Brendan deposited $3,967 in an account earning 5% interest compounded annually.
To the nearest cent, how much interest will he earn in 5 years?

There is 20% decrease in the number of people who went to the pool over these four weeks.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.

Attendance of pool in first week of July = 1120

In second week, 125 fewer people joined.

Thus, attendance in second week is = 1120-125 = 995

In third week, 130 more people joined.

Thus, attendance in third week is = 995+130 = 1125

In fourth week, 229 fewer people joined.

Thus, attendance in fourth week is = 1125-229 = 896

Difference of attendance in first and fourth week = 1120-896 = 224

Percentage decrease = (Decrease number/Initial number)×100%

= (224/1120)×100%

= 0.20×100%

= 20%

Thus, there has been a 20% decrease over the four weeks.

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x = 3 is the true solution to 2 ln e superscript ln 5 x baseline = 2 ln 15, using the concept of simplification.

Make something simpler by simplifying it. In mathematics, reducing an expression, fraction, or issue to a simpler form is referred to as simplification. With calculations and solutions, the problem is made simple.

In order to achieve consistency in efforts, costs, and time, procedures must be simplified. It gets rid of variation and variety that is superfluous, harmful, and unproductive. It is termed simplification to use and interpret the function in order to make it simpler or easier to grasp.

The equation can be simplified by using the fact,

ln(eˣ) = x

This gives,

2 ln(5x) = 2·ln(15)

Comparing arguments, we see that,

5x = 15

x = 3

Check if it is true or not:

2 ln(e^(ln(5·3))) = 2·ln(15)

2 ln(e^2.70805) = 2·2.70805

2 ln(15) = 5.41610

and,

2·2.70805 = 5.41610

So, it is true.

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Answer:

The answer is 71

What is chemist?

A chemist is a person who specializes in the science of chemistry, which is the study of matter and its properties, structure, composition, behavior, and the changes it undergoes. Chemists are trained in the scientific discipline of chemistry and use their knowledge to study and manipulate matter. This can include anything from the analysis of materials for their chemical makeup, to the development of new products and processes. Chemists can work in a variety of fields, including pharmaceuticals, materials science, biochemistry, research and development, and more. They must be well-versed in the principles and theories of chemistry, as well as in the practical aspects of their work. Through their work, chemists contribute to the advancement and application of science.

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Answer: the answer is 15

Step-by-step explanation:

Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

An inequality is a mathematical statement that shows the relative size of two values.

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

What is inequality?

An inequality is a mathematical statement that shows the relative size of two values.

What is linear inequality?

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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The function, f(x) = -50 and g(x) = -17

A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

Instance: f(x) = x/2 ("f of x equals x divided by 2")

we are given that f(x) = -3[tex]x^{2}[/tex] -2 and g(x) = 4x - 1

we need to find f(4) and g(-4)

f(4) = -3([tex]4^{2}[/tex]) - 2

f(4) = -3*16 - 2

f(4) = -48-2

f(4) = -50

g(x) = 4x - 1

g(-4) = 4 *-4 -1

g(-4) = -16-1

g(-4) = -17

The function f(x) = -50  and g(x) = -17

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The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .

total length of four-bit strings = 16

Let S represent the collection of all four-bit bit strings.

Let A represent the occurrence of a randomly generated string beginning with 1.

Let B represent the scenario where a string created at random contains two consecutive 0s.

S has 8 strings that begin with the letter "1."

P( A ) = 8 / 16 = 1 / 2

Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100

P(A ∩ B)  = 3 / 16

Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,

3/16 / 1/2

= 3 / 8

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Answer:

congruence is compatibility or agreement while equal is the same or equivalent to one another.

Answer:

5x + 16

Step-by-step explanation:

First you have to distribute the 2 into the parentheses

2 times x is 2x

2 times 6 is 12

so now the equation is

2x + 12 + 3x + 4

add the 2x and 3x and that is 5

so now the equation is...

5x + 12 + 4

add 12 + 4 and that is 16

so now the answer is

5x + 16

Either the slope intercept form or the point-slope form can be used to express the equation of a line-, the line's equation is - 3x - 5.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two distinct points on a line can be used to calculate the slope of any line.

The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.

According to our question-

the points are given as

(x1,y1)=0,-5

(x2,y2)=-3,4

m = y2-y2/x2-x2

Hence, the line's equation is - 3x - 5.

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It will be 13min until there are 20 grams of the element remaining.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, and is the initial amount, b is the decay factor, and y is the final amount.

