the polynomial is P(x) = 4(x-1)(x-(3-3i))(x-(3+3i)). However, since we want the y-intercept to be negative, we can multiply the entire polynomial by -1 to get P(x) = -4(x-1)(x-(3-3i))(x-(3+3i)).

For more such questions on Polynomial.

https://brainly.com/question/29623585#

#SPJ11

Answer:

The dilated image has half the dimensions of the pre-image

So the pre-image is dilated by a scale factor of 1/2 (0.5)

Step-by-step explanation:

The side lengths of the dilated image is related to the preimage by a division of 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where we have

Pre-Image = PQRS

Image = P''Q'R'S'

From the figure, we can see that

The side lengths of P''Q'R'S' is half of the side lengths of PQRS

This means that

(x, y) = 1/2(x, y)

Hence, the transformation is (x, y) = 1/2(x, y)

Read more about transformation at

brainly.com/question/27224272

#SPJ1