1 - Determine whether the given function is even, odd, or neither.a. [tex]f(x) = x ^{3} \times x ^{2} - 4[/tex]b. [tex]f(x) = 4x^{2} + x^{4} [/tex]2 - Evaluate the piece wise function at the given value of the independent variable. (picture)

The distance between two points (a,b) and (c,d) is given by

Here u = (-1,6) and v=(-9,6)

Hence the distance is given by

The balance due on the note at the date of maturity is $1012.49

Given,

Principal  = $2000

Int rate(r) = 5%

Effective date April 1

The partial payment date May 1

Maturity date June 1

partial payment is being made on May 1

Interest from April 1 to May 1 for 30 days and is calculated as:

$2000 x 0.05 x (30/365) = $8.21

Interest Amount deducted from the principal = $2000 - $8.21 = $1991.79

Amount applied to the principal = $1000 - $8.21 = $991.79

Principal  due = $2000 - $991.79 =$1008.21

Interest on new principal $1008.215 will be for (61` - 30 ) is 31 days

interest due = $1008.21 x 0.05 x (31/365) = $4.28

Account due on maturity (Total due) is $1012.49

The principal is the amount of  debt originally borrowed that  remains unpaid. This amount does not include accrued unpaid interest related to the debt. The term can also refer to a principal participant in a contract or other  transaction. Home loan equity is the amount of money originally borrowed by the lender, and  it can also refer to the amount of money remaining when the loan is paid off.

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Is HALLOW is double consonant. Yes, HALLOW is double consonant.

Given that,

We have to prove is HALLOW is double consonant.

What is double consonant?

A double consonant is a term that contains two consecutive consonant letters. For instance, the double consonant "nn" in tunnel. Words with a suffix, like "beginning," are usually found to have double consonants.

In conclusion, if a word has:

Syllable count: 2

Vowel one is short.

between each vowel, only one consonant sound is made.

Double that consonant after that! Like any other spelling rule in English literacy, this spelling strategy should be taught to pupils to help them learn how to double consonants together with other rules.

Here,

In hallow there is "ll"

Therefore, HALLOW is double consonant.

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The function has an even degree if the the number of turns is an odd number.

The function has a negative leading coefficient if the behavior of the graph goes to the negative infinity.

From the choices, only this graph satisfied the conditions.

The graph has 3 turns (an odd number)

and it goes to the negative infinity.

0.6 is a decimal and it can be converted to fraction by moving the dot to the right sides and dividing by the number of zero that existed by the dot movement to the right.

The percentage of her adult height has a girl attained at age 12 is 94.39 %

The percentage of adult height attained by a girl who is x years old can be modeled by

f(x) = 61 + 35 log (x - 3)

where x represents the girl's age and f(x) represents the percentage of her adult height.

The percentage of her adult height a girl attained at age 12

f(12) = 61 + 35 log (12 -3) = 61 + 35 log 9

f(12) = 61 + 35 *0.954 = 94.39

Now, f(12) = 94.39 %

The logarithmic function used to model the percentage of adult height attained by a girl from ages 5 to 15, inclusive, Height increases rapidly at a young age and then increases more slowly.

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We are given the following word problem.

"The difference of b and 2 is less than 25"

Let us convert t

We will write it as follows:

Answer:

Either B or D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the general form of the absolute value function is

y = a | x - h | + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (2, 3 ) then

y = a | x - 2 | + 3

to find a substitute any other point on the graph into the equation

using (1, - 1 ) , then

- 1 = a | 1 - 2 | + 3

- 1 = a | - 1 | + 3

- 1 = a + 3 ( subtract 3 from both sides )

- 4 = a

then

f(x) = - 4 | x - 2 | + 3

The remaining area of the cream cheese pack will be 255.9 cm³.

The volume of a cylinder is -

V = πr²h

Given is a packet has an internal diameter of 14cm and and internal depth of 2cm internally.

The volume of the cream cheese pack will be -

V[C] =  πr²h

V[C] =  π(d/2)²h

V[C] = 3.14 x 7 x 7 x 2

V[C] = 307.2

For six equal sectors, the volume of each sector = 307.2/6 = 51.3 cm³.

Remaining volume = 307.2 - 51.3 = 255.9 cm³

Therefore, the remaining area of the cream cheese pack will be 255.9 cm³.

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1) Examining this rational equation. And then solving it.

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

3/4x-3/4-1/2=2-6x

2)Combining like terms, let's isolate the x terms on the left side

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

3)To add these fractions let's calculate the Least Common Multiple of the denominators:

27/4x -5/4=2+0

27/4x -5/4+5/4=2+5/4

27/4x=13/4 Multiplying both sides by four to eliminate the fraction.

