What is a gradient in mathematics

The Reagan doctrine of American activism in the Third World was most particularly exercised in Nicaragua and Grenada. These countries became focal points of U.S. involvement and intervention.

The Reagan doctrine, implemented during the presidency of Ronald Reagan in the 1980s, aimed to counter Soviet influence and promote American interests in the Third World. This doctrine was characterized by a strong anti-communist stance and support for anti-communist governments and movements. Among the various countries where the Reagan doctrine was applied, Nicaragua and Grenada stand out as prime examples.

In Nicaragua, the Reagan administration actively supported the Contras, a rebel group fighting against the Sandinista government. The Contras were seen as a counterforce to the left-wing Sandinistas, who were aligned with the Soviet Union and Cuba. The United States provided financial and military assistance to the Contras, including covert operations, in an effort to undermine the Sandinista regime.

Grenada, a small island nation in the Caribbean, also witnessed American intervention under the Reagan doctrine. The United States launched Operation Urgent Fury, invading Grenada and overthrowing the government, with the stated objective of protecting American citizens and restoring democracy.

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Answer:

9/12 and 10/12

Step-by-step explanation:

Lowest common denominator = Lowest common multiple for denominators only

Lowest common multiple of 4 and 6 is 12

3/4 × 3/3 = 9/12

5/6 × 2/2 = 10/12

So our final answer is

9/12 and 10/12

Hope this helped and have a good day

Answer:

75/100 and 100/120

Step-by-step explanation:

3 × 25 = 75 and 4 × 25 = 100. So 75/100. You can choose any numbers. If i choose 9 by example: 3 × 9 = 27 and 4 × 9 = 36. So 27/36 = 3/4.

First, we should identify the coordinates of the vertices of the triangle UVW.

The coordinates of the vertices are:

U(0,3)

V(6,6)

W(6, 0)

We can find the coordinates of the resulting triangle after dilation, given that the center of dilation is the origin using the relationship:

Where k is the scale factor

Applying this rule to the original coordinates of the triangle UVW, we have the new coordinates to be:

Hence, the coordinates of the resulting triangle are:

U'(0, 1)

V'(2,2)

W'(2,0)

Answer:

Option D

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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The coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

The given parameters are

Number of pen = 2

Unit price = $2

This means that the total amount spent is

Total amount = Number of pen * Unit price

Evaluate the product

Total amount = 2 * 2

Evaluate the product

Total amount = 4

So, the coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

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I do not agree. To find how fast Spotify is downloading songs, divide the number of songs already downloaded by how long the playlist has been downloading.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

For example, assume that you are downloading a playlist that has 100 songs. 80 songs have been downloaded in the past two hours. In order to determine the rate at which songs are downloaded, divide 80 by 2.

Speed = 80 / 2 = 40 songs per hour

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Answer:

2 in 542 is in the ones place/column and the 2 in 324 is in the tens place/column

Answer:

The 2 in 542 is in the ones place so its value is only 2, the 2 in 324 is in the tenths place, its value is 20.

Step-by-step explanation:

Answer:

the answer is t=47°

Step-by-step explanation:

72°-25°=47°

Answer:

t = 47°

Step-by-step explanation:

72° appears to be equal to t + 25°

Therefore, you subtract 25° from 72° to get 47°

Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975% in the compound interest.

When interest is earned on a loan or investment, it is earned on both the principal and any accumulated interest, which is known as compound interest. In other words, interest is added to the principal, and the resulting sum is then used to determine future interest. Compounding causes an investment or loan to increase more quickly than it would with simple interest, where just the principal is charged interest. Compounding may occur daily, monthly, quarterly, annually, or at any other interval.

To compare the plans of the two accounts we have:

Rate = ( 1 + rate / n)ⁿ - 1

where, n is the compounded period.

For plan A:

Effective annual interest rate = (1 + (0.5%/4))⁴ - 1 ≈ 0.5025%

For Plan B, we have:

Effective annual interest rate = (1 + 3.5%)¹- 1 = 3.5%

Comparing the two we see that Plan B offers higher rates by:

3.5% - 0.5025% ≈ 2.9975%.

Hence, Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975%.

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The rectangle with an area of 24cm^2 and a perimeter of 20 cm can have dimensions of either 4cm x 6cm or 6cm x 4cm.

To find the dimensions of the rectangle, we first set up two equations based on the given information:

A = L x W and P = 2L + 2W.

We substitute the values of the area and perimeter and simplify the equations to get

L x W = 24cm^2 and L + W = 10cm.

We then use the second equation to solve for L in terms of W and substitute the expression for L into the first equation.

This leads to a quadratic equation, which we solve to get the possible values of W.

We then use the expression for L to find the corresponding values of L for each value of W.

Thus, we find that the rectangle can have dimensions of either 4cm x 6cm or 6cm x 4cm.

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Let the time taken to read the whole be y

If he reads 1/8 of the whole book (x), it can be expressed as,

If it takes Adam to read x/8 of a book in 1/6 hours,

To read the whole book, it will take Adam,

Hence, it will take 1 1/3 hours for Adam to read the whole book.

The length of one side of the rhombus is 17 units. It's worth noting that the length of a side can also be found by using either of the diagonals since they are both equal in a rhombus. However, in this case, we used the Pythagorean theorem to demonstrate the relationship between the diagonals and the sides

In a rhombus, the diagonals intersect at right angles and bisect each other. Let's denote the length of one side of the rhombus as "s."

The diagonals of the rhombus have lengths of 16 and 30 units. Let's label them as "d1" and "d2" respectively.

Since the diagonals bisect each other, they form four congruent right triangles within the rhombus. The sides of these right triangles are half the lengths of the diagonals. Therefore, we can set up the Pythagorean theorem for one of the right triangles:

\((d1/2)^2 + (d2/2)^2 = s^2\)

Plugging in the values of the diagonals, we have:

\((16/2)^2 + (30/2)^2 = s^2\)

\(8^2 + 15^2 = s^2\)

\(64 + 225 = s^2\)

\(289 = s^2\)

Taking the square root of both sides, we find:

s = √289

s = 17

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The radius of the circle is 24 units.

We know that for an arc defined by an angle θ on a circle of radius R, the area is:

A = (θ/360°)*π*R²

Here we can see that the area of the sector is 432π and the angle is 270°, then we can replace that in the formula above so we get:

432π = (270°/360°)*π*R²

432 = (3/4)*R²

(4/3)*432 = R²

√576 = R

24 = R

The radius is 24 units.

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Answer:

-6/5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-2-(-14))/(0-10)

m=(-2+14)/-10

m=12/-10

simplify

m=-6/5

Answer:

I think it would be 0. I hope this helps!

The largest interval I over which the solution is defined is (-∞, ∞).               I = (-∞, ∞)

To solve the given initial-value problem, we can use the method of separation of variables as follows:
1. Separate the variables by moving all terms with y to the left side of the equation and all terms with x to the right side:
y/y' = ex/x
2. Integrate both sides of the equation with respect to their respective variables:
∫y/y' dy = ∫ex/x d
ln(y) = ex + C
3. Solve for y:
y = e^(ex + C)
4. Use the initial condition y(1) = 9 to find the value of C:
9 = e^(e + C)
C = ln(9) - e
5. Substitute the value of C back into the equation for y:
y = e^(ex + ln(9) - e)
6. Simplify the equation:
y = 9e^(ex - e)
7. The largest interval I over which the solution is defined is (-∞, ∞), since there are no restrictions on the values of x or y therefore, the solution to the initial-value problem is y(x) = 9e^(ex - e) and the largest interval I over which the solution is defined is (-∞, ∞).

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Answer:

-21, -16, 4, 9

Step-by-step explanation:

-3: f(-3) = 5(-3)-6 = -15-6 = -21

-2: f(-2) = 5(-2)-6 = -10-6 = -16

2: f(2) = 5(2)-6 = 10 - 6 = 4

3: f(3) = 5(3)-6 = 15 - 6 = 9

Answer:

11, 12.5, 10.6

Step-by-step explanation:

2y > 18.8

y > 9.4

given values which are true :-

11, 12.5, 10.6

To solve this, We need to solve the equation with each given value of y

\( \sf \: 2y > 18.8 \\ \sf \: 2 \times 8.2 > 18.8 \\ \sf16.4 > 18.8 \\ \boxed{ \tt \: false}\)

\( \sf \: 2y > 18.8 \\ \sf \: 2 \times 9.4 > 18.8 \\ \sf18.8 > 18.8 \\ \boxed{ \tt \: false}\)

\( \sf \: 2y > 18.8 \\ \sf \: 2 \times 11 > 18.8 \\ \sf22 > 18.8 \\ \boxed{ \tt \: true}\)

\( \sf \: 2y > 18.8 \\ \sf \: 2 \times 12.5 > 18.8 \\ \sf25> 18.8 \\ \boxed{ \tt \: true}\)

\( \sf \: 2y > 18.8 \\ \sf \: 2 \times 10.6> 18.8 \\ \sf21.2> 18.8 \\ \boxed{ \tt \: true}\)

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

According to medical research, teenagers' need to sleep,  (0.60, 0.70, and 0.80) is higher than 0.50, so they are less likely to occur.

The value of g that is least likely to occur is 0.50.

The article in the school newspaper claims that 50% of the 1,200 students at the high school are not getting enough sleep,

which would mean that P = 0.50.

However, the sample of 50 students is likely to differ from the population of 1,200 students,

So it's possible that the proportion of students in the sample who do not get enough sleep is different from 0.50.

The other values of g (0.60, 0.70, and 0.80) are higher than 0.50, so they are less likely to occur.

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In a case whereby a ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the time the ball is thrown will it strike the​ ground at t = 2.5 or -3.5.

Height of building = 140 ft

Initial velocity, u = 16 ft/sec

the equation given is

h = -16t² -16t +140

h(t) = -16t² -16t +140

AT h(t) = 0 , We can divide by -2 and have

(8t² + 8t - 70) = 0

8t² + 8t - 70 = 0

Then if we solve with quadratic equation formula where  a=8, b=8, c=- 70 then the root will be -7/2 and 5/2 then  t = 2.5 or -3.5

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complete question;

A ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the height of the ball h in feet after t seconds is given by the equation h equals negative 16 t squared minus 16 t plus 140. how long after the ball is thrown will it strike the​ ground?

The missing values in the ratio table are:

The equivalent ratios in the order they appear in the table are:

Ratios that are the same when compared are referred to as equivalent ratios. To determine whether two or more ratios are equivalent, they can be put side by side.

An equivalent ratio is, for instance, 1 : 2 and 2:4.

Divide or multiply both amounts by the same number to arrive at an equivalent ratio. The method is the same as determining equivalent fractions.

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Inductive reasoning: Reasoning that takes specific information and makes a broader generalization that is considered probable while that conclusion may not be 100% guaranteed.

Deductive reasoning: when you take two true statements to form a conclusion. It is used in science.

The argument is INDUCTIVE.

Since it is inductive, the last question is not applicable.

It is weak.

In this representation, the numbers are placed from left to right in order of most pounds eaten to fewest pounds eaten.

To plot the number of pounds eaten each week on a number line and order them from most pounds eaten to fewest pounds eaten, we'll consider the negative rational numbers representing the weight in pounds of doggie treats eaten by Darius. Here's an example ordering:

1. -3.5
2. -2.7
3. -2.5
4. -1.8
5. -1.2
6. -0.9
7. -0.5
8. -0.2

To visualize this on a number line, let's place these numbers accordingly:

```
-3.5                    -2.7        -2.5
    |---------------------|-----------|
-1.8       -1.2         -0.9         -0.5   -0.2
 |-----------|-----------|-----------|
```

In this representation, the numbers are placed from left to right in order of most pounds eaten to fewest pounds eaten. Each number is marked with a vertical line segment, and the length of the line segment corresponds to the magnitude of the number. The numbers are positioned such that they are evenly spaced along the number line.

Please note that this is just one possible ordering and arrangement of the numbers on the number line. The exact values and spacing may vary based on the actual data.

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The total amount that Williana's mother would spend to buy the glass table top is $120.04.

The first step is to determine the area of the glass table top.

Area of a hexagon = [(3√3)/2] x a²

a = side length

2.598 x 27.75² = 2000.68 in²

Cost of the table top = 2000.68 in² x 0.06 = $120.04

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Answer:

\(h=16inches\)

Step-by-step explanation:

From the question we are told that:

Base of  flag \(l_b=8inch\)

Area of flag \(A=64 inch^2\)

Generally the equation for a triangle is mathematically given by

 \(Area=\frac{1}{2}l_b*h\)

Therefore

 \(h=\frac{2A}{l_b}\\h=\frac{2*64}{8}\)

 \(h=16inches\)

Therefore the hieght of the ship is  mathematically given as

 \(h=16inches\)

The quotient expressions when simplified are (20x + 6)/5x = 4 + 6/5x and 49x² - 28x - 14 ÷ 7x = 7x - 4 - 2/x

Expression 1

To divide 20x + 6 by 5x, we can use long division or the shortcut method of factoring out the common factor.

Using the shortcut method, we can factor out 5x from the numerator:

(20x + 6)/5x = 4 + 6/5x

Therefore, the simplified expression is: (20x + 6) / (5x) = 4 + 6/5x

Expression 2

Here, we divide each of the term by 7x

So, we have

49x² - 28x - 14 ÷ 7x = 7x - 4 - 2/x

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There are three ways to name an angle--by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

You can name a specific angle by using the vertex point, and three points on each of the angle's rays or by letter or number written. The name of the angle is simply the three letters representing those points, with the vertex point listed in the middle. You can also name angles by looking at their size. Right angles are 90 degrees. Acute angles are less than 90 degrees. Obtuse angles are greater than 90 degrees, but less than 180 degrees, which is a straight angle, or a straight line.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 850\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years \end{cases} \\\\\\ 850 = 500[1+(0.1)(t)] \implies \cfrac{850}{500}=1+0.10t\implies \cfrac{17}{10}=1+0.10t \\\\\\ \cfrac{17}{10}-1=0.10t\implies \cfrac{7}{10}=0.10t\implies \cfrac{7}{(10)(0.10)}=t\implies 7=t\)