write any ten ordered pairs in which the first elements is country the second element is its capital​

If all the dimensions of a cube increase by a factor of 3/2, the surface area will increase by a factor of 9/2.

If all the dimensions of a cube increase by a factor of 3/2, then the new dimensions of the cube will be 3/2 times the original dimensions.

Let's say the original side length of the cube was "s". Then the new side length would be (3/2)*s.

The surface area of a cube is given by the formula 6s^2, where s is the side length.

So the original surface area of the cube would be:

6s^2

And the new surface area of the cube would be:

6(3/2s)^2
= 6(9/4)s^2
= 27/2 s^2

To find how many times greater the new surface area is compared to the original surface area, we can divide the new surface area by the original surface area:

(27/2 s^2) / (6s^2)
= (9/2)

So the new surface area is 9/2 times greater than the original surface area.

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The volume of granola a cylindrical container can hold 5451.6 cubic centimeters if containers have a diameter of 20 cm and a height of 17. 4 cm.

The number of unit cubes (cubes of unit length) that can fit inside a cylinder determines its volume.

Identifying the radius (r) and height (h)
r = 10 cm
h = 17.4 cm

Calculating the volume (V) using the formula V = πr²h
V = π × (10 cm)² × 17.4 cm
V ≈ 3.14 × 100 cm² × 17.4 cm
V ≈ 5451.6 cm³

Approximately, a container will hold 5451.6 cubic centimeters of granola.

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The equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.

To solve for x in 3/5 (30 x - 15) = 72, we can first simplify the left side by distributing the 3/5:

3/5 (30 x - 15) = 18 x - 9

Now we can solve for x by setting the right side equal to 72:

18 x - 9 = 72

Adding 9 to both sides:

18 x = 81

Dividing by 18:

x = 4.5

So we know that option E is one of the correct answers.

To check which of the other options have the same value of x, we can substitute x = 4.5 into each equation and see if it simplifies to 72:

A. 18 x - 15 = 72

18(4.5) - 15 = 72

81 - 15 = 72 (not equivalent)

B. 50 x - 25 = 72

50(4.5) - 25 = 200 - 25 = 175 (not equivalent)

C. 18 x - 9 = 72

18(4.5) - 9 = 72 (equivalent)

D. 3 (6 x - 3) = 72

3(6(4.5) - 3) = 3(24) = 72 (equivalent)

Therefore, the equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.

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The value of the reflex angle in this figure is 273 degrees

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

In this given figure, there's acute angle and an obtuse angle, therefore a reflex angle must be present.

To find the reflex angle in the figure, we have to trace the green part of the figure which will give us;

180° + 93°

i.e the sum of angle on a straight line with an obtuse angle

Reflex angle = 180 + 93 = 273°

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Where the function f(x) = x² + 2x - 3 is given, note that the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4. See the attached graph.

To find the minimum and maximum points of the function f(x), we can complete the square:

f(x) = x^2 + 2x - 3

= (x + 1)^2 - 4

We can see that the function is in the vertex form f(x) = a(x - h)^2 + k, where the vertex is (-1, -4).

Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the vertex is the minimum point. Therefore, the minimum value of the function f(x) is -4.

To find the x-intercepts, we can set f(x) = 0:

(x + 1)^2 - 4 = 0

(x + 1)^2 = 4

Taking the square root of both sides, we get:

x + 1 = ±2

x = -1 ± 2

Therefore, the x-intercepts of the function f(x) are x = -3 and x = 1.

In summary, the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4, which occurs at the vertex (-1, -4).

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To get 51 using the numbers 8, 5, 6, and 7 exactly once each, you can use the following mathematical expression:

(8 x 6) - 7 + 5 = 51

How it works:

1. Multiply 8 by 6 to get 48: (8 x 6) = 48

2. Subtract 7 from 48 to get 41: 48 - 7 = 41

3. Add 5 to 41 to get 51: 41 + 5 = 51

Therefore, (8 x 6) - 7 + 5 = 51.

Answer:

Step-by-step explanation:

8 x (7 - 5) + 6 = 51

Answer:

The numerical values of the circumference and area are equal

Step-by-step explanation:

Circumference: 12.57

Area: 12.57

12.57=12.57

Hope this helps! :)

The height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.

To find the z-score associated with the 96th percentile, we need to find the z-score such that the area to the right of it under the standard normal distribution is 0.96. Using a standard normal distribution table or calculator, we find that the z-score is approximately 1.75.

Next, we can use the z-score formula to find the height of a 16-year-old boy in the 96th percentile:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.

Plugging in the values we have:

1.75 = (x - 68.3) / 2.9

Multiplying both sides by 2.9, we get:

x - 68.3 = 5.075

Adding 68.3 to both sides, we get:

x = 73.375

So the height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.

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Hello!

In this question, we are asked to find which set of points are solutions to our equation: 7x + 4y = -23

In order to find which points are solutions to our equation, we will plug the values into our equation and solve. If both sides of the equation are equal, the point will be a solution.

Note: Our coordinate point is in the format of (x,y), so we will plug in the values according to its variable.

Solve:

(-1,-4):

Plug in coordinate.

7(-1) + 4(-4) = -23

Simplify.

-7 - 16 = -23

-23 = -23

Since it is equal, (-1,-4) is a solution.

(2,6):

Plug in coordinate.

7(2) + 4(6) = -23

Simplify.

14 + 24 = -23

38 = -23

Since it is not equal, making it false, (2,6) is not a solution.

(-5,3):

Plug in coordinate.

7(-5) + 4(3) = -23

Simplify.

-35 + 12 = -23

-23 = -23

Since it is equal, (-5,3) is a solution.

(6,-7):

Plug in coordinate.

7(6) + 4(-7) = -23

Simplify.

42 - 28 = -23

14 = -23

Since it is not equal, making it false, (6,-7) is not a solution.

Answer:

The solutions to the equation are: (-1,-4) and (-5,3).

To solve this problem, we will use the formula for exponential decay as follows: V = P * e^(-rt) where V is the value after t years, P is the initial value, r is the annual interest rate as a decimal, and t is the time in years.

What is Depreciation: Depreciation is dependent on a number of estimates.The method in which companies determine the depreciation value of their assets is different from one another. Some companies may use a straight line method of depreciation and another may count the depreciation according to asset's production value. What is exponential decay: An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time .Given that a brand new Audi R8 is purchased for $148,700 before taxes, and the car depreciates at a rate of 8%, we can find how much it will be worth in 5 years. Using the formula for exponential decay, we have V = P * e^(-rt) where     P = $148,700r = 0.08t = 5. Therefore,V = $148,700 * e^(-0.08 * 5), V = $148,700 * e^(-0.4)V ≈ $82,429.61. Therefore, the car will be worth approximately $82,429.61 in 5 years.

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Using the triple integral to find the volume of the solid bounded by the parabolic cylinder is 32/15 cubic units.

The given solid is bounded by the parabolic cylinder y = 2x², the plane z = 0, the plane z = 2, and the plane y = 4.

To find the volume of the solid using a triple integral, we can set up the integral as follows:

∫∫∫E dV

where E is the region of integration in three dimensions.

Region E can be described as:

0 ≤ z ≤ 2

0 ≤ y ≤ 4

0 ≤ x ≤ √(y/2)

Therefore, the triple integral can be written as:

∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz

Evaluating the integral gives us the volume of the solid:

V = ∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz = 32/15

Hence, the volume of the solid is 32/15 cubic units.

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1. Myla bought an item for P2,500 and decided to sell it with a 2% markup. The selling price will be P2,500 + (2% of P2,500) = P2,500 + P50 = P2,550.

2. Joan sold her old iPhone for P5,000 at an 8% markdown rate. To find the markdown and the original cost, we first calculate the markdown: P5,000 = 92% of original price. So, the original price was P5,000 ÷ 0.92 ≈ P5,434.78. The markdown is P5,434.78 - P5,000 = P434.78.

3. The student assistant bought an item for P520 and sold it for P550. The markup is P550 - P520 = P30.

4. Mother earned P120 on an item at a 60% markdown. Let X be the original price, then X * 60% = P120. X = P120 ÷ 0.60 = P200. So, the mother bought the item for P200.

5. The cost of a t-shirt from the manufacturer is P400. If Loan wants a 30% markup based on the selling price, we'll let X be the selling price, then X - 30% of X = P400. So, 0.7X = P400. X = P400 ÷ 0.7 ≈ P571.43. Loan's selling price will be P571.43.

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The negation of each of these statements in terms of quantifiers without using the negation symbo

a) There exists at least one x such that x is not greater than 1.
b) There exists at least one x such that x is not less than or equal to 2.
c) For all x, x is less than 4.
d) For all x, x is greater than or equal to 0.
e) There exists at least one x such that either x is not less than or equal to -1 or x is not greater than 2.
f) For all x, x is not less than 4 and x is not greater than 7.

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Step-by-step explanation:

If we let A be the event that Trevor studies for at least 50 minutes, and let B be the event that he passes his Algebra test, then we know:

P(A and B) = 0.88

P(A) = 0.92

We want to find the probability that Trevor passes his Algebra test given that he studied for at least 50 minutes, or in other words, we want to find P(B|A).

We can use Bayes' theorem to find this probability:

P(B|A) = P(A and B) / P(A)

Substituting in our values, we get:

P(B|A) = 0.88 / 0.92

Simplifying this fraction, we get:

P(B|A) = 0.9565

Therefore, the probability that Trevor passes his Algebra test given that he studied for at least 50 minutes is approximately 0.9565.

The expression (x + 1)(x - 3) represents the Area of base of the prism.

a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.

According to question:

The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).

We can find the height of the prism by dividing the volume by the area of the base:

B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)

Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.

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the area of the circle is 615. 4 m²

The formula that is used to calculate the area of a circle is expressed with the equation.

We have the equation as;

A = πr²

Such that the parameters are given as;

From the diagram shown, we have that;

A = unknown

r = 14m

Now, substitute the values, we get;

Area = 3.14 ×14²

Find the square value

Area = 3.14(196)

Multiply the values

Area = 615. 4 m²

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Two balloons A and B apart 150km with given angle of elevation represents observer A is at a distance of  122.5 km approximately from balloon.

Number of observers = 2

Distance between two observers A and B = 150km

Angles of elevation are 42° and 76°.

Let us consider 'h' be the height of the balloon

Let the distance from observer A to the balloon x.

Use trigonometry to find the value of x.

From observer A, the angle of elevation to the balloon is 42°.

This means that the height of the balloon above observer A is ,

h = x ×  tan(42°)

From observer B,

The angle of elevation to the balloon is 76°.

This means that the height of the balloon above observer B is ,

h = (150 - x) × tan(76°)

Since both expressions give the same value for h, set them equal to each other,

⇒ x × tan(42°) = (150 - x) × tan(76°)

Simplifying this equation, we get,

⇒ x × (0.9004 ) = (150 - x) × 4.0107

⇒ 0.9004x = 601.605 - 4.0107x

⇒ 4.9111x = 601.605

⇒ x ≈ 122.5 km

Therefore, the distance from observer A to the balloon as per given angle of elevation is approximately 98.3 km.

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The coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

To find the coordinates of the point P on the directed line segment AB that partitions AB in the ratio 1:3, we can use the concept of section formula.

