help help help help help help help help help help help help help help help help help help help help help help help help help help ​

Help Help Help Help Help Help Help Help Help Help Help Help Help Help Help Help Help Help Help Help Help

Answers

Answer 1

Answer:

1. \((x-6)^{2}\)

2. \((x +11)^2\)

3. \((x-4y)^{2}\)

4. \((5x - y)^2\)

Step-by-step explanation:

1. \(x^{2} -12x +36\) ---> \((x-6)^{2}\)

2. \(x^{2} +22x + 121\) ---> \((x +11)^2\)

3. \(x^{2} -8xy+16y^{2}\) ---> \((x-4y)^{2}\)

4. \(25x^2-10xy + y^2\) ---> \((5x - y)^2\)


Related Questions

Please help meeee! Need the answer for the first box, no phony answers please! Thanks for your help, and happy holidays!

 Please help meeee! Need the answer for the first box, no phony answers please! Thanks for your help,

Answers

Answer:

y=2(x+5)^2-4.

Step-by-step explanation:

By solving a little bit, we get the vertex to be (-5, -4). Plugging the info given and the vertex into the vertex form, we get y=2(x+5)^2-4. You have a happy holiday season, too!


Note Figure is not drawn to scale.
If r= 2 cm and h = 2 cm, what is the surface area,
in terms of r?

Answers

Answer:

your answer is...

Step-by-step explanation:

50.265482457437

I used my calculator

The table represents the function fix).
f(x)
X
-3
-2
−1
0
1
2
3
-3
0
3
69
9
What is (3)?
09

The table represents the function fix).f(x)X-3-210123-303699What is (3)?09

Answers

F(3) is equal to 9, based on the given table and the corresponding values of x and f(x). Option D.

To find the value of F(3) based on the given table, we look at the corresponding x-value of 3 and find its corresponding f(x) value.

From the table, we see that when x = 3, f(x) = 9. Therefore, F(3) = 9.

The table shows the values of x and their corresponding f(x) values. We can see that when x increases by 1, f(x) also increases by 3. This indicates that the function has a constant rate of change, where the change in f(x) is always 3 units for every 1 unit change in x.

Given that F(3) represents the value of the function when x = 3, we look at the x-values in the table and find the corresponding f(x) value. In this case, when x = 3, f(x) = 9.

Therefore, the value of F(3) is 9. Option D is correct.

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Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below.


Three lines of math. The first line, StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis. The second line, StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half EndFraction x minus x plus 4. The third line StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half EndFraction x plus 4.

StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half Endfraction x minus x plus 4.

StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half Endfraction x plus 4.

When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ?


–1

–negative StartFraction one-half EndFraction

0

StartFraction one-half EndFraction. BRAINIEST

Answers

When she subtracts 4 from both side of the equation, then she gets the value of x is 0.

What is expression?

Expressions means the idea of expressing numbers using letters or alphabets without specifying their actual values, the expression is the statement consisting variable, numbers, and arithmetical operation.

Given that, Karissa begins to solve the equation,

1/2(x-14)+11 = 1/2x-(x-14)

1/2x-1/2(14)+11 = -1/2x-x+4

1/2x-7+11 = -1/2x+4

1/2x+4 = -1/2x+4

1/2x+1/2x = 4-4

x = 0

Hence, When she subtracts 4 from both sides, then x = 0

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I Agree With The Other Person

What is the probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute?

Answers

The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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Fill in the blank A ____ is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution
answer options are
histogram
frequency polygon
scatterplot
normal quantile plot

Answers

Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.


What is a Normal Quantile Plot?

A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.

It plots sample data versus a theoretical normal distribution.

In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.

A normal quantile plot can be used to evaluate the following:

Whether or not a data set is normally distributedA data set's skewnessA data set's outliersA data set's center and spread whether or not a transformation is required to make a data set normally distributed.      

The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.

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2409÷61 as a fraction

Answers

Answer:

así es es una fracción si necesita la respuesta me avisa

Compute the flux of F⃗ =3(x+z)i⃗ +2j⃗ +3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane

Answers

It seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

To compute the flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane, we can use the surface integral.

The surface integral of a vector field F⃗ over a surface S is given by the formula:

∬S F⃗ · dS = ∬S F⃗ · (n⃗ dS)

where F⃗ is the vector field, dS is the differential area vector, and n⃗ is the unit normal vector to the surface.

In this case, the surface S is given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0. We can parameterize this surface as:

r(x, z) = xi⃗ + yj⃗ + zk⃗ = xi⃗ + (x^2+z^2)j⃗ + zk⃗

To find the normal vector n⃗ to the surface, we can take the cross product of the partial derivatives of r(x, z) with respect to x and z:

n⃗ = ∂r/∂x × ∂r/∂z

= (1i⃗ + 2xj⃗) × (0i⃗ + 2zj⃗)

= -2xz i⃗ + 2zj⃗ + 2xk⃗

Now, we can calculate the flux:

∬S F⃗ · (n⃗ dS) = ∬S (3(x+z)i⃗ + 2j⃗ + 3zk⃗) · (-2xz i⃗ + 2zj⃗ + 2xk⃗) dS

= ∬S (-6x^2z - 4xz + 6xz^2 + 6xz) dS

= ∬S (-6x^2z + 2xz + 6xz^2) dS

To evaluate this integral, we need to determine the limits of integration for x, y, and z.

Since the surface is defined by 0≤y≤16, x≥0, z≥0, we have:

0 ≤ y = x^2 + z^2 ≤ 16

Simplifying the inequality, we get:

0 ≤ x^2 + z^2 ≤ 16

From this, we can see that x and z both range from 0 to 4.

Now, we can evaluate the flux:

∬S (-6x^2z + 2xz + 6xz^2) dS = ∫∫ (-6x^2z + 2xz + 6xz^2) dA

where dA is the differential area.

Integrating over the limits 0 ≤ x ≤ 4 and 0 ≤ z ≤ 4, we can calculate the flux.

However, it seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

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Ava opened a account first oak with 5000$. Zoe started an account with 4000$ l. No additional deposit or withdrawal from this account. Hiw much more money will be in avas account than zoes at the end of three years

Answers

Answer:

This isnt much of an answer just something to help-

Try doing A(1 + B)^I

What is the value of 3x+4?

Answers

Answer:

7x

Step-by-step explanation:

add the numbers 3+4

and add the x

find the acute angle between the lines. round your answer to the nearest degree. 6x − y = 2, 5x y = 7

Answers

The acute angle between the lines 6x - y = 2 and 5x + y = 7 is approximately 55 degrees.

To find the acute angle between two lines, we need to determine the angle between their direction vectors.

First, let's rewrite the given lines in slope-intercept form:

Line 1: 6x - y = 2 => y = 6x - 2

Line 2: 5x + y = 7 => y = -5x + 7

The direction vector of Line 1 is (6, -1), and the direction vector of Line 2 is (5, -1).

To find the angle between two vectors, we can use the dot product formula:

cos(theta) = (v · w) / (|v| |w|)

where v and w are the direction vectors of the lines, and |v| and |w| are their magnitudes.

Calculating the dot product:

v · w = (6 * 5) + (-1 * -1) = 30 + 1 = 31

Calculating the magnitudes:

|v| = sqrt(6^2 + (-1)^2) = sqrt(36 + 1) = sqrt(37)

|w| = sqrt(5^2 + (-1)^2) = sqrt(25 + 1) = sqrt(26)

Plugging the values into the formula:

cos(theta) = 31 / (sqrt(37) * sqrt(26))

Using an inverse cosine function to find theta:

theta ≈ acos(31 / (sqrt(37) * sqrt(26))) ≈ 54.8 degrees

Rounding to the nearest degree, the acute angle between the lines is approximately 55 degrees.

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The lines shown below are perpendicular

The lines shown below are perpendicular

Answers

Answer:

Slope of green line:

\(m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} \)

Slope of red line:

\(m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} \)

The slopes of these two lines are negative reciprocals of each other.

Therefore, the correct answer is True (A).

Someone please help me. ASAP

Someone please help me. ASAP

Answers

Answer:

x = 6

Step-by-step explanation:

we both know you dont wanna know how you just want the answer

Answer:

6

Explanation:
Add like terms and make x alone.

I hope this helps you!!

can someone help me with this

can someone help me with this

Answers

Answer:

Total Area = 1200 in^2

Step-by-step explanation:

There is a triangle and a rectangle.

Arca Triangle: Area = 1/2 * Base* Height

Area = 1/2 * 40 in * 30 in = 600 in^2

Area Rectangle: Area = Length* Width

Area = 30 in * 20 in = 600 in^2

Total Area = Area Rect + Area Tri

Total Area = 600 in^2 + 600 in^2 = 1200 in^2

can someone help me with this

equivalent ratio of given ratio to form​

Answers

Answer:

not enough context

HELP MEEEE PLEASE i don't know how to do this

HELP MEEEE PLEASE i don't know how to do this

Answers

Answer:

5 hours

Step-by-step explanation:

35x+25 = 40x

25=5x

x= hours

how would you solve this equation?

how would you solve this equation?

Answers

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

how many solutions are there to square root x =9

Answers

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Please help.
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.

Please help.Is algebra.PLEASE HELP NO LINKS OR FILES.I don't want links.

Answers

Answer:

question 12 is answer B

question 13 is -8x^3

Step-by-step explanation:

exponent rule \(\frac{a^m}{a^n} = a^(^m^-^n^)\)

Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 90% of adults will have an IQ score higher than what value?

Answers

The IQ score that is higher than 90% of the population is 112.8.

We know that the IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 10.

Let X be the random variable representing the IQ scores. We want to find the value x such that 90% of the observations lie above x.

Using the standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile as 1.28.

The z-score formula is z = (x - μ) / σ, where μ is the mean, σ is the standard deviation and x is the value we want to find.

Plugging in the values, we get 1.28 = (x - 100) / 10. Solving for x, we get x = 100 + 12.8 = 112.8.

Therefore, the IQ score that is higher than 90% of the population is 112.8.

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very confusing i know
Center (-10, -4), Point on Circle: (4,2)
h=
k=
r^2=
Fill in the parenthesis for the equation of the circle:
(Blank 1)² +(Blank 2)²= (Blank 3)

*Just type what you would write in the parentheses with no spaces

Answers

Answer:

(x + 10)² + (y + 4)² = 232

Step-by-step explanation:

Given Center = (-10, -4)Point on circle = (4, 2)To find The equation of circleSolution

Remember the standard equation of circle:

(x - h)² + (y - k)² = r², where (h, k) is the center and r is radius

We have

h = -10, k = -4

Use distance formula (Pythagorean theorem) to work out the length of the radius. We know that radius is the distance from the center to any point on the circle.

Here we are finding the distance between points (-10, -4) and (4, 2)

r² = (-10 - 4)² + (-4 - 2)² r² = 14² + 6²r² = 232

So the equation is:

(x + 10)² + (y + 4)² = 232

in forecasting, there is more than one use for linear regression. what are they? check all that apply.

Answers

Casual relationship forecasting and Time series forecasting uses linear regression in forecasting.

Linear regression is a statistical tool used in forecasting to model the relationship between a dependent variable and one or more independent variables. Some of the common uses of linear regression in forecasting are:

Predictive modeling: Linear regression can be used to build a predictive model that estimates the value of the dependent variable based on the values of the independent variables..Trend analysis: Linear regression can be used to analyze the trend of the dependent variable over time.Forecast accuracy evaluation: Linear regression can be used to evaluate the accuracy of a forecasting model by comparing the predicted values to the actual values of the dependent variable. Causal analysis: Linear regression can be used to identify the causal relationship between the independent variables and the dependent variable. .

Therefore, linear regression is a versatile tool in forecasting, with many useful applications for predicting future values, analyzing trends, evaluating accuracy, and identifying causal relationships.

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The complete question is :

In forecasting, there is more than one use for linear regression. What are the? Check all that apply.

1. Causal relationship forecasting

2. Time series forecasting

Enter the solutions from least to greatest.
(X+ 1)(3x + 4) = 0
lesser x =
greater x =

Answers

Answer:

Lesser x = -4/3

Greater x = -1

Step-by-step explanation:

By the Zero Product Property, the roots are found by setting each factor equal to 0:

x+1 = 0

x = -1

3x+4 = 0

3x = -4

x = -4/3

So, the lesser x is -4/3 and the greater x is -1.

Find the length of MN

Answers

Answer:

Is there supposed to be a screenshot?

then again this is your first question .....................

For a sequence of statements, compute their complexity functions individually and add them up for (j=0;j

Answers

If the sequence of statements is executed within a loop where `j` ranges from 0 to `n`, the overall time complexity is O(n).

To compute the complexity function for a sequence of statements where the variable `j` ranges from 0 to `n`, we need to analyze the complexity of each individual statement and then sum them up.

Let's assume the time complexity of each statement is as follows:

Statement 1: O(1)

Statement 2: O(1)

...

Statement `n`: O(1)

Since all the statements have a time complexity of O(1), we can say that each statement takes constant time regardless of the input size.

Now, we need to consider the loop where `j` ranges from 0 to `n`. In each iteration of the loop, the sequence of statements is executed. Therefore, the time complexity of the loop will depend on the number of iterations.

The loop `for j in range(n)` runs `n` times. In each iteration, the sequence of statements is executed. Since each statement has a time complexity of O(1), the total complexity of the sequence of statements executed in each iteration is O(1).

Therefore, the time complexity of the loop is given by:

O(1) * n = O(n)

Finally, since the loop is the only part that depends on the input size `n`, the overall time complexity of the sequence of statements is O(n).

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Complete Question

For a sequence of statements, compute their complexity functions individually and add them up for (j=0; j < n; j++). Write the complete question.

2) Bobby has 3 apples and 5 oranges. Mary has 2 apples and
one orange. If Bobby eats an orange and then combines
what he has with Mary, what do they have together?

Answers

Answer:

3 apples and 6 oranges.

Step-by-step explanation:

5-1=4

4+2=6

0+3=3

6 apples and 3 oranges

What is the rate of change between (3.4,-0.1) and (3.5,0.1)?

What is the rate of change between (3.4,-0.1) and (3.5,0.1)?

Answers

The rate of change between the points (3.4, -0.1) and (3.5, 0.1) is 2.

How to find rate of change?

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.

The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity.

Therefore,

rate of change = Δy / Δx

rate of change = y₂ - y₁ / x₂ - x₁

Hence, let's find the rate of change of (3.4,-0.1) and (3.5,0.1).

rate of change = 0.1 + 0.1 / 3.5  - 3.4

rate of change = 0.2 / 0.1

rate of change = 2

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Whitney is a car saleswoman. Her weekly pay is $375 plus 3.5% of her total sales for the week. Whitney sells x dollars’ worth of cars during the week.

Answers

Whitney's weekly pay is $375 plus 3.5% commission on her total sales for the week (represented by x). The equation for her weekly pay is Weekly Pay = $375 + 0.035x.

To calculate Whitney's total weekly pay, we need to add her base salary and the commission she earns from her sales. The base salary is a fixed amount of $375. The commission is calculated as 3.5% of her total sales, represented by the variable x.

The equation to determine Whitney's weekly pay can be expressed as: Weekly Pay = $375 + (0.035 x)

In this equation, x represents the total sales made by Whitney during the week. To calculate her commission, we multiply the total sales (x) by 0.035, which is equivalent to 3.5%.

Adding the base salary and the commission gives us Whitney's total weekly pay. The equation allows for flexibility in accounting for different levels of sales, as the commission is directly proportional to the total sales amount.

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GIVING BRAINLIEST!! PLS HELP :((

At least 2 sides of equal length, 2 pairs of parallel sides, & at least 2 right angles.

Which shapes have all the properties shown? Select All That Apply.

A) Isosceles triangle
B) Parallelogram
C) Rectangle
D) Right Triangle
E) Square
F) Trapezoid

Answers

Answer:

A parallelogram is a quadrilateral with 2 pairs of parallel opposite and equal sides. Similarly, the opposite angles in a parallelogram are equal in measure

Step-by-step explanation:

Answer: Parallelogram

Rectangle

Square

Step-by-step explanation:

f(x, m, s) = 1 √278² exp (-2/2 (x-m) ²) 28² Write a function in the form of gauss(x, m=0, s=1) for computing the Gaussian density. Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. Give the name of question5b (c) x-0, m-2, s-1. Give the name of question5e (d) x=0, m=2, s=2. Give the name of question5d (e) x=3, m-3, s-3.

Answers

Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.

To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.

First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:

Principal = $1,000

Rate of interest per period = 8% / 4 = 2% per quarter

Number of periods = 12 quarters

Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)

                           = $1,000 * (1 + 0.02)^12

                           ≈ $1,166.41

Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):

Principal = $1,000

Rate of interest per period = 2% per quarter

Number of periods = 8 quarters

Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)

                         = $1,000 * (1 + 0.02)^8

                         ≈ $1,165.16

Finally, we add the two values to find the total value of the account on January 1, 2021:

Total value = Value after three years + Value after two years

                ≈ $1,166.41 + $1,165.16

                ≈ $2,331.57

Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.

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Determine if y varies directly with x. Give the constant of variation, when appropriate. (picture below)A) Does y vary directly with x? B) What is the constant of variation? Look at the picture and describe it considering the following? Which example violates the professional scope of practice? A dental hygienist decides to take x-rays in addition to your dental cleaning.A nurse gives you specific instructions on how to take a medication that your doctor prescribed to you.A receptionist helps you to your car.A doctor decides to sit behind the front desk and schedules another doctor's patients' appointments. Use the word SMART goal in a sentence: Why were the Vikings so successful in annexing territory? What military tactics did they use? Petra Kelly wrote, "Nonviolence is stronger than violence." This sentence includes ________________________.A) a correctly punctuated direct quotationB) a correctly punctuated indirect quotationC) no quotation at allD) one or more punctuation errors What is the author's purpose in writing the first passage of the Passing of the Buffalo?to entertain while telling a story about the buffaloto persuade younger generations to fight the white man.to persuade the reader to save the buffaloto inform younger generations how the buffalo were killed. !!PLEASE HELP!! QUESTION ON MY PAGE NEED HELP AND USE THIS!!!!Problem-Based Task: On the ShelfKareem wants to put up a small corner shelf in his room. The shelf is in the shape of a right triangle. Oneleg of the triangle is 2 inches shorter than the other leg. The longest side of the shelf is 10 inches long. Kareem needs to find the area of the shelf so that he knows if he has enough paint to cover the top of theshelf. The area of a triangle is A=1/2 bh.Let the length of the long leg equal x. How can the length of the short leg 10 pointsbe expressed in terms of x? *(x)(x + 2)(x - 2)Be what is an organism that has the ability to use an atmospheric gas to produce an organic nutrient How did President Hoover respond to the challenges of the Great Depression? A. He ended World War I to bring American servicemen home. B. He gave World War I veterans bonuses they had been promised. C. He did nothing because he believed the economy would turn around. D. He made government money available to banks and railroads. According to your textbook, a listener anxious about an upcoming exam, worried about a recent argument with a friend, or distracted by cold air in the classroom would be experiencing any person planning to begin a fitness program should first have a medical exam. any person planning to begin a fitness program should first have a medical exam. true false Select the correct product (x2+4) (x2-4)x4 16x4+16x2+8x+16x2 8x 16 Which is less, 3,074 rounded to the nearest ten, or 3,074 rounded to the nearest hundred? Nosotros___alumnos buenos. Whats the missing word why are stockout costs difficult to determine? suggest an approach that might be used to estimate them. what is the commission Use Green's Theorem to evaluate the line integral along the given positively oriented curve. C 3y + 7e (x)^1/2 dx + 10x + 7 cos(y2) dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2 use newton's method to approximate the root of x^4 - 2x^3 5x^2 - 6 = 0 in the interval [1, 2] to 6 decimal places. Do we still need to worry about genocide and events similar to the Holocaust in our modern world?