Factor the following standard form trinomials in x*2 + bx + c form. First look for the number pairs that multiply to c (sign included). Second, see which of those pairs ALSO adds up to b [sign included]. Third, use those numbers to write the factored form in (x + r) (x + s) form. *work please*​

The modification to a research study that will result in a narrower confidence interval is option D is correct choice

The modification to a research study that will result in a narrower confidence interval is option D: decreasing the confidence level and increasing the sample size. By decreasing the confidence level, we are willing to accept a lower level of certainty in our results, which can lead to a narrower interval. Increasing the sample size also leads to a narrower interval as it reduces the variability in our data and increases the precision of our estimates.

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To find the rate at which average cost is changing when 176 belts have been produced, we need to first find the rate at which the average cost is changing when x belts have been produced.

We know that C(x) = 720 + 37x - 0.068x²We can find the average cost by dividing the total cost by the number of units produced. Average cost = Total cost / Number of units produced Let's consider that x belts have been produced. Then the total cost of producing these x belts is C(x).

Thus, the average cost per belt can be calculated as follows: Average cost = C(x) / x The rate at which the average cost is changing when x belts have been produced is given by the derivative of the average cost with respect to the number of belts produced (x).So, we need to differentiate the equation for average cost with respect to x to find the rate at which the average cost is changing.

Thus, the derivative is given by average cost'(x) = (C(x) / x)'Now, the derivative of the cost function C(x) is given as follows:

C'(x) = 37 - 0.136xaverage cost'(x) = (C(x) / x)'= (720 + 37x - 0.068x²) / x '= [37x² - 2x(720 + 37x) - x²(0.068)] / x²= (37x - 1440 - 0.068x²) / x²Putting x = 176, we get: average cost'(176) = (37(176) - 1440 - 0.068(176²)) / 176²= 13.064

Therefore, when 176 belts have been produced, the average cost is changing at 13.064 dollars per belt for each additional belt.

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Answer:

B

Step-by-step explanation:

Answer:

To complete the square for the quadratic expression x^2 + 16x + 22, we need to add and subtract (16/2)^2 = 64 inside the parentheses. This gives us (x^2 + 16x + 64) - 64 + 22, which can be simplified to (x + 8)^2 - 42. So, the expression x^2 + 16x + 22 can be rewritten as a perfect square by completing the square as (x + 8)^2 - 42.

Step-by-step explanation:

To find the function that describes the frog population at time x weeks, let's analyze the given data:

Week 1: Population = P

Week 2: Population = Px

We can observe that the population increases by a factor of x from week 1 to week 2. Therefore, we can conclude that the growth factor is x.

(a) The function of the form f(x) = Pax that describes the frog population at time x weeks is:

f(x) = P * x^x

(b) The growth factor in this situation is x, which means each week's population is obtained by multiplying the previous week's population by x.

(c) Each tree frog requires 10 square feet of space, and the park has an area of 6.2 square miles. We can calculate the total area available in the park in square feet:

1 square mile = 52802 square feet

6.2 square miles = 6.2 * 52802 = 327166.4 square feet

Now, let's calculate the space required by the frog population after 12 weeks:

Week 12: Population = P * 12^12

Space required = Population * 10 square feet

Space required after 12 weeks = (P * 12^12) * 10 square feet

If this space required exceeds the size of the park (327166.4 square feet), then the frog population has outgrown the park. We can perform a similar calculation for 14 weeks.

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Answer:

b, quadratic with constant second difference of 96

Step-by-step explanation:

The function is cubic with a constant third difference of 96.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Using differences:

X            f(x)             first difference          second difference             third

3            39                        -                                    -                                -

5            187             (187-39)/2= 74                       -                                -

7            551            (551-187)/7-5 = 182     182 - 74/2 = 54                   -

9           1227          (1227-551)/(9-7)=338   338-182/2=78          78-54/2 = 12

11           2311           (2311-1227)/2=542      542-338/2=102       102-78/2 = 12

According to table,

The function is cubic, because the third average change rate is constant of 12.

12>0, so the third difference is >0 then -96 is false.

Thus, the function is cubic with a constant third difference of 96.

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In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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Step-by-step explanation: First, you have to multiply the numerators, for example, 1/2 x 1/4. 1x1=1. Then the denominator. 2x4=8. So, 1/2x1/4=1/8

Answer:

What Is Your Dogs Name. - Don't have one :(

Or If You Dont Have One And When You Get It What Will You Name It. - I would name it Beau :3

Answer:

\(\overline {DE} \parallel \overline{AB}\) because \(\frac{EC}{DC} = \frac{AC}{BC}\).

Step-by-step explanation:

According to the Theorem of Thales and definition of proportionality, \(\overline {DE} \parallel \overline{AB}\) if and only if \(\frac{EC}{DC} = \frac{AC}{BC}\). If we know that \(EC = 15\,cm\), \(DC = 20\,cm\), \(BC = 36\,cm\) and \(AC = 27\,cm\), then we have the following result:

\(\frac{15\,cm}{20\,cm} = \frac{27\,cm}{36\,cm}\)

\(\frac{3}{4} = \frac{3}{4}\)

Hence, \(\overline {DE} \parallel \overline{AB}\).

Therefore, the 300th term of the sequence is 2748. The correct choice is option A: 2748.

To find the 300th term of the sequence using the explicit formula, we need to identify the first term (a1) and the common difference (d).

Looking at the given sequence:

57, 66, 75, 84, 93, ...

We can see that the first term (a1) is 57, and the common difference (d) is 66 - 57 = 9.

Now, we can use the explicit formula to find the 300th term (a300):

an = a1 + (n - 1) * d

Substituting the values:

a300 = 57 + (300 - 1) * 9

a300 = 57 + 299 * 9

a300 = 57 + 2691

a300 = 2748

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To find the limit of a rational function as x approaches infinity or negative infinity, you should analyze the degrees of the numerator and denominator and use the above rules to determine the limit.

The limit of a rational function as x approaches infinity or negative infinity can be found by analyzing the degrees of the numerator and denominator of the function.

If the degree of the numerator is less than the degree of the denominator, the limit as x approaches infinity or negative infinity is 0. This is because the denominator will grow at a faster rate than the numerator, causing the fraction to approach 0.

If the degree of the numerator is greater than the degree of the denominator, the limit as x approaches infinity or negative infinity is infinity or negative infinity, depending on the signs of the leading coefficients of the numerator and denominator. This is because the numerator will grow at a faster rate than the denominator, causing the fraction to approach infinity or negative infinity.

If the degree of the numerator is equal to the degree of the denominator, the limit as x approaches infinity or negative infinity is the ratio of the leading coefficients of the numerator and denominator. This is because the leading terms of the numerator and denominator will grow at the same rate, causing the fraction to approach the ratio of the leading coefficients.

Therefore, to find the limit of a rational function as x approaches infinity or negative infinity, you should analyze the degrees of the numerator and denominator and use the above rules to determine the limit.

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Answer:

C.

Step-by-step explanation:

A negative number divided by a negative number is a positve number.

Answer:

c and d

Step-by-step explanation:

The age of Bryson today is 11 1/3 years

From the question, we have the following mathematical statements:

Bryson's dad age = 38

Bryson's dad age = 4 + 3 * Bryson's age

Represent Bryson's age with x

So, we have the following equation

Bryson's dad age = 38

Bryson's dad age = 4 + 3x

substitute the known values in the above equation, so, we have the following representation

4 + 3x = 38

Evaluatet the like terms

3x = 34

Divide by 3

x = 11 1/3 years

Hence, Bryson's age as per the mathematical statement is 11 1/3 years

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Answer:

it's answer is 2

Step-by-step explanation:

take the reference angle as 60°

base (b) = x

hypotenuse (h) = 4

Now

cos 60 ° = b / h

1/2 = x / 4

1/2 * 4 = x

Therefore x = 2

Hope it will help :)❤

It would take 11 attendees to cause the company to break even. The company's total expenses would be 180 + 17 x = 180 + 17 × 11 = 297 and the company's total revenues would be 53 x = 53 × 11 = 583.

To write a system of equations to describe the situation, we can let x represent the number of attendees that register for the seminar.

The total expenses for the company can be calculated as 180 + 17x, and the total revenues can be calculated as 53x. Therefore, the equation that describes the company's situation is 180 + 17x = 53x.

To solve for the number of attendees that would cause the company to break even, we can solve the equation using substitution. Subtract 180 from both sides to get 17x = 180, then divide both sides by 17 to get x = 10.59, which we can round up to x = 11.

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One common unit of measure that serves as a conversion factor between linear and angular measurements is the radian (rad).

A radian is defined as the angle subtended at the center of a circle by an arc of the circle equal in length to the radius of the circle.

Since the circumference of a circle is 2π times the radius, there are 2π radians in a full circle. Therefore, one can use the following conversion factors

1 radian = 180/π degrees (approx. 57.3 degrees)

1 degree = π/180 radians (approx. 0.01745 radians)

These conversion factors allow you to convert between linear measurements (such as arc length or circumference) and angular measurements (such as angles in degrees or radians) when dealing with circular motion or rotational systems.

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Answer:

the answer is c I pretty sure

There are 16 people who share the worm.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this illustration, Vince brought 6 boxes of worms to use as bait while fishing with his friends if each person uses exactly 3 8ths of a box of worms

The number of people who shared the works will be:

= Number of worms / Amount collected by each person

= 6 ÷ 3/8

= 6 × 8/3

= 16

In conclusion, 16 people shared it.

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The graph of the function g(x) = −|x + 3| − 2 is added as an attachment

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

g(x) = −|x + 3| − 2

The above expression is an absolute value function that hs the following properties

Next, we plot the graph

See attachment for the graph of the function

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Answer: The first 3 options(LJ, JK, and KL)

Step-by-step explanation:

The last option isn't right since R is a plane, not a point on a segment.

The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

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Answer:

\(0\leq y\leq 8\)

Step-by-step explanation:

because it cant go below x-axis with is y = o and nothing above 8

The function can produce any y-value between 0 and 8, including both 0 and 8 (option a).

The range of a function refers to the set of all possible output values, or y-values, that the function can produce. To identify the range of the function shown in the graph, we need to determine the highest and lowest y-values that the graph reaches.

Looking at the graph, we can see that the highest point on the graph is at y = 8, and the lowest point is at y = 0. Therefore, the range of the function is from y = 0 to y = 8.

In other words, the function can produce any y-value between 0 and 8, including both 0 and 8. We can express this range using interval notation as [0, 8].

So, the correct answer is option A: 0 ≤ y ≤ 8.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

c

Step-by-step explanation:

The more variable the data, the less accurate the sample mean will be as an estimate of the population mean. In statistical analysis, accuracy is important. Statistical analysis is a method of gathering and examining data to uncover useful information.

A sample mean is a numerical estimate that represents a data set's central tendency. The population mean, on the other hand, is a statistical measure that represents the mean value of the entire population. The difference between the two lies in the fact that sample mean is computed on a subset of the population whereas population mean is calculated for the entire population. If the variability of the sample data is large, the sample mean becomes less accurate as an estimate of the population mean.

As a result, the more variable the data, the less accurate the sample mean will be as an estimate of the population mean.Therefore, it is essential to examine the variability of the data in order to better estimate the population mean. The greater the variability in the data, the more difficult it becomes to identify the true population mean and the less accurate the sample mean is as an estimator of the population mean.

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Based on proportions, the numbers of students in the senior form and junior form are 615 and 885, respectively.

Proportion refers to the equation of two ratios.

Proportion is a fractional value depicted using ratios, percentages, fractions, and decimals.

The percentage of senior form students in the school = 41%

The percentage of junior form students = 59% (100% - 41%)

The additional percentage of junior over senior students = 18% (59% - 41%)

The additional number of junior form students over the seniors = 270

Proportionately, if 18% = 270, the total number of students (both junior and senior) = 1,500.

Therefore, the number of senior and junior students is as follows:

Check:

The difference in the numbers = 270 (885 - 615)

Thus, using proportions, we can state that there are 1,500 students in the school, consisting of 615 seniors and 885 juniors.

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Answer: The solutions of the absolute value equation are given by:

x = -41 and x = 49.

What is the absolute value function?

The absolute value function is defined by:

|x| = x, x >= 0.

|x| = -x, x < 0.

The absolute value function measures the distance of a point x to the origin, that is, the distance to x = 0. From this, we get that |x| = a can mean either that:

x = a, or;

x = -a.

In this problem, the equation is given by:

Hence:

0.2|x - 4| = 9

|x - 4| = 45

The first possible solution is:

x - 4 = 45

x = 49.

The second possible solution is:

-x + 4 = 45

-x = 41

x = -41.

Hence the solutions are x = -41 and x = 49.

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Step-by-step explanation: