A + A = 2
B + B = 3
A + B x 2 = ?​

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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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:4 minutes

Step-by-step explanation:

16/4 is 4

36/9 is 4

64/16 is 4

Answer:

300 students were surveyed.

Step-by-step explanation:

Well, we know that 57% of students like blue, so that leaves 43% who like red. By simply dividing 129 by 43, we get 3, so know we can conclude that 1% is equal to 3 students. Knowing this, we can multiply 3 by 57 to get 171. Adding these up, we get 300, and we can verify this, by simply finding the difference between 57 and 43, which is 14. Now that we also know that 1% is equal to 3 students, we can multiply 14 by 3, to get 42, which is also the difference between 171 and 129.

Answer:

c ) 7/3

Step-by-step explanation:

Answer:

$60

Step-by-step explanation:

45 x 100/75 = 60

Answer:11.25

Step-by-step explanation:

45×0.75 45-33.75=11.25

Approximately 0.37 mg of beryllium-11 will remain after 130 seconds.

The radioactive decay formula is, as follows:

\(N(t) = N0e^{(- { \lambda} t)}\)

where N(t) is the amount of radioactive material at time t, N0 is the initial amount of radioactive material, λ is the decay constant, and e is the mathematical constant approximately equal to 2.71828.

The decay constant can be calculated from the half-life as:

λ = ln(2) / half-life

For beryllium-11, the decay constant is:

λ = ln(2) / 13.81 s = 0.0502 s⁻¹

Using the formula, we can calculate the amount of beryllium-11 remaining after 130 seconds:

\(N(130) = 230 e^{(-0.0502 \times 130 )} = 0.37 mg\)

Therefore, 0.37 mg of beryllium-11 will remain after 130 seconds.

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The simplified ratio of total marbles to red marbles is 27 to 8

In this question, we have the following parameters

Blue marbles = 24

Red marbles = 16

White marbles = 14

The above parameters mean that

Total marbles = sum of the individual marbles

Substitute the known values in the above equation, so, we have the following representation

Total marbles = 24 + 16 + 14

Evaluate

Total marbles = 54

The ratio is then represented as

Ratio = Total : Red

This gives

Ratio = 54 : 16

Simplify ratio

Ratio = 27 : 8

Hence, the simplified ratio is 27 : 8

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Answer:

16 trees

Step-by-step explanation:

1. First, let's find the positive factors of 352.

2. Now, let's find the two factors that have one number 6 more than the other.

3. Okay, 16 and 22 have one number that's 6 more than the other. Since the number of rows exceeds the number of trees per row by 6, 22 is the number of rows, and there are 16 trees in each row.

It's asking  would not be a solution soo

(-10, -9) as you can see

You're welcome thank me later

Answer:

14×7=98

188-98=90 so she had 90 left

Answer:

see explanation

Step-by-step explanation:

Joshua has made his error in the first step in the application of Pythagoras' theorem.

the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.

let the hypotenuse be h , then

h² = 7² + 7² = 49 + 49 = 98 ( take square root of both sides )

h = \(\sqrt{98}\)

since the figure is a square then each of the 3 sides is \(\sqrt{98}\)

the perimeter (P) is the sum of the 5 sides of the figure, that is

P = 3 × \(\sqrt{98}\) + 7 + 7 ≈ 29.7 + 14 = 43.7 ft

The calculated equation of the line parallel to y = -x - 5 that passes through (-2, 2) is y = -x.

To find the equation of the line parallel to y = -x - 5 that passes through (-2, 2),

We first note that any line parallel to y = -x - 5 will have the same slope as this line, which is -1

Using the point-slope form of the equation of a line, we can write the equation of the line we're looking for as:

y - y1 = m(x - x1)

where m is the slope (-1 in this case),

So, we have

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

Evaluate

y - 2 = -x - 2

Adding 2 to both sides, we get:

y = -x

Therefore, the equation of the line parallel to y = -x - 5 that passes through (-2, 2) is y = -x.

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Answer:  B. 142°.

Step-by-step explanation:

Given: OP is an angle bisector of ∠QOR and ∠QOP = 71°.

We know that an angle bisector divides an angle into two equal parts.

So, if OP is an angle bisector of ∠QOR and ∠QOP = 71°.

Then, the angle measure of ∠QOR = Twice of ∠QOP

⇒ Angle measure of ∠QOR = 2 (71°)

⇒ Angle measure of ∠QOR = 142°

Hence, correct option is B. 142°.

The answer of the given question based on the matching  the equation with the graph is , Y=3x -5 , Y= -5x + 3  , Y= x - 1  , Y= (x + 3)² -2  , Y= 1/2x + 2 , Y= x .

An equation is  mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by equal sign (=). The LHS and RHS may contain numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. The purpose of an equation is to solve for the value of an unknown variable.

Equations are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are essential for modeling and solving real-world problems and are a fundamental tool for understanding the natural world.

Here are the equations that match the graphs in the given image:

Y=3x -5 (Line passing through points (0,-5), (1,-2), and (2,1))

Y= -5x + 3 (Line passing through points (0,3) and (1,-2))

Y= x - 1 (Line passing through points (0,-1) and (1,0))

Y= (x + 3)² -2 (Parabola opening upwards with vertex at (-3,-2))

Y= 1/2x + 2 (Line passing through points (0,2) and (2,3))

Y= x (Line passing through points (-2,-2), (0,0), and (2,2))

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Answer:

square root of seven

Step-by-step explanation:

multiply the numbers inside the radicals to get fourth root of 49. simplify the radical and get square root of 7

Answer:

Step-by-step explanation:

y = − 3 /2 x  +  7/ 2

Step-by-step explanation:

The given expression is:

       12x + 8y = 28

Problem;

 Express in slope-intercept format;

   Solution:

The equation of a straight line is given as;

     y = mx + c

where y is the y-coordinate

          m is the slope

          x is the x-coordinate

          c is the intercept

 To solve this problem simply express the given equation as that of a straight line.

     12x + 8y = 28  in the form y = mx + c

      12x + 8y = 28  

   take 12x to the other side;

          8y  = 28 - 12x

divide by 8 to isolate the y;

           \(\frac{8y}{8} = \frac{28}{8} - \frac{12x}{8}\)

            y  = \(\frac{7}{2} - \frac{3x}{2}\)

Re-arranging gives;

           y = \(\frac{-3x}{2} + \frac{7}{2}\)

This is the slope-intercept form.  

Answer:

16

Step-by-step explanation:

4:2

2x4 = 8

4x4=16

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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On solving the provided question, we can say that Probability(A and B) = P(A)P(B|A) and P(E or F) = P(E) + P(F) - P(E and F)

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

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

P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).

Using the general multiplication rule, we have

P(E and F) = P(E)P(F|E)

.392 = P(E)(.7)

P(E) = .56

   P(E and F) = P(F)P(E|F)

.392 = P(F)(.56), so

P(F) = .7

P(E or F) = P(E) + P(F) - P(E and F)

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Answer: x= 1/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x−5(x−1)=2x−(2x−3)

x−5(x−1)=2x+−1(2x−3)(Distribute the Negative Sign)

x−5(x−1)=2x+−1(2x)+(−1)(−3)

x−5(x−1)=2x+−2x+3

x+(−5)(x)+(−5)(−1)=2x+−2x+3(Distribute)

x+−5x+5=2x+−2x+3

(x+−5x)+(5)=(2x+−2x)+(3)(Combine Like Terms)

−4x+5=3

−4x+5=3

Step 2: Subtract 5 from both sides.

−4x+5−5=3−5

−4x=−2

Step 3: Divide both sides by -4.

−4x /−4 = −2 /−4

x = 1/2

Answer:

The 4th term of the linear sequence = 3

Step-by-step explanation:

First term, a = -9

Common difference, d = -5 - (-9)

= -5 + 9

= 4

d = 4

The 4th term of the linear sequence = a + (n - 1)d

where,

n = 4

a + (n - 1)d

= -9 + (4 - 1)4

= -9 + (3)4

= -9 + 12

= 3

The 4th term of the linear sequence = 3

If Given f(x) = 1/2 (3 - x) ^ 2 , the value of f(15) is 72.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

The given function is:

f(x) = 1/2 (3 - x)²

To find the value of f(15), we need to substitute 15 for x in the function:

f(15) = 1/2 (3 - 15)²

Here, we subtract 15 from 3 to get -12 in the parentheses, and then we square it to get 144. We can simplify the expression further by multiplying 144 by 1/2, which gives us 72:

f(15) = 1/2 (144)

f(15) = 72

Therefore, the value of f(15) is 72.

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The base of the function given 2(4)ˣ+5 is 4ˣ

The base of an exponential function. If f(x) = ax, then we call a the base of the exponential function. The base must always be positive. Base 1. If f(x) is an exponential function whose base equals 1 – that is if f(x)=1x.

Given is a function, 2(4)ˣ+5, we need to find the base of the function,

With the multiplication of 4ˣ with 2, the rate at which f(x) changes is 2 times larger. Now it is added by 5, by adding 5 the value of f(x) is always 5 greater than the value of f(x).

This reverses the value of y for each corresponding value of x and increases the rate at which f(x) changes 8 times that of the original function.

Hence, the base of the function given 2(4)ˣ+5 is 4ˣ

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The system of equations for the given situation is;

⇒ $8x + $6y = $29

And, x = y + 1

Where, x is number pounds of Ham and y is number of pound of Cheese.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The cost Ham per pound = $8

The cost of cheese per pound = $6

Steve bought x pounds of ham and y pounds of cheese, and the total cost was $29

Now,

Since, Steve bought x pounds of ham and y pounds of cheese, and the total cost was $29.

So, We can formulate;

⇒ $8x + $6y = $29

And, He bought 1 pound more of ham than of cheese.

So, We can formulate;

⇒ x = y + 1

Thus, The system of equations for the given situation is;

⇒ $8x + $6y = $29

And, x = y + 1

Where, x is number pounds of Ham and y is number of pound of Cheese.

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Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

Answer:

Step-by-step explanation: