Write an absolute value equation that has the given solution of -2 and 10.

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Option A and B : This statements is generally false in probability theory.

A. P(A ∪ B) = P(A) + P(B) - This statement is generally false in probability theory. This is known as the inclusion-exclusion principle, which states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.

B. P(A | B) = P(A) - This statement is generally false in probability theory. In general, P(A | B) is not equal to P(A) because the occurrence of event B affects the probability of event A.

C. P(A ∩ B) = P(A)P(B) - This statement is generally true in probability theory. This is known as the independent events rule, which states that the probability of the intersection of two independent events is equal to the product of their individual probabilities.

D. P(A | B) + P(A' | B) = 1 - This statement is generally true in probability theory.

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Let A and B be any two events. Which of the following statements, in general, are false? P(A∣B)+P(A∣B)=1                                                                                                                                    

A. P(A ∪ B) = P(A) + P(B)

B. P(A | B) = P(A)

C. P(A ∩ B) = P(A)P(B)

D. P(A | B) + P(A' | B) = 1

The rewritten statements are 1. ∀x∃y¬P(x, y), 2. ∃y∃x¬(P(x, y)∨Q(x, y)), 3. (∃x∃yP(x, y)∨∃x∃y¬Q(x, y)), and 4. ∃x(∀y∀z¬P(x, y, z)∧∀z∀y¬P(x, y, z)).

1. ∀x∃y¬P(x, y) - This statement states that for all x, there exists a y such that P(x, y) is not true. This rejects the statement "there exists x such that for all values of y, P(x, y) is true."

2. ∃y∃x(¬P(x, y)∧¬Q(x, y)) - This statement states that there exists a y and x such that both P(x, y) and Q(x, y) are not true. This rejects the statement, "for all the values of y and x, either P(x, y) or Q(x, y) will be true."

3. ∃x∀y¬P(x, y)∨∃x∀y¬Q(x, y) - This statement states that either there exists x such that for all y, P(x, y) is not true or there exists x such that for all y, Q(x, y) is not true. This rejects the statement, "for all the values of x, there exists y such that both P(x, y) and Q(x, y) will be true."

4. ∀x(¬∃y∃zP(x, y, z)∧¬∃z∀yP(x, y, z)) - This statement states that for all x, it is not the case that there exists y and z such that P(x, y, z) is true, and it is also not the case that there exists z such that for all y, P(x, y, z) is true. This rejects the statement "for all x, either there exists y and z such that P(x, y, z) is true, or there exists z such that for all y, P(x, y, z) is true."

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--The given question is incomplete; the complete question is

"Rewrite each of these statements so that negations appear only applied to predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives).

1. ¬∃x∀yP(x, y)

2. ¬∀y∀x(P(x, y)∨Q(x, y))

3. ¬(∃x∀y¬P(x, y)∧∀x∀yQ(x, y))

4. ¬∀x(∃y∃zP(x, y, z)∨∃z∀yP(x, y, z))"--

Answer:

Jackets cost $69.90.

Step-by-step explanation:

1. Multiply $233 by 70% (.70 as a decimal) to find how much less the jacket is.

2. Subtract that answer from the cost of the jacket.

233 * .70 = 163.1

233.00

163.10

$69.90

You can also multiply $233 by 30% and not have to subtract because your answer would BE the cost (70% + 30% = 100%).

233 * .30 = 69.90                 $69.90

Step-by-step explanation:

a= c-b pls let me know if it is correct or not

The area of Nick's grandfather's yard is 8/15 m²

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.

Given that, Nick's grandfather grows tomatoes in a section of his yard that is 4/5 meter long and 2/3 meter wide.

We have to find the area of the section,

Considering the section as a rectangular section,

Area of a rectangle = length × width

= 4/5 × 2/3

= 8/15

Hence, the area of Nick's grandfather's yard is 8/15 m²

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Answer:

I think you would add the numbers then divide by 2

Step-by-step explanation:

Answer:

1. Is a continuous random variable

2. Is a discrete random variable

3. Is not a random variable

Step-by-step explanation:

1. The exact Weight of quarters in circulation in the united states is a continuous random variable. This is because a random variable such as this can take uncountable and infinite number of values.

2. The shoe sizes if humans is an example of discrete random variable. This is a discrete random variable because it has countable number of values.

3. Political party affiliation is not a random variable.

Thank you!

A quadrilateral is a shape with four sides

The indicated measures are A = 56, B = 128, C = 100 and D = 76

The angles in a quadrilateral add up to 360 degrees.

So, we have:

4n + 5n + 6 + 9n + 2 + 8n - 12 = 360

Collect like terms

4n + 5n + 9n + 8n = 360 - 6 - 2 + 12

Evaluate the like terms

26n = 364

Divide through by 26

n = 14

From the figure, we have:

A = 4n

B = 9n + 2

C = 8n - 12

D = 5n + 6

So, we have:

A = 4 * 14 = 56

B = 9*14 + 2 = 128

C = 8*14 - 12 = 100

D = 5*14 + 6 = 76

Hence, the indicated measures are

A = 56, B = 128, C = 100 and D = 76

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9514 1404 393

Answer:

  (a)  -4

Step-by-step explanation:

The picture is fuzzy, but perhaps you want to evaluate ...

  \(-1\left|\dfrac{2}{3}-4\right|\div\dfrac{5}{6}=-1\left|-\dfrac{10}{3}\right|\div\dfrac{5}{6}\\\\=-\dfrac{10}{3}\div\dfrac{5}{6}=-\dfrac{20}{6}\div\dfrac{5}{6}=-\dfrac{20}{5}=\boxed{-4}\)

The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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Answer:

do you mean scientific notation ?

2.097152 x \(10^{6}\)

Step-by-step explanation:

The equation is n(n+1) = n + n+1 +29. The two consecutive integers are 6, 7 or -5, -4

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that: the product of two consecutive integers is 29 more than their sum.

Let the first integer and second  integer be n and n+1 respectively

We can write the equation as:

n(n+1) = n + n+1 +29

n² + n = 2n + 30

n² + n - 2n - 30 = 0

n² + - n - 30 = 0

(n - 6) (n + 5) = 0

n - 6 = 0 or n + 5 = 0

n = 6 or n = -5

Thus, n+1 = 7 or n+1 = -4

Therefore, the two  integers are 6, 7 or -5, -4

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The graph of the function is the set of all points (x,y) in the plane that satisfies the equation y=f(x) y = f ( x ) . ... The y value of a point where a vertical line intersects a graph represents an output for that input x value.

Answer:

Constant

Step-by-step explanation:

In a population of values having a normal distribution with (μ = 126.7) and (σ = 78.3), and we intend to draw a random sample of size (n = 242),

(i) The probability that a single randomly selected value is greater is than 119.2 is 0.54

(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is 0.932

As per the question statement, a population of values has a normal distribution with (μ = 126.7) and (σ = 78.3) and we intend to draw a random sample of size (n = 242).

We are required to calculate:

(i) The probability that a single randomly selected value is greater is than 119.2

(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2

Let us assume that, a random variable "X" follows normal distribution with mean (μ = 126.7), standard deviation (σ = 78.3) and a sample size of (n = 242).

(i) The probability that a single randomly selected value is greater is than 119.2 is,

P (X > 119.2) = [1 - P(X < 119.2)]

= [1 - P{(X - μ)/σ < (119.2 - 126.7)/78.3}]

= [1 - P{Z < (-0.096)}]

= (1 - 0.462)...[Using Excel Function "NORMSDIST (-0.096)]

= 0.538

≈ 0.54

(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is.

P(X bar > 119.2) = [1 - P( < 119.2)]

= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/(78.3/√242)}]

= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/5.033}]

= [1 - P{Z < (-1.49)}]

= (1 - 0.068)...[Using Excel Function "NORMSDIST (-1.49)]

= 0.932

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The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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The expression is

\(6^{-2}\) < \(\frac{1}{6} ^{-2}\) , \(6^{-1}\)< \(\frac{1}{6} ^{-1}\), \(6^{-2}\)< \(6^{-1}\)

Here we have to find the expression

a) \(6^{-2}\) and \(\frac{1}{6}^{-2} }\)

= 1/6² and 6²

= 1/ 36 and 36

= 1/36 < 36

So \(6^{-2}\)< \(\frac{1}{6} ^{-2}\)

b) \(6^{-1}\) and \(\frac{1}{6} ^{-1}\)

= 1/6 and 6

= 1/6 < 6

So \(6^{-1}\) < \(\frac{1}{6} ^{-1}\)

c) \(6^{-2}\) and \(6^{-1}\)

= 1/36 and 1/6

= 1/36 < 1/6

So \(6^{-2}\) < \(6^{-1}\)

Therefore the expression is \(6^{-2}\)< \(\frac{1}{6} ^{-2}\) , \(6^{-1}\) < \(\frac{1}{6} ^{-1}\) , \(6^{-2}\) < \(6^{-1}\).

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Therefore, in response to the given query, we can state that R(-1)'s inequality possible spectrum is thus: [0, 10]

A connection between two expressions or numbers that is not equivalent in mathematics is referred to as an inequality. Thus, disparity results from inequity. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and disparity are not the same. Use the not equal sign most frequently when two numbers are not identical. (). Values of any size can be contrasted using a variety of disparities. By changing the two sides until only the factors are left, many straightforward inequalities can be answered. However, a number of factors support inequality: Both parts' negative numbers are divided or added. Exchange the left and the right.

The equation can be used to describe the candle's length, R(t):

R(t) = 11 - 1.1t

where t represents how long the light has been burning, in hours.

We must determine t in terms of R in order to determine the negative of R(t):

R = 11 - 1.1 t = (11 - R)/1.1 t = (11 - R)

R(t)'s inverse function is thus:

\(R^{(-1)}(R) = (11 - R)/1.1\)

0 ≤ R ≤ 11

So, R(-1)'s scope is as follows:

[0, 11]

0 ≤ R ≤ 11

Inputting these limits into the equation for R(-1) yields the following results:

\(R^{(-1)}(0) = 11/1.1 = 10\\R^{(-1)}(11) = 0/1.1 = 0\)

R(-1)'s possible spectrum is thus:

[0, 10]

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Answer:

There is no picture

Step-by-step explanation:

Answer:

Domain: - ∞ < x < ∞

Range: y > 0

Asymptote: y = 0

y-intercept: 1

Step-by-step explanation:

The DOMAIN is the set of possible input values, so in this case it is the set of possible x values.  For this function the set of input values is not restricted, so this is why we say that the domain can be ANY value by denoting it as - ∞ < x < ∞.  Another way of stating this would be to say

x ∈ R, which means x belongs to the set of real numbers. Real numbers are any number (positive, negative, zero, irrational, rational, whole etc.) except imaginary numbers.

The RANGE is the set of values the function takes, i.e. the output.  As this function is an exponential function, the function is always positive.  Hence the range is y > 0 or f(x) > 0.

An ASYMPTOTE is a line that the curve approaches, as it heads towards infinity (or negative infinity).  Asymptotes can be horizontal, vertical or oblique.   For this function, there is a horizontal asymptote at y = 0:  this is because as x tends to negative infinity, the curve approaches (tends to) zero (but never actually gets there).

The y-intercept is the y-coordinate of the point where the curve crosses the y-axis, i.e. when x = 0.  If you input x = 0 into the function y = 5^x you get y = 1.  Therefore, the y-intercept of y = 5^x is y = 1

Answer:

Therefore, mom had the better unit rate, as she paid less per book than dad did.

Step-by-step explanation:

To determine who had the better unit rate, we need to divide the cost by the number of books for each parent.

For mom, the unit rate would be:

$19.85 ÷ 8 books = $2.48 per book

For dad, the unit rate would be:

$15.00 ÷ 6 books = $2.50 per book

Therefore, mom had the better unit rate, as she paid less per book than dad did.

To further explain, the unit rate is the cost per unit of measure, in this case, the cost per book. When comparing two different unit rates, the one with the lower cost per unit is the better value. In this scenario, mom paid $0.02 less per book than dad did, making her unit rate better.

Answer:

exact form: 5/3

decimal form: 1.6 (6 is repeating)

mixed number form: 1  2/3

Step-by-step explanation:

Answer:

1 2/3

Step-by-step explanation:

1 1/4 x  1 1/3 = 5/4 x 4/3 = (5x4)/(4x3) = 20/12 = 5/3 = 1 2/3

The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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Answer:

Part A: 84 boxes

Part B: Explained below

Part C: 2 layers of boxes high

6 boxes width per layer

7 boxes length per layer

Step-by-step explanation:

Part A:

In terms of height, we can see that there are 3 boxes

In terms of width, we can see that there are 4 boxes.

In terms of length, we can see that there are 7 boxes.

Thus, number of boxes = 3 × 4 × 7 = 84 boxes

Part B:

What I've just done in part A is same as V = l × w × h

Thus is because if we take one strip vertically, we will see just height and length.. But since they are stacked and of same size, we will just multiply by the number of rows that make up the width to get the total number of boxes that form the prsim.

Part C:

Since he wants it to be 2 layers high, we can only put 1 box on another one.

Now, he wants the width to be less than 14 inches,which means that there should be less than 14/2 = 7 boxes. So let's adopt 6 boxes along the width.

He wants the length to be less than 30 inches. This means that the length should be less than 30/2 = 15 boxes

Since we know that the height has 2 layers, it means number of boxes along the width and length = 84/2 = 42 boxes

Let's find multiples of 42 and they are;

1, 2, 6, 7, 21, 42.

Looking at these multiples, the most appropriate to use will be 6 and 7.

Thus,he can use 6 boxes as width per layer and 7 boxes as length per layer

Thus, he will stack the boxes as follows;

2 layers of boxes high

6 boxes width per layer

7 boxes length per layer

To solve for j, cross multiply:

4 x 45 = 18 x j

180 = 18j

Divide both sides by 18:

j = 10

j=10

if you dont need an explanation dont read this:

firstly you reduce the 4/18 by 2 (basically simplifying) , which then becomes 2/9..

then you cross the 2 by 45 and 9 to j (you multiply 2x45 and 9xj=9j)

so it equals to 90=9j

then you divide both sides by 9

j=10

The quartiles of the distribution are given as follows:

The sample size of the distribution is of:

n = 40.

The first quartile is the value that is greater than 25% of the distribution, hence it is the value at the position which is 25% of the sample size, hence:

The second quartile is the value that is greater than 50% of the  distribution, hence it is the value at the position which is 50% of the sample size, hence:

The third quartile is the value that is greater than 75% of the  distribution, hence it is the value at the position which is 75% of the sample size, hence:

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===========================================================

Explanation:

The fact that we have the phrasing "randomly-selected" in there is a big clue that we are working with a sample, and not a population. If 40 people represented the population, then we wouldn't be randomly selecting anyone. Everyone would be surveyed. No random process needed. We don't need to worry about the order of those surveyed.

However, we are applying a random selection process to form this sample. A statistic is some value that measures a sample. For instance, xbar is the sample mean which is a sample statistic. The xbar value estimates mu, which is a greek letter. Mu is the population mean and a population parameter.

To remember the difference between the two terms parameter and statistic, one useful memory trick is to think of it like this:

As the name "statistics" implies, it is the study of how to estimate a population based on a sample. After gathering the sample, we compute a statistic, which in turn estimates a parameter. So that explains why your math course and textbook has that label.