Annie has $9,000 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will she earn in 2 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$

Answer:

Step-by-step explanation:

To solve the equation |5-4r| = 17, we need to consider two cases:Case 1: 5 - 4r is positiveIf 5 - 4r is positive, then we have:5 - 4r = 17Subtracting 5 from both sides, we get:-4r = 12Dividing both sides by -4, we get:r = -3So if 5 - 4r is positive, then the solution to the equation is r = -3.Case 2: 5 - 4r is negativeIf 5 - 4r is negative, then we have:-(5 - 4r) = 17Simplifying the left side by distributing the negative sign, we get:-5 + 4r = 17Adding 5 to both sides, we get:4r = 22Dividing both sides by 4, we get:r = 5.5So if 5 - 4r is negative, then the solution to the equation is r = 5.5.Therefore, the solution set of the equation |5-4r| = 17 is {-3, 5.5}.To show this solution set on a number line, we can draw a number line and mark the points -3 and 5.5 with open circles, since these values are not included in the solution set. Then, we shade the part of the number line between -3 and 5.5, since any value of r in this interval satisfies the equation. The resulting number line looks like this:

So the solution set of the equation is the interval (-3, 5.5).

Answer:

w

Step-by-step explanation:

When deciding best course of action for accomplishing a task, I consider factors like time, resources, efficiency, effectiveness etc.

In both, the decision-making process involves weighing different options and determining most appropriate course of action based on tthe specific circumstances.

Just like considering factors like time, resources, efficiency and effectiveness when deciding best way to accomplish a task; when solving quadratic equation, we wil consider factors like complexity, availability of different methods and level of precision required.

So, by evaluating these factors, we are able to select most appropriate method for solving the quadratic equation in same way I am able to select the most appropriate approach for accomplishing a task in my daily life.

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Answer:

Step-by-step explanation:

Let's first expand the left side of the given equation:

(2x+5)a + (x+3)b = 2x+4

2xa + 5a + xb + 3b = 2x + 4

Now, let's group the terms with x and the terms without x:

(2a + b)x + (5a + 3b) = 2x + 4

We can see that the coefficients of x are equal on both sides, so we can equate the coefficients of x and the constant terms separately:

2a + b = 2 (1)

5a + 3b = 4 (2)

Solving these two equations, we get:

a = 2/7

b = 8/7

Now, we can substitute these values of a and b into the expression (a-b)^2 and simplify:

(a-b)^2 = (2/7 - 8/7)^2

= (-6/7)^2

= 36/49

Therefore, the value of (a-b)^2 is 36/49.

The distance between the points A (3, 3) and B (6, 6) include the following: 4.24 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Note: Each interval on the coordinate plane represent 1 unit.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(6 - 3)² + (6 - 3)²]

Distance = √[(3)² + (3)²]

Distance = √[9 + 9]

Distance = √18

Distance AB = 4.24 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: c

Step-by-step explanation:

p−5/p−1

This is the simplified value ^

Step-by-step explanation:

Answer:

1. First, add the x coordinates and divide by 2.

2. Second, add the y coordinates and divide by 2.

3. Take each result to get the midpoint.

Step-by-step explanation:

Example:

Find the midpoint of (1,6)(5,10)

x=1+5=6/2=3

y=6+10=16/2=8

Midpoint: (3,8)

Answer:

1/16

Step-by-step explanation:

The probability of selecting an Independent on the first draw is 5/16, since there are 5 Independents out of 16 total members.

Assuming that the first person selected is an Independent, there are now 4 Independents left out of 15 total members for the second draw. So the probability of selecting a second Independent given that the first person selected was an Independent is 4/15.

Therefore, the probability of selecting two Independents in succession is:

(5/16) * (4/15) = 1/16

So the probability of selecting two Independents is 1/16 or approximately 0.0625.

Answer:

[tex]y=4[/tex]

Step-by-step explanation:

To calculate the quantity produced from fabrication and finishing hours for Stoneage Surfboards, you would need to have additional information such as the production rate or efficiency of the fabrication and finishing processes. Without specific data on the production rate, it is not possible to determine the exact quantity produced.

However, if you have the production rate, you can use the following formula:

Quantity Produced = Production Rate × Fabrication and Finishing Hours

For example, if the production rate is 5 surfboards per hour and you have 8 hours of fabrication and finishing time, the calculation would be:

Quantity Produced = 5 surfboards/hour × 8 hours = 40 surfboards

Remember to adjust the units and variables based on the specific information and units of measurement used in Stoneage Surfboards' production processes.

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The statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.

This principle is known as the exclusive disjunction, which means that the truth value of p v q is only true if either p or q is true, but not both.

In other words, if both p and q are true, then the statement p v q is still considered true because only one of them needs to be true for the whole statement to be true. This concept is essential in the study of logic as it helps to clarify the relationship between different statements and propositions.

Furthermore, this principle is often used in mathematics, computer science, and other fields that rely heavily on logical reasoning. It enables us to make accurate predictions and draw valid conclusions from a set of given premises or statements.

In conclusion, the exclusive disjunction is a crucial concept in the study of logic that helps us understand the truth value of compound claims. Therefore, the statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.

In the study of logic, the statement "p ∨ q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim p ∨ q is, as a whole claim, true" is actually false. This is because the given description refers to the "inclusive" sense of the disjunction (OR) operator, rather than the exclusive sense.

In logic, there are two types of disjunctions: inclusive and exclusive. The inclusive disjunction, represented by p ∨ q, is true when at least one of p or q is true. This means that if both p and q are true, the compound claim p ∨ q is also true, which matches the given description in the question.

On the other hand, the exclusive disjunction, represented by p ⊕ q or p XOR q, is true only when either p or q is true, but not when both are true. If p and q are both true, then the compound claim p ⊕ q is false.

So, the statement in the question actually describes the inclusive disjunction, not the exclusive disjunction, and is therefore false.

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Characteristics that are harmful to a species tend to decrease in frequency from generation to generation because these characteristics usually have a low survival value for the species.

Option 2.

Characteristics that are harmful to a species are numerous and some of them affect species in many ways.

Some of the harmful characteristics to species include the following;

Poor genetic diversity - species that are not diverse will not survive long the nearest future as tend to go into extinct.

Poor habitat ; species with limited habitation will not survive long.

Poor reproductive rate - this factor does not favour species wide spread and fast growth

Predators - this factor kill and reduce the number of available species

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The simulation that can best be used to compute the probability would be one that randomly generates a large number of outcomes and records the number of games it takes for Janet to win in each simulation.

A simulation that randomly generates a large number of outcomes and records the number of games it takes for Janet to win in each simulation can be used to compute the probability of it taking at least six games for her to win.

By running the simulation many times and calculating the proportion of simulations in which Janet wins after six or more games, an estimate of the probability can be obtained.

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Answer:

A) The lower portion of the lungs has more oxygen than perfusion.

Step-by-step explanation:

The distance between the center of the circle and the given point is 13 units.

The distance between the center of the circle (0, 0) and the given point (-5, 12) should be equal to the radius of the circle.

Using the distance formula,

d= √(-5-0)² + (12-0)²

d = √25 + 144

d = √169

d = 13 unit

Therefore, the distance between the center of the circle and the given point is 13 units.

Any point on the circle will have a distance of 13 units from the center.

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In the question it ask for a slope of -6 so the answer is D.

Answer:

Step-by-step explanation:

if CB = 1/2 of AB it is understood that it is half of an equilateral triangle and AC is the height, three sides and three congruent angles, the sum of the internal angles of a triangle is 180°, therefore 180:3=60° , but the height divides the angle A in two therefore 30°, C is a right angle so 90°

The water tariff for Mogale City in August 2022 is R18 per kl, so her water bill excluding VAT will be R144.

Mrs Mabaspacked is a registered resident and she used 14 kt of water for the month of August 2022. The first 6 kl of water is free for registered residents, so she will only be charged for the remaining 8 kl. The water tariff for Mogale City in August 2022 is R18 per kl, so her water bill excluding VAT will be 8 kl x R18/kl = R144.

Water used: 14 kl

Free water: 6 kl

Water used after deduction of free water: 14 kl - 6 kl = 8 kl

Water tariff: R18 per kl

Water bill excluding VAT: 8 kl x R18/kl = R144

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The range of the exponential function [tex]f(x) = -4^x + 1[/tex] is given as follows:

y < 1.

The function for this problem is given as follows:

[tex]f(x) = -4^x + 1[/tex]

The horizontal asymptote is given as follows:

y = 1.

Due to the negative symbol, the function is decreasing, hence the inequality representing the range of the function is given as follows:

y < 1.

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Answer:

2

Step-by-step explanation:

The explanation is attached below.

So the base of the ladder is moving away from the wall at a rate of 3/4 feet per minute when the top of the ladder is 4 feet from the ground.

We can use the Pythagorean Theorem to relate the ladder's length to the distance it is from the wall. Let's call the distance from the wall "x", and the length of the ladder "y". Then:

x^2 + y^2 = 5^2

We can take the derivative with respect to time of both sides of this equation, using implicit differentiation:

2x(dx/dt) + 2y(dy/dt) = 0

Now we can plug in the values we know and solve for the rate at which the base of the ladder is moving away from the wall (which is the same as the rate at which x is increasing):

x = sqrt(5^2 - 4^2) = 3

y = 4

dx/dt = 1 (given)

dy/dt = ?

Plugging in these values, we get:

2(3)(1) + 2(4)(dy/dt) = 0

Simplifying:

6 + 8(dy/dt) = 0

Solving for dy/dt:

dy/dt = -6/8 = -3/4

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The measure of Angle WBK, the angles are supplementary,

complementary, adjacent, vertical, or part of a triangle.

The measure of Angle WBK (represented by b).
1. Identify the relationships between the angles: the angles are supplementary, complementary, adjacent, vertical, or part of a triangle or other polygon.
2. Write an equation using the angle relationships:  if two angles are supplementary, the sum of their measures is 180 degrees. If Angle WBK is supplementary to Angle WBL, we would write the equation b + m(WBL) = 180, where m(WBL) represents the measure of Angle WBL.
3. Solve the equation: the values into the equation and solve for b, the measure of Angle WBK.

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The gradient of the trail you hiked up is approximately 754.6 ft/mi. This means that for every mile you hiked horizontally, the elevation increased by about 754.6 feet.

The gradient of the trail is essentially the steepness of the trail, or the rate at which the elevation changes per unit of horizontal distance. To find the gradient in ft/mi, we need to calculate the total change in elevation and divide it by the total horizontal distance.
The total change in elevation is the difference between the elevation at the summit and the elevation at the trail head, which is:
6,849 ft - 645 ft = 6,204 ft

The total horizontal distance of the trail is 8.2 mi. To convert the total change in elevation to ft/mi, we divide it by the total horizontal distance
6,204 ft / 8.2 mi = 754.63 ft/mi
Rounding this to the tenths place gives us:
Gradient = 754.6 ft/mi

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The value of the volume of Sphere A is expressed as: 128π

The formula to calculate the volume of a sphere is given as:

V = ⁴/₃πr³

Where:

V is volume

r is radius

The radius of sphere A is: r_A = 2r_b

Radius of Sphere B is: r_B

Volume of sphere B = 16π

Thus:

⁴/₃πr_B³ = 16π

r_B³ = 12

r_b = ∛12

V_A = ⁴/₃π(2 * ∛12)³

V_A = ⁴/₃π * 8 * 12

= 128π

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Answer:

infinite

Step-by-step explanation:

because if you were to graph it or something 1 could go to 10 like 1 could fit into ten without exeeding the limit going to low or to high

Main Answer:The correct answer is "equality of three or more population means."

Supporting Question and Answer:

What is the purpose of the one-way analysis of variance (ANOVA) test?

ANOVA helps to assess whether these differences are statistically significant by comparing the variation between the groups to the variation within the groups.

Body of the Solution:The one-way analysis of variance (ANOVA) is used to test for" the equality of three or more population means". ANOVA compares the variation between the groups (due to differences in means) to the variation within the groups (due to individual differences within each group) to assess whether the observed differences in means are statistically significant. Therefore, the correct answer is:

"equality of three or more population means."

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The correct expansion of (x + 4y)³ using the binomial theorem is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

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

(x + 4y)³

The binomial theorem of expansion states that

Given that an expression is (a + b)ⁿ, the current term is

ⁿCₓ * (a)ˣ * (b)ⁿ ⁻ ˣ

Using the above as a guide, we have the following:

(x + 4y)³ = ³C₀ (x)⁰(4y)³ +³C₁ (x)¹(4y)² + ³C₂ (x)²(4y)¹ + ³C₃ (x)³(4y)⁰

Rewrite as

(x + 4y)³ = [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

This means that the correct expansion is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³

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Answer:

x=23

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

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