0³ 1 + sin 04 ex 1 - tan ex do dx 1 √ [1 + (In 1)²] dt

Answer:

  2. ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36

  3. see below for synthetic division

  4. complex roots: ±3i

  5. see the second attachment for a graph (has no symmetry)

Step-by-step explanation:

2. The Rational Root Theorem tells you possible rational roots are the form of ...

  ±(divisor of constant term) / (divisor of leading coefficient)

Here, we're lucky in that the leading coefficient is 1. The constant is 36, and its divisors are 1, 2, 3, 4, 6, 9, 12, 18, 36. Possible rational roots, according to the Rational Root Theorem are ...

  ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36

__

3. When actually searching for possible roots, it is useful to narrow down this list of 18 candidates. We can do this using Descarte's Rule of Signs and a couple of other simple tests. The rule of signs has us look at the signs of the coefficients. They are ...

  + + + + +

There are no sign changes, hence no positive real roots. This means we're looking at negative roots only.

We know that p(0) = 36, the constant term. We can evaluate p(-1) simply, by reversing the signs of the odd-degree coefficients and adding them up:

  1 -4 +13 -36 +36 = 10

So p(0) = 36 and p(-1) = 10. The average rate of change is -26, so we expect p(-2) to be zero or less. That value (-2) may be a good first choice for a possible root.

The synthetic division for the root -2 is shown in the first attachment. It shows a remainder of 0, so -2 is a root. The polynomial with the corresponding factor divided out is ...

  q(x) = x^3 +2x^2 +9x +18

__

We can apply the above steps to this polynomial. It will have no positive real roots. The value of q(0) is 18, and the value of q(-1) is -1 +2 -9 +18 = 10. The average rate of change between these points is (18 -10)/(0 -(-1)) = 8, so we expect the function to be zero or negative between x=-2 and x=-3.

Further, we observe that the ratio of the first two coefficients is 1 : 2, the same as the 9 : 18 ratio of the last two coefficients. This suggests we can factor this polynomial by "grouping."

  q(x) = (x^3 +2x^2) +(9x +18) = x^2(x +2) +9(x +2) = (x^2 +9)(x +2)

So, without doing any more synthetic division, we have found a second root at x = -2. This means -2 is a double root.

Our factorization so far is ...

  p(x) = (x +2)^2(x^2 +9)

__

4. The remaining polynomial factor (x^2 +9) has only complex roots:

  x^2 +9 = 0

  x^2 = -9

  x = ±√(-9)

  x = ±3i . . . . the complex roots

__

5. The graph is shown in the second attachment, along with the graph of the final quadratic factor.

The leading coefficient is positive and p(x) is of even degree, so it will have a general U shape, going to +∞ for large positive and negative values of x.

Since x = -2 is a double root, the graph touches the x-axis there, but does not cross it.

The graph of p(x) shows no symmetry.

______

Comment on the graph

With modern graphing calculator software it is entirely feasible to start by graphing the polynomial, then reading the (rational) roots from the graph. The same calculator can effectively divide out those roots. If the result is a quadratic, its vertex form equation can be read from the graph, making it easy to find any additional real or complex roots.

This graph shows ...

  p(x) = (x +2)^2·q(x)

  q(x) = x^2 +9

Answer:

320 pages.

Step-by-step explanation:

We can simply multiply and add to find how many pages are in the book.

So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.

Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:

\(\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320\)

The answer choice which represents a function among the given answer choices is; Choice B.

According to the given task content; the table which represents a function among the given answer choice is to be identified.

Recall that a function can be defined as a relation in which case; each input value is assigned not more than one value.

By observation, only the answer choice B has a combination of input and output values in which case; each input value is assigned only one output value.

Hence, since a function is a relation which is characterized by assigning only one output value to each input value; the correct answer choice is; Choice B.

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The sample is Stratified Random Sample

A large company surveys 100 employees by taking random samples of 101010 managers and 909090 non- managerial employees.

To find the what type of sample is this?

Now, According to the question:

"A stratified random sampling involves dividing the entire population into homogeneous groups called strata (plural for stratum). Random samples are then selected from each stratum. ... A random sample from each stratum is taken in a number proportional to the stratum's size when compared to the population. "

The managers group (101010) is one strata of sampling, and the other group of non-managerial employees (909090) is another strata. We're taking one sample from each group .

Hence, the sample is Stratified Random Sample

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Answer:

51% of 200 =

102

Step-by-step explanation:

51           x     200  =  10200

100                  1  =      100       10200/100 = 102

percentages is out of 100

Another way:

51/100 is .51 so just multiply it by 200!

.51 x 200 = 102

Hope this helps you out! :)

Answer:

Step-by-step explanation:

How you get 51% of 200 is by multiplying 51 by 200 then dividing the value of 51 times 200 by 100.

51 ⋅ 200 = 10200 ÷ 100 = 102 Steps

So, 51% of 200 equals 102 Steps

Hope this helps! <3

Answer:

Step-by-step explanation:

22.9

To perform a hypothesis test on the proportion of people who subscribe to a cable television service versus others, we need to check the following conditions:

1. Random Sampling: Ensure that the sample is randomly selected, which means each person has an equal chance of being selected. This is important to avoid biases and ensure the sample is representative of the population.

2. Independence: If sampling without replacement, the sample size (n) should be less than 10% of the population size (N) to assume independence. This is called the 10% Rule. Independence is important because the outcome of one person's choice should not affect another person's choice.

3. Normality: We need to ensure that the sampling distribution of the sample proportion (p-hat) is approximately normal. This can be checked using the success-failure condition, which states that both np and n(1-p) should be greater than or equal to 10. This ensures that the distribution is sufficiently normal to apply the z-test.

To help the student, remind them to:

1. Verify that the sample is random.
2. Check the independence condition by confirming the sample size is less than 10% of the population size.
3. Check the normality condition by calculating np and n(1-p) and making sure both values are greater than or equal to 10.

It is crucial to check these conditions because if they are not met, the hypothesis test's results may not be valid or reliable. Meeting these conditions ensures that the statistical methods applied are appropriate and provide accurate results for making conclusions.

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The expected weight less than 5 oz to the nearest whole number is 700 oranges

According to the Empirical Rule, a normally distributed random variable includes the following:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Mean = 6

Standard deviation = 0.5

95% of weights:

Based on the Empirical Rule, within 2 standard deviations of the mean.

Lower weight limit

= 6 - 2(0.5)

= 5

Upper weight limit

= 6 + 2(0.5)

= 7

Therefore, the interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

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Answer: Product = 2\(x^{2}\)-8x

Step-by-step explanation:

2x(x-4)

First we want to expand the brackets by multiply the contents of the bracket by 2x

2x * x = 2\(x^{2}\)

2x * (-4) = -8x

Put these together

Product = 2\(x^{2}\)-8x

In order to identify these mentioned terms, it is important that each of them is defined.

Diameter: It is a line that passes through the center of the circle from one endpoint to another. It is two times the radius of the circle

Radius: It is a line drawn from the center of the circle to one endpoint of the circle.

It is half of the diameter.

Chord: It is a line drawn from one endpoint of the circle to another but does not necessarily pass through the center. Diameter is an example of a chord, but a chord does not have to be a diameter

Arc: It is a segment of the circumference of a circle

Circumference: is the total distance around the circle

From the diagram above:

|AB| is a diameter

|OA| or |OB| is the radius

|CD| is the chord

Arc CD is indicated on the diagram

If a circle has a radius of 2 cm:

Diameter = 2 x radius

Diameter = 2 x 2

Diameter = 4 cm

Therefore, if a circle has a radius of 2 cm, the diameter is 4 cm

Answer: i took a screen shot hope it helps

Step-by-step explanation:

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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h'(1) is equal to -2V54.

To find h'(1), we need to differentiate the function h(x) with respect to x and evaluate it at x = 1.

Given:

h(x) = V54f(x)

f(1) = -5

f'(1) = -2

First, let's find the derivative of h(x) using the chain rule:

h'(x) = d/dx [V54f(x)] = V54 * d/dx [f(x)]

Now, we substitute x = 1 into the expression to evaluate h'(1):

h'(1) = V54 * d/dx [f(x)] | x=1

Since we know f(1) = -5 and f'(1) = -2, we can substitute these values:

h'(1) = V54 * d/dx [f(x)] | x=1

      = V54 * f'(1)

      = V54 * (-2)

      = -2V54

Therefore, h'(1) is equal to -2V54.

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Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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Answer:

BC=FE=5

BC=5

BA=DE=11

angle A= angle D=27

Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.

The value of x is 8.5 cm

The complete question is in the image

The given parameters are:

y = 12 cm

\(\theta = 45^o\)

The value of x is calculated using the following sine ratio

\(\sin(\theta) = \frac xy\)

This gives

\(\sin(45^o) = \frac x{12}\)

Multiply by 12

\(x = 12 * \sin(45^o)\)

Evaluate

x = 8.5

Hence, the value of x is 8.5 cm

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The required  the average daily census for this period is 12.

A Average can be characterized as the amount of all numbers isolated by the all out number of values. A mean can be characterized as a normal of the arrangement of values in an example of information. At the end of the day, a normal is likewise called the math mean. It is known as a mean to Depict the average.

there were 2,200 inpatient service days.

Number of days between this period = 184 days

So, average daily census = 2200/184

11.95

⇒ 12 up to whole number.

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To calculate Bill's total wages, we need to determine the earnings for each category of hours worked and then sum them up. The correct answer is B) $680.00.

Regular rate (40 hours): $10.00 per hour * 40 hours = $400.00

Time and a half (8 hours): $10.00 per hour * 1.5 * 8 hours = $120.00

Double time (8 hours): $10.00 per hour * 2 * 8 hours = $160.00

Now, we can calculate the total wages by adding up the earnings from each category:

Total wages = Regular rate + Time and a half + Double time

Total wages = $400.00 + $120.00 + $160.00

Total wages = $680.00

Therefore, the correct answer is B) $680.00.

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Answer:

????

Step-by-step explanation:

Answer:

it's 3/50

Step-by-step explanation:

Answer:

3/50

Step-by-step explanation:

the fraction 6/100 can simplify to 3/50

Answer:

8.75

Step-by-step explanation:

\(\frac{3}{4} +\sqrt{64} \\\\\frac{3}{4} +8\\\\\frac{3+32}{4} \\\\\\\\\frac{35}{4}\) 35/4 simply(8\(\frac{3}{4}\)) then turn into a decimal which would be 8.75

1) Tash is multiplying each number of the bracket while Taylor solves the bracket first and then applied multiplication.

2) The solution to the expression 7(x + 2) is 7x + 14.

According to the distributive property the same expression can be written in different ways by using the parenthesis or common multiplications.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Part(1),

Taylor's solution is,

5(9 + 2)

5(11)

Tash's solution is,

5(9 + 2)

5(9) + 5(2)

Tash is multiplying each number of the bracket while Taylor solves the bracket first and then applied multiplication.

Part(2),

The solution to the expression 7(x + 2 is,

E = 7(x + 2

E = 7x + 14

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The mean mass of the women given the conditions are 52.5 kg and 54 kg

(a) a woman of mass 60kg leaves the group

Given that

Women = 15

Mean mass = 53 kg

So, we have

Total mass = 15 * 53 kg

Total mass = 795 kg

When a mass of 60 kg leaves, we have

Mean mass = (795 - 60)/(15 - 1)

Mean mass = 52.5 kg

(b) a woman of mass 69kg joins the original group ​

Given that

Women = 15

Mean mass = 53 kg

So, we have

Total mass = 15 * 53 kg

Total mass = 795 kg

When a mass of 69 kg joins, we have

Mean mass = (795 + 69)/(15 + 1)

Mean mass = 54 kg

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Answer:

They're all false??? Do them on a calculator!

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

the assumption here being that if we were to graph the traveling of the car the miles will be on y-axis usually whilst the minutes on the x-axis usually, so is simply asking for the slope, and since the car began at 0 miles at 0 minutes, at the origin of our graph, then the rise and run are pretty much those values above.

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3\frac{1}{2}}~,~\stackrel{y_2}{2\frac{1}{3}}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2\frac{1}{3}}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{3\frac{1}{2}}-\underset{x_1}{0}}} \implies \cfrac{ ~~ 2\frac{1}{3} ~~ }{3\frac{1}{2}}\implies \cfrac{~~ \frac{ 7}{3 } ~~}{\frac{7}{2}}\implies \cfrac{7}{3}\cdot \cfrac{2}{7}\implies \boxed{\cfrac{2}{3}}\)

The value of Tim's house at the start of 2018 is £146410

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

Initial value = 100,000

Rate of increase = 10%

The value of the house x years after 2014 can be represented as the following exponential function

Value = Initial value * (1 + rate)ˣ

So, we have

Value = 100000 * (1 + 10%)ˣ

2018 is 4 years after 2014

This means that x = 4

So, we have

Value = 100000 * (1 + 10%)⁴

Evaluate

Value = 146410

Hence, the value is #146410

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The lower bound of the confidence interval is 0.55.

A confidence interval for a proportion is a range of values that is likely to contain a population proportion with a certain level of confidence.

Construct a confidence interval of the population proportion at the given level of confidence x equals = 540, n equals = 900, 96% confidence.

The value of p is;

\(\rm p=\dfrac{x}{n}\\\\p =\dfrac{540}{900}\\\\p=0.6\)

The standard error of the proportion is:

\(\rm \sigma_p=\sqrt{\dfrac{p(1-p)}{n}} \\\\ \sigma_p=\sqrt{\dfrac{0.6(1-0.6)}{540}} \\\\ \sigma_p=\sqrt{\dfrac{0.6\times 0.4}{540}} \\\\ \sigma_p=\sqrt{\dfrac{0.24}{540}} \\\\ \sigma_p=\sqrt{0.00044}\\\\ \sigma_p=0.02\)

The critical z-value for a 94% confidence interval is z = 2.04

The margin of error (MOE) can be calculated as:

\(\rm Margin \ of \ error=\sigma_p \times z =2.04 \times0.02 =0.04\)

Then, the lower bound of the confidence interval is;

\(Lower \ bound =p-x\times \sigma_p=0.6-0.04=0.55\)

Hence, the lower bound of the confidence interval is 0.55.

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The type of sampling technique described is stratified random sampling.

In stratified random sampling, the population is first divided into homogeneous subgroups or strata based on some criteria, such as age, gender, income, or education level. In this case, the population was grouped according to age. Then, a random sample is selected from each stratum.

By doing so, the sample represents the entire population better than simple random sampling, as each subgroup is represented proportionally to its size in the population. This technique ensures that there is less variation within each subgroup, which can result in more precise estimates of the population parameters.

In summary, stratified random sampling is a type of probability sampling technique where the population is divided into subgroups, and a random sample is selected from each subgroup.

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