Here, we have

This is a compound decay problem, which goes by the formula:

F = P(1-r)ˣ

Where

F is the future amount (we want it to be 20)

P is the present amount (240 now)

r is the rate of decay per minute (17.4% = 17.4/100 = 0.174)

x is the time it takes (what we want to find)

Substitute all values in the formula and we get

20 = 240(1-0.174)ˣ

20 = 240(0.826)ˣ

0.0833 = 0.826ˣ

㏑0.0833 = ㏑0.826ˣ

㏑0.0833 = x ㏑0.826

x = ㏑0.0833/㏑0.826

x = 13

Hence, it will be 13min until there are 20 grams of the element remaining.

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Answer:

x ≥ 5

Step-by-step explanation:

5 + 2 (2x - 3) ≥ 3x + 4

5 + 4x - 6 ≥ 3x + 4

-1 + 4x ≥ 3x + 4

4x ≥ 3x + 5

x ≥ 5

By looking at the definition of mutually exclusive and independent event, the statement for both events are true.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.

(a) True. The given event is both mutually exclusive as well as independent

(b)True. The given event is both mutually exclusive as well as independent

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Answer:

2400

Step-by-step explanation:4152 is just 173% of d.

We create an equation d = 4152/1.73

after solving you get 2400.

Answer:

Breadth = 10 ft

Step-by-step explanation:

Given information,

→ Perimeter (P) = 50 ft

→ Length (L) = 15 ft

→ Breadth (B) = ??

Now we have to,

→ find the required value of Breadth.

Formula we use,

→ P = 2(L + B)

Then the required Breadth will be,

→ P = 2(L + B)

→ 50 = 2(15 + B)

→ 30 + 2B = 50

→ 2B = 50 - 30

→ B = 20/2

→ [ B = 10 ft ]

Hence, required Breadth is 10 ft.

The number of pounds of clay used to make 21 small vases is 10 and one half pounds.

Sandy uses three and one half pounds of clay to make 7 small vases. Using proportion, the number of pounds of clay that she can use to make 21 small vases can be calculated as follows;

Therefore,

7 small vases = 3 1 / 2 pounds of clay(7 / 2)

21 small vases = ?

cross multiply

pounds of clay used to make 21 small vases = 7 / 2 × 21 ÷ 7

pounds of clay used to make 21 small vases = 147 / 2 ÷ 7

pounds of clay used to make 21 small vases =  147 / 2 × 1 / 7

pounds of clay used to make 21 small vases = 21 / 2

Therefore,

pounds of clay used to make 21 small vases = 10 1 / 2

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The perimeter of the image is 70 meters and its area is 210 square meters.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter.

Area=(1/2)×base× height

=(1/2)×21×20

=210 square meters

Perimeter=a+ b+ c

=21+20+29

=70meters

Therefore, The perimeter of the image is 70 meters and its area is 210 square meters.

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Total number of ways four people line up in the straight line with the given condition is equal to 18 ways.

As given in the question,

Total number of people = 4

Given condition :

First position can not occupied by youngest person:

First position occupied in 3 ways

Second position occupied in 3 ways

Third position occupied in 2 ways

fourth position occupied in 1 ways

Total number of ways = 3 × 3 × 2 × 1

                                  = 18 ways

Therefore, the number of ways four people stand in straight line is equal to 18 ways.

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So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

The valid bounding condition for the sum of the subset problem is:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

This means that each item can either be included in the subset (x[i] = 1) or not included in the subset (x[i] = 0).

The sum of the weights of the items in the subset should not exceed the maximum capacity constraint, m. So the bounding condition for the weight of the subset is:

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

This means that the sum of the weights of the items in the subset should be less than or equal to the maximum capacity constraint.

So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

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The value of the side AC is 40 if the points  B, D, and F are midpoints of

the sides of ΔACE.

The midpoint theorem states that in order to determine the midpoints of a triangle's sides, "a line segment linking any two of its midpoints is said to be parallel to the triangle's third side and also half the length of the third side."

Divide the distance between the two endpoints by 2, then do it again. The two terminal x coordinates can alternatively be combined, then the result divided by two. Draw a line from a midway to the opposite corner. The centroid of a triangle is the point at where the three medians intersect.

Given,

The points B, D, F are midpoints of the sides of a triangle ACE.

And also given that,

EC =32 and DF=20, AC=?

So, FD=1/2(AC)

AC=2(FD)

AC=2(20)

AC=40

Therefore, the value of the side AC is 40 if the points  B, D, and F are

midpoints of the sides of ΔACE.

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The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

In an alternative method, a linear polynomial over a field from which the coefficients are extracted is equalized to zero to produce a linear equation. The values that, when used as placeholders for the unknowns, result in the equality being true are the solutions to this kind of equation.

In this specific situation, where the variable is appropriately referred to as the unknown, the term "linear equation" frequently applies indirectly.

The Cartesian coordinates of a point on the Euclidean plane can be read as each solution in the case of two variables.

Given equation is:

-4x+y=16

For x-intercept, y=0

-4x+0=16

-4x=16

x= -4

The x-intercept has an ordered pair (-4, 0)

For y-intercept, x=0

-4(0)+y=16

y=16

The y-intercept has an ordered pair(0,16)

Therefore, The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

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The unidentified term is 3m.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, an equation (x-0.2n)² = x-1.2mn+0.04n²

We know that, (a-b)² = a²-2ab+b²

Comparing the given equation with the above identity, we get,

a = x, b = 0.2n and 2ab = 1.2mn

Therefore, 2x×0.2n = 1.2mn

x = 3m

Hence, the unidentified term is 3m

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4 inches is the rim's radius

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The value of n when is divided by 6 and it gives 42 is 252

Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division and 12 divided by 4 gives 3 in each group. This means that 3 and 4 are factors of 12

When dividing a number by another number that is not it's factor, there will be remainder for example 12 divided by 5 . It will give 2 remainder 2. This is because 5 is not a factor of 12.

Similarly, n divided by 6 to give 42. This means that 42 and 6 are factors of n

Therefore to find n we multiply 42 and 6.

n = 42×6

n = 252

therefore the value of n is 252

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The perimeter of the right triangle shown is given by the following option:

39 units.

The perimeter of a figure is composed by the sum of the lengths of the outer edges of the figure.

The sides of the right triangle in this problem are given as follows:

Then, applying the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 5² + 17²

h = square root(5² + 17²)

h = 17.7.

The hypotenuse is the third side length of the triangle, hence it's perimeter is calculated as follows:

5 + 17 + 17 = 39 units.

(I suppose there was a typing mistake on the options).

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Answer:

its D

Step-by-step explanation:

30

Answer:

$1944

Step-by-step explanation:

18x12=216

216x$9=$1944

Answer:

£1944

Step-by-step explanation:

The area of the floor is 216 feet²

18 x 12 = 216

216 x 9 = 1944

8 ÷ 640 x 100,000 = 12,500 defective computer chips

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Points of inflection does this curve have is:

Concave Up: [tex]$\left(-\infty,-\sqrt{\frac{5}{3}}\right),\left(\sqrt{\frac{5}{3}}, \infty\right)$[/tex]

Concave Down: [tex]$\left(-\sqrt{\frac{5}{3}}, \sqrt{\frac{5}{3}}\right)$[/tex]

Points of Inflection: [tex]$(-1.2910,2.1111),(1.2910,2.1111)$[/tex]

To find the concavity of a function?

We need to take the second derivative.

y' = 4x^3 - 20x

y'' = 12x^2 - 20

Finding the points of inflection involves setting the second derivative equal to 0. Add 20 over, divide by 12, and take the square root. The positive and negative square roots of 5/3 are the potential points of inflection.

Setting up a number line can help to determine concavity. Let's plug in -2 into the second derivative. From this, we have found that from negative infinity to the negative square root of 5/3, the graph is concave up, as f''(-2) > 0. f''(0) < 0, so from the negative square root of 5/3 to the positive square root of 5/3, the graph is concave down. f''(2) is also > 0, and therefore from the positive square root of 5/3 to infinity, the graph is concave up.

Since the graph shifted direction at both potential points of inflection, they are both actually points of inflection. To find the y-values for each point of inflection, plug the x-value back into the original polynomial equation.

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Answer:

5

Step-by-step explanation:

The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."

Using this definition, we can simplify the expression "10^log5" as follows:

10^log5 = 10^y

Where "y" is the exponent to which the base "10" must be raised to produce the result "5."

To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:

log(10^y) = y

Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:

log(5) = y

Solving for "y," we find that "y = log(5)."

Therefore, the expression "10^log5" can be simplified to:

10^log(5) = 10^(log(5)) = 5

So the simplified result is 5.

Answer:

[tex]A \approx 38 \, \textrm{cm}^2[/tex]

Step-by-step explanation:

The area of a triangle is defined as:

[tex]A_\triangle = \dfrac{1}{2}bh[/tex]

where [tex]b[/tex] is the length of its base and [tex]h[/tex] is its height.

So, we can plug the given values into this formula along with the inch to centimeter conversion to get the answer to this problem.

[tex]A=\dfrac{1}{2}\left(4.75\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)\left(2.5\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)[/tex]

And simplify.

[tex]A \approx 38 \, \textrm{cm}^2[/tex]