P(x)= 1/2x^2+3x-4x^3x+6x^4-1 write in standard form, is it polynomial, what degree, type, and leading coefficient is it?

As per the given stem and leaf plot, the range of the stem and leaf plot is 4.

The term stem and leaf plot in math is referred as a type of table where the stem (or first column) represents the first place values of numbers and the leaves (or second column) represent the final place value of the numbers.

Here we given the following stem and leaf plot data.

Now we have to find the range of the stem and plot.

As we all know that range is defined as the maximum and minimum number in the data set.

While we looking into the given data, we have identified the the minimum number is 14 and the maximum number is 18.

Then the range is calculated as,

=> 18 - 14 = 4.

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The variability in your data collection is measured by the standard deviation. It reveals the average distance between each score and the mean.

How to interpret a standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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Answer:

a_n = -15 (n - 4) (for all terms given)

Step-by-step explanation:

a_n = -15 (n - 4) (for all terms given)

45, 30, 15, 0, -15, -30, -45, -60, -75, -90, -105, -120, -135, -150, -165, ...

To search for the nth sequence, replace n with the desired term.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

The outcome of multiplying a number by itself produces the original number, which is the square root of that number. Squares and square roots are a few of examples of exponents. Try to visualize nine. Furthermore, this can be written as 3x3.

Here,

A quadratic function is one where an equation has two roots.

A quadratic function's two roots are equal if D=0.

D (discriminant) = 0 such that b24ac = 0 is needed in order for the roots of a polynomial function to be equal.

As a result, if an equation has two roots, a quadratic function is what it is.

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The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 . Quadratics can be defined using a polynomial equation of the second degree.

The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.

here ,

=  [tex]3x^{2}[/tex] + 36x + 81 = 0

= 3x² + 27x + 9x + 81

= 3x(x+9) + 9(x+9)

= (3x+9)(x+9)

= 3(x+3)(x+9)

The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 .

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Whole numbers are closed under addition and multiplication. If we add and  multiply any two whole numbers, the result will be a whole number.

What are Whole numbers ?
The numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Whereas Integer: A counting number, zero, or the negative.

If we add any two whole numbers, the result will be a whole number. For example, 2 + 4 = 6 and 6 is a whole number.

Therefore, whole numbers are closed under addition.

If we multiply any two whole numbers, the result will be a whole number. For example, 2 × 4 = 8 and 8 is a whole number.

Therefore, whole numbers are closed under multiplication.

Also , Whole numbers are not closed under Subtraction and division.

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5.7 gallons of paint is required to cover an area of 2000 square feet

Given,

The quantity of paint = 2 gallons

Area covered by 2 gallons of paint = 700 square feet

We have to find the quantity of paint required to cover 2,000 square feet;

Here,

Area covered by 1 gallon of paint = Given area / Quantity of paint

= 700 / 2 = 350 square feet

Now,

Quantity of paint required to cover 2000 square feet;

2000 / Area covered by 1 gallon of paint = 2000 / 350 = 40 / 7 = 5.7 gallons

That is,

We need 5.7 gallons of paint to cover 2000 square feet.

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The given question is incomplete. Completed question is given below;

two gallons of paint will cover 700 square feet. How many gallons of paint are needed to cover 2,000 square feet ?

Answer:

Option D. No solution

Step-by-step explanation:

There is no value of x that makes the equation be true since an absolute value can never be negative.

No solution

Answer:

OptionD)

Step-by-step explanation:

[tex]x + 4 = -6\\x=-6-4\\x=-10\\[/tex]

Since there is no options with -10 only

The correct answer is OptionD)

Answer:

$25000

Step-by-step explanation:

100% - 34% = 66%

We know that

66% = $16,500

We have to find 1%

16500 divided by 66 = $250

Then we have to find the 34%

250 times 34 = $8500

Then we add both numbers to find their previous year's revenue

$16500 + $8500 = $25000

So, their previous year's revenue is $25000

The percent error in zookeeper's prediction on baby elephant's weight is 13.79%.

What is percentage error?

Percentage error is the difference between the estimated value and the actual value compared to the actual value, expressed as a percentage. So the percent error is the relative error multiplied by 100.

Uses of percentage error:

The main purpose of calculating percent error is to analyze how close the measured value is to the actual value. This is part of a comprehensive error analysis.

Solution:

Percent error = (Actual weight - Predicted weight/Predicted weight)x100

Percent error = (264 - 232/232) x 100

Percent error = ( 32/232) x 100

Percent error = 0.1379 x 100

Percent error = 13.79%

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Answer:

25%

Step-by-step explanation:

[tex](1/2)^2=1/4 \\ \\ \frac{1}{4} \times 100=25\%[/tex]

The similarity ratio of first polygon to second polygon is 4 : 1.

If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name given to this usual ratio. The ratio of any pair of corresponding sides is the ratio of any two similar figures. Simply put, when two figures are found to be similar, all of their associated side pairs have the same ratio.

Given,

Two polygons given,

Ratio of PQRS polygon = 20

Ratio of EFGH polygon = 5

Similarity ratio,

20 : 5

Simplifying,

4 : 1

The similarity ratio of first polygon to second polygon is 4 : 1.

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Examples of inverse relationships are :  As the speed of the car increases the time taken to cover certain distance decreases and  More buses on the road less space on the road.

inverse relationships

An inverse relationship, also known as a negative relationship, is a contrary correlation between two variables such that they move in opposite directions. For example, we have two variables X and Y. As X increases, Y decreases and as Y increases, X decreases .The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.

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The height of pyramid when given the volume and area is estimated as; H = 3 * V / a²

How is the height of the a square pyramid determined?

H = 3 * V / A_b

In which,

H - height of pyramid;

V- volume of pyramid

A_b - base area of pyramid; A_b = a²,

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Answer:

⭐ AAS = Angle-Angle-Side

⭐ I don't know what AES is.

Step-by-step explanation:

AAS is a triangle congruence statement you use to say that 2 triangles are congruent ≅ (the same).

Here's how to determine if 2 triangles are congruent by AAS:

Congruent side lengths and congruent angles are often denoted by tick marks.

⭐ Example:

The probability of both events occurring is 0.18.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

Since the person goes to store to buy clothes. the probability of the events are independent. the probability of buying a hat is 0.25. the probability of buying a pair of gloves is 0.72.

The probability of both events occurring will be:

= P(hat) × P(glove)

= 0.25 × 0.72

= 0.18

The probability is 0.18.

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C) 2x+y=10 is the line has an X intercept of 5 and Y intercept of 10

To find the eqaution of line whose X intercept and Y intercept is given we will use line intercept form of line

The equation of line with A units of X intercept and  B units of

Y intersect is given by:

  [tex]\frac{x}{A} + \frac{y}{B} =1[/tex]   ----(i)

 given that A= 5 (X intercept) and B= 10 (Y intercept)

 so equation (i) reduces to

  [tex]\frac{x}{5}+\frac{y}{10} =1[/tex]

so 2x + y = 1*10

so the equation of the line is 2x+y=10

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Complete question:

Which equation has an X intercept of 5 and a Y intercept of 10?

A) 3x+2y=10

B) 5x+7y=2

C) 2x+y=10

D) 11x+7y=9

Step-by-step explanation:

a linear function is defined as

y = ax + b

the variable x is only occurring with the exponent of 1.

this represents a straight line in a graphic representation (hence the name "linear").

if the exponent of the variable x is not 1, then it is not a linear function

P : y = 3/x + 2³

it is not linear.

the exponent of x = -1, as 1/x = x^-1. -1 is different to 1, which would be needed as exponent of x to make it linear.

Q : y = (1/3)x² + 3

it is not linear.

the exponent of x = 2. and 2 is different to 1, which would be needed as exponent of x to make it linear.

Answer:

Step-by-step explanation:

domain

all real numbers, because the graph keeps going to the left and to the right

range

y ≥ 1 because the function starts in y = 1 and then keeps going up

Answer: 7 dollars

Step-by-step explanation:

i think

Answer: A dollar is 100 cents, so you would add the 5 dimes and 12 quarters together. A dime is 10 cents so 10x5 is 50, so you would have 50 cents in dimes. A quarter is 25 cents, so you would multiply 12x25 and you would get 300 and you add those both together to get 350 cents. A dollar is 100 cents so you would have 3 dollars and the remaining 50 cents would stay 50 cents! <33

Step-by-step explanation:

Answer: Strong Negative Correlation

Step-by-step explanation:

The First step in adding and subtracting the rational expression is making the denominator equal .

The Rational Expression is defined as the expression that is written in the p/q form , where q ≠ 0 .

Let us understand adding and subtracting of the rational expression by an Example .

For Example : add the rational expressions 2/3 and 1/4 .

The First Step in adding them is to make the denominator equal ,

to make the denominator equal , we take LCM ,

the LCM of 3 and 4 is 12 ,

the rational expression become ⇒ 8/12 and 3/12 .

On adding , we get ; (8 + 3)/12 = 11/12 .

On subtracting , we get ; (8 - 3)/12 = 5/12 .

Therefore , making the denominator equal is the first step for adding and subtracting rational expressions .

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Yuki would have typed more than Neil at 10:30 AM and the inequality is 45×90+45 × x < 90 × x

We know that Neil started 90 minutes earlier than Yuki by subtracting the time difference So that tells us that

at 10:30 AM Neil would have typed 45 times 90. After x minutes he would have typed 45*90+45*x and Yuki would have typed 60*x.

Words typed by Yuki will be greater than those that will be Words typed by Neil

45×90+45 × x < 90 × x

When we will try in  Solving the above inequality would give us

x >90

it means that 90 minutes after 10:30 AM

Yuki would type more than Neil.

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The median of 1 to 99 is 50.

The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.

The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.

Median= 99+1/2 = 100/2 = 50th term, which in this case is 50.

Thus, the median of 1 to 99 is 50.

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The amount that should be paid by Siti for the bag is $46.50. A discount is a reduction in the price of a product or service. It can be expressed as a percentage or as a fixed amount.

Discounts can be offered for a variety of reasons, such as to encourage customers to buy a product or to clear out inventory. They may be offered to certain groups of customers, such as students or seniors, or they may be available to all customers.

To find out how much Siti paid for the bag, you can use the following formula:

Discounted price = Original price * (1 - discount percentage)

Plugging in the values given in the problem, we get:

Discounted price = $50 * (1 - 7%) = $50 * 0.93 = $46.50

Therefore, Siti paid $46.50 for the bag.

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Therefore , the solution to the problem is  factors of the given equation comes out be (x-14)(x+3).

By joining two expressions with the equivalent sign, a mathematical statement known as an equation is produced. The equation 3x - 5 = 17 is an illustration. By solving this equation, we can determine that the value of the variable x is 4.

Here,

In the given question the equation is given as  [tex]x^{2}[/tex]-11x-42.

Given  polynomial : [tex]x^{2}[/tex]-11x-42

Thus we factorise the given equation

First:

=> [tex]x^{2}[/tex]-14x+3x-42

Second:

=> x(x-14)+3(x-14)

=> (x-14)(x+3)

thus factors comes out to be

(x-14) and (x+3)

Therefore , the solution to the problem is  factors of the given equation comes out be (x-14)(x+3).

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Answer:

3. B

4. C

Tell me if you need an explanation, I can add it for you :D

For a w10×15 cantilevered beam of A - 36 steel subjected to loading as in the attached image, slope at B is 0.0042rad and displacement at B is 0.034ft.

For w10×15, moment of inertia I = 68.9in⁴ and for A - 36 steel, Young's modulus E = 29e3 ksi

Slope at B

θB = P₂x³/ (2EI) + P₁l³/ (2EI)

θB = (5 × 6³ + 9 × 12³)/ (2 × 29 × 10³ × 68.9)

θB = 0.0042rad

Displacement at B

yB = P₂x³(3l - x)/ (6EI) + P₁l³(3l - l)/ (6EI)

yB = ( 5 × 6³ × (3 × 12 - 6) + 9 × 12³ × 2 × 12)/ (6 × 29 × 10³ × 68.9)

yB = 0.034ft

--The question is incomplete, answering to the question below--

"The W10×15 cantilevered beam is made of A - 36 steel and is subjected to the loading shown.

1. Determine the displacement at B, if P1 = 9kip and P2 = 5kip

2. Determine the slope at B, if P1 = 9kip and P2 = 5kip"

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