The function f(x) is a cubie function and a limited table of values is provided below. Write the equation of the cubic polynomial in standard form.

The given expression 3x + 2.5 (4x + 2) is equivalent to 13x + 5.

The given question is a polynomial in one variable. Polynomials in one variable are algebraic expressions that depend on only one variable. The given expression is also dependent only on the variable, x.

In order to find its equivalent, we need to expand it. To expand it, we multiply the terms inside the bracket with the 2.5 outside. By doing so, we will get -

= 3x + (2.5*4x) + (2.5*2)

= 3x + 10x + 5

= 13x + 5

Hence, we find out that 3x + 2.5 (4x + 2) is equivalent to 13x+5.

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Answer:C

Step-by-step explanation:

The answer is c because of the following:

-5 + 7 = 2

so 3/x= 2

we can put two in x's place and x in 2 place and get 3/2= x

If an outfit consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes, then 144 different outfits Ayden can make.

In the given question we have to find how many different outfits can ayden make.

Ayden has 6 shirts, 4 pairs of pants, 3 ties, and 2 pairs of shoes.

We have to choose outfit for interview consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes.

We have to choose 1 shirt and he has 6 shirts. So he can choose different shirts in 6 ways.

Similarly;

We have to choose 1 pair of pants and he has 4 pair of pants. So he can choose different pair of pants in 4 ways.

We have to choose 1 tie and he has 3 ties. So he can choose different ties in 3 ways.

We have to choose one pair of shoes and he has 2 pair of shoes. So he can choose different pair of shoes in 2 ways.

So the total different outfits that he select = 6*4*3*2 = 144

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The solution to this system of equations is x = 5 and y = 2.

Given:

5x + 2y = 29 and  x + 4y = 13.

on solving eq 1 - 5*eq 2:

5x + 2y - 5(x+4y) = 29  - 13*5

5x + 2y - 5x - 20y = 29 - 65

2y - 20 y = 29 - 65

-18y = -36

18y = 36

divide by 18 on both sides

18y/18 = 36/18

y = 36/18

y = 2

substitute y = 2

5x+2y =  29

5x + 2*2 = 29

5x + 4 = 29

5x = 29-4

5x = 25

divide by 5 on both sides

x = 25/5

x = 5

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Ratio is the relation between two amounts that shows the number of times one value contains within the other.

What is Ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of vegetables contains eight tomato and six carrots, the tomato-to-carrot ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of carrots to tomato is 6:8 (or 3:4), while the proportion of tomato to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive.

Solution:

Ratio is the relation between two amounts that shows the number of times one value contains within the other.

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The 5 positive integers are 3,3,4,4,16, for them mode is 3 and 4, a median is  4 and mean is 6.

The median is a middle number of sequence, more precisely when the series is shorted descending to ascending order the middle term is median.

Let the number 3 repeats m times,

The number 4 repeats n times,

and any other number is x,

Mean of series is 6, therefore,

(3m+4n+x)/5 = 6

3m+4n +x = 30

Since, mode of 5 number is 3 and 4

So, the value of m can be 2 and value of n can also be 2,

3(2) + 4(2) + x = 30

x = 30-14

x = 16

Therefore, the 5 numbers are 3,3,4,4,16

And median for this number is 4 and mean is 6.

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The expression represents a  model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres will be 28 + 14 = 7 (4 + 2). The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres.

The expression will be written as,

28 + 14 = 7 (4 + 2)

Therefore, the expression represents a  model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres will be 28 + 14 = 7 (4 + 2). The correct option is D.

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The simplified expression of the radical expression ∛54 is 3∛3

Expression:

Expression is also known as equation is the combination of number, variable and the mathematical operator.

Given,

Here we have the radical expression ∛54.

Now, we have to simplify the expression and to find the simplest form of it.

Here we have to radical expression

=> ∛54.

Now, we have to expand this equation, then we get,

=> ∛(27 x 3)

We know that the value of ∛27 = 3,

Therefore, when we apply these on the expression, then we get,

=> 3∛3.

Therefore, the simplified expression is 3∛3.

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Answer:

13 - 6(2)

Step-by-step explanation:

I found this out because, since you have to subtract the 6 from the 13, the 13 will go first:

13 -

Then, you figure out what the 6 and two times means. It means 6 x 2, or 6(2):

13 - 6(2).

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The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

Given that,

The lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

We have to find identify the container's dimensions and maximum volume.