27x=13 Dividing both sides by 13 to get the value of x

x =13/27

S={13/27}

2) For those 2 equations there was a single solution for x. We can say that there is one solution to these equations.

A way to pinpoint a point's location on the planet is through the use of a coordinate system. In most coordinate systems, a point's location is determined by two numbers called a coordinate. Each of these values represents the separation between the point and the origin, a fixed point of reference.

A two-dimensional number line, such as two perpendicular axes, can be thought of as a coordinate system.

The x-axis stands for the horizontal axis, and the y-axis for the vertical axis.

A coordinate system's origin is its centre (in which the lines intersect). The axes cross if x and y are both 0.

The coordinates of the origin are (0, 0).

for the posed query.

"English score" is one of the independent variables on the x-axis.

The dependent variables "History score" are displayed on the y-axis.

The scattered points are used to plot the graph for the provided table.

Take note of these two points on the graph:

(x₁, y₁) = (60, 65) (60, 65)

(x₂, y₂) = (61, 61) (61, 61)

The slope will then be;

m = (y2 - y1)/(x2 - x1) is the slope.

the values in.

m = (61 - 65)/(61 - 60) (61 - 60)

m = -4

The slope is -4.

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If x is the number of 30 days period, the cost of gift cards after x days unused is,

And for the second gift card:

The equation for x is,

Solve the equation for x.

So after 20 unused days, the value of cards are equal.

(b)

Substitute 20 for x in equation 95 - 4x to determine the value of the card.

So the value of cards, when they are equal, is $15.

We were given the following information:

Sample of men = 80, 45% of the sample owned cats (36 men owned cats)

Sample of women = 80, 55% of the sample owned cats (68.75 women owned cats)

The significance level is 0.025

We will calculate the test statistics as shown below:

The function for the cost C(x) of printing the newsletter is :

C(x) = 75 + 0.25x

In this question, we have been given the cost of producing a newsletter is an initial charge of $75 for formatting and editing plus $0.25 for printing each copy.

We need to express the cost C(x) of printing the newsletter as a function of x i.e., the number of copies printed.

Here $75 is the fixed cost.

And the cost of printing 'x' copies would be 0.25x

So, we get a function C(x) = 75 + 0.25x

Therefore, the function for the cost C(x) of printing the newsletter is :

C(x) = 75 + 0.25x

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Confidence interval is written as

Sample proportion +/- margin of error

The formula for determining margin of error is

where

z represents the z score corresponding to the confidence interval

p represents the sample proportion. It also means the probability of success

q represents the probability of failure

q = 1 - p

p = x/n

where

n represents the number of samples

x represents the number of success

From the information given,

n = 325

x = 260

p = 260/325 = 0.8

q = 1 - p = 1 - 0.8 = 0.2

To determine the z score, we would subtract the confidence level from 100 to get alpha, a

Thus

a = 1 - 0.99 = 0.01

a/2 = 0.01/2 = 0.005

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.005 = 0.995

The z score corresponding to the area on the z scores table is 2.576. Thus, the z score for a 99% confidence interval is 2.576

Thus, the 99% confidence interval is

Thus,

the lower limit is

0.8 - 0.057 = 0.743

the upper limit is

0.8 + 0.057 = 0.857

Answer:

Interval notation:

Set-builder notation:

Plot of the solution:

Step-by-step explanation:

First, let's put the solution of the inequality into simpler words. We're looking for values of x that are between 5 and 8, including 5 and excluding 8.

This way, the interval notation for the solution is:

As a set, we would read the solution as: "The set of all x's, such that x is greater or equal than -5 and less than 8 than 0". In set builder notation, this is:

The plot of the inequality would be:

Where the full end represents a square bracket and the empty end represents a parentheses.

Answer:

712 = 360944128

20 = 8000

25 = 15625

27 = 19683

Step-by-step explanation:

A cube number is a number that is the product of three numbers which are the same. In other words, if you multiply a number by itself and then by itself again, the result is a cube number.

Answer:

$3.5

Explanation:

Let the cost of 1 kg of apples = x

Let the cost of 1 kg of bananas​ =y

Claire bought 5 kg of apples and 2 kg of bananas and paid altogether $22.

Dale bought 4 kg of apples and 6 kg of bananas and paid altogether $33.

We set up the system of linear equations as a matrix below:

We then solve for the variables x and y as follows.

We proceed to simplify further.

Therefore:

x=3 and y=3.5.

The cost of 1 kg of bananas​ is $3.5.

The volume of the steel after the hole is cut is 32inches³.

