please help me with this

The result to the factorization of the polynomial is 3x (x + 10) (x - 10).

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.

= 3x³ - 300x

= 3x(x²) - 300x

= 3x(x²) - 3x(100)

= 3x(x² - 100)

= 3x(x² - 10²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );

where

= 3x (x+10) (x−10)

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a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

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When eight more than the quotient of a number 'b' and 25 is greater than 6 then the inequality representing the value of b is b > -50.

The expression used to represents :

Quotient of a number b and 25 is equal to b / 25

Next step is :

8 more than the b / 25 is equal to ( b / 25 ) + 8

Then ,

( b / 25 ) + 8  is greater than 6 is given by

⇒ ( b / 25 ) + 8 > 6

Simplify the above inequality for 'b' we get,

⇒ ( b / 25 )  > 6 - 8

⇒ ( b / 25 )  > -2

Multiply both the side by 25 we get,

⇒ b > - 2 × 25

⇒ b > -50

Therefore, the inequality representing the value of 'b' for the condition of quotient and a number is equal to b > -50.

The above question is incomplete , the complete question is:

8 more than the quotient of a number b and 25 is greater than 6 , then the value of b is ?

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The value of sin a + cos a is √7/2.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows

Here we have

sin a × cos a = 3/8  

Multiply with 2 on both sides

=> 2(sin a × cos a) = 2(3/8)

=> 2 sin a cos a = 3/4  

Add sin²a + cos²a on both sides

=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a    

As we know (a + b)² = a²+ b² + 2ab  

=> (sin a + cos a)² = 3/4 + 1

=> (sin a + cos a)² = 7/4

=> sin a + cos a = √7/2

Therefore,

The value of sin a + cos a is √7/2.

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Answer:

c

Step-by-step explanation:

9/10

I would need to work at least 27 hours to make enough money to reach my goal.

What are arithmatic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

Let's start by finding the amount of money I receive from my allowance and how much more money I need to make to reach my goal:

Allowance per month = $60

Amount of money I need for social life = $260

Additional amount of money I need to make = $260 - $60 = $200

Now, let's divide the additional amount of money I need to make by the amount I make per hour to find how many hours I need to work:

$200 ÷ $7.50 per hour = 26.67 hours

Since we can't work a fraction of an hour, we need to round up to the nearest whole number.

Therefore, I would need to work at least 27 hours to make enough money to reach my goal.

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Answer:

The function f: A -> B is defined by:

f(x) = { 11, if x = -1 or x = 2,

-1, if x = 0,

-2, if x = 1,

0, if x = 3 or x = 4 }

The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.

To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.

To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.

Therefore, the function f is one-to-one and onto both.

Answer: [tex]36/\pi[/tex] or approximately 11.4592

Step-by-step explanation:

The distance around a circle equals its circumference.

The circumference equation is: C = 2[tex]\pi[/tex] * r where r = radius.

Now, we know that the distance around the circle is 36 so C = 36

Using the equation, we have 36= 2[tex]\pi[/tex]*r

Now, we solve for r by dividing by 2[tex]\pi[/tex] to both sides.

r = [tex]36/2\pi[/tex] which equals [tex]18/\pi[/tex] which is approximately 5.7296

Now, since radius is half of the diameter, we need to multiply this by 2.

This finally gives us the answer of diameter = [tex]36/\pi[/tex] which is approximately 11.4592

The company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.

To predict the number of T-shirts with problems in a shipment of 3,000 short-sleeved and 3,000 long-sleeved T-shirts, we can use the proportion of T-shirts with problems in the random sample as an estimate of the proportion of T-shirts with problems in the population.

For short-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 4/60 = 0.067. For long-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 1/60 = 0.017.

To estimate the number of short-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of short-sleeved T-shirts in the shipment:

Estimated number of short-sleeved T-shirts with problems = 0.067 x 3,000 = 201

Similarly, to estimate the number of long-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of long-sleeved T-shirts in the shipment:

Estimated number of long-sleeved T-shirts with problems = 0.017 x 3,000 = 51

Therefore, the company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.

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Object is kind of a vector with the same size as the coefficients in the linear regression model.

In the least squares optimization target, the sum of squared errors (SSE) is typically minimized with respect to the coefficients of the linear regression model. The gradient of the SSE with respect to the coefficients is a vector that provides the direction of steepest ascent, or the direction in which the SSE increases the most rapidly. Setting this gradient vector to zero and solving for the coefficients yields the least squares solution to the linear regression problem.

Therefore, in this context, " " is likely a vector of coefficients that are being optimized to minimize the SSE.

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The probability of selecting three numbers in increasing order is 1/3, which means that in one out of every three trials, we will select three numbers in increasing order.

Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. In this problem, we are asked to find the probability of selecting three numbers in increasing order from a range of 0 to 1.

Let's compute the probability of selecting three numbers in increasing order. Since the total number of possible outcomes is infinite, we need to use a continuous probability distribution to compute the probability. In this case, we can use the uniform distribution, which assumes that each number between 0 and 1 is equally likely to be selected.

The probability of selecting "a" as the smallest number is a/1 = a.

The probability of selecting "a" as the largest number is (1-a)/1 = 1-a.

The probability of selecting "a" as the middle number is 2(1-a)a, which is the product of the probability of selecting "a" and the probability of selecting "b" or "c" from the remaining range.

Therefore, the probability of selecting three numbers in increasing order is the sum of these probabilities:

P(increasing order) = ∫₀¹ (a * (1 - a) + (1 - a) * a + 2a(1 - a))da

P(increasing order) = ∫₀¹ 2a(1 - a)da

P(increasing order) = 2∫₀¹ a - a²da

P(increasing order) = 2[(a²/2) - (a³/3)] from 0 to 1

P(increasing order) = 2[(1/2) - (1/3)] = 1/3

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The mean score of all the ninth graders in the city is equal to 81.84 ( round to two decimal places )

Number of schools in the city = 3

Result of the mean score of the ninth grade students are

Glenwood     78       269

Central City   93       321

Lincoln High  66       161

Given mean score by PR manager = 81

Correct mean score is calculated as

= ( 78 × 269 + 93 × 321 + 66 × 161 ) / ( 269 + 321 + 161 )

= ( 20982 + 29853 + 10626 ) / 751

= 61461 / 751

= 81.84 ( round to two decimal places )

Therefore, the mean score of the ninth grade students of all the schools in the city is given by 81.84 ( round to two decimal places ).

The above question is incomplete , the complete question is:

In a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean score on test Number of ninth graders

Glenwood     78       269

Central City   93       321

Lincoln High  66       161

The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81 . Of course, that is incorrect.

a. What is the mean score for all ninth graders in the city? Round to two decimal places.

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The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the quadrilateral be represented as ABCD

Now , the coordinates of ABCD is given as

A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )

Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin

Substituting the values in the equation , we get

A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )

On simplifying the equation , we get

The coordinates of A' is = A' ( -2 , 4 )

The coordinates of B' is = B' ( 4 , 4 )

The coordinates of C' is = C' ( 6 , -2 )

The coordinates of D' is = D' ( 0 , -2 )

Hence , the dilated figure is solved

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Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.

For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., [tex]^{n} C_{r} = \frac{n!}{(n-r)!.r!}[/tex]

A combination is a way of selecting items from a collection where the order of selection does not matter.

We will have to apply the formula separately for vegetarian and meat items.

Combinations available

A. 1 vegetarian item and 2 meat items              

    [tex]^{5} C_{1} and ^{4} C_{2}[/tex]                                 (In combination "and" means to multiply)                                                                                        

   = [tex]\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}[/tex]

   = [tex]\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}[/tex]

   = 5.3.2

   = 5.6

   = 30

B. 2 vegetarian items and 1 meat item

    [tex]^{5} C_{2} and ^{4} C_{1}[/tex]

   = [tex]\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}[/tex]

   = [tex]\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}[/tex]

   = 5.2.4

   = 10.4

   = 40

C. 3 vegetarian items and no meat item

   = [tex]^{5} C_{3} and ^{4} C_{0}[/tex]

   = [tex]\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1[/tex]

   = 5.2

   = 10

Now, we will add all the different combination

Total combinations = 30+40+10

                                = 80 different type of dinners

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Answer:

None

Step-by-step explanation:

Let's clarify that a radical symbol beside a number means what number squared (or to the power of 2) can give me the number in the symbol.

In this case it would be 4 because

[tex]4*4=16[/tex]

A method I use is to find the square root is dividing the number in the radical symbol 2 times

First by the original number, and then by the product of the last equation. It will not always work, but it works in some cases like this one.

[tex]\frac{16}{2} = 8\\ \\\frac{8}{2}=4\\ \\\sqrt{16}=4[/tex]

Second step, multiply 4 by 4, which equals 16.

Since the square root of 16 is 4, you can substitute 4 in the rest of the equations instead of the radical expression.

None of the following equations equal 16, which means none of the following equations if equal to [tex]\sqrt{16} *4[/tex]

The solution of the system of equations is (4, -3)

Here we want to solve the next system of equations:

y = -(1/2)x - 1

y = (1/4)x - 4

Graphically.

To do so, we just need to graph both of these lines on the same coordinate axis and find the point where the lines intersect. Below is the graph of the system of equations, there we can see that the lines intersect at the point (4, -3), so that is the solution of the system.

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The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

we graphed the function y = 3x - 4

now, the required coordinates are, which satisfies the graph function.

as, we get,

(-1, -7), satisfies the graph function

(0, -4) , satisfies the graph function

(1, -1), satisfies the graph function

Hence, The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4

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Ken total annual income is $ 55,401.98.

What has compounded annually?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.

The completely randomized design, in which participants are assigned to treatment groups at random, is the most basic type of experimental design. The main benefit of using this method is that it minimizes the influence of chance and eliminates bias. This approach makes use of probability theory, which gives statistical analysis a strong foundation.

Given that Roth IRA has a present value of $524,856.00. The rate of interest is 3.4% per annum.

A = P(1+r)^t

A = amount

P = principal

r = rate of interest

t = time

The amount after 15 years is

A = 524,856.00(1+3.4%)¹⁵

A = 866658.9925

The total interest is  866658.9925 - 524,856.00 = $341802.99

The average interest per annum is (341802.99 /15) =22786.866

The annual income is 22786.866 + 32,615.12 = 55,401.986

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The required coordinates of B are (0, 6) for the given parabola.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.

To determine the coordinates of B, we can use the information given in the problem.

A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).

The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.

Therefore, we can set x = 0 in both equations to find the y-coordinate of B.

For f(x), we have:

f(0) = a × 0² + b × 0 + c = c

For g(x), we have:

g(0) = 3 × 0 + 6 = 6

Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:

c = 6

So, the coordinates of B are (0, 6).

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Answer:

Point (-3, 3) is not a solution to the system of equations

2y+x=3

y=x+0

Step-by-step explanation:

2y + x = 3

y = x + 0

2(3) + (-3) = 3

6 - 3 = 3

3 = 3

The point works in the first equation.

3 = -3 + 0

3 = -3

The point does not work in the second equation.

She travel  31.25 miles we calculate it by multiply by speed and time

Speed indicates how quickly something or someone is moving. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example because the distance is measured in metres (m) and the time is measured in seconds (s).The formula can be rearranged in three ways:

speed = distance ÷ time

distance = speed × time

time = distance ÷ speed

To calculate one of the variables (speed, distance or time) we need the other two.

As given in Question she cycled at speed 12 1/2 miles per hours

12 1/2  can be written as 12.5 miles per hours

and she cycled for 2 1/2 hours which can be written as 2.5 hours

and to find the distance how much she total travel we have to multiply the speed and time

distance = 12.5x2.5 = 31.25 miles

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Answer: height = 1.91 m

Step-by-step explanation: Using the formula

V=πr2h

Solving for h

h=V

πr2=37.5

π·2.52≈1.90986m

Answer:

i think it x = 0 and x = 5

Step-by-step explanation:

[tex]y = {x}^{2} - 4x + 2[/tex]

[tex]y = x + 2[/tex]

[tex]x + 2 = {x}^{2} - 4x + 2[/tex]

[tex]0 = {x}^{2} - 4x + 2 - x - 2[/tex]

[tex]0 = {x}^{2} - 5x[/tex]

[tex]0 = x(x - 5)[/tex]

[tex]x = 0[/tex]

(or)

[tex]x - 5 = 0[/tex]

[tex]x = 5[/tex]

To get the total number of different ways, multiply 1,536 x 18 = 7,344.

7,344 different ways. Raven has 19 choices for drinks, 12 choices for appetizers, and 8 choices for desserts. The formula for calculating the number of different ways is 19 x 12 x 8 = 1,536. Since Raven needs to pick 3 drinks, 3 appetizers, and 2 desserts, the formula is 3 x 3 x 2 = 18. To get the total number of different ways, multiply 1,536 x 18 = 7,344.

The formula can be used to calculate the number of different ways to combine any number of choices. For example, if Raven had 24 choices for drinks, 15 choices for appetizers, and 7 choices for desserts, the formula would become 24 x 15 x 7 = 3,240. If Raven still had to pick 3 drinks, 3 appetizers, and 2 desserts, the total would be 3 x 3 x 2 = 18. Multiplying 3,240 x 18 = 57,720 different ways.

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Answer:

Step-by-step explanation:

To find the volume of the container, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height. Plugging in the given values, we get:

V = π * 8.1^2 * 17.9 = 1146.4 cm^3

Since the sample contains 0.04 g of the trace element per cubic centimeter of water, the amount of trace element in the entire container can be found by multiplying the volume of the container by the concentration of the trace element:

0.04 g/cm^3 * 1146.4 cm^3 = 45.86 g

So Samir has collected approximately 45.9 g of the trace element, rounded to the nearest tenth.

Answer:147.6g

Step-by-step explanation

Answer:

second option

Step-by-step explanation:

an exponential function modelling the situation has the form

y = a [tex](b)^{x}[/tex]

to find a and b use ordered pairs from the table

using (0, 11000 )

11000 = a [tex](b)^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then

a = 11000 , so

y = 11000 [tex]b^{x}[/tex]

using (1, 9350 )

9350 = 11000 [tex]b^{1}[/tex] = 11000b ( divide both sides by 11000 )

[tex]\frac{9350}{11000}[/tex] = b

b = 0.85

then exponential function is

y = 11000 [tex](0.85)^{x}[/tex]

In  ΔABC, we can conclude that m∠A < m∠C and m∠B < m∠A < m∠C. Hence, options a. and d. are the accurate solutions.

The angle opposite to the longest side of the triangle is the largest angle of the triangle, similarly, the angle opposite to the smallest side of the triangle is the smallest angle of the triangle.

In the given ΔABC, we have,  

The longest side = AB = 3.1

The angle opposite to side AB = m∠C

The smallest side = AC = 2.9

The angle opposite to side AC = m∠B

side CB = 3

The angle opposite to side CB = m∠A

We have,

side AC < side CB < side AB

m∠B < m∠A < m∠C

From the given relations in the options provided, we get,

a. m∠A < m∠C

d. m∠B < m∠A < m∠C

are correct interpretations.

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The complete question is -

Select all the angle relationships in △ABC that are correct.

The data is symmetric because some students have phones and some do not. The correct option is B.

A histogram is a simplified representation of the distribution of numerical data. The phrase was first used by Karl Pearson at the outset.

Rectangles are used in a histogram, a type of visual representation of statistical data, to show how frequently data points occur throughout a range of subsequent numerical intervals of equal width.

In the most common sort of histogram, the independent variable and dependent variable are shown along the horizontal axis and the vertical axis, respectively.

The histogram is a frequently used graphing tool. It is used to summarize data that is measured on an interval scale, whether it be continuous or discontinuous.

It is widely applied to give the primary properties of the data distribution a practical way to be illustrated.

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Answer: B. The data is symmetric because some students have phones and some do not.

Step-by-step explanation: