Please help me with this

President Harry S. Truman, in his address before a Joint Session of Congress on March 12, 1947, was advocating the Truman Doctrine.

This policy emphasized the commitment of the United States to support free peoples who were facing subjugation either from armed minorities or external pressures.

During this time, the world was grappling with the aftermath of World War II and the growing influence of the Soviet Union. Truman's speech marked a significant shift in U.S. foreign policy, as he outlined the need to counter the expansion of communism and protect democratic nations. The Truman Doctrine sought to provide economic and military assistance to countries threatened by communism, with the goal of containing its spread.

Truman's address laid the foundation for subsequent actions such as the Marshall Plan and the creation of the North Atlantic Treaty Organization (NATO). While the Berlin airlift, which occurred later in 1948, was a response to the Soviet blockade of West Berlin, it was not directly advocated in Truman's speech. The Marshall Plan, implemented in 1948, aimed to aid the economic recovery of war-torn European countries, and it was a crucial component of the broader strategy outlined in the Truman Doctrine.

In summary, President Truman's speech on March 12, 1947, advocated the Truman Doctrine, which emphasized the support of free peoples facing subjugation by armed minorities or external pressures. This policy set the stage for subsequent initiatives like the Marshall Plan and the establishment of NATO, as the United States sought to counter the expansion of communism and protect democratic nations.

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The volume of the cylinder in cubic centimeters is 251.2 cm^3.

The volume of a cylinder is expressed as:

V = πr²h

V = base area * height

Given the following

Base area =  16π centimeters

Height = 5cm

Substitute into the formula to have:

V = 16(3.14) * 5

V = 251.2 cm^3

Hence the volume of the cylinder in cubic centimeters is 251.2 cm^3.

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Look at screenshot because it wouldn't let me upload the text.

Answer:

D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)

Step-by-step explanation:

hope this helps

Answer:  D has the largest perimeter

Step-by-step explanation:

The top numbers of fractions describe the vertex and  the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.

A.

P = 2(11) + 2(3)

P = 22+6

P=28

B.

P = 2(4) + 2(9)

p = 8 +18

P = 26

C.

P = 2(5) + 2(9)

P = 10 +18

P = 28

D.

P =  2(8) + 2(7)

P = 16 +14

P = 30

Answer:

Domain: \(t \geq 0\)

Range: \(v \geq 550\)

Step-by-step explanation:

Given

\(v = 550 + 16.5t\)

Required

Determine the domain and the range

Solving for domain:

From the question, we understand that t represent years.

Because years can't be negative;

Then, we can conclude that the domain, t is:

\(t \geq 0\)

Solving for Range:

We solved domain to be \(t \geq 0\)

This implies that the minimum value of t is \(t = 0\) and the maximum is infinity

Substitute 0 for t in \(v = 550 + 16.5t\)

\(v = 550 + 16.5(0)\)

\(v = 550 + 0\)

\(v = 550\)

Hence;

The range is \(v \geq 550\)

Answer:

90π sq cm

Step-by-step explanation:

2πrh = 2π(5)(9) = 90π sq cm

The compound inequality that does not belong with the other three include the following: D. a < 6 or a > -9.

The graph of this inequality is the only one with overlapping rays that represent all real numbers.

In Mathematics and Geometry, an inequality is a relation that compares two (2) or more numerical data, number, and variables in an algebraic equation based on any of the inequality symbols;

Next, we would evaluate the given inequalities for a as follows;

a > 4 or a < -3      ⇒ 4 > -3

a < -2 or a > 8      ⇒ 8 > -2

a > 7 or a < -5      ⇒ 7 > -5

a < 6 or a > -9      ⇒ -9 > 6

In conclusion, we can logically deduce that only the inequality a < 6 or a > -9 that has one interval and overlapping rays that represent all real numbers.

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The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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The recursive definition for the amount of the blood pressure medicine in Hareem's bloodstream after n hours can be defined as :

a. a1=25, an= 0.40an-1 + 25

Base Case:

The initial amount of medicine in Hareem's bloodstream after 0 hours is 25 mg.

Recursive Step:

The amount of medicine in Hareem's bloodstream after n hours can be calculated by taking 60% of the amount of medicine in his bloodstream after (n-1) hours, and then adding 25 mg.

To write this recursive definition in mathematical notation:

M(n) = 25 mg, if n = 1

M(n) = 40 mg, if n = 6

M(n) = M(n-1) + (60% * M(n-1)), if n > 6

This recursive definition represents the amount of the blood pressure medicine in Hareem's bloodstream after n hours. The base case sets the initial amount of medicine, and the recursive step calculates the amount of medicine at each hour by taking 60% of the previous amount and adding 25 mg.

The correct option is a. a1=25, an= 0.40an-1 + 25

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Answer:

Divide both sides by 22.

\frac{3y}{2}=x

2

3y

=x

2 Switch sides.

x=\frac{3y}{2}

x=

2

3y

Answer:

x=10

Step-by-step explanation:

5x-10 and 3x+10

+10 +10

5x and 3x+20

-3x -3x

2x and 20

divide by 2 on both sides

x=10

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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The probability that only two individuals will suffer from the side effect is 0.0453 and the probability that at least two individuals will suffer from the side effect is 0.9555, using Poisson Distribution.

A Poisson distribution is a discrete probability distribution that describes the probability of a number of discrete events occurring in a fixed interval of time. In this case, the fixed interval of time is the population of 1000 individuals who are inoculated with the vaccine.

(a) The probability that only two individuals will suffer from the side effect is given by the equation:

P(X=2) = (\(e^-10 * 10^2\))/2! = 0.0453

(b) The probability that at least two individuals will suffer from the side effect is given by the equation:

P(X≥2) = 1 - P(X=0) - P(X=1)

= 1 - (\(e^-10 * 10^0\))/0! - (\(e^-10 * 10^1\))/1!

= 0.9555

Therefore, the probability that only two individuals will suffer from the side effect is 0.0453 and the probability that at least two individuals will suffer from the side effect is 0.9555.

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Answer: x = 18

explanation: By adding 11 and 7 you get 18

Answer:

Step-by-step explanation:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Answer:

8 floor tickets and 7 balcony tickets.

Step-by-step explanation:

f+b=15

25f+17.50b=322.50

Answer:

8 floor tickets, 7 balcony tickets

Step-by-step explanation:

F + B = 15

25F + 17.50B = 322.50

The cash price of her purchase would be $5262.79

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + \dfrac{r}{n})^{nt}\)

The Present value = C [1 - (1+i)^(-n)]/i

C = the amount of payment per period

i = interest rate

n=number of payments

In this problem we have;

C = $174.80

i = 12% per year compounded monthly

 = 12/(12 x 100)

 = 0.01

n = 3 x 12 = 36 months

Present Value = 174.80[1  - (1+0.01)^(-36)]/0.01

Cash price = $5262.79

Hence, the cash price of her purchase would be $5262.79

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Answer:

z*(z - 3) = 520

Step-by-step explanation:

Use the following representations:

Width:  W  

Length:  L = W + 3, or W = L - 3

Area = L*W = L*(L - 3) = 520

Equation b) is the correct one:  z*(z - 3) = 520

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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The equation -x + y = 5 can be represented in the y = mx + b form as y = x + 5. This form allows us to easily identify the slope and y-intercept of the line represented by the equation.

To express the equation -x + y = 5 in the y = mx + b form, we need to isolate y on one side of the equation.

Starting with -x + y = 5, we can rearrange the equation by moving the -x term to the other side:

y = x + 5

Now the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, the coefficient of x is 1, which gives us a slope of m = 1. This means that for every unit increase in x, y will increase by 1. The positive slope indicates that the line will slant upward as we move from left to right.

The constant term in the equation is 5, which gives us the y-intercept, b = 5. The y-intercept is the value of y when x is 0, which in this case is the point (0, 5) on the y-axis.

In the y = mx + b form, the equation -x + y = 5 can be written as y = x + 5. We can quickly determine the slope and y-intercept of the line that the equation represents using this method.

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The statue of the cat is 14 meters tall.

If the ladder is 6 meters tall and it casts a shadow that is 3 meters long and the statue of a cat casts a shadow that is 7 meters long, then we can use the concept of similar triangles to determine the height of the statue of the cat.

The ratio of the height of the ladder to the length of its shadow is 6/3 = 2.

We can also assume that the ratio of the height of the statue of the cat to the length of its shadow is also 2.

so, the height of the statue of the cat can be calculated by:

height of statue of the cat = (2 * shadow length of the statue of the cat) = (2 * 7) = 14 meters

Therefore the statue of the cat is 14 meters tall.

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The amount of calories provided from fat and carbohydrates is 1210 calories.

The number of calories left over is 290 calories.

These calories come from proteins.

The amount of protein in this meal is not specified, so we cannot calculate it.

The amount of calories provided from fat and carbohydrates: Fat provides 9 calories per gram, so 90g of fat would provide 9 x 90 = 810 calories. Carbohydrates provide 4 calories per gram, so 100g of carbs would provide 4 x 100 = 400 calories. So, the total amount of calories provided from fat and carbohydrates is 810 + 400 = 1210 calories.

The number of calories left over: 1500 calories - 1210 calories = 290 calories. These calories come from proteins.

The amount of protein in this meal: The amount of protein in this meal is not specified, so we cannot calculate it.

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The first two approximations are y(0.2) ≈ 2.4 and y(0.4) ≈ 1.92.

Euler's method is a numerical method used to approximate the solutions of ordinary differential equations (ODEs) with a given initial value.

The method involves breaking down the solution into smaller intervals and approximating the solution at each interval using the derivative at the current point. Specifically, for the initial value problem y'(t) = f(t,y(t)), y(t0) = y0, with a time step size of delta t, Euler's method proceeds as follows:

y1 = y0 + delta t * f(t0, y0)

In the given problem, the ODE to be solved is y'(t) = -y and the initial value is y(0) = 3. Therefore, we have f(t,y) = -y and y0 = 3. The time step size is given as delta t = 0.2, which means we need to compute the values of y at t = 0.2 and t = 0.4 using Euler's method.

Applying the formula for the first approximation, we get:

y1 = y0 + delta t * f(t0, y0) = 3 + 0.2 * (-3) = 2.4

So, the first approximation of y at t = 0.2 is y1 = 2.4.

For the second approximation, we need to use y1 as the initial value and compute y2 as follows:

y2 = y1 + delta t * f(t1, y1) = 2.4 + 0.2 * (-2.4) = 1.92

Therefore, the second approximation of y at t = 0.4 is y2 = 1.92.

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The possible values of the solutions to the inequality 5x + 5 ≥ −9 are: I, II, and III.

To find the possible values of the solution to a given inequality, solve the inequality given using the properties of equality to isolate the variable.

Given the inequality:

5x + 5 ≥ −9

Subtract 5 from both sides:

5x + 5 - 5 ≥ −9 - 5 [subtraction property of inequality]

5x ≥ -14

Divide both sides by 5

5x/5 ≥ -14/5

x ≥ -2.8

This means that all the possible values of x are greater than or equal to -2.8.

1, 4, and 6 are greater than -2.8, therefore, the values of the solutions are: I, II, and III.

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Answer:

Step-by-step explanation:

\(a = \frac{2b+1}{3b-1}\)

b = 2/3

\(2b + 1 = 2*\frac{2}{3}+1\\\\=\frac{4}{3}+1\\\\=\frac{4}{3}+\frac{3}{3}\\\\=\frac{7}{3}\\\\3b-1 = 3*\frac{2}{3}-1\\\\=2- 1 = 1\\\\\\\)

\(a = \frac{2b+1}{3b-1}\\\\a=\frac{\frac{7}{3}}{1}\\\\=\frac{7}{3}\\\\\)

a = 7/3

b)

\(\frac{2b+1}{3b-1}=a\\\\\)

Cross multiply,

2b + 1 = a*(3b - 1)

2b + 1 = a*3b - 3*a

2b + 1 = 3ab- 3a

2b = 3ab - 3a - 1

2b - 3ab = -3a  - 1

b(2 - 3a) = -3a - 1

\(b =\frac{-3a - 1}{2 - 3a}\)

Answer:

  124/999

Step-by-step explanation:

A recurring decimal fraction can be expressed as a rational number by using the recurring digits in the numerator and an equal number of 9s in the denominator:

  \(0.\overline{124}=\dfrac{124}{999}\)

This fraction cannot be reduced.

_____

Additional comment

If the recurring digits don't start at the decimal point, then you can determine the fraction by ...

In this case, you would get ...

  \(1000x = 124.\overline{124}\\\\1000x-x=124.\overline{124}-0.\overline{124}=124\\\\x=\dfrac{124}{999}\)

To approximate the real solutions of the equation x^4 - 2x + 5x - 2 = 0 using a graphing utility, we can plot the equation on a graph and observe where it intersects the x-axis. By doing so, we can determine the x-values that correspond to the real solutions.

Using a graphing utility, we input the equation and set the x-axis limits between -10 and 10. After plotting the graph, we observe the points where the curve intersects the x-axis. These x-values are the approximate real solutions of the equation.
Upon analyzing the graph, if there are any points where the curve intersects the x-axis, we can note those x-values as the approximate real solutions. If there are no intersections, then there are no real solutions
Therefore, we select the answer choice that corresponds to the x-values where the curve intersects the x-axis. If there are no intersections, we select the answer choice stating that there are no real solutions.
In this case, since we don't have the graph or its details, I am unable to determine the real solutions or whether they exist. Please input the specific x-values obtained from the graphing utility, and I will be happy to assist you further.

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Answer:

Option A

Step-by-step explanation:

2x^2+10x+12

Divide through by 2

x^2 +5x+6=0

x^2 +3x+2x+6

x(x+3)+2(x+3)=0

(x+2)(x+3)=o

x=-2 or x=-3

Answer:

A

Step-by-step explanation:

I believe its A cause i just did the same question

Answer:

I got 5/16 as my answer

Step-by-step explanation:

I used a calculator to solve the equation :/

The fraction of the original action figures will Natasha and her 3 friends each receive is (1/15).

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Total number of action figures = x

Number of action figures left = (1/5)x

The number of action figures received by each friend.

= (1/5)x ÷ 3

= (1/15)x

Thus,

Each friend received (1/15) of the original action figures.

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