We know that,

2(x+y)=4

x+y=2

Now,

Volume is π(x/2)²y

=π(x²/4)(2-x)

=π(f(x))

Now, volume will be maximum when f(x) will be max,

f(x)=x²/4(2-x)

f'(x)=2x(2-x)-x²

f'(x)=4x-3x²

We get,

f'(x)=0

4x-3x²=0

x(4-3x)=0

x=0, 4-3x=0

x=4/3

y value is 2-4/3=6-4/3=2/3

Therefore, The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

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The value of m from the above expression  is  - 100

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In the given expression 1/4 m + 9 = -16, the m is equal to -100.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

1/4 m + 9 = -16,

Simplify the expression to find the value of m,

1/4 m  = -16 - 9

1/4 m = -25

m = -100

The value of m for the given expression 1/4 m + 9 = -16, is -100.

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The total number of different colorings possible are c)3120.So, correct option is c.

We know very well that Probability is the defined  as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We need to take care that each vertex of convex pentagon has been assigned a color.

We are given that we can choose 6 colors , and we need to take care that the ends of each diagonal must have different colors.

So, we need to try all different combinations,

Let PQRST are the vertex of the pentagon.

Let vertex P be any vertex, then vertex Q be one of the diagonal vertices to P, R be one of the diagonal vertices to Q, and so on. We consider cases for this problem.

In the case that,

R has the same color as P,

S has a different color from P

and so,

T has a different color from P and S.

In this case, the choices are

P = 6

Q = 5

R = 1

S = 5

T = 4

So, total number of combinations are =6 x 5 x 1 x 5 x 4 = 600 combinations.

Similarly, R has a different color from P and

S has a different color from P,

In this kind of situations,

P has 6 choices,

Q has 5 choices,

R has 4 choices

S has 4 choices,

and T has 4 choices,

So, total number of combinations  is

=> 6 x 5 x 4 x 4 x 4 = 1920

Next case,  R has a different color from P and S has the same color as P, So,

P has 6 choices,

Q has 5 choices,

R has 4 choices,

S has 1 choice, and

T has 5 choices,

=> total number of combinations=6 x 5 x 4 x 1 x 5 = 600

On Adding all those combinations up, we get

=> 600 + 1920 + 600 = 3120

Hence, total colorings are c)3120.

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(Complete question) is:

Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?

A.2520 B.2880 C.3120 D.3250 E.3750

The data can be thought of as a random sample from the population of interest. So the option a is correct.

In the given question we have to find the most important condition for sound conclusions from statistical inference is usually.

The given statements are:

(a) the data can be thought of as a random sample from the population of interest.

(b) the population distribution is exactly Normal.

(c) the data contain no outliers.

The results of the hypothesis testing will still be accurate even if the population distribution is not perfectly normal, according to the Central Limit Theorem.

Statistical techniques can be used to identify and prevent outliers if the data contains them.

However, the results of the hypothesis testing will not be reliable for non-random samples.

The data can be thought of as a random sample from the population of interest. So the option a is correct.

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The right question is:

The most important condition for sound conclusions from statistical inference is usually that

(a) the data can be thought of as a random sample from the population of interest.

(b) the population distribution is exactly Normal.

(c) the data contain no outliers.

The standard deviation of X is about 2.38.

Suppose X is normally distributed with mean of 5. If P (X ≤ 3) = 0.2

We need to find the standard deviation of X

We can use a z-table or a graphing calculator to find the z-value that is associated with a probability to 0.20 (you should get a z-value of about z = -0.84). Then use the z-value formula

z = (x−μ) /σ

−0.84 = (3−5) /σ

−0.84 = −2/σ

σ = -2/-0.84

σ  = 2.38

Solving for the standard deviation ( σ ) you should get a value of about 2.38. Therefore, the standard deviation of X is about 2.38.

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The biconditional statement,

→ If a polygon is a triangle, then the polygon has exactly three sides.

→ If a polygon has exactly three sides then it is a triangle.

Given statement;

If a polygon has three sides, then it is a triangle. If a polygon is a triangle, then it has three sides.

The biconditional of the given statement is,

→ If a polygon is a triangle, then the polygon has exactly three sides.

→ If a polygon has exactly three sides then it is a triangle.

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The half life for this radioactive substance is 40.76 years

As we know that radioactive decay is a first order reaction

For first order reaction, we can write

N = [tex]N^{0}[/tex][tex]e^{-kt}[/tex]

Where N = Amount of substance at time ‘t’

N0 = Initial amount of substance

K = rate constant for first order reaction

t = time in years

Now, as per the question,

This substance is decaying at a rate of 1.7% that means 98.3% will remain after decaying.

For time t = 1 years , N/[tex]N^{0}[/tex] = 0.983

Therefore, we have

N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]

0.983 = [tex]e^{-k }[/tex]

-k = ln(0.983)

-k = -0.017

K = 0.017 [tex]year^{-1}[/tex]

Now for half life, We can write N/[tex]N^{0}[/tex] = 0.5

Therefore, N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]

              0.5 = [tex]e^{-0.017t}[/tex]

ln(0.5) = -0.017t

-0.693 = -0.017t

t = 0.693/0.017 = 40.76 years

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The value of x is 11

What is supplementary angle ?

Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.

Angles ∠1 and ∠7 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.

∠ 1 = ∠ 7

∴2x + 5 = 4x - 17

4x - 2x =17+5

 2x = 22

   x = [tex]\frac{22}{2}[/tex]

   x = 11

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We get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.

Given that,

The equation is q²+ 5/6q+---

We have to find to create a flawless quarte trinomial, finish the quadrilateral.

We know that,

Take the equation

q²+ 5/6q+---

By adding some thing we get the quadratic equation.

The missing term we add is 5/2×6

We get

q²+ 5/6q+(5/6×2)²

q²+ 5/6q+(5/12)²

We can write as

(q+5/12)²

Therefore, we get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.

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Using Expanded form formula,

the Expanded form of 1005 is { (1000×1 ) + (1×5)}.

Expanded from:

Breaks a number into its digits and expands to display the value of each digit.

For example, an extended form of 943 is

9 × 100 + 4 × 10 + 3 × 1 = 900 + 40 + 3

Find expanded form:

To write a number in expanded form:

All numbers must be displayed as the product of the number and the digit value.

we have given that,

Number = three power of ten and five = 1000+5

= 1005

Expanded from of given number is

one's place number is 5 and its expanded

from 1× 5

ten's place number is zero and it's expanded form 10×0

hundred's place number is zero and it's expanded form is 100×0

thousand's place number is 1 and it's expanded from is 1,000× 1

so, the expanded from of given number is

= (1,000× 1 ) + (100×0) + (10×0)+(1× 5)

=( 1,000× 1) + (1× 5) = 1,000 + 5

Hence , required form is result occurred.

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Jason's down payment is calculated to be 41250 if he bought the house for 275,000

Down payment is a term used to describe an initial payment made when something is bought on credit.

The original price of the house that Jason Aldeen bought is 275,000. Jason made a down payment of 15%. This means Jason Aldeen paid 15% of the original cost of the house. Therefore,

Jason's down payment is 15% of $275000

Down payment = 15% × 275,000

Down payment = 15/100 × 275000

Down payment = 0.15×275000

Down payment = 41250

Therefore; the down payment on the house bought by Jason Aldeen is calculated to be 41250

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10 units is the length of the line segment

Given that: the graph of the line segment from negative 6 comma negative 5 to 0 comma 3. Thus:

point 1 (-6, -5) => x1 = -6, y1 = -5

point 2 (0, 3) => x2 = 0, y2 = 3

Length of x-axis (x): x2 -x1 = 0-(-6) = 6

Length of y-axis (y): y2 -y1 = 3-(-5) = 8

Let the length of the line segment be L

Using Pythagorean Theorem:

L² = x² + y²

L² = 6² + 8²

L² = 36 + 64

L² = 100

L = √100 = 10 units

Therefore, the length of the line segment is 10 units. The 3rd option is the answer

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Answer:

36

Step-by-step explanation:

5(x-y)=18

5x-5y=18

To make it 10x-10y we multiply entire equation by 2

5x-5y=18

*2. *2.  *2

10x+10y=36

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The number 5 can be either a geometric sequence or a arthimetic sequence

A geometric sequence is a series in which each term is found by multiplying the preceding term by the same value. Its general term is. aₙ= a₁rⁿ⁻¹.

The r represents the common ratio, and a is the initial term. r is found by taking any term in the sequence and dividing it by its preceding term.

The example of a geometric sequence with 5 as initial term is

5, 10, 20, 40.....

In an arithmetic sequence, the difference between consecutive terms is always the same.

aₙ = a + (n - 1)d

The example of a arithmetric sequence with 5 as initial term is

5, 7, 9, 11 .....

Therefore, The number 5 can be either a geometric sequence or a arthimetic sequence.

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With a one-way ANOVA, you are comparing the T Statistic with the T critical value.

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z-test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

The critical value should be compared to the test statistic. The alternative hypothesis should be accepted in place of the null hypothesis if the test statistic is more extreme in the alternative's favor than the critical value. The null hypothesis should not be rejected if the test statistic is less extreme than the critical value.

Thus, with a one-way ANOVA, you are comparing the T Statistic with the T critical value.

The question is incomplete, the complete question is"

With a one-way ANOVA, you are comparing the _____ with the _____.

A. T Statistic with the T critical value

B. F Statistic with the F critical value

C. Correlation coefficient with the confidence interval

D. Outlier with the 4th quartile outer-most limit

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Answer:

18/25

Step by step explanation:

Answer: 18 cents - 72%

There is a total of 190 ways to share apples between them.

What is a ball-and-urn method?

The ball-and-urn method often referred to as stars-and-bars, sticks-and-stones, or dots-and-dividers is a typical combinatorial method.

It is used to resolve issues of the following type: in how many different ways can one divide 'k' undifferentiable items into 'n' distinct bins?

Use the ball-and-urn method,  Let Alice get 'x' apples, Becky get 'y' apples, and Chris get 'z' apples.

⇒x + y + z = 24

We can manipulate this into an equation that can be solved using the ball-and-urn method

All of them get at least 2 apples, so we can subtract 2 from x, 2 from y, and 2 from z.

⇒(x - 2) + (y - 2) + (z - 2) = 18

Let x' = x - 2, y' = y - 2, z' = z - 2.

⇒ x' + y' + z' = 18

We can allow either of them to equal 0, hence this can be solved by the ball-and-urn method.

By the ball-and-urn method, we get

 [tex]$\binom{18 + 3 - 1}{3 - 1} = \binom{20}{2} = \ 190}$.[/tex]

Hence, there are 190 ways to split the apples among them.

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Answer:  4 hours and 10 minutes per week

Step-by-step explanation:

She exercises for 5 days per week (week days only).

(5/6 hr/day) x 5 days = 25/6 = 4.17 hours = 4 hours and 10 minutes per week

When formula =D2/E2 is enter in Excel spreadsheet then we receive an error which is #DIV/0! .

Excel spreadsheet Error :

Microsoft Excel shows #DIV/0. Error when dividing a number by zero (0). This happens when you enter a simple formula like =5/0, or when the formula refers to a cell that contains 0 or is blank, as shown in this image.

Easiest way to suppress #DIV/0! The error is using the IF function to evaluate the existence of the denominator. If 0 or no value, display 0 or no value as the result of the formula instead of

#DIV/0.

For example, use =IF(A3,A2/A3,0) to return 0 if the formula returning the error is =A2/A3

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Using the exponential function given y = 7.1(1.03)ˣ, the amount produced in 2006 was 7.8 billion pounds and the estimated amount in 2014 is 9.8 billion pounds

An exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

In the function given;

y = 7.1(1.03)ˣ

a) What is the estimated number in 2006

We can find the value of x in 2006 as

2006 - 2003 = 3

x = 3

Let's substitute the values into the formula above;

y = 7.1(1.03)³

y = 7.76 ≅ 7.8 billion pounds

b)

The cheese produced in 2014

x = 2014 - 2003 = 11

Plug in the value

y = 7.1(1.03)¹¹

y = 9.83 ≅ 9.8 billion pounds

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The estimate of the total cheese production in 2006 is 7.8 billions of pounds.

The estimate of the total cheese production in 2014 is 9.8 billions of pounds.

[tex]y =7 .1( {1.03})^{x} [/tex]

Where,

The total cheese production in 2006;

x = 3 years

[tex]y =7 .1( {1.03})^{x} [/tex]

[tex]y =7 .1( {1.03})^{3} [/tex]

[tex]y =7 .1(1.092727)[/tex]

y = 7.7583617 billions of pounds

Approximately,

y = 7.8 billions of pounds

The total amount of cheese produced in 2014;

x = 11

[tex]y =7 .1( {1.03})^{x} [/tex]

[tex]y =7 .1( {1.03})^{11} [/tex]

[tex]y =7 .1(1.3842338707244)[/tex]

y = 9.8280604821435

y = 9.8 billions of pounds

In conclusion, the estimated production of cheese in 2006 and 2014 are 7.8 and 9.8 billions of pounds respectively.

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