The total weight of the drawing is 960 oz

The volume of the shape that is being drawn is the difference in the volume of the rectangle and the volume of the hole. Th volume of an object is the amount of space that is in the object.

A rectangular prism is a three dimensional object that has 6 faces, 12 edges and 8 vertices.

Volume of a rectangular prism = length x width x height

3.77 x 9.32 x 1 = 35.14 inches³

The shape of the hole would be a cylinder. Thus, the formula for the volume of a cylinder would be used to determine the volume of the hole.

Volume of a cylinder = πr²h

Where:

3.14 x 1² x 1 = 3.14 inches³

Volume of the steel after the hole is cut = 35.14 inches³ - 3.14 inches³ = 32inches³.

Total weight of the drawing = 32 inches x 30 = 960 oz

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Answer:

48.214 bars

Step-by-step explanation:

112.5 hars * (150 bars / 350 hars) = 48.214 bars

To determine the area of the shaded region we first need to calculate the area of the whole circle, then we need to calculate the area of the circular sector of 60º, then finally we will calculate the area of the triangle and subtract the area of the triangle from the area of the circular sector, this will be the area of the part that isn't painted. Finally we can subtract the area that isn't painted by the area of the circle to determine the shaded region.

To calculate the area of the circle we will do as follows:

The circular sector can be calculated by the following expression:

All of the sides of the triangle are equal, so we can use the following expression:

Now we will subtract the area of the triangle from the area of the sector to determine the area that isn't shaded.

To finish we will subtract the area that isn't shaded from the area of the circle.

The area of the shaded region is 67.6 cm²

4 sheets of paper cost's $14 how much will with be for 11 1/2 sheets of paper?

we have that

Applying proportion

14/4=x/11 1/2

Convert 11 1/2 to an improper fraction

11 1/2=23/2

substitute

14/4=x/(23/2)

x=(23/2)*(14/4)

x=$40.25

therefore

teh answer is $40.25

For this problem we know that the salary per week is 500 and he gets a commission of 4% for each sale over 800. During one week the total sales are 1330 and we want to estimate the gross earnings for the week.

Taking in count the info given we can set up the following equation for the total amount recieved:

Where A represent the amount recieved and S the sales. For this case S=1330 and replacing we got:

Hello there. To solve this question, we'll have to remember some properties about polynomials.

We want to express the following 3rd degree polynomial as a product of linear factors:

Knowing that -1 is a zero.

For this, there are two ways of determining the other roots and hence the linear factors.

Remember that a polynomial is written as a product of linear factors if

Where x1, x2 ... are the roots of the polynomial.

It is also called the canonical form of the polynomial.

First way: divide g(x) by (x - (-1)), that is (x + 1)

We'll use the long division method for polynomials:

At the top of x + 1 in the diagram below, we add the terms that, when multiplied by the bottom expression, gives us a term that can be subtracted from g(x).

We have a x³ factor, so we want to multiply it first by x² in order to cancel out:

Now we have a -4x² factor, so we multiply it by -4x in order to cancel out:

Finally, multiply it by a 29 in order to cancel the first 29x term:

Hence we say that

Now, we want to factorize the quadratic expression in the right hand side, writing it as a product of linear factors as well:

As said before, we can take the roots of the expression and write it in canonical form. Since it is a quadratic expression, we have this easier formula to find the roots:

Plugging a = 1, b = -4 and c = 29, we'll get

Notice the radical is a negative number, hence it cannot be factored in terms of real linear factors.

We say that for an expression

It is not reducible over R (real numbers) if

Therefore the final answer is:

We could also use the following method to find this answer:

It is called the Horner-Ruffini method, that we dispose the coefficients and the roots in the following manner

Multiply the first coefficient by the root and add it to the second number in the line. Repeat the process until you reach the last number.

Therefore the result of this division is the polynomial:

As we found before.

Given the definitions of

blocking is the arranging of experimental units in groups (blocks) that are similar to one another

replication experiment is typically performed by obtaining test results on 20 samples of the same material and then calculating the mean, standard deviation, and coefficient of variation

randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects

in Control Experiment all variable factors have been kept constant and which is used as a standard of comparison to the experimental component in a controlled experiment

since

the sampling group could be either in group a or b (aspirin or placebo)

this expample is a blocking experiment

Correct answer

option A

Answer:

The linear equation is;

Explanation:

Given that the function f(x) is a linear function;

let us derive the values of m and b.

At x=-1, f(-1)=-3;

At x=2, f(2)=6;

subtract equation 1 from 2;

let's substitute the value of m into equation 2;

Therefore, since we have the values of m and b we can substitute to get the equation f(x);

The linear equation is;