Let's assume the coordinates of point P are (x, y). According to the section formula, the coordinates of P can be calculated as follows:

x = (3x2 + 1x1) / (3+1) = (37 + 1(-1)) / 4 = (21 - 1) / 4 = 20/4 = 5

y = (3y2 + 1y1) / (3+1) = (38 + 12) / 4 = (24 + 2) / 4 = 26/4 = 13/2 = 6.5

Therefore, the coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

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The angle measure of L in the triangle is approximately 75°.

Based on the given table, we can see that the ratio of the opposite leg length to the adjacent leg length for an angle measure of 75° is approximately 3.73. Looking at the triangle in the question, we can see that the side opposite to angle L is the hypotenuse and the adjacent leg is LK.

Therefore, the ratio of the opposite leg length to the adjacent leg length for angle L is equal to the ratio of the hypotenuse length to the length of segment LK.

From the figure, we can see that the length of segment LK is approximately 3.2 units. Therefore, the length of the hypotenuse is approximately 3.73 times the length of segment LK, or:

hypotenuse length ≈ 3.73 × 3.2 ≈ 11.9

Therefore, the angle measure of L is approximately 75°.

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The mean number of miles the hiker walked for the 6 days was 6.5 miles.

To calculate the mean or average of a set of numbers, we add up all the numbers and then divide the sum by the number of items in the set. In this case, we have the number of miles the hiker walked on each of the six days. To find the total number of miles the hiker walked, we simply add up all the numbers

8 + 5 + 7 + 2 + 9 + 8 = 39

Next, we divide the total number of miles by the number of days (which is 6) to get the average or mean number of miles the hiker walked per day:

Mean number of miles = Total number of miles / Number of days

= 39 / 6

= 6.5

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Answer: 6

Step-by-step explanation:42/7=6

Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

To answer your question about how many cups of water Abby should add to make 1 gallon of punch, let's first convert all the given measurements to cups. One gallon is equivalent to 16 cups.

1. Orange juice: Abby uses 2 quarts of orange juice. Since there are 4 cups in a quart, she uses 2 x 4 = 8 cups of orange juice.

2. Lemon juice: Abby uses 1 cup of lemon juice.

3. Pineapple juice: Abby uses 2 1/2 pints of pineapple juice. There are 2 cups in a pint, so she uses (2 1/2) x 2 = 5 cups of pineapple juice.

Now, let's add up the cups of orange juice, lemon juice, and pineapple juice: 8 + 1 + 5 = 14 cups. Since Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

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The probability of the event not happening is 5/83.

Here, probability refers to the likelihood of a given event occurring and that the inequality f(x) > 3g(x) holds for all x > 0.

If the probability of an event happening is 88/83, then the probability of the event not happening is 1 minus the probability of the event happening. This can be expressed as:

1 - 88/83

To simplify this expression, we can first find a common denominator for 1 and 88/83, which is 83/83:

83/83 - 88/83

-5/83

Therefore, the probability of the event not happening is 5/83.

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To find the percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race, we'll use the following formula:
Percent Error = (|(Measured Value - Actual Value)| / Actual Value) * 100

Here, the Measured Value is the stopwatch's time (32.4 seconds), and the Actual Value is the electronic touchpad's time (32.36 seconds).

Step 1: Calculate the absolute difference between the measured and actual values:
|32.4 - 32.36| = 0.04

Step 2: Divide the absolute difference by the actual value:
0.04 / 32.36 = 0.001236

Step 3: Multiply the result by 100 to get the percentage:
0.001236 * 100 = 0.1236%

The percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race is approximately 0.124%.

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The radian measure -1.7 pi is equivalent to -306 degrees.

To find the percent error of the stopwatch's measurement, we need to compare it to the more precise electronic touchpad measurement. The formula for percent error is:

percent error = (|measured value - actual value| / actual value) x 100%

In this case, the measured value is 32.4 seconds, the actual value is 32.36 seconds, and the absolute difference between them is 0.04 seconds. Plugging these values into the formula, we get:

percent error = (|32.4 - 32.36| / 32.36) x 100% = 0.124%

Therefore, the percent error for the stopwatch's measurement is 0.124%. This means that the stopwatch's measurement was very close to the actual value, with an error of only 0.124% of the actual value.

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The expression that fits perfect for the given requirement is 5z + 7.50, under the condition that a food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole.

Here we have to apply the principles of solving algebraic equations, due to the expression provided.

From the  given information, here the food truck owner charges z dollars per burrito combo along with $1.50 for a side of guacamole.

According to the information it is given that the  expression is  5(z+1.50)  which helps to state the total cost of 5 burrito combos and 5 sides of guacamole.

Lets now formulate the expression for the given required equation

= 5(z + 1.50)

= 5z + 7.50.

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A food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole. The expression 5(z+1.50) represents the total cost of 5 burrito combos and 5 sides of guacamole. What expression also represent the cost of 5 burrito combos and 5 sides if guacamole that cost 1.50 each.

Answer:

This function is an exponential function because the base is a constant and the exponent is a variable.

This new function W(x) = 22 - (11/8) * (x - 16)² will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall.

To modify the function W to model the new arch with dimensions of 32 inches wide and 44 inches tall, we need to adjust the formula to reflect the new proportions.

Currently, the function W is defined as:

W(x) = h/2 - h/(2a) * (x - a)²

Where h is the height of the arch and a is half of the width of the arch.

To modify the function for the new arch, we need to adjust the value of a to reflect the new width of 32 inches. Since a is half the width, we have:

a = 32/2 = 16

We also need to adjust the value of h to reflect the new height of 44 inches. Therefore, the new function for the arch would be:

W(x) = 44/2 - 44/(2*16) * (x - 16)²

Simplifying this expression, we get:

W(x) = 22 - (11/8) * (x - 16)²

This new function will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall. The parabolic shape of the function will remain the same, but the specific coefficients in the function have been adjusted to reflect the new proportions of the arch.

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In 2029, there will be an estimated A, 8.66 billion people in the world.

C, t = (ln(N/N₀))/k is the equation rewritten to solve for t.

Part A:

Using the given exponential growth model, find the population in 2029 as follows:

N = N₀e^kt

N₀ = 7.95 billion (present population)

k = 1.08% = 0.0108 (rate of increase)

t = 2029 - 2022 = 7 (number of years)

N = 7.95 billion × e^(0.0108×7)

N ≈ 8.66 billion

Therefore, the world's population is expected to be 8.66 billion in 2029. Answer choice A is correct.

Part B:

To solve for t, isolate it on one side of the exponential growth model equation. Taking the natural logarithm of both sides:

ln(N/N₀) = kt

Divide both sides by k:

t = ln(N/N₀)/k

Therefore, the equation rewritten to solve for t is t = (ln(N/N₀))/k. Answer choice C is correct.

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All the angles of the Rhombus if B-A=20 is angle A = angle C = 80°, and angle B = angle D = 100°.

In a rhombus ABCD, if angle B minus angle A equals 20 degrees (B-A=20°), we can find the degree measures of all the angles.

Step 1: Recognize that in a rhombus, opposite angles are equal. Therefore, angle A = angle C and angle B = angle D.

Step 2: Remember that the sum of the angles in any quadrilateral is 360 degrees. In a rhombus, since the opposite angles are equal, we can represent this as: 2A + 2B = 360°

Step 3: Use the given information, B - A = 20°, to solve for one of the angles. For this, rearrange the equation to isolate B: B = A + 20°

Step 4: Substitute the expression for B from step 3 into the equation from step 2: 2A + 2(A + 20°) = 360°

Step 5: Solve the equation for angle A. 2A + 2A + 40° = 360° → 4A + 40° = 360° → 4A = 320° → A = 80°

Step 6: Now that we have angle A, use the expression from step 3 to find angle B: B = 80° + 20° = 100°

Step 7: Since A = C and B = D, we can now state all the angles of the rhombus ABCD: angle A = angle C = 80°, and angle B = angle D = 100